Transfer learning for transportation system
resilience estimation using floating car data

A thesis presented in part fulfilment of the requirements of the Degree ofMaster of Science in Transportation Systems at the Department of Civil, TUM
School of Engineering and Design, Technical University of Munich.

Supervisor

M.Sc. Qinglong Lu
M.Eng. Cheng Lyu
Prof. Dr. Constantinos Antoniou
Chair of Transportation Systems Engineering

Submitted by

Ningkang Yang

Submitted on

Munich, 09.05.2023

Abstract
Understanding the reaction of a transportation system under extreme events is significant
for evaluating the resilience of the system. However, collecting traffic data after a natural
disaster is usually expensive and the data volume is always insufficient for building a robustmodel. In this thesis, an unsupervised pattern extractor is proposed to extract the patterns oftransportation resilience from grid-wise aggregating floating car data (FCD), which improves
the transferability of deep learning models and enables the prediction of target cities to learn
resilience patterns from other cities. The unsupervised pattern extractor is a combination of
the k-shape time series clustering method and the Bayes inference method. The k-Shapemethod is used to capture the similarity of pre-disaster patterns between different cities while
the Bayes inference method is used to generate the posterior distribution for the traffic volume
at each time step for the time series of each cluster.
To verify the effectiveness of our method, we conducted a case study under the context of the
COVID-19 pandemic using the grid traffic volume resulted from aggregating floating car dataof three cities, in which the source domain cites include Antwerp and Bangkok, and the target
domain city is Barcelona. Results show that the extracted resilience patterns by our method
can improve the prediction performance of transfer learning neural networks at both grid andmacro levels with less pre-disaster information and limited data volume. Furthermore, we
explored the impact of grid size through a sensitivity analysis and discussed the balance
between data stability and data volume. The results show that our method achieved better
performance as the grid size increased, although the data volume decreased.

Transfer learning for transportation system resilience estimation using floating car dataiAcknowledgement
First of all, I would like to express my sincere gratitude to my supervisors at the Chair of Transportation Systems Engineering (TSE) at the Technical University of Munich (TUM), who provided me with unconditional support. Thanks to Cheng Lyu’s guidance on the methodologies
and to Qinglong Lu’s guidance on experiment design and thesis writing. During this thesis, I
developed a strong interest in scientific research and significantly improved my research abilities and understanding of traffic data analysis and transportation system resilience. I also
want to thank Vishal Mahajan and Prof. Dr. Constantinos Antoniou for their advice in themidterm presentation of this thesis, which helped me to recognize my shortcomings.
Additionally, I would like to express my gratitude to all of my friends and teachers at TUM
for their help in both daily life and studies. I really appreciate TUM for providing me with aconducive learning environment. During this one and a half years, I have gained abundant
expertise and met many like-minded friends. This study experience would be the most precious wealth of my life, which will continuously inspire me to become a better person andresearcher in the rest of my life.
Last but not least, I would like to express my gratitude to my family, in particular to my parents,
for their understanding and unconditional support.

Transfer learning for transportation system resilience estimation using floating car dataii

Contents
1 Introduction .......................................................................................................

1

1.1 Motivation ..................................................................................................

1

1.2 Objectives and Contributions........................................................................

2

1.2.1 Research Objectives.........................................................................

2

1.2.2 Contributions ...................................................................................

2

1.3 Thesis Structure .........................................................................................

3

2 Literature Review ...............................................................................................

4

2.1 Definitions of Transportation System Resilience..............................................

4

2.2 Features of Transportation System Resilience ................................................

4

2.3 Tasks and Methodologies in Different Research Branches of Transportation
Resilience..................................................................................................

6

2.3.1 Assessment Metrics Exploration.........................................................

6

2.3.2 Resilience Regression Model .............................................................

6

2.3.3 Causal Impact Analysis .....................................................................

7

2.3.4 Resilience Patterns Prediction............................................................

7

2.4 Transfer Learning Strategies ........................................................................

8

2.5 Literature Gaps ..........................................................................................

8

3 Methodology .....................................................................................................

9

3.1 Floating Car Data .......................................................................................

9

3.1.1 Characteristics of FCD ......................................................................

9

3.1.2 Data Availablility ...............................................................................

9

3.2 Overview and Basic Assumption................................................................... 10
3.3 Time Series Clustering ................................................................................ 11
3.3.1 Distance Measures of Time Series ..................................................... 11
3.3.2 K-Shape Time Series Clustering ........................................................ 14
3.4 Bayes-Based Shape Extractor ...................................................................... 15
3.5 Neural Networks ......................................................................................... 17
3.5.1 Multi-Layer Perceptron (MLP)............................................................. 17
3.5.2 Recurrent Neural Network (RNN) ....................................................... 18
3.5.3 Long Short-Term Memory (LSTM) ...................................................... 18
3.6 Transfer Learning........................................................................................ 20
4 Case Study ....................................................................................................... 21
4.1 Background ............................................................................................... 21
4.2 Study Area................................................................................................. 22
4.3 Data Description......................................................................................... 26
4.3.1 Macroscopic Traffic Volume Resilience Patterns ................................... 26
4.3.2 Microscopic Traffic Volume Resilience Patterns .................................... 28
5 Experiment Setup .............................................................................................. 33
5.1 Data Preprocessing .................................................................................... 33
5.2 Experiment Settings.................................................................................... 34

Transfer learning for transportation system resilience estimation using floating car dataiii

6 Results and Discussions ..................................................................................... 36
6.1 Results of Source Domain Model.................................................................. 36
6.1.1 Average Resilience Patterns .............................................................. 36
6.1.2 Results of Neural Networks ............................................................... 40
6.2 Results of Target Domain Model ................................................................... 43
6.3 Sensitivity Analysis ..................................................................................... 46
6.3.1 Average resilience patterns................................................................ 46
6.3.2 Source Domain Sensitivity Analysis .................................................... 49
6.3.3 Target Domain Sensitivity Analysis ..................................................... 51
6.4 Ablation Experiment Analysis ....................................................................... 55
6.4.1 100m × 100m Grid Size .................................................................... 55
6.4.2 200m × 200m Grid Size .................................................................... 57
7 Conclusion ........................................................................................................ 59
7.1 Main Contributions and Findings................................................................... 59
7.2 Limitations ................................................................................................. 60
7.3 Outlook ..................................................................................................... 60
Bibliography ........................................................................................................... 62

Transfer learning for transportation system resilience estimation using floating car dataiv

List of Figures
Figure 1

Measure of resilience—conceptual definition, adapted from [1]. .....................

1

Figure 2

Structure of Thesis...................................................................................

3

Figure 3

Schematic of performance of a resilient system, adapted from [2]. .................

5

Figure 4

The framework of the proposed method...................................................... 10

Figure 5

Time series alignment under ED and DTW ................................................. 12

Figure 6

Heatmap of cumulative distance matrix and warping path ............................. 13

Figure 7

K-shape time series cluster for grid floating car data .................................... 15

Figure 8

Example of Bayes resilience patterns extraction. Here we marked an example of resilience pattern extraction with a single time step. The samples ofeach time step form a data set. For each cluster di, the resilience pattern
extraction process is repeated Nd times. .................................................... 16

Figure 9

Sample of a feed-forward neural network .................................................... 17

Figure 10 Sample of a recurrent neural network ......................................................... 18
Figure 11 Sample of a long short-term memory network. ............................................ 19
Figure 12 The transfer learning process. ................................................................... 20
Figure 13 ANTWERP road network .......................................................................... 23
Figure 14 BANGKOK road network .......................................................................... 24
Figure 15 BARCELONA road network ...................................................................... 25
Figure 16 Grid floating car data................................................................................ 26
Figure 17 ANTWERP traffic volume time series ......................................................... 27
Figure 18 BANGKOK traffic volume time series.......................................................... 27
Figure 19 BARCELONA traffic volume time series...................................................... 28
Figure 20 ANTWERP traffic volume heatmap (grid size: 100m × 100m unit: veh/day) .... 29
Figure 21 BANGKOK traffic volume heatmap (grid size: 100m × 100m unit: veh/day)..... 30
Figure 22 BARCELONA traffic volume heatmap (grid size: 100m × 100m unit: veh/day). 31
Figure 23 Traffic volume heatmap (grid size: 200m × 200m unit: veh/day)..................... 32
Figure 24 Within-Cluster Sum of Square of different number of clusters (Grid size:

100m × 100m) ........................................................................................ 36
Figure 25 Samples of pre-disaster clusters (Grid size: 100m × 100m) .......................... 38

Transfer learning for transportation system resilience estimation using floating car datav

Figure 26 During-disaster clusters and average resilience patterns (Grid size: 100m ×100m) .................................................................................................... 39
Figure 27 The macro level prediction and true values in source domain (Grid size:

100m × 100m) ........................................................................................ 42
Figure 28 The macro level prediction and true values in target domain (Grid size: 100m×100m) .................................................................................................... 45
Figure 29 Within-Cluster Sum of Square of different number of clusters (Grid size:

200m × 200m) ........................................................................................ 46
Figure 30 Samples of pre-disaster clusters (Grid size: 200m × 200m) .......................... 47
Figure 31 During-disaster clusters and average resilience patterns (Grid size: 200m ×200m) .................................................................................................... 49
Figure 32 The macro level prediction and true values in source domain (Grid size:

200m × 200m) ........................................................................................ 51
Figure 33 The macro level prediction and true values in target domain (Grid size: 200m×200m) .................................................................................................... 53

Transfer learning for transportation system resilience estimation using floating car dataviList of Tables
Table 1

Characteristics of the distance measures ..................................................... 14

Table 2

Data volume ............................................................................................. 33

Table 3

Data valid rate .......................................................................................... 34

Table 4Model architecture..................................................................................... 35

Table 5

Source domain loss (Grid size: 100m × 100m) ............................................ 40

Table 6

Target domain loss (Grid size: 100m × 100m) .............................................. 43

Table 7

Source domain loss (Grid size: 200m × 200m) ............................................ 49

Table 8Target domain loss (Grid size: 200m × 200m) .............................................. 51

Table 9MAPE of the models in macro level traffic volume resilience patterns prediction 55

Table 10 Source domain ablation experiment (Grid size: 100m × 100m) ...................... 56
Table 11 Target domain ablation experiment (Grid size: 100m × 100m) ....................... 56
Table 12 Source domain ablation experiment (Grid size: 200m × 200m) ...................... 57
Table 13 Target domain ablation experiment (Grid size: 200m × 200m) ....................... 57

Transfer learning for transportation system resilience estimation using floating car datavii

1. Introduction
1.1. Motivation
The frequent natural disasters have led to numerous socio-economic problems for the past
decades. Under the impact of natural disasters, transportation infrastructure is often at significant risk [3]. Natural disasters in transportation systems can highly damage the systems’
performance and impact citizens’ travel behavior directly or indirectly. Thus, understanding
the resilience of transportation systems under extreme events to bring the systems back to anormal state in a timely manner becomes imperative [4].
According to [1], resilience refers to the capacity of a system to avoid shocks, to absorb theshock when it happens, and to restore within a specific time after a shock event. They further
proposed a “resilience triangle” as the measurement for this process. As shown in Figure 1,
the performance of the system drops sharply after the occurrence of the shock events at t0 .
After reaching the lowest point, the system gradually recovers to a new equilibrium at t1 .

Figure 1 Measure of resilience—conceptual definition, adapted from [1].

The “resilience triangle” theory provides opportunities for researchers to investigate the resilience of transportation systems. Although several studies have applied various methods tomodel the resilience of transportation systems during natural disasters, the research scopeof these studies is often limited, and most of their models are non-transferable. Moreover,most current studies only rely on local traffic detection data from fixed locations, which fails
to reflect the resilience patterns of the entire network and can only focus on certain natural
disaster events. For example, [5] applied a logistic function to model the resilience of the New
York City transportation system under the Hurricanes through taxi trip data and subway ridership data; [6] used snowplow data and traffic speed detectors data to analyze the resilienceof city road network after the snow storm through some performance index.

Transfer learning for transportation system resilience estimation using floating car data1

In order to build more comprehensive models, the floating car data (FCD) is receiving increasing scholarly attention in these years, which makes it possible to apply artificial neuralnetworks to predict the resilience patterns of transportation systems. However, for a single city road network, the limited historical data and insufficient data volume always present
significant challenges to traffic prediction tasks, and the temporal domain shift among cities
increases the difficulties of applying transfer learning. Therefore, little research focuses ontransportation resilience pattern prediction.
To address the gap in this research area, this thesis proposed a transferable model for predicting transportation system resilience using FCD. The proposed model consists of a resilience
pattern extractor and artificial neural networks, which can alleviate the temporal domain shift
among different cities and enable effective transfer learning for the target domain. By applying
the proposed method, this study seeks to contribute to the development of more transferable
and effective models for transportation system resilience prediction.

1.2. Objectives and Contributions
1.2.1. Research Objectives
The overall objective of this thesis is to predict the resilience patterns of the transportation
system using FCD through the transfer learning method. Specific objectives are listed below:

1.

Explore the dynamics of the resilience triangle of the transportation system under thenatural disasters through the time series of FCD.
a.

Extract the resilience patterns of the networks that contain different pre-disasterfeatures.

b.
2.

Discuss the features of extracted resilience patterns.

Propose a transferable model to describe and predict transportation resilience by using
pre-disaster FCD.

3.

Explore and analyze the performance and transferability of different machine learningmodels in the resilience estimation task.

1.2.2. Contributions
The contributions of this thesis are listed below:
1.

The thesis proposed a transferable method to address the temporal domain shift byaggregating the traffic volume resilience patterns from different cities. The proposed
method achieved better transfer learning performance than traditional neural networks
under limited data conditions.It overcomes the challenges of post-disaster data collec-

Transfer learning for transportation system resilience estimation using floating car data2

tion and limited historical data and provide timely predictions of both macro and local
resilience patterns of cities.
2.

This thesis proposed a model for predicting resilience patterns of large-scale city roadtransportation at the grid level. Through the analysis and observation of both micro andmacro prediction results, the proposed model can learn stable traffic volume resilience
trends at the grid level while resisting the interference of some unstable trends, showing
more robust predictive performance than traditional neural networks.

3.

This thesis also discusses the impact of grid size on the predictive performance ofthe model, and analyzes the importance of data quantity and stability to the model.
The proposed model can achieve better transfer learning performance by enhancing
data stability with fewer data than traditional neural networks. This further reduces therequirement for the volume of training data and alleviates the conflict between datastability and volume in traffic prediction tasks.

1.3. Thesis Structure
The overall structure of this thesis is illustrated in Figure 2, and the rest of this paper is structured as follows: Chapter 2 reviews the related literature, provides comprehensive definitionsof transportation resilience, and summarizes the tasks and methods in the previous studies
on transportation resilience research. Chapter 3 proposes the proposed framework of theapplied method and describes the components of the method respectively. Chapter 4 introduces the background of the case study and describes the used floating car data. Chapter 5
describes the experimental setup. Chapter 6 presents and discusses the experiment results
and some further experiments. Chapter 7 concludes the main findings and contributions of
this thesis and discusses potential future research directions.

Figure 2 Structure of Thesis

Transfer learning for transportation system resilience estimation using floating car data3

2. Literature Review
In this chapter, we first clarify the basic concepts of transportation system resilience; Then
we summarize the features of transportation system resilience; In the third section, we review
the tasks in different research branches of transportation resilience and their methodologies;
In the fourth section, we introduce the categories and strategies of transfer learning.

2.1. Definitions of Transportation System Resilience
Resilience is physically expressed as the ability of an object to recover its shape. For the past
decades, this concept has been extended to various fields, such as climate analysis, psychology, economics, and engineering research. For example, [1] proposed the "4R" frameworkand initially presented a method to quantify system resilience. Based on their proposed concept in Section 1.1, many researchers have further proposed various definitions of resiliencein the field of transportation.
[7] defined transportation resilience as the endurance and recovery capacity of transportation systems under the extreme disruptions. In order to describe the resources cost of theresilience process, transportation systems resilience is further extended to the ability of atransportation system to absorb shocks and gradually provide the needed service with its
basic structure and function within an acceptable time and cost after a disturbance event [2].
Besides, [8] took the riskiness of shocks into consideration and introduced the concept of risk
into the definition of system resilience. They emphasize that the degradation parameters andrecovery time of the disruption that the transportation system withstands should be within
an acceptable range. In the temporal dimension, the definition of transportation system resilience should also consider both their short-term and long-term adaptability, which describe
the ability of the transportation system to respond in the short term and to transform in thelong term [9]. Based on the aforementioned definitions, [10] have proposed a comprehensive
definition of traffic resilience:" The ability of a system to resist, reduce and absorb the impacts
of a disturbance (shock, interruption, or disaster), maintaining an acceptable level of service(static resilience), and restoring the regular and balanced operation within a reasonable period of time and cost (dynamic resilience)."2.2. Features of Transportation System Resilience
The definition of system resilience contains various aspects, and these aspects have beensummarized by [1] as four characteristics (4R): robustness, redundancy, resourcefulness andrapidity. Figure 3 illustrates the schema of the system resilience. Robustness describes theability of a system or unit to withstand a certain level of stress without suffering degradation and to maintain its functionality; Redundancy describes the extent to which the system
Transfer learning for transportation system resilience estimation using floating car data4

contains replaceable components in the event of degradation and loss of functionality; Resourcefulness describes the capacity of system resilience to achieve stability through theavailable resources during the recovery phase; Rapidity describes the time consumption of asystem to minimize losses and satisfy priorities.

Figure 3 Schematic of performance of a resilient system, adapted from [2].

Based on the 4R, more characteristics of the resilience of the transportation system resilience
were proposed, such as adaptability, preparedness, reliability, and vulnerability. Among them,
adaptability emphasizes the flexibility of the system to learn from previous shock events andbecome more robust to better adapt to new stresses [11, 12]; Preparedness refers to thedegree to which the system is prepared for a catastrophic event before being shocked, withthe aim of reducing the negative impact of the shock event on the system [13]; Reliability
measures the probability that the network will still be able to meet part of the demand aftera disruptive event [14]. In the context of transportation systems vulnerability is defined as
the sensitivity of the road system to events that could lead to a significant reduction in roadservice capacity [15]. Although these features are actually the further complement of the 4R,
they are not comprehensive enough to describe system resilience.
Therefore, this thesis applies 4R as the features of system resilience and extends the definition of 4R to transportation systems field:•

Robustness is defined as the ability of the transportation system to satisfy primary traffic
demand under a certain level of stress.

•

Redundancy refers to the capacity of a transportation system to provide alternative routes
or services for the traffic demand in the early stage of the disaster.

•

Resourcefulness describes the ability of a transportation system to provide enough service
for the potential traffic demand during the recovery phase.

•

Rapidity is the ability of a transportation system to reach a new equilibrium state after adisruptive event in a short time.

Transfer learning for transportation system resilience estimation using floating car data5

2.3. Tasks and Methodologies in Different Research Branches ofTransportation Resilience
The introduction of the above concepts and characteristics has inspired many scholars toanalyze transportation system resilience from various aspects. The tasks of system resilience analysis can be divided into several categories: Assessment metrics exploration,
resilience regression model developing, causal impact and resilience patterns prediction. Different methods usually need to be applied for different tasks, including regression models,statistical time series models, and deep learning methods.

2.3.1. Assessment Metrics Exploration
In order to quantify the resilience of systems, considering different disaster types and considering different aspects, numerous scholars have developed different indicators. For instance,[16] introduced a framework to evaluate the impact of floods on road traffic disruption. They
used traffic flow betweenness centrality, overall travel time, and person-minute delay as resilience indicators. They explored the importance of intersections of major roads and networks during hazardous events and identified priority intervention locations. Meanwhile, [17]defined the resilience of a system as the ratio of the system’s recovery level to the loss it
suffered and used the system delivery function to quantify this resilience indicator. [18] proposed an importance-impedance-based rail transit network resilience measurement, using
variables such as node betweenness centrality, passenger volume, and travel time among
different origin-destination pairs under varying levels of impact to define the extent of degradation of rail transit networks during extreme events. Some scholars further used optimization algorithms to calculate system resilience metrics under optimized recovery measures
for transportation networks. [19] used the expected mean of the area between the actual
performance curve and the target performance curve for different stages of transportation
network system performance during disasters as the resilience index. They proposed an OD pair connectivity optimization model based on different resilience actions and calculated
the resilience index for each stage of the transportation network under optimized measures.
However, these methods cannot flexibly consider the time of each stage of the micro-level
resilience pattern, and the complexity of calculating the indicator increases when considering
complex urban networks.

2.3.2. Resilience Regression Model
It has been proven that the logistic model can simulate natural growth. [5] analyze the numberof taxi trips and subways ridership in New York City before and after the impact of Hurricanes,
and applied a logistic function to model the recovery rate. They divided the city into six zones
according to the degree of impact and fitted the resilience models for each zone. The regression models require low computational resources and can reflect the approximate trends ofthe resilience patterns. However, their model failed to capture the temporal dependencies of
the resilience patterns and cannot reflect the seasonality of the model. [3] developed a timedependent recovery rate regression model based on Cox’s proportional hazards regression
Transfer learning for transportation system resilience estimation using floating car data

6

model. The independent variables of their model are region, type of natural disaster, andpost-disaster reconstruction cost, while the dependent variable is the post-disaster reconstruction duration. They conducted a case study in New South Wales, Australia, and used
the likelihood function to calculate the cumulative probability of time to the recovery of transport infrastructure. However, their model only considered the overall recovery time, i.e., therapidity of system, and did not consider the other resilience features, which means that theirmodel failed to describe the specific impact of disasters at different stages.

2.3.3. Causal Impact Analysis
The other type of task is to analyze the causal impact of disasters. The causal impact aims toestimate the causal effect of a particular intervention on the outcome of an event. The widelyused methods in transportation resilience causal impact analysis are statistical time seriesmodels. By comparing with the prediction of the system performance under a no-disaster
scenario, the effect of the disaster could be captured. The autoregressive integrated moving
average (ARIMA) model has high efficiency in stable time series analysis and prediction [20].
[21] applied ARIMA model to predict the short-term GDP of the no-earthquake scenario by
the pre-disaster time series. They focused on the post-disaster macroeconomic recovery ratio(RE) by comparing the simulated GDP and actual value. The Bayesian structural time series(BSTS) model is another method for inferring causal impact. The BSTS model allows theresearchers to add regression components and estimate their potential contributions through
Bayes methods. [7] applied BSTS to infer the non-disaster ridership of four public stations
and used a regression tree to explore the relationship between the resilience of the rail transit
system and possible influencing factors, such as built environment, socioeconomic disparities
and the COVID-19 cases. [22] calculated dynamic time warping (DTW) distance to measure
the similarity between the smooth historical data and the shocked serial data. They measured
the resilience of the ecosystem by developing disturbance magnitude, recovery strength andrecovery rate as the resilience metrics. However, These models usually require long-term
historical data and the performance of the non-disaster scenarios prediction tasks cannot be
guaranteed.

2.3.4. Resilience Patterns Prediction
The above conventional methods are usually used to estimate the resilience of certain disaster events. These models are non-transferable and can hardly be applied in large-scale
scenarios. Currently, deep learning methods such as recurrent neural network (RNN), Long
Short-Term Memory (LSTM), and temporal convolutional network (TCN) have achieved great
success on time series prediction tasks. They provide vital support to predict the whole resilience patterns directly. [23] proposed a bidirectional diffusion graph convolutional layer topredict the transportation system resilience patterns under extreme weather. Their researchalso provided the performance of RNN-based methods, which shows that the RNN-based
methods still have strong prediction performance. However, training a deep neural network
is usually time-consuming, and the insufficiency of the data is always a challenging problem.
Thus, transfer learning methods are widely used in traffic prediction tasks. Due to the limited

Transfer learning for transportation system resilience estimation using floating car data7

knowledge about the transferability of the GNNs, this thesis only adopts conventional neuralnetwork methods as one of the components for traffic prediction tasks.

2.4. Transfer Learning Strategies
The distributions of the traffic data are usually inconsistent among different cities, which is theso-called domain shift. However, most machine learning methods require the training data
and test data to obey the same distribution. A challenge for traffic forecasting is insufficient
data [24] and using past traffic data for a data imputation is always unreliable [25]. Hence,transfer learning methods are popular in traffic data mining tasks. According to [26], transfer
learning techniques can be divided into three categories: inductive transfer learning, transductive transfer learning, and unsupervised transfer learning. The differences between thesetechniques depend on the availability of the labels and the similarity of the tasks between
the source domain and the target domain. In the transportation system resilience predictiontask, the main purpose of transfer learning is to use the prediction knowledge from the other
cities to improve the learning of the target city, which corresponds to the definition of theinductive transfer learning task. [27] summarized the characteristics of three main transfer
learning strategies: transfer without fine-tuning, fine-tuning with freezing transferred layers
and fine-tuning without freezing transferred layers. Their results show that the second strategy requires fewer transferred layers and can achieve better performance in the prediction
tasks. Although under the third strategy the model converges more rapidly, the overfitting
problem significantly affects its performance.

2.5. Literature Gaps
Based on the above literature review, this thesis aims to address the following literature
gaps.

1.

Few works have used transfer learning for transportation resilience prediction and proposed solutions for temporal domain shift.

2.

Few works have performed large-scale resilience patterns prediction at the grid level.

3.

Few works have developed general approaches for transportation resilience prediction
and focused on the predictive performance of the models.

Transfer learning for transportation system resilience estimation using floating car data8

3. Methodology
In this chapter, we first review the concepts and characteristics of FCD in Section 3.1. In therest sections, we introduce the components of the proposed method sequentially. Section 3.2
presents the overall framework of the proposed method and basic assumptions; Specifically,
Section 3.3 introduces the time series clustering methods; Section 3.4 describes the application of the Bayes method; Section 3.5 introduces several conventional neural networks;
Finally, Section 3.6 introduces the transfer learning process.

3.1. Floating Car Data
3.1.1. Characteristics of FCD
To build a robust model that can describe the resilience patterns for the entire city road network, the input traffic data of the proposed model should be able to cover as wide as an urban
area and provide specific details to reflect the citizen’s travel patterns and behavior. Nowadays, floating car data (FCD), which is collected by Global Position System (GPS)-equipped
vehicles, play a vital role in traffic data mining [28]. Compared to traditional methods of obtaining traffic data, the FCD can be provided by various types of vehicles in the whole cityroad network in real time. Therefore, the floating car data has a broader coverage and ismore flexible as road sensors and traffic cameras are always fixed [29], which overcomessome technical and terrain limitations of certain areas or sections. In addition, the FCD includes dimensions, such as positions, speed, time and traffic volume, which strongly support
the research on intelligent transportation systems (ITS) [30]. Therefore, we applied grid FCD
as the input to the proposed model.

3.1.2. Data Availablility
For the input grid FCD, the grid size should be appropriately selected to provide sufficient andstable data for the machine learning models. The grid FCD usually contains traffic volume
and average speed. For traffic volume data, which is sensitive to the number of vehicles
connected, a relatively large grid size could increase the order of magnitude and alleviate theinstability of the data. However, the city road network is sparse, and applying a large gridsize can further reduce data volume after data cleaning. For average speed data, which is
not affected by the number of floating vehicles, a small grid size can be applied to guarantee
a sufficient data volume. However, the speed data fail to reflect the resilience patterns forsome types of disasters. In this thesis, we applied traffic volume to represent the system’s
performance and paid more effort into data cleaning to maintain as much data as possible forthe proposed model.

Transfer learning for transportation system resilience estimation using floating car data

9

3.2. Overview and Basic Assumption
The proposed method of this thesis combines time series clustering, Bayes methods, andartificial neural networks (ANN). This method aims to perform traffic volume resilience patterns prediction on the test set and target domain data set using only pre-disaster data. The
framework of the method is presented in Figure 4, which outlines the steps involved in themethod.

Figure 4 The framework of the proposed method.

In order to predict traffic volume resilience patterns using only pre-disaster data, some prompt
features of the resilience patterns are necessary, which can only be extracted from the training
data, as both the pre-disaster sequence and the during-disaster sequence of the training set
are given. To match the extracted features to the pre-disaster data set, the approach forresilience pattern extraction should depend on the pre-disaster data. Although the distributionof overall traffic volume time series varies from city to city, there are still similarities among
the pre-disaster patterns at the grid level. Therefore, we presented the basic assumptionthat grids with similar pre-disaster characters tend to have similar resilience patterns. To
capture the similarities of the pre-disaster data, we applied the k-shape time series clustering
method to cluster the pre-disaster time series of the training set. In order to extract general
resilience patterns, we mixed the pre-disaster part of the raw grid traffic volume FCD fromdifferent cities as the input to the k-shape method. Then, the clusters, each containing similar
pre-disaster time series from different cities, are generated, and the corresponding duringdisaster time series of the elements in each cluster could be labeled based on the clusteringoutcomes of their pre-disaster parts. In this way, the clusters of resilience patterns can befurther generated.
Based on the “resilience triangle” model, for each cluster of resilience patterns, an overall
resilience pattern can be observed. To extract the overall resilience pattern, we applied theBayes method for each cluster to provide inference for the posterior distribution of duringdisaster traffic volume time series at each time step. Thus, for the grids in the same cluster,traffic volume distributions of each time step can be obtained. In order to extract unbiased
Transfer learning for transportation system resilience estimation using floating car data10

features, the mean value of the distributions is denoted as the extracted prompt features. The
sequence of extracted prompt features represents the average resilience pattern for eachcluster.
Then, the clustered pre-disaster time series and their corresponding average resilience patterns are joined together and fed into different neural networks to predict the actual resilience
patterns. In this way, the pre-trained models can be obtained. For the test set, only predisaster data is given. The pre-disaster data of the test set is first matched to the corresponding cluster directly and then joined together with the corresponding average resilience
patterns extracted from the training set as the input of the neural network.

3.3. Time Series Clustering
In order to find the homogeneity of grids in a city road network, we applied time series
clustering to identify the girds with similar pre-disaster patterns. Here we define a data
set of traffic volume time series in a n-grid road network as G = {g1 , g2 , ..., gn }. The
pre-disaster part of the data set is P = {p1 , p2 , ..., pn } and the resilience patterns of thedata set is R = {r1 , r2 , ..., rn }. The pre-disaster time series P is divided into k clusters

C = {c1 , c2 , ..., ck }, where ci = {pj |j ∈ [1, n]}. Based on the aforementioned basic assumption in Section 3.2, the cluster set of resilience patterns D = {d1 , d2 , ..., dk } can begenerated, in which each cluster di should contain the resilience patterns r from the samegrids as the cluster ci in C , i.e., di = {rj |j ∈ [1, n]}. On the one hand, for the time series in the same cluster, their patterns, trends and other characteristics are similar. On theother hand, the data from different clusters are heterogenous in some features. Thus, themeasurement of similarity between time series directly highly determines the performance ofclustering. The similarity between two pre-disaster time series can be also the described as
distance [31].

3.3.1. Distance Measures of Time Series
Euclidean distance (ED)[32] and time dynamic warping (DTW) [33] are two popular distancemeasures for time series clustering. The main difference between them is evident in thealignment of the time series and the time complexity, as shown in Figure 5. ED can bedirectly calculated through the sum of squared differences between two sequences PS ={s1 , s2 , ..., sm } and PQ = {q1 , q2 , ..., qm } in a point-to-point way as follows:vumuX
ED (PS , PQ ) ≡ t(si − qi )2

(3.1)

i=1

ED is a simple and competitive measure for time series clustering, with a time complexity of
only O(m). However, when the lengths of the time series are different or when the time series
are not aligned at the same time points, ED is not robust enough to reflect the real distance
between two time series, i.e., ED fails to achieve shift-invariance. [34].

Transfer learning for transportation system resilience estimation using floating car data

11

Figure 5 Time series alignment under ED and DTW

In contrast, DTW can handle the unequal length and unaligned time series. As shown in Figure 6, in the DTW algorithm, an m-by-m cumulative distance matrix M needs to be calculated
and a warping path W = {w1 , w2 , ..., wn }, n ≥ m through the matrix represents the distance
between two time series, which is given by the following formula:

v
u n
uX
DT W (PS , PQ ) = min t
wi

(3.2)

i=1

The warping path is selected from M by a dynamic programming process. Given a distancemeasure D between two time points, the elements of the cumulative distance Matrix M aregiven as follows:

M (i, j) =











D (si , q0 ) + M (i − 1, 0),

j=0

D (s0 , qj ) + M (0, j − 1), i = 0







 D (si , qi ) + min{M (i − 1, j), M (i, j − 1), M (i − 1, j − 1)}, others(3.3)

Although the DTW algorithm has achieved the best performance in many kinds of research,
the time complexities for DTW and the dynamic programming process of calculating minimum
time warping path are both O(m2 ). Therefore, applying DTW to a time series clustering
algorithm requires a long calculation time for a large time series data set and leads to low
efficiency. In this thesis, due to the large data volume, DTW is applied for evaluating theTransfer learning for transportation system resilience estimation using floating car data12

performance of the model rather than time series clustering.

Figure 6 Heatmap of cumulative distance matrix and warping path

To tradeoff the time complexity and the robustness of the model, in this thesis, we applied kShape algorithm for time series clustering [35]. The similarity measure of k-Shape algorithm
is the Shape-based distance (SBD). The SBD is calculated through coefficient normalized
cross-correlation (N CCc ) between two time series. According to [35], when computing the

N CCc , one of the sequences PQ = q1 , q2 , ..., qm keeps static and the other sequence PS =s1 , s2 , ..., sm slides over Q to calculate the inner product of their overlapping part for each shiftof PS . Since PS can slide both forward and backward, a total of 2m-1 slides can be generated,which can result in 2m-1 N CCc . The cross-correlation CCk (PS , PQ ) can be computed as:

CCk (PS , PQ ) =Pm−k P
l=1

Sl+k · PQl ,CC (P , P ) ,
Q
S
−k

k≥0

(3.4)

k<0

Where k is the sliding length of sequence PS . When k ≥ 0, the direction of sliding is forward
and when k ≤ 0, the backward sliding of PS can be seen as the forward sliding of PQ . Then,N CCc is defined as follow equation:
CCk (PS , PQ )N CCc = p
R0 (PS , PS ) · R0 (PQ , PQ )Transfer learning for transportation system resilience estimation using floating car data

(3.5)

13

And the SBD is derived as:

SBD(PS , PQ ) = 1 − maxkCCk (PS , PQ )p
R0 (PS , PS ) · R0 (PQ , PQ )

!
(3.6)

The time complexity of SBD is O(m2 ) due to the computation of CCk (PS , PQ ). In order toincrease the efficiency of the calculation, [35] optimizes the computation of SBD by using a
Fast Fourier Transform, which reduces the time complexity of SBD to only O(mlog(m)). The
characteristics of the above distance measures are summarized in Table 1:
Table 1 Characteristics of the distance measures

Distance measure

Time complexity

Shift-invariance

ED

O(m)

False

DTW

O m2

True

SBD

O(mlog(m))



True

3.3.2. K-Shape Time Series Clustering
K-means algorithm are one of the renowned methods for time series clustering [36]. According to [37], the basic steps of the k-means clustering procedure are as follows:
Step 1: Specify the number of K clusters to assign.
Step 2: Randomly initialize K centroids within the feature space.
Step 3: Assign each data point to its closest centroid based on a distance measure.
Step 4: Compute the new average centroid of each cluster.
Step 5: Repeat step 3 and step 4 until the centroids no longer change or the maximum
iterations is reached.
K-Shape algorithm is a k-means-based partitional clustering method with SBD as the distancemeasure, and the centroids are calculated by solving a maximization problem [38]. Based on
Equation 3.4, the centroids of k-Shape can be computed as follow:

2µk ∗ = argmax
µk

X

X


Pi ∈ckPil · µkl (3.7)

l∈[1,m]Where µk ∗ = µk+1 is the new centroid based on the optimization and Pi is the ith time series
from P , i.e., Pi = pi .
By applying k-Shape time series clustering method, the pre-disaster time series P is divided
into k clusters C = {c1 , c2 , ..., ck }, where ci = {pj |j ∈ [1, n]}. For the pre-disaster time

Transfer learning for transportation system resilience estimation using floating car data14

series in each cluster ci , the label i is assigned to their corresponding resilience patterns
from G and the new cluster of resilience patterns di = {rj |j ∈ [1, n]} is generated. Finally, as
presented in Fig 7, k clusters of resilience patterns are extracted from G. In the next section,
we introduce how to extract the shape of resilience patterns for each cluster.

Figure 7 K-shape time series cluster for grid floating car data

3.4. Bayes-Based Shape Extractor
Assuming that for each resilience patterns cluster di , the number of elements is N and theduration of the resilience phase is Nd days. Therefore, for each time step dit in di , a maximumof N values can be sampled. Therefore, for each cluster, Nd data sets are generated, which
represent the days of the resilience patterns. In order to represent the resilience patterns foreach cluster, a Bayes inference method is implemented to generate the posterior distribution
Transfer learning for transportation system resilience estimation using floating car data15

for each data set. The parameter field of each data set is denoted as θ, and the calculationof Bayes inference is given as follows:
posterior

likelihood

priorz }| { z}|{z }| { p (dit | θ) · p(θ)∝ p (dit | θ) · p(θ)
p (θ | dit ) =p (dit )| {z }(3.8)

evidence

where

P (dit | θ) = P
=

n
o 
(1)
dit , . . . , dit (Ni ) | θ

N
Y



P dit (j) | θ

(3.9)

j=1

Here, for each time step dit in cluster di , p(dit |θ) represents the likelihood function and p(dit )is a normalizing constant called evidence. p(θ) is the prior distribution for the parameter θ.
In our research, we applied Gaussian distribution as posterior distribution and uniform priors
for both µ and σ . For k clusters, k · Nd posterior distributions are computed. An exampleof Bayes resilience patterns extraction is presented in Figure 8 and for each posterior, weapplied the mean value mu as the representing resilience patterns.

Figure 8 Example of Bayes resilience patterns extraction. Here we marked an example of resilience pattern extraction with asingle time step. The samples of each time step form a data set. For each cluster di, the resilience pattern extraction process
is repeated Nd times.

Transfer learning for transportation system resilience estimation using floating car data16

In the next section, we summarize the architecture of different neural networks and clarify
how these networks are implemented for the prediction tasks.

3.5. Neural Networks
By applying the k-Shape clustering and Bayes method, prior knowledge about resilience patterns is extracted, which enriches the features for the pre-disaster data of the test set andtransfer learning data set. In order to acquire deep embedding of the features and accomplish prediction task, deep learning models with the prediction heads are applied to automatically learn the prediction parameters. In this thesis, two kinds of deep learning models wereapplied, namely multi-layer perceptron (MLP) and recurrent neural networks (RNNs). For
RNNs, we used a conventional recurrent neural network (RNN) and long short-term memory(LSTM), which are variants of RNN.

3.5.1. Multi-Layer Perceptron (MLP)
MLP is a basic type of feed-forward neural network (FNN). As presented in Fig 9, the nodesof FNN are connected in a directed graph without a circular structure. The inputs of FNN
only flow from the input layer through hidden layers to the output layer in one direction andthe length of inputs and outputs is fixed. The computation of each hidden layer hl is given as
follows:

hl = f wlT xl + bl

(3.10)

Where xl is the input of the current layer, wl represents the weight matrix of the lth layer, bldenotes the bias vector and f is the non-linear activation function.

Figure 9 Sample of a feed-forward neural network

Transfer learning for transportation system resilience estimation using floating car data17

In this thesis, the inputs of the MLP are the joined sequences comprising the pre-disastertime series and the corresponding Bayes resilience patterns. The outputs are the predictedresilience patterns and the labels are the actual resilience patterns.

3.5.2. Recurrent Neural Network (RNN)
In contrast to FNN, in RNNs, the parameters are shared between different time steps to allow
the model to handle the variable-length sequence. As shown in Figure 10, the inputs areprocessed one by one through time in the RNN model, and for each layer, the inputs are not
only the features of the current time, but also the hidden features from the last time step, sothat the RNN can capture the temporal dependency of the time series. The computation of
the hidden feature ht and output yˆt is given as follows:
TT
ht = fh xt Whx+ ht−1 Whh+ bhTŷt = fy ht Wh + by
(3.11)

T is the weight matrix of the input x , W T denotes the weight matrix of the hidden
Where Whxthhfeatures ht−1 from the last time step, WhT is the weight matrix of the ht , yˆt is the output andbh and by represent the bias. fh and fy are non-linear activation functions.

Figure 10 Sample of a recurrent neural network

In this thesis, the inputs of the RNN are also the joined sequences comprising the pre-disastertime series and the corresponding Bayes resilience patterns. Only the outputs from the last
few layers are optimized to predict the resilience patterns.

3.5.3. Long Short-Term Memory (LSTM)Long short-term memory (LSTM) is a variant of RNN, which is designed to solve the gradientproblem in order to remember more information from the past by alleviating the gradientproblem. In RNN, the outputs can only be optimized through hidden features. Once theweights are smaller than zero or larger than one, based on the backward propagation throughtime (BPTT) and chain rule, the successive derivations of the latest outputs can result in their
gradients to the previous inputs converging either zero or infinity when predicting for longsequence. Therefore, the previous information is challenging to propagate to distant future

Transfer learning for transportation system resilience estimation using floating car data18

units. As shown in Figure 11, an LSTM unit contains a memory cell, an input gate, a forgetgate and an output gate. The memory cell is introduced to aggregate the past and current
information, the flow of which is adjusted by the gate units so that the information can beselectively transmitted to the following LSTM units to keep a long-term temporal dependency.
The equations for an LSTM cell are as follows:

it = σ (Wix xt + Wih ht−1 + bi )ft = σ (Wf x xt + Wf h ht−1 + bf )ct = ft ⊙ ct−1 + it ⊙ tanh (Wcx xt + Wch ht−1 + bc )(3.12)

ot = σ (Wox xt + Woh ht−1 + bo )ht = ot ⊙ tanh (ct )yt = Wyh ht + by
Where it , ft , ot denote the input gate, forget gate and output gate respectively, ct is thememory cell, ht represents the hidden state, xt is the input of current time step and yt is theoutput of current time step. For the learning parameters, W denotes the weight matrix andb is the bias. ⊙ denotes the Hadamard product. For activation functions, σ is the sigmoid
function and tanh is the hyperbolic tangent function.

Figure 11 Sample of a long short-term memory network.

Transfer learning for transportation system resilience estimation using floating car data

19

3.6. Transfer Learning
In the transfer learning experiment, the input data is only the pre-disaster grid floating car
data from the other city. As the framework presented in Figure 12, the input traffic volume
time series is first assigned to the corresponding cluster by measuring their SBD to the cluster
centers of each group. The corresponding resilience patterns are then matched to the input
data, and the joined sequences comprising the pre-disaster time series and the resilience
patterns extracted from the cities of the source domain model are fed into the pre-trainedneural networks with frozen parameters. Each pre-trained neural network is stacked with a
MLP for parameter learning. Through this transfer learning process, the transfer learningmodel can predict the resilience patterns only with the pre-disaster data from the other city.
from the other city.

Figure 12 The transfer learning process.

In this thesis, transfer learning was implemented on all of the pre-trained neural networks
from the source domain, aiming to explore and analyze how the extracted average resilience
patterns affect the performance of both the source and target domain models. As the transfer
learning data set is only the FCD from one city, the data volume is far less than the source
domain data set. Besides, the input pre-disaster time series of the transfer learning experiment is different from the source domain models. Specifically, the sequence length of the
inputs is shorter than in the source domain model, which means that they contain fewer predisaster patterns. Therefore, the transfer learning model should overcome both insufficient
data volume and less historical data. As mentioned before, the average resilience patterns
are extracted from the mixed FCD, which means that they balanced the different temporal
distributions of the grid traffic volume and are the embeddings of them in a common feature space so that the model could capture the target city traffic volume distribution fromthe pre-disaster input and the resilience trend from the average resilience patterns. In thisway, we seek to alleviate the domain shift by the unsupervised machine learning methods
before training a neural network and further improve the robustness of the transfer learningmodels.
Transfer learning for transportation system resilience estimation using floating car data20

4. Case StudyIn this chapter, we introduce the case study for our experiment, which is conducted in thecontext of the COVID-19 pandemic. Section 4.1 presents the background and related literature of the case study. Section 4.2 describes the situation of the study areas and Section 4.3
provides a description of the floating car data used in the study.

4.1. Background
COVID-19 virus emerged in late 2019 and spread globally in 2020, posing enormous challenges to public health and economies around the world. As of December 2022, approximately 650 million people worldwide have been infected with COVID-19 and over 6 million
died. Although modern cities have ever experienced pandemics before, the knowledge ofurban resilience under the impact of pandemics is still limited. The blind adoption of travel
control and the urban lockdown has still led to unpredictable consequences, greatly stalling
economic development and reducing the quality of life of citizens [39]. In the future, transportation systems are still likely to face pandemic challenges. Therefore, it is imminent tounderstand the resilience of urban transportation systems under the impact of the pandemic,
which can help governments to react more quickly to the pandemic and to take more effective
pandemic intervention measures in order to ensure the satisfaction of travel demands andlogistics trade under the pandemic.
Unlike natural disasters, the COVID-19 pandemic did not destroy the transportation infrastructure directly but affected travel behaviors and limited the travel opportunities of citizens
indirectly. In order to protect the health of citizens and reduce the economic losses caused by
the pandemic, governments of different countries and regions have taken a series of emergency measures. Among them, the lockdown of event venues, short-term travel control ofcitizens, and quarantine policies are the most commonly used measures. According to [40],the mobility of the population is sensitive to the government’s stay-at-home announcement,
which changed the travel behavior and limited the travel opportunities of citizens, significantly
reducing traffic demand for a period. Citizens may or have to choose to stay at home andreduce the possibilities of travel because of the government-imposed lockdown policies andthe possibilities offered by businesses to work from home.
Under the pandemic control policies, the traffic volumes of many cities showed a sharp decline and then gradually recovered as the control measures were relaxed. Although "resilience triangles" showed in most of the city road networks, the impact of COVID-19 varied greatly in different cities due to their differences in topology and response policies [41].
Therefore, some researchers analyze the resilience patterns for certain cities. [42] applied the
speed reduction index (SRI) as an indicator to investigate the traffic on a small road network

Transfer learning for transportation system resilience estimation using floating car data21

in South Africa during the COVID-19 pandemic. Their study shows that under the strictest
lockdown policy, i.e., with an alert level (AL) equal to AL5, the traffic system experienced little
congestion. In their research, as the alert level decreased to AL1, the performance of thetransportation system recovered gradually but still failed to return to its pre-pandemic state[42]. However, they only implemented the experiment in a small test zone and did not exclude the impact of citizen relocation. The advances in communication and transportation
technologies allow people to remote work and obtain necessary household around their residence area, so some citizens could choose to move to the outskirts of the city. However,with the reopening of urban amenities, some people were inspired to move to the urban
core. [43]. Since the coverage of COVID-19 is broader than natural disasters, the resilienceof urban transportation systems should be considered on a large scale. [44] explored thechanges of citizens’ travel behavior before and during the pandemic by traffic volume data
at a city level. Their results show that traffic volumes at urban intersections during the pandemic were generally lower than before the pandemic, and the distributions of morning andevening peak hours of traffic volumes were flatter during the pandemic. In addition, there
were fixed morning and evening peak hours at city intersections in specific months before
the outbreak, while the peak hours became blurred in specific months during the pandemic.
Their results illustrate that the COVID-19 pandemic radically changes citizens’ travel behavior
and only considering the situation for a certain city is inadequate to understand the changed
scenario.
Therefore, learning from the experience of other cities and studying how to transfer the knowledge of resilience patterns from them is essential. In our research, we applied the proposed
method on the grid traffic volume FCD from three cities: Antwerp, Bangkok and Barcelona.
We used the data of Antwerp and Bangkok for source domain model training and the FCDfrom Barcelona for transfer learning. In the next section, we introduce the basic situation andthe pandemic intervention measures of these cities.

4.2. Study Area
During the COVID-19 pandemic, the transportation systems of these three cities showed different resilience patterns, which depend on their pandemic intervention policies and the rateof disease transmission. The cities where cases first appear tended to implement prevention
measures earlier to slow the spread of the disease and the cities that took measures later
might be more severely affected. Overall, all these three cities implemented strict prevention
measures in March 2020 and gradually eased these measures in mid-2020. Now, we introduce the basic situation and pandemic intervention policies of these three cities: Antwerp,
Bangkok and Barcelona, respectively.
Antwerp is the largest city in Belgium, which is located in the Antwerp Province in the Flemish
region with a geographical coordinate of 51°15’N and 4° 24’E. As presented in Figure 13, theroad network of Antwerp has a radial structure with a relatively dense road network in the city
Transfer learning for transportation system resilience estimation using floating car data22

center and a sparse road network in the outskirts.

Figure 13 ANTWERP road network

In order to combat the spread of the COVID-19 virus, Belgium implemented lockdown polices
on March 18, 2020. The lockdown measures affected schools, restaurants, and workplacesacross the entire nation. The traffic volume of the Antwerp road network decreased sharply
under the pandemic intervention measures, and until May 4, 2020, as the lockdown measures
were gradually eased, some urban amenities were allowed to reopen and the traffic volume
started to recover.
The second city is Bangkok, the capital of Thailand, which is located in the center of thecountry with a geographical coordinate of 13°45’N and 100° 29’E. As presented in Figure 14,
the road network of Bangkok has a ring structure and the roads within the ring have a mix ofTransfer learning for transportation system resilience estimation using floating car data23

grid and radial layouts.

Figure 14 BANGKOK road network

The pandemic intervention measures in Bangkok were implemented since January 3, 2020,
when the Thai Ministry of Public Health started to screen the temperature and issue healthdeclaration cards to travelers. On March 3, 2020, the Thai government started to prohibit
large gatherings and close schools and entertainment venues. Shortly after the closure, thegovernment imposed a curfew since March 26 and until May 17, 2020, the entertainment
places were allowed to reopen. Because of the timely implementation of pandemic intervention policies, the transportation system of the Bangkok road network was relatively lessaffected by the pandemic and showed more resilient patterns.
Barcelona is the city for the transfer learning experiment in this research, which is located on
Transfer learning for transportation system resilience estimation using floating car data24

the northeast coast of Spain with a geographical coordinate of 41°23’N and 2° 11’E. As presented in Figure 15, Barcelona has a comprehensive network structure that consists mainlyof ring and radial roads, and some blocks in the city center have a grid structure.

Figure 15 BARCELONA road network

The government of Spain implemented lockdown measures since March 14, 2020 and extended the measures until April 26. After that, the prevention measures began to ease andon May 11, 2020, citizens were gradually allowed to resume social activities. During the
pandemic, the traffic volume of Barcelona experienced a sharp decline and then gradually
recovered at an unstable rate.
The governments of these cities have all implemented strict prevention policies and achieved
remarkable results. In the next section, we introduce the grid traffic volume FCD used in thisTransfer learning for transportation system resilience estimation using floating car data25

thesis and present the resilience patterns of these cities through data.

4.3. Data Description
The grid traffic volume floating car data is provided by HERE [45] and was used for NeurIPS
Traffic4cast competitions [46]. Half of the data of each city is from February 02, 2019, to June30, 2019, before the appearance of the COVID pandemic and the other half is from February
02, 2020, to June 30, 2020, during the first outbreak of the pandemic. Therefore, the datacontains 180 days of pre-COVID patterns and 181 days during and after the first outbreak
patterns. As shown in Figure 16, the data for our experiment is a (288,495,436,4) tensor
for one day. The first three-dimension encode the number of 5-min time intervals and thenumber of 100m×100m grids for each city and the four channels encode the traffic volume
of four directions of each grid. In our experiment, we merged the time interval into one day
to avoid multiple seasonality and then applied two different grid sizes, i.e., 100m square and200m square, to evaluate the stability of the traffic volume FCD.

Figure 16 Grid floating car data

4.3.1. Macroscopic Traffic Volume Resilience Patterns
The traffic volume time series of the whole cities are presented in Figure 17, 18 and 19
respectively. Compared with their pandemic intervention timeline, it can be observed thatthey have different patterns before and during the pandemic.
As shown in Figure 17, the trend of traffic volume time series of Antwerp was relatively stable
before the COVID pandemic. In the first half year of 2019, the values showed a slightly

Transfer learning for transportation system resilience estimation using floating car data26

increasing trend and remained at the same level in the first three months of 2020. After that,the government of Antwerp implemented pandemic preventive measures in March 2020, andthen the traffic flow experienced a sharp decline and then reached its minimum point, which
was only half of the pre-disaster level, by the end of March and maintained a low level fora period. In early May, as the preventive policies were eased, the traffic volume gradually
recovered with a slightly accelerating trend. By the end of June, the overall traffic volume in
Antwerp had recovered to and even surpassed its pre-pandemic level.

Figure 17 ANTWERP traffic volume time series

As presented in Figure 18, the trend of traffic volume of Bangkok was relatively stable before
April 2019 and then declined slightly. In early 2020, because of the timely prevention measures, the traffic volume had a slightly decreasing trend and declined to the minimum pointat the beginning of April. On March 2020, the curve recovered gradually but failed to reach
its original state. The traffic volume of Bangkok did not show a sharply decreased during the
pandemic and has an overall decreasing trend.

Figure 18 BANGKOK traffic volume time series

Transfer learning for transportation system resilience estimation using floating car data27

Figure 19 shows the traffic volume patterns in Barcelona. Unlike the previous two cities, thecurve in 2019 fluctuated with an overall ascent trend and the traffic volume was relatively
stable in early 2020. Then a plunge showed in the curve since the implementation of the
lockdown policies in March and remained at a low level. After the end of the lockdown, thetraffic volume showed an erratic upward trend and recovered to the pre-pandemic level in thelast week.

Figure 19 BARCELONA traffic volume time series

From the macro level, the overall traffic volume in each of the three cities has different trends
and resilience patterns. However, from a microscopic view, the grids of each city containvarious patterns, and for different cities, some grids of them could contain the same patterns.
The smaller the grid size, the more the patterns. In other words, when we evaluate thepatterns for the whole city, we consider the maximum grid size. However, the small grid size
could increase the instability and complexity of data. Therefore, it is necessary to evaluate
the transportation system resilience patterns in different grid sizes.

4.3.2. Microscopic Traffic Volume Resilience Patterns
In order to precisely show the changes in microscopic traffic volumes for each city at different resilience stages, for each city, four heatmaps are presented below for each stage. As
shown in Figure 20, 21, 22, and 23, the pre-disaster heatmap is generated using the data in
2019, while the minimum point heatmap reflects the average traffic volume patterns during
the lockdown policies. The post-disaster heatmap is extracted from the last week of the dataset.
For a 100×100m grid size, the traffic patterns for the city can be presented more detailedly,
which is beneficial for capturing the changes in traffic volume as well as traffic congestion.
As shown in Figure 20, the overall traffic volume of Antwerp is mainly concentrated on thecentral circular road network and extended outwards. During the pre-pandemic period, there
were traffic hot spots with high traffic volume in the city center and circular road network.

Transfer learning for transportation system resilience estimation using floating car data

28

Further research is required to determine whether these areas are at high congestion risk.
During the lockdown period, the traffic volume of the main arterials decreased significantly,
while the traffic volume of some dispersed grids in the periphery remained stable. In the
post-pandemic period, traffic volume on the main arterials and in the city center recoveredand even exceeded the pre-pandemic level. The average traffic volume patterns in Antwerp
remained at pre-pandemic levels.

Figure 20 ANTWERP traffic volume heatmap (grid size: 100m × 100m unit: veh/day)Figure 21 illustrates the traffic volume distribution of Bangkok, which was mainly distributedon the peripheral circular and radial road networks of the city. During the pre-pandemic period, the traffic volume was primarily concentrated on the main roads close to the intersections
and intersections. During the lockdown period, the traffic volume of the city center decreased
significantly, and the traffic volume of the circular road network also experienced a certain degree of reduction. However, on some road sections near the intersections, the traffic volume
still remained at a high level. In the post-pandemic period, the traffic volume on the circularTransfer learning for transportation system resilience estimation using floating car data29

road network showed a trend of recovery to the pre-pandemic level, but the traffic volume of
the city center still had a gap compared to the pre-pandemic level. Compared to Antwerp, theimpact of the lockdown measures on the traffic volume of Bangkok was relatively mild, andthe average traffic volume was close to its normal level.

Figure 21 BANGKOK traffic volume heatmap (grid size: 100m × 100m unit: veh/day)

As presented in Figure 22, the traffic volume on the main roads of Barcelona was relatively
evenly distributed before the pandemic, and there were some grid clusters with high traffic
volume around the main roads. During the lockdown period, the traffic volume on the main
roads decreased significantly, but the traffic volume in some grid clusters did not show too
much change. In addition, more clusters with relatively high traffic volume appeared in the
periphery of the city, which reflects a trend of citizens moving to the outskirts of the city. In
the post-pandemic period, the traffic volume of the main road network has basically returned
to pre-pandemic levels, and the number of traffic-dense clusters in the periphery increased
compared to before the pandemic.
Transfer learning for transportation system resilience estimation using floating car data

30

Figure 22 BARCELONA traffic volume heatmap (grid size: 100m × 100m unit: veh/day)From the heatmaps with 100m × 100m grid size, some mobility trends of citizens as well as
the level of traffic density can be observed. In addition, some grids from different cities had
similar resilience patterns, which can facilitate inter-city knowledge transfer. The heatmaps
also reveal that the road network of each city is sparse, which results in a large amount ofinvalid grid data for each city. Moreover, for smaller grid sizes, the trends of some grids with
low traffic volume are usually unstable and require more data-cleaning efforts.

Transfer learning for transportation system resilience estimation using floating car data31

(a) ANTWERP traffic volume heatmap(b) BANGKOK traffic volume heatmap(c) Barvelona traffic volume heatmap

Figure 23 Traffic volume heatmap (grid size: 200m × 200m unit: veh/day)Figure 23 illustrates the distribution of traffic volume in our study cities using a 200m × 200m
grid size. On the one hand, the traffic volume is averaged to larger grid cells, which results
in a reduction of the traffic volume density in some grids and also decreases the amount ofvalid data for our model. On the other hand, a larger grid size can help to reduce the numberof grids with unstable trends and also the noise of the grid FCD, which can better reflect theoverall transportation system patterns. Although the number of available data is decreased
when using a larger grid size, the percentage of valid data is higher compared to smaller grid
sizes. Both large grid size and small grid size have their own advantages and disadvantages.
In the next chapter, we will present our experimental process and results and discuss theperformance of our model under different grid size conditions.
Transfer learning for transportation system resilience estimation using floating car data32

5. Experiment Setup
5.1. Data Preprocessing
Data preprocessing involves several steps: (1) aggregate the traffic volume into one-hourintervals; (2) pad and join the data based on the grid size (2) reshape the data to three
dimensions (cities, samples, time steps); (3) set a threshold to eliminate part of abnormal
data; (4) run a k-shape clustering for each city and delete the abnormal cluster; (5) normalize
the rest data and reshape the data for source domain cities to the shape (samples, time
steps) and shuffle the data. (6) shuffle the data of the target domain city. (7) For both thesource domain and target domain, 60% of the data are used for training, 20% are used fortesting and the rest 20% for validation.
After the data preprocessing, the data splitting is shown in Table 2. Although the grid area has
been increased fourfold, we are still able to extract a sufficient amount of data from the FCD
dataset, which represents 60% of the 100m × 100m dataset. For the source domain cities,
we used 180-day pre-disaster traffic volume FCD to predict the 181-day resilience patterns.
For the target domain task, we used only 50 days of pre-disaster data to predict 181-day
resilience patterns. Therefore, the total input sequence length of the source domain timeseries is 361 and 231 of the target domain.
Table 2 Data volume

Data

Antwerp+Bangkok

Barcelona

Grid size

100m × 100m

200m × 200m

100m × 100m

200m × 200m

Training set(48881,361)(30634,361)(14370,231)(8805,231)

Test set(16295,361)(10213,361)(4791,231)(2935,231)

Validation set(16295,361)(10213,361)(4791,231)(2935,231)

Total(81471,361)(50700,361)(23952,231)(214675,231)

For 100m × 100m grid size, each city contains 495 × 436 grid cells and each grid contains
the traffic volume time series from four different directions, which means that for each city,
there is a maximum of 863280 traffic volume time series can be extracted. For 200m × 200m
grid size, each city contains 248 × 218 grid cells after padding and each grid also contains
the traffic volume time series from four different directions. Therefore, the dataset of each city
contains a maximum of 216256 time series. Based on the data cleaning results, the valid rateof the datasets can be derived as Table 3:

Transfer learning for transportation system resilience estimation using floating car data

33

Table 3 Data valid rate

Data

Antwerp+Bangkok

Barcelona

Grid size

100m × 100m

200m × 200m

100m × 100m

200m × 200m

Total data volume

1726500

432512863280216256

Valid data volume

81471

50700

23952

14675

Valid rate

4.71%

11.72%

2.77%

6.78%

For 100m × 100m grid size, the valid rate of the Antwerp+Bangkok dataset is 4.71%, and thevalid rate of the Barcelona dataset is only 2.77%. However, when the grid size is extended to200m × 200m, the valid rate of the datasets is 11.72% and 6.79% respectively, which is 2.5
times higher than the 100 m * 100 m grid size.

5.2. Experiment Settings
The architectures of the neural networks are shown in Table 4. Our experiment is deployed ina Windows 11 System with 32 GB RAM and NVIDIA RTX 3080 Laptop Graphics Cards (16GB). The data processing and modeling are performed using Python 3.8 with Tslearn package for k-Shape time series clustering, Pymc package for Bayes method, Pandas, Numpy,
and Pytorch package for deep learning. For more effective learning, we employed the ReLU
activation function, Adam optimizer, Mean Square Error (MSE) loss function, EarlyStoping
technique and learning rate decay technique. For learning rate decay, the initial learning rate
is set to 0.001, and we applied the step decay schedule with the decay rate of 0.75 per 50
steps. The batch size for all models is taken as 64.
For our proposed model, we first applied a Bayes patterns extractor to generate the average
resilience patterns for each cluster, the sequence length of which is 181. Therefore, the input
sequence length of each neural network is the sum of the pre-disaster sequence length andthe average resilience patterns length, which is 361. And for the ablation experiment, we
directly feed the pre-disaster sequence into the neural network with the same architecture as
our proposed model. For each RNN, we added a feedforward network as the prediction headto generate the output. For transfer learning, the parameters of all models were frozen, andtheir outputs were fed into a feedforward neural network for fine-tuning.

Transfer learning for transportation system resilience estimation using floating car data

34

Table 4 Model architecture
Model

Number of Layers

Hidden Size

RNN Predition Head

Input Sequence Length

Output Sequence Length

361

181

361

181

180

181

180

181

Layer 1 = 256
Bayes+MLP

3

Layer 2 = 128
Layer 3 = 181

Bayes+RNN
Bayes+LSTM

3Bayes+BiLSTM

Layer 1 = 16

Layer 1 = 256

Layer 2 = 16

Layer 2 = 128

Layer 3 = 16

Layer 3 = 1

Layer 1 = 256
Bayes+MLP

3

Layer 2 = 128
Layer 3 = 181

RNN
LSTM
BiLSTM

3

Layer 1 = 16

Layer 1 = 256

Layer 2 = 16

Layer 2 = 128

Layer 3 = 16

Layer 3 = 1

For model performance evaluation, we employed Mean Absolute Error (MAE), Mean Absolute
Percentage Error (MAPE), and Time Dynamic Warping Distance (DTW) as metrics, which aredefined as:n

1 X
Yi − Ŷi
M AE =
n×t

(5.1)

v
u n 
2
1u
1X
RM SE = tYi − Ŷi
t n

(5.2)

i=1

i=1

n

DT W =

1X
|Wi |
n

(5.3)

i=1

Where Yi refers to the ground truth, Ŷi represents the predictions, n denotes the numberof samples, t is the total prediction length, and Wi is the warping path length between the
ground truth and predictions (see Section 3.3.1).

Transfer learning for transportation system resilience estimation using floating car data35

6. Results and Discussions
This chapter summarizes the performance and characteristics of our models. The first two
sections present the results and performance of the models using 100m × 100m grid size
datasets in both the source and target domains. In section 6.3, we conduct a sensitivity
analysis of the models using 200m × 200m grid size datasets. Finally, in section 6.4, we
present the results of the ablation experiment.

6.1. Results of Source Domain Model
6.1.1. Average Resilience Patterns
The number of clusters in this thesis was defined by the Elbow method. The Elbow method
involves plotting the within-cluster sum of squares (WCSS) against the number of clusters.
WCSS is the sum of the squared distance between each point and the centroid in a cluster,and the "elbow" of the WCSS curve is selected as the number of clusters to use. As shownin Figure 24, we picked four clusters rather than three clusters as the number of clusters forthe normalized source domain training pre-disaster data to generate more average resilience
patterns.

0.21

WCSS

0.20
0.19
0.18
0.17
2

3

4
5
6
Number of clusters

7

Figure 24 Within-Cluster Sum of Square of different number of clusters (Grid size: 100m × 100m)

Transfer learning for transportation system resilience estimation using floating car data36

Based on the WCSS curve, the k-shape method was applied to cluster the pre-disaster timeseries into four clusters. Figure 25 presents 50 samples of pre-disaster time series in eachcluster. As shown in Figure 25(a) and 25(b), the first two clusters contained the normalized
traffic volume pre-disaster time series with overall stable trends, while the elements of thelast two clusters (see Figure 25(c) and 25(d)) contained some unstable trends. In addition,
an apparent bolded trend curve can be observed among the samples of each cluster, whichmeans that some time series in the same cluster have high similarity, and the shades of color

Normalized traffic volumereflect the number of similar time series in these samples.
1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01

Normalized traffic volume(a) Cluster 0 (pre-disaster)

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01

Normalized traffic volume(b) Cluster 1 (pre-disaster)

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01(c) Cluster 2 (pre-disaster)

Transfer learning for transportation system resilience estimation using floating car data37

Normalized traffic volume

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01(d) Cluster 3 (pre-disaster)Figure 25 Samples of pre-disaster clusters (Grid size: 100m × 100m)

According to the clustering results of the pre-disaster time series, the resilience patterns
can also be correspondingly divided into four clusters. Figure 26 presents the samples ofduring-disaster time series and the extracted average resilience patterns from all elementsin each cluster. Consistent with pre-disaster clusters, an apparent bolded trend curve canalso be observed among the samples of each cluster. The average resilience patterns reflect
the possible normalized traffic volume with the highest degree of confidence in each cluster. As shown in Figure 26(a), the average resilience patterns of cluster 0 showed a slightly
downward trend in mid-March 2020 and a slow upward trend since April 2020. In contrast,
the average resilience patterns of cluster 1 (see Figure 26(b)) presented a more distinct “resilience triangle” shape. The extracted time series in Figure 26(c) and 26(d) had an overall

Normalized traffic volume

downward trend and slight resilience patterns.
1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series(a) Resilience patterns of cluster 0

Transfer learning for transportation system resilience estimation using floating car data

38Normalized traffic volume

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series

Normalized traffic volume(b) Resilience patterns of cluster 1

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series

Normalized traffic volume(c) Resilience patterns of cluster 2

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series(d) Resilience patterns of cluster 3

Figure 26 During-disaster clusters and average resilience patterns (Grid size: 100m × 100m)

The above-presented average resilience patterns of each cluster are the output of the unsupervised resilience patterns extractor and also part of the input to the neural networks.
In the next subsection, we summarize and discuss the results of the source domain neuralnetworks.

Transfer learning for transportation system resilience estimation using floating car data396.1.2. Results of Neural Networks
Table 5 summarizes the performance of different models under different metrics when predicting traffic volume resilience patterns at the grid level. DTW measures the similarity between
time series, MAE measures the difference between prediction and actual value of each time
step, and RMSE emphasizes the impacts of the significant errors.
Table 5 Source domain loss (Grid size: 100m × 100m)

Model & Input features

DTW

MAE

RMSE

BMLP (180+181)

260.60717.22340.0486

BRNN (180+181)

273.541

19.13444.745BLSTM (180+181)

262.951

17.49840.887BBiLSTM (180+181)

261.848

17.74741.504In the source domain, it is evident from the results that the Bayes patterns extractor-based
MLP model (BMLP) achieved the best performance under all three metrics. In contrast, theBayes patterns extractor-based RNN (BRNN) model performed worst. The Bayes patterns
extractor-based LSTM model (BLSTM) and Bayes patterns extractor-based BiLTSM model(BBiLSTM) achieved similar performance close to BMLP. For DTW, the performance of the
BMLP, BLSTM, and BBiLSTM were almost identical, with a difference of less than 1%, while
the performance of BRNN was worse. It appears that the BRNN model failed to capture
the similarity of the traffic volume time series. For MAE, the BLSTM and BBiLSTM models
achieved similar performance as the BMLP model, while the MAE of the BRNN model was
significantly lower than other models, which means that the BRNN model had a relatively
poor prediction accuracy. For RMSE, the BMLP and BLSTM models had relatively low valuesof around 40, significantly lower than the value of the BRNN model. The BBiLSTM model
showed an RMSE value of 41.504 which is slightly larger than the BLSTM model. The RMSE
values show that the prediction of the BMLP and BLSTM model were less influenced bysignificant errors than BiLSTM and BRNN models.
It can be noticed that the BMLP model exhibited more robust prediction performance in our
experiment than RNN-based models in the source domain. The possible reason could be thecumulative error caused by the long prediction length. In RNN-based models, the BLSTM and
BiLSTM performed better than BRNN because the gate mechanism can enhance the ability of
the LTSM-based model to capture the long-term temporal dependencies and achieve similar
performance as the BMLP model.

Transfer learning for transportation system resilience estimation using floating car data40

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
MLP
BMLP

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:MLP
MAPE:BMLP(a) MLP model

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
RNN
BRNN

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:RNN
MAPE:BRNN(b) RNN model

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
LSTM
BLATM

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:LSTM
MAPE:BLSTM(c) LSTM modelTransfer learning for transportation system resilience estimation using floating car data41

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
BiLSTM
BBiLSTM

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:BiLSTM
MAPE:BBiLSTM(d) BiLSTM model

Figure 27 The macro level prediction and true values in source domain (Grid size: 100m × 100m)

To visualize the overall absolute error of the models, the line charts of Figure 27 present
the prediction curves of our models and the Bayes ablated models (refer to Section 6.4 formore details). It can be observed from the line chart that the predictions of the Bayes-basedmodel are almost consistent with the ground truth. As shown in Figure 27(a), the BMLP
exhibited strong robustness over the entire forecasting interval but visible bias in predicting
the peak value for the first month. Additionally, it had relatively low precision at the time steps
with significant changes in trends, and the occurrence times of error were relatively random,which indicates that the BMLP can not capture the dependency between adjacent time steps
but have a strong ability in learning the overall shape of the resilience patterns. As shown in
Figure 27(b), the BRNN performed well in the prediction from January to March. However, themodel showed relatively poor performance when predicting the period with large fluctuations,
i.e., April and May. This result suggests that the BRNN has limitations in capturing the longterm dependencies of the sequence and is not sensitive enough to the changes in the trendsof the time series. The BLSTM model was relatively robust on the overall prediction interval,
as displayed in Figure 27(c). Compared to BMLP, BLSTM performed better in peak value
prediction. In contrast to BRNN, BLSTM can capture significant changes in trends. However,the BLSTM was unstable in predicting the valley values of each period in our experimentand focused more on the trends with large traffic volumes. As shown in Figure 27(d), theBBiLSTM performed better in predicting peak-to-peak values in the first few months. However,for the prediction from mid-March to the end of May, BiLSTM continuously overestimated thetraffic volume. Although BiLSTM can capture future temporal dependencies, the upward trend
during the recovery phase might lead to the overestimation of the redundancy and robustnessof the transportation systems.
In order to quantify and compare the performance of different models in different experiments
for the macro-level prediction, we further introduced the mean absolute percentage error(MAPE) as the metric. The bar charts of Figure 27 present the MAPE of different neural
Transfer learning for transportation system resilience estimation using floating car data42

networks for each time step. For the proposed models, BMLP and BLSTM achieved betteroverall performance than BRNN and BBiLSTM in MAPE. For RNN-based models, BRNN
and BBiLSTM showed better predictive performance in the first three months and relatively
large MAPE in April and May, while BLSTM had a stable performance in the whole prediction
length. For BMLP, although some significant bias in the line chart can be observed in the firstmonth, the large absolute traffic volume keeps the MAPE in a small range.
In general, our models showed strong robustness in predicting the overall traffic volume of thecity in the source domain, and each model has its advantages and disadvantages. Therefore,
the models should be selected under the consideration of specific tasks and goals.

6.2. Results of Target Domain ModelIn the target domain, the input was only 50 days of the Barcelona pre-disaster traffic volume
time series, and a feedforward neural network was stacked to each pre-trained model forfine-tuning. Table 6 lists the prediction performance comparison of different models under
different metrics at the grid level.
Table 6 Target domain loss (Grid size: 100m × 100m)

Model & Input features

DTW

MAE

RMSE

BMLP (50+181)

309.585

20.45882.508BRNN (50+181)

317.416

21.58084.702BLSTM (50+181)

311.488

20.83085.225BBiLSTM (50+181)

311.215

21.50184.558In general, similar to the results of the source domain models, the BMLP showed the strongest
robustness across all three metrics, while the BRNN performed the worst, and the BLSTM
and BBiLSTM exhibited similar performance. The DTW results were consistent between thetarget and source domains. The BMLP-based transfer learning model still exhibited the mostprominent performance in capturing the similarity between traffic volume time series. BLSTM
and BBiLSTM exhibited similar DTW performances, which were close to BMLP. However, the
BRNN still performed poorly in learning time series similarity. The MAE results show thatboth BLSTM and BMLP achieved high accuracy in our traffic volume prediction task, while
BBiLSTM and BRNN had approximately 4% lower prediction accuracy. In terms of RMSE,
BMLP achieved significantly lower errors than other models. Although BLSTM exhibited thehighest accuracy in MAE error, BBiLSTM and BRNN models were less affected by significant
errors. Compared to the source domain tasks, the performance of the BRNN was closer toother models. In the source domain, the performance of BRNN and other models differs byapproximately 5% in terms of the DTW metric. However, in the transfer learning experiment,
the gap had narrowed to approximately 2-2.5%. Regarding MAE, the performance of BRENN
was even closer to BBiLSTM and exhibited better performance than in the source domain.
Transfer learning for transportation system resilience estimation using floating car data

43

For RMSE, BRNN’s performance surpassed BLSTM and was close to BBiLSTM. This result
suggests that although RNN models have a relatively poor ability to capture the similarityof traffic volume time series at the micro level, they exhibited good generalization ability inpredictive accuracy.

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
MLP
BMLP

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:MLP
MAPE:BMLP(a) MLP model

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
RNN
BRNN

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:RNN
MAPE:BRNN(b) RNN model

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
LSTM
BLATM

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:LSTM
MAPE:BLSTM(c) LSTM modelTransfer learning for transportation system resilience estimation using floating car data44

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
BiLSTM
BBiLSTM

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:BiLSTM
MAPE:BBiLSTM(d) BiLSTM model

Figure 28 The macro level prediction and true values in target domain (Grid size: 100m × 100m)

From a macro perspective, all four models achieved robust prediction performance for relatively stable trends but exhibited particular bias in predicting the valleys of the overall resilience pattern, as shown in the line charts of Figure 28. Figure 28(a) illustrates the prediction results of the BMLP model in the target domain. It can be observed that the BMLP
model had generally robust performance and better prediction for the periods with significant
trend changes. Figure 28(b) shows that although the BRNN model could capture the overall
trend of the time series, its predictive ability for the valleys of the resilience patterns is poor.
Compared to the BRNN model, as shown in Figure 28(c), the BLSTM model captured the
downward trend of the resilience patterns better but overestimated the robustness and resourcefulness of the transportation systems. Figure 28(d) shows the prediction results of theBBiLSTM, which showed a more robust performance in predicting the traffic volume of therecovery phase of the time series than the BLSTM.
However, as shown in the bar charts, all of the target domain models experienced large
MAPE when the traffic volume was relatively low. Due to the inconsistency of traffic volume
distribution between the source domain cities and Barcelona and the instability of data dueto the small grid size, the models may show poor prediction performance for the grids andperiods with small traffic volume. The influence of low data stability on the RNN-based models
may be more significant than MLP because the predictions of RNN-based models highly
depend on the correlation between traffic volumes at different time steps. On the other hand,
MLP does not consider the dependency between the prediction results. Additionally, as theamount of the input pre-disaster information decreased in the transfer learning, the stabilityof the grids could significantly determine the quality of the model’s input, which is particularly
important for the prediction performance of the models. Therefore, to analyze the impact ofgrid size on models’ prediction performance, we conducted a sensitivity analysis for the input
data with a grid size of 200m × 200m.

Transfer learning for transportation system resilience estimation using floating car data45

6.3. Sensitivity Analysis
6.3.1. Average resilience patterns
As shown in Figure 29, the elbow points of the WCSS curve appeared when the number ofclusters was 3 and 4. Similar to the previous experiment, we picked four rather than three
as the number of clusters for the normalized source domain training pre-disaster data to
generate more average resilience patterns.

0.21

WCSS

0.20
0.19
0.18
0.17
2

3

4
5
6
Number of clusters

7

Figure 29 Within-Cluster Sum of Square of different number of clusters (Grid size: 200m × 200m)

Figure 30 presents 50 samples of pre-disaster time series in each cluster, which is generated
through the k-shape method. As shown in Figure 30(a), 30(b), and 30(c), the first threeclusters contained the normalized traffic volume pre-disaster time series with overall stable

Normalized traffic volume

trends, while the elements of the last cluster (Figure 30(d)) contained some unstable trends.
1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01(a) Cluster 0 (pre-disaster)

Transfer learning for transportation system resilience estimation using floating car data46

Normalized traffic volume

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01

Normalized traffic volume(b) Cluster 1 (pre-disaster)

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01

Normalized traffic volume(c) Cluster 2 (pre-disaster)

1.0
0.8
0.6
0.4
0.2
0.0

2019-01-02

2019-02-01

2019-03-03

2019-04-02

Time step (t)2019-05-02

2019-06-01(d) Cluster 3 (pre-disaster)Figure 30 Samples of pre-disaster clusters (Grid size: 200m × 200m)

Figure 31 presents the samples of during-disaster time series and the extracted average
resilience patterns from all elements in each cluster. As shown in Figure 31(a), the average
resilience patterns of cluster 0 showed a slightly downward trend in mid-March 2020 and aslow upward trend since April 2020. In comparison, the average resilience patterns of cluster
1 and cluster 2 (see Figure 31(b) and 31(c)) had a slightly upward trend since January 2020and presented a more distinct “resilience triangle” trend. Consistent with the small grid size

Transfer learning for transportation system resilience estimation using floating car data47

experiment, the extracted time series in Figure 31(d) had an overall downward trend andNormalized traffic volumeslight resilience patterns.
1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series

Normalized traffic volume(a) Resilience patterns of cluster 0

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series

Normalized traffic volume(b) Resilience patterns of cluster 1

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series(c) Resilience patterns of cluster 2

Transfer learning for transportation system resilience estimation using floating car data48

Normalized traffic volume

1.0
0.8
0.6
0.4
0.2
0.0

2020-01-02

2020-02-01

2020-03-02

2020-04-01

Time step (t)average resilience patterns

2020-05-01

2020-05-31

2020-06-30

during-disaster time series(d) Resilience patterns of cluster 3

Figure 31 During-disaster clusters and average resilience patterns (Grid size: 200m × 200m)

6.3.2. Source Domain Sensitivity Analysis
Table 7 presents the performance of proposed methods in the source domain under different
metrics for the input data with a grid size of 200m x 200m. Overall, the BMLP model still
outperformed the other three models in all three metrics, and the performance gaps among
the models became more significant (see Table 5).
Table 7 Source domain loss (Grid size: 200m × 200m)

Model & Input features

DTW

MAE

RMSE

BMLP (180+181)

422.888

27.91072.265

BRNN (180+181)

457.91633.76391.761BLSTM (180+181)

441.835

30.10480.205BBiLSTM (180+181)

433.92229.41984.595

For DTW, the BRNN performed the worst, with the error approximately 8% larger than BMLP,
5.5% larger than BBiLSTM, and 3.6% larger than BLSTM. However, in our previous experiment, the performance of BRNN was only about 2.5% lower than BMLP and about 2% lower
than BLSTM and BBiLSTM. This finding indicates that increasing the grid size and reducing
the data volume can improve the differences in the neural networks’ performance to learn
time series similarity. For MAE, the accuracy of BRNN was 22% lower than BMLP, while theperformances of BLSTM and BBiLSTM were similar, which were between BRNN and BMLP.
Compared to the previous experiments, the performance gaps of MAE between the networks
became more significant, but the accuracy of BBiLSTM exceeded BLSTM. For RMSE, BMLP
achieved the best performance. Unlike the previous experiments, BRNN performed worse
than BLSTM. Additionly, the performance of BLSTM was better than BBiLSTM, which indicates that BLSTM was less affected by significant errors in data with a larger grid size thanother models.

Transfer learning for transportation system resilience estimation using floating car data49

At the macro level, the prediction performance of the neural networks is shown in Figure
32. Compared to the results of the previous experiments with a small grid size (see Figure27), the performance of BRNN on the resilience patterns prediction became worse, whileother models still achieved robust prediction performance. As shown in Figure 32(a), BMLP
performed relatively well throughout the entire prediction interval. However, a visible bias
occurred when predicting the peak of the first month, as in the previous experiment. Figure32(c) shows that the ability of BLSTM to predict the valley values of resilience patterns had
decreased compared to the previous experiment. Compared to the bar charts of Figure 32(d)and Figure 27(d), it can be clearly observed that the robustness of BBiLSTM in predicting
valley values and time steps with significant changes in trend had improved.

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
MLP
BMLP

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:MLP
MAPE:BMLP(a) MLP model

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
RNN
BRNN

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:RNN
MAPE:BRNN(b) RNN modelTransfer learning for transportation system resilience estimation using floating car data50

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
LSTM
BLATM

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:LSTM
MAPE:BLSTM(c) LSTM model

2020-01-02

MAPE (%)

Anwerp+Bangkok
traffic volume (1e6 vehs)

1.5
1.25
1
0.75
0.5
0.25
0
-0.25
-0.5
2020-02-01

2020-03-02

Prediction curve
Ground Truth
BiLSTM
BBiLSTM

2020-04-01

Time step (day)2020-05-01

2020-05-31

10
5
0
5
10
2020-06-30

MAPE bar
MAPE:BiLSTM
MAPE:BBiLSTM(d) BiLSTM model

Figure 32 The macro level prediction and true values in source domain (Grid size: 200m × 200m)

6.3.3. Target Domain Sensitivity Analysis
Table 8 presents the performance of the proposed methods under different metrics for thetarget domain experiment when the grid size was 200m*200m. Overall, BMLP showed themost robust performance among all models.
Table 8 Target domain loss (Grid size: 200m × 200m)

Model & Input features

DTW

MAE

RMSE

BMLP (50+181)

440.76729.04975.771

BRNN (50+181)

453.75231.33

80.998BLSTM (50+181)

450.47830.65180.478BBiLSTM (50+181)

445.89630.38477.429Transfer learning for transportation system resilience estimation using floating car data

51

For DTW, although the gap between each neural network and BMLP became more significant compared to the previous experiment (see Table 6), the difference between BRNN and
BLSTM, and between BBiLSTM and BLSTM, had decreased. For MAE, compared to theexperiment with a small grid size, the performance of BBiLSTM had improved relative to
BRNN and BLSTM. For RMSE, BRNN and BLSTM show similar performance, while BBiLSTM outperformed them by approximately 4%. Since a large grid size can contain a large
traffic volume and result in a decrease in the input data volume, which can impact the neuralnetwork’s performance, therefore, in the sensitivity analysis of the source domain, the values
DTW, MAE, and RMSE of the models were higher than those in the previous source domain
experiment. In the target domain, the model’s DTW and MAE were also higher than in theprevious experiment. However, it can be noticed that the RMSE of the models is lower thanthe previous target domain experiment. Although the data volume for training in the target
domain of the sensitivity experiment is only 8805, the number of significant errors is lower
than the transfer learning of the previous transfer learning experiment. This finding indicatesthat increasing the grid size improves the stability of grid traffic volume time series.

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
MLP
BMLP

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:MLP
MAPE:BMLP(a) MLP modelTransfer learning for transportation system resilience estimation using floating car data52

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
RNN
BRNN

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:RNN
MAPE:BRNN(b) RNN model

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
LSTM
BLATM

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:LSTM
MAPE:BLSTM(c) LSTM model

2020-01-02

MAPE (%)

Barcelonatraffic volume (1e5 vehs)

5
4
3
2
1
0
-1
-2
-3

50
40
30
20
10
0
10
20
30
40
50
2020-02-01

2020-03-02

Prediction curve
Ground Truth
BiLSTM
BBiLSTM

2020-04-01

Time step (day)2020-05-01

2020-05-31

2020-06-30

MAPE bar
MAPE:BiLSTM
MAPE:BBiLSTM(d) BiLSTM model

Figure 33 The macro level prediction and true values in target domain (Grid size: 200m × 200m)

Transfer learning for transportation system resilience estimation using floating car data

53

Figure 33 shows the prediction results of transfer learning of various neural networks in thesensitivity analysis experiment. Compared to Figure 28, although the predictive performanceof BMLP was almost similar to the previous experiment, the performance of RNN-based models had improved compared to the previous transfer learning experiment. The RNN-basedmodels could capture more information and temporal dependencies on resilience patterns
and became more robust in predicting the months with significant changes in trends. Among
RNN-based models, BRNN achieved the best prediction performance at the macro level,
which was inconsistent with the previous experimental results. The possible reason is that
BRNN had a better generalization ability for grids with unstable trends, while BiLSTM and
BLSTM focused more on these grids. Therefore, BRNN could better express stable trends at
the macro level.
Table 9 displays the average MAPE loss of the during disaster time series for the experimentswith different grid sizes in predicting traffic volume resilience patterns at the macro level.
Comparing the different Bayes patterns extractor-based models, the evidence suggests that
BMLP achieved the best prediction performance in both the source and target domains forthe 100m x 100m grid size experiment, and the BRNN performed the worst. However, inthe sensitivity experiment, BLSTM and BBiLSTm performed better in the source domain than
BMLP. BLSTM and BRNN outperformed BMLP in the target domain. This evidence indicatesthat increasing the grid size can enhance the temporal correlation of resilience patterns andfacilitate RNN-based models to capture temporal dependencies more accurately. Comparedwith the micro-level results, it can be inferred that BMLP had a better explanation ability for
unstable time series of grid data, while RNN-based models failed to handle the unstable
grid information. However, the ability of the RNN-based models to capture the temporaldependence made them a better prediction than BMLP on a macro-level when the proportionof stable time series data increases.

Transfer learning for transportation system resilience estimation using floating car data

54

Table 9 MAPE of the models in macro level traffic volume resilience patterns prediction

MAPE

100m × 100m

200m × 200m

Model
Source domain

Target domain

Source domain

Target domain

MLP

3.73%

11.91%

2.67%

14.39%

BMLP

1.91%

11.33%

2.22%

9.66%

RNN

2.99%

12.85%

4.59%

15.26%

BRNN

2.39%

15.74%

5.43%

7.12%

LSTM

2.89%

15.29%

3.37%

17.05%

BLSTM

1.89%

14.18%

1.93%

8.72%

BiLSTM

1.98%

18.08%

3.67%

22.04%BBiLSTM

2.18%

15.47%

1.97%

10.61%On the other hand, increasing the grid size can reduce the input data volume of the models.
By comparing the prediction results of the source domain experiments, we found that when
the data volume was relatively sufficient, the model with a larger data volume (100 m x 100
m grid size) performed better generally. However, in cases of insufficient data volume, thetransfer learning performance of Bayes patterns extractor-based models in the sensitivity
experiment far exceeded that of the original experiment. This result suggests that increasing
the grid size can help stabilize the traffic volume time series and significantly impacted theperformance of our Bayes patterns extractor-based models.

6.4. Ablation Experiment Analysis
In the previous section, we discussed the transfer learning performance of the proposed
Bayes patterns extractor-based models. To evaluate the contribution of the Bayes patterns
extractor, we further conducted an ablation experiment by removing the Bayes patterns extractor from the proposed models and directly training different types of neural networks (MLP,
RNN, LSTM, and BiLSTM) to predict the traffic volume resilience patterns.

6.4.1. 100m × 100m Grid Size
Table 10 lists the prediction results of the proposed methods and the ablation experimentmodels in the source domain with a 100m × 100m grid size. It can be observed that theresilience patterns extracted by the Bayes patterns extractor could improve the overall per-Transfer learning for transportation system resilience estimation using floating car data55

formance of RNN-based models while did not improve the performance of MLP. Although in
RNN-based models, the improvement of BRNN compared to RNN was insignificant, BLSTM
and BBiLSTM outperformed LSTM and BiLSTM in all metrics. The possible reason is that the
memory capability of RNN for pre-disaster information is inferior to LSTM and BiLSTM when
the prediction length is long.
Table 10 Source domain ablation experiment (Grid size: 100m × 100m)

Model & Input features

DTW

MAE

RMSE

MLP (180)

258.456

17.29039.888BMLP (180+181)

260.60717.22340.0486

RNN (180)275.61419.37144.916

BRNN (180+181)

273.541

19.13444.745

LSTM (180)273.553

18.88444.033BLSTM (180+181)

262.951

17.49840.882BiLSTM (180)266.64817.96342.597BBiLSTM (180+181)

261.848

17.74741.504

Table 11 shows the prediction results of the proposed methods and the ablation experimentmodel in the target domain under different metrics. As evident from the table, our proposedmodels showed stronger robustness in transfer learning. For DTW, compared to the Bayescomponent ablated models, BMLP, BRNN, BLSTM, and BBiLSTM models performed betteron capturing time series similarity by 4.6%, 7.0%, 6.2%, and 3.3%, respectively. The accuracyof proposed models also improved by 6.0%, 3.8%, 9.2%, and 4.9% in MAE. Moreover, for
RMSE, the accuracy of our models increased by 1-3%.
Table 11 Target domain ablation experiment (Grid size: 100m × 100m)

Model & Input features

DTW

MAE

RMSE

MLP (50)

319.442

21.67983.732

BMLP (50+181)

309.585

20.45882.508RNN (50)

332.087

22.401

82.213

BRNN (50+181)

317.416

21.58084.702

LSTM (50)333.43622.74587.104BLSTM (50+181)

311.488

20.83085.225BiLSTM (50)

330.359

22.54787.788BBiLSTM (50+181)

311.215

21.50184.558From the results of both Table 10 and Table 11, we can conclude that the proposed methods
enhanced the performance of RNN-based models in the source domain and improved thetransfer learning performance of all models.

Transfer learning for transportation system resilience estimation using floating car data56

6.4.2. 200m × 200m Grid Size
Table 12 lists the prediction results of the proposed methods and the ablation experimentmodels in the source domain with a 200m * 200m grid size. It is observed that the Bayes
patterns extractor improved the prediction performance of MLP, LSTM, and BiLSTM, while it
did not improve the overall prediction performance of RNN.
Table 12 Source domain ablation experiment (Grid size: 200m × 200m)

Model & Input features

DTW

MAE

RMSE

MLP (180)

425.39728.49973.701BMLP (180+181)

422.888

27.91072.265

RNN (180)

463.90733.75587.998BRNN (180+181)

457.91633.76391.761

LSTM (180)447.590

31.13884.824BLSTM (180+181)

441.835

30.10480.205BiLSTM (180)448.240

31.19184.537BBiLSTM (180+181)

433.92229.41984.595

Table 13 displays the results of the proposed models and the ablation experiment models in
the target domain with a 200m*200m grid size. According to the table, the proposed models
exhibited a more robust ability to capture the time series similarity and more precise prediction accuracy. Compared to the Bayes component ablated models, BMLP, BRNN, BLSTM,
and BBiLSTM models had better prediction performance by 5.4%, 7.7%, 5.7%, and 7.7%,
respectively, in terms of DTW. The accuracy of the proposed models also improved by 5.9%,
7.5%, 6.9%, and 7.4% in MAE and by 7.0%, 8.8%, and 11.1%, respectively, in RMSE.
Table 13 Target domain ablation experiment (Grid size: 200m × 200m)

Model & Input features

DTW

MAE

RMSE

MLP (50)466.852

31.29883.757

BMLP (50+181)

440.76729.04975.771

RNN (50)487.63133.05486.694

BRNN (50+181)

453.752

31.33480.998LSTM (50)483.80733.01587.595BLSTM (50+181)

450.47830.65180.478BiLSTM (50)476.700

32.10386.023BBiLSTM (50+181)

445.89630.38477.429The results of Table 12 and Table 13 illustrate that the proposed Bayes patterns extractorbased models can significantly improve the prediction ability of traffic volume resilience patterns when the data volume is insufficient and pre-disaster information is limited.

Transfer learning for transportation system resilience estimation using floating car data57

From the macro perspective, the proposed models achieved superior performance in predicting overall traffic volume than the Bayes component ablated models in almost all metrics (seeTable 9). In the experiment with a 100m x 100m grid size, the BMLP, BRNN, and BLSTM
models in the source domain achieved lower MAPE losses than MLP, RNN, and LSTM models by 1.8%, 0.6%, and 1%, respectively. In the target domain, BMLP, BLSTM, and BBiLSTM
models showed lower MAPE losses than MLP, LSTM, and BiLSTM models by 0.6%, 1.1%,
and 2.6%, respectively. In the experiment with a 200m × 200m grid size, the BMLP, BLSTM,
and BBiLSTM had lower losses than MLP, LSTM, and BiLSTM models by 0.5%, 1.4%, and1.7% in the source domain, respectively. In the target domain, the MAE losses of the BMLP,
BRNN, BLSTM, and BBiLSTM models were reduced by 4.73%, 8.14%, 8.33%, and 11.43%,
respectively. It can be noticed that MLP, RNN, LSTM, and BiLSTM models showed a significant decline in performance in the target domain when the grid size increased. However, theBayes pattern extractor-based models demonstrated an increasing prediction performancein such conditions. This result suggests that our Bayes pattern extractor-based models exhibited better robustness for more stable data and enhanced the transferability of the neuralnetworks when predicting traffic volume resilience patterns. Additionally, by comparing Figures 27, 28, 32, and 33, we can infer that Bayes pattern extractor-based models primarily
contributed to the model’s robustness in predicting peak and valley values. Although theBayes component ablated models (MLP, RNN, LSTM, BiLSTM) could learn temporal dependencies between different patterns, they all continuously overestimated or underestimatedthe traffic volume in predicting the overall city resilience patterns. The reason could be theover-capturing of the local unstable traffic trends, which made them fail to express the global
traffic volume trends. In long-term prediction tasks, the accumulative error also was a limitation for RNN-based models (RNN, LSTM, and BiLSTM). However, introducing the Bayes
pattern extractor can provide global information to the neural networks and makes the input
grid time series more stable, which could enhance the models’ robustness in predicting theoverall traffic volume at the macro level. On the other hand, as the traffic volume floating car
data highly depends on the number of vehicles connected, which can increase the instabilityof data with a small grid size. However, the extracted resilience patterns might prevent themodels from learning such unstable trends. Hence, some models’ performance did not show
significant improvements at the grid level.

Transfer learning for transportation system resilience estimation using floating car data58

7. Conclusion
This thesis aims to build a transferable model for capturing and predicting transportation systems resilience patterns using floating car data. The method proposed in this thesis includes
an unsupervised resilience patterns extractor and different kinds of neural networks. By conducting a case study under the context of the COVID-19 Pandemic, we have proven theeffectiveness of our proposed model and achieved satisfactory results.

7.1. Main Contributions and Findings
In this thesis, we applied grid traffic volume FCD as the model inputs and sought to capture
the transportation resilience patterns from the FCD by a series of machine learning methods.
The proposed framework in Section 3.2 combines both unsupervised machine learning methods and supervised deep learning methods. The unsupervised machine learning methods
include the time series clustering method and the Bayes inference method. Through thesemethods, we created prompt features for the grids with homogeneous resilience patterns
and formed the average resilience patterns as the additional input of the neural networks.
In the experiments, we evaluated the performance of different neural networks and further
discussed the pros and cons of them through ablation analysis and sensitivity analysis experiments.
Additionally, the average resilience patterns extracted from the mixed FCD enable the models
to learn the experience from other cities. In the existing literature, the inputs to the models forthe resilience pattern prediction tasks are mostly only the traffic data at the local level or only
the macro level traffic data. In our experiment, the extracted resilience patterns from different
cities were proven helpful in enriching the features of the input data and could provide macro
information for the deep learning models. Therefore, our proposed methods also achieved
robust performance at the macro level.
Moreover, we conducted a sensitivity analysis (see Section 6.3) to explore the importanceof data stability. In our experiment, although the values of a larger grid size dataset werelarger and the input data volume was decreased, the models achieved less RMSE than theexperiment with a small grid size in the target domain.
More importantly, we explored and analyzed the performance and transferability of the models with different neural network components in the transportation resilience prediction task.
By conducting an ablation experiment (see Section 6.4), we found that our models achieved
better performance in almost all situations of the transfer learning experiments. When increased the grid size, our models exhibited a more robust performance with only thousandsof input data at the macro level, while the traditional neural networks experienced a drop in

Transfer learning for transportation system resilience estimation using floating car data59

performance.

7.2. Limitations
Although the proposed method achieved satisfactory performance in our case study, there
are still limitations require further research.
1.

The extracted resilience patterns allowed the proposed method to learn experiencesfrom different grids and cities, and we successfully applied it in our case study. However, the COVID-19 pandemic lasted for a relatively consistent duration globally. Therefore, the proposed method has not been proven effective between the time series withdifferent disaster duration. In reality, most disasters have different duration, and collecting data with the same disaster duration requires considerable effort and is not always
practical.

2.

This thesis assumed that cities with similar pre-disaster traffic volume patterns would
exhibit similar resilience patterns during the pandemic. Therefore, we applied time series clustering to capture the similarity of the grids. However, the performance of timeseries clustering depends on how similar are the pre-disaster patterns between different grids and cities. In this thesis, we only collected floating car data from two cities forresilience patterns extraction, which cannot guarantee that each grid from the target
city could have the right category to correspond. Therefore, collecting resilience patterns from more cities to enrich pre-disaster pattern categories can potentially enhance
the model’s performance.

3.

This paper only used traffic volume to measure the resilience patterns of the transportation system but did not consider other features of the floating car data. However, traffic
volume floating car data is probably unstable at the grid level and highly depends on
the number of GPS-equipped vehicles. Therefore, features like average speed should
also be considered. Furthermore, this paper only considered the similarity of the data
itself but neglected the spatial similarity between grids. Therefore, introducing spatial
features may help classify grids more precisely and extract resilience patterns moreaccurately.

7.3. Outlook
Considering the limitations of the proposed method, future efforts should be paid in several
potential research directions.
1.

Learn a deep embedding for the extracted resilience patterns. In order to address
the problem of potential differences in the duration of resilience patterns between different cities it is necessary to learn deep embeddings of the extracted resilience patterns.

Transfer learning for transportation system resilience estimation using floating car data60

A feasible solution is to first perform the Bayes-based feature extraction on the grids
from the same city after time series clustering between different cities. Then, using a
representation learning method to learn the embeddings of resilience patterns of thesame cluster from different cities.
2.

Increase the sources of Floating Car Data. In our case study, we only extracted theresilience patterns of the FCD data from two cities, but some grids in the target city did
not belong to any cluster. Therefore, collecting FCD data from more cities to generate
more clusters and extract more types of resilience patterns is necessary.

3.

Enrich the input features for the model. For pandemics, demand loss is the reason
for the performance decline of the transportation system. However, for other disasters,
the average speed is also an important feature that can reflect the resilience patterns ofurban transportation systems. Moreover, even though some grids have the same predisaster patterns, their difference in spatial structures may result in entirely different
resilience patterns. Thus, clustering of node features (node degree, node centrality,
graphlets) should also be considered as a future research direction.

Transfer learning for transportation system resilience estimation using floating car data61

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Declaration

I hereby confirm that the presented thesis work has been done independently and using only the sources
and resources as are listed. This thesis has not previously been submitted elsewhere for purposes ofassessment.

München, 09.05.2023, Signature