# Sustainability Measurement of Transportation Systems in China: A System-Based Bayesian Network Approach

Authors: Wu Jiang; Zhou Huan
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Sustainability has been a challenging issue in the transportation industry, which necessitates obtaining a better measurement of transport sustainability performance. To appropriately measure performance, this paper presents a hybrid approach based on the hierarchical Bayesian network model (BNM) and Principal Component Analysis (PCA). The proposed BNM encompasses social, economic, environmental, and technological dimensions, where each dimension consists of various subdivisions. The Conditional Probability Table of the model is determined by PCA. Twenty-three sustainable transportation indicators involved in the different stages of traffic management are used to kick off the calculation and probability propagation. The results show that the overall transport sustainability of the selected cities is generally at a medium level, indicating that there is much room for further improvement. The sustainability-economic coupling analysis exhibits the nonlinear relationship between sustainability and economic level, revealing that economic growth does not necessarily lead to the enhancement of the transport sustainability. Additionally, the sensitivity analysis reveals that “Accessibility,” “Serviceability,” “Reliability,” and “Innovation” demonstrate an upward trend, indicating their great effect on transportation sustainability. Last, the policy implications of this study can not only offer a solution for the current needs of transportation systems but also serve as more transparent decision-making to develop a sustainable transportation system in the future.


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## Body

## 1. Introduction

Socioeconomic progress, dramatic population growth, and urbanization in recent decades have led to continually growing demand for travel and freight in transportation worldwide, imposing a huge burden and significant challenges on transportation systems [1, 2]. Indeed, increasing transport volumes have resulted in the degradation of both human habitat and the environment; with 103.13 million tons of CO2 emissions in 2018, China was the largest CO2 emitter in the world [3], and transportation was responsible for 25% of the total energy-related CO2 emissions and 65% of the liquid fuel consumption in 2016. The degree of haze pollution suggested to be related to vehicle emissions has been considerably aggravated, especially in the Beijing-Tianjin-Hebei region. Additionally, chronic stresses such as severe congestion and inadequate accessibility critically affect social efficiency and quality of life and ultimately affect the sustainability of our transport systems and society as a whole [4]. In response to these disturbances, the United Nations introduced Sustainable Development Goals [5], and promoting sustainable industrialization was identified as one of the key factors to support economic development and human wellbeing [6]. Achieving sustainability has become a common vision, and traffic policy-makers and practitioners show increasing interest in it and view it as an emerging and essential part of the bigger picture of sustainability.The sustainability of transportation systems, as a multifaceted concept, is normally perceived as a compound system capability, which is believed to be the ability of transportation systems to meet society’s transport and mobility needs safely, support a vibrant economy, and establish relationships without sacrificing other essential human or ecological values, today or in the future [7–10]. To reach a sustainable transportation system, policy-makers are required to comprehensively and appropriately measure the current conditions and continuously monitor the sustainability performance of a transportation system [11]. Measuring transport sustainability may contribute to easy-to-understand results, make stakeholders quickly observe and compare the effects of a proposed traffic management strategy, and readily track trends in transportation system performance towards or away from sustainability [12]. Finally, meaningful decision-making and proper action taking can lead to a more sustainable transportation system.Thus, measuring the sustainability of transportation systems has become an increasingly important topic for traffic policy-makers. However, the measurement of sustainability is a sophisticated and challenging task [13]. A transportation system is highly dynamic, complex, and transdisciplinary in nature [14]. Meanwhile, sustainable transportation is a multiattribute issue in which various indicators from all sustainability dimensions and their subdivisions should be fully taken into account and appropriately chosen [15]. Additionally, the development of sustainable transportation is associated with a great amount of complexity and uncertainty, which makes it more laborious to measure [16]. These eminent challenges lead to an important question: how can suitable quantitative methods be applied to measure the sustainability of a transportation system from a comprehensive point of view?Numerous studies applied different methods to deal with the transport sustainability. Mahdinia et al. [4] used the Principal Component Analysis method to measure the transport sustainability of fifty states in the USA. De Gruyter et al. [17] used equal weighting method to assess the sustainability of urban public transit systems of several cities in Asia and the Middle East region. Alonso et al. [18] developed a composite index by using equal weighting method to measure the transport sustainability of twenty-three cities in European countries. Stefaniec et al. [19] studied the sustainability of inland transportation in China by applying a triple bottom line-based network DEA approach. Rajak et al. [20] used a fuzzy logic method to evaluate the systems performance of sustainable transportation. Jeon et al. [9] demonstrated an application of Multiple Criteria Decision Making (MCDM) approach for evaluating transportation sustainability at the planning level in the Atlanta region. Baghizadeh et al. [21] developed a G/M/S/M queuing system to optimize transportation system in sustainable logistic for the first time. Ling et al. [22] focused on the sustainability of urban transportation development in China from behavioral perspective. Afrin and Yodo [23] presented a Bayesian network model for probabilistic estimation of traffic congestion. Baghizadeh et al. [24] focused on the resilient route to increase the flexibility of the transportation networks to minimize all costs. Chan et al. [25] focused on the sustainability of public transportation through an examination of user behavior after real-time GPS tracking application.Many studies developed hybrid methods. Shiau and Liu [26] used Fuzzy Cognitive Map (FCM) and Analytic Hierarchy Process (AHP) to develop the cause-effect relationship for sustainability evaluation of Taipei city. Bray et al. [27] developed a hybrid model with a fuzzy set and DEA to measure the freight transport efficiency. Awasthi and Chauhan [28] presented a hybrid model with AHP and Dempster–Shafer (D-S) theory to evaluate the impact of sustainable transportation on city planning. Staš et al. [29] combined the balanced scorecard (BSC) with Analytical Network Process (ANP) to measure the performance of the green transport initiative in the European automotive industry. Sayyadi and Awasthi [30] presented an integrated approach based on system dynamics and ANP for evaluating sustainable transportation policies.Prior researches elucidated two limitations. First, a few number of indicators [9, 19, 25] had been used, or sustainability frameworks were mostly confined to few dimensions [4, 22], such as economic, social, and environmental. Second, equal weighting method [17, 18] or AHP method [26, 28] has some limitations in measuring sustainable transport. Equal weighting method assigns equal importance to various indicators; however, this is not the case in reality. AHP based on expert judgment may introduce subjective elements. Therefore, there remains a pressing need for an appropriate method to interpret the complex goal of sustainable transport through using a diverse range of indicators.Sabet et al. [31] developed a consistent framework to objectively evaluate and compare the travel performance of eleven global cities. Baghizadeh et al. [32] suggested a multiperiod and multiproduct Mixed-Integer Nonlinear Programming (MINLP) model considering transportation discount systems for a sustainable supply chain. Inspired by these ideas, we propose a system-based Bayesian network model for probabilistic measuring multidimensional transport sustainability and comparing cities with a consistent framework. The main contributions of this paper are twofold.First, this paper proposes a novel approach with more mathematical rigorousness to probabilistically evaluate the sustainability of a transportation system at the city level. We integrate Bayesian network and Principal Component Analysis (PCA) in this hierarchical model. The Bayesian network is recognized as an excellent tool for tackling probabilistic measurement of multiple variables. PCA is a data-driven statistical method for weighting; their combination can achieve a more powerful effect. This integrated method can appropriately capture complex system’s multidimensional and dynamic attribute in measuring system sustainability and reduce the subjectivity at the same time. In this way, we demonstrate an improved methodology to manage multiattribute decision problem with dynamic characteristics and a great amount of uncertainty. This enriches the decision-making toolkit for transport managers, policy-makers, and other relevant stakeholders.Second, this paper develops a robust four-layer hierarchical Bayesian network model (BNM) to interpret transport sustainability from a broader and exhaustive perspective. The proposed model encompasses three dimensions, namely, economic, social, and environmental, and adds the fourth technological dimension as an important pillar. Furthermore, we consider various multidimensional indicators involved in different stages of design, construction, operation, management, and innovation. This best utilizes available potentially rich sources of statistical data to identify abstract-related sustainability.The rest of this paper is organized as follows. Section2 introduces the methodology, including the fundamental theory of the Bayesian network, constructing the structure of the Bayesian network model, and the procedure of setting the Conditional Probability Table of the Bayesian network model based on Principal Component Analysis. Section 3 and Section 4 elaborate upon case studies and empirical findings from the model inference, which lead to managerial and practical implications. Finally, Section 5 provides conclusions of the study, implications, limitations, and guidance for future research.


## 2. Methodology

### 2.1. Theory of Bayesian Network

A Bayesian network model (BNM), also called a Belief network model, is a combination of graph theory and probability theory [33]. It is composed of a directed acyclic graph (DAG) and a joint probability distribution (JPD) [34]. DAG, also known as the structure of the BNM, consists of nodes and arcs between nodes. Nodes represent different random variables, and arcs represent the association relationship within the variables [35, 36]. The relations represented by DAG allow JPD to be specified by the Conditional Probability Table (CPT) of each node [37]. The essence of BNM is to compute the posterior probability distribution of target variables conditioned on input variables [38–40].For the purpose of mathematically representing BNM, we letV = {X1, X2, …, Xn} be the set of variables in a given BNM, and the conditional dependence among variables is represented by the topology of the network. As shown in Figure 1, an outgoing arc from X1 to X4 indicates that X1 is the parent node of X4, and X4 is the child node of X1. In general, there are three kinds of nodes in BNM: (1) root nodes are those nodes without parent nodes, (2) leaf nodes are those nodes without child nodes, and (3) intermediate nodes are those nodes with both parent and child nodes [35]. For example, in Figure 1, the root nodes are X1, X2, and X3, the leaf node is X8, and the intermediate nodes are X4, X5, X6, and X7.Figure 1
An illustrative example of a BNM with eight variables.The association relationships among variables in BNM can be measured by their CPTs [37]. The general expression for full JPD of BNM can be written as follows:(1)PB1,B2…Bn=∏i=1nPBiParentsBi.The design of a BNM involves two steps: determining the structure and setting the CPT for the nodes. Generally, the available methods of designing a BNM can be classified into three categories [41]. The first method is to learn the structure and the CPT entirely on training data. As a data-driven approach, the prominent advantage of this method is rigorousness and objectivity. Nevertheless, it has demanding requirements on both the quantity and quality of the training data. The second method depends entirely on expert prior knowledge for both structure and the CPT. Obviously, the outcome of this method may have discrepancies with the real status due to the limitation in knowledge acquisition [37]. The third method is a combination of the first two methods as a compromise.In this paper, we consider the third method. In fact, a large strand of literature has accumulated on this theme, which can serve as effective prior knowledge for structure learning of a BNM. Moreover, PCA can be applied to determine the CPT of the proposed model. PCA is a multivariate statistical method and is commonly recognized as one of the most useful tools in sustainability studies [42]. The principles of PCA are to construct weights in the indices based on the correlation between the indicators. Owing to its data-driven nature, the subjectivity problem of weighting can be solved [15]. This hybrid method can combine the advantages of BNM and PCA to achieve a more powerful effect. In this way, the proposed BNM can increase the adaptability of the outcome while reducing the subjectivity of the BNM design as much as possible.


### 2.2. Constructing the Structure of the Model

For the structure of the BNM, we design a four-layer hierarchical topology. The top layer is the ultimate goal layer; achieving sustainability is the ultimate goal that the transportation system pursues as mentioned before. The second layer includes the four sustainability dimensions. The third layer is the attribute layer consisting of twelve system attributes related to the four dimensions, and the fourth layer is the indicator layer consisting of multiple indicators. In this proposed BNM, sustainability can be set as a “leaf node,” whose quantitative assessment can be achieved from probabilistic inference from the “root node.” The indicators act as elements of root nodes to kick off the calculation and probability propagation in the BNM (Figure2).Figure 2
Hierarchical layout of the BNM.


#### 2.2.1. Dimension Layer

The purpose of the dimension layer is to establish the macrolevel dimension that directly contributes to the overall system sustainability. At this level, the reasoning process is based on established frameworks and commonly agreed-on definitions proposed in the sustainability engineering field.Many studies have proposed a sustainability framework that includes three main pillars: society, economy, and environment [43–46]. It is noteworthy that the technological dimension is added as the fourth basic dimension in this study based on the powerful momentum presented in transportation development [47, 48]. In other words, the four essential dimensions, including social, economic, environmental, and technological dimensions, outline the four essential abilities of being sustainable (Figure 3). They are generally applied in transportation systems and interpreted as follows:Social dimension: urban transportation is a public product that should satisfy the basic interests of residents in a manner that is consistent with safety and human health [2, 19]. Moreover, it should be equally beneficial for all residents at various socioeconomic levels, especially for the elderly and the disabled.Economic dimension: this dimension indicates that urban transport operates efficiently and supports a vibrant economy [43, 46]. Economic vitality is important to transport systems. The former can nurture the latter. Conversely, sustainable transportation plays a significant role in improving productivity and work opportunities, reducing economic operating costs, facilitating economic development, and finally promoting the sustainable development of the overall economy.Environmental dimension: this dimension indicates that sustainable transportation should be environmentally friendly [43, 44]. Traffic-related emissions and energy consumption should be reduced within the scope of resources and ecological carrying capacity. The negative externalities or threats to the ecological environment should be controlled as much as possible.Scientific and Technological Dimension: the aim of this dimension is to emphasize the powerful momentum of science and technology present in the sustainable development of transport system. In particular, the application of cutting-edge technology in the transportation sector is showing a booming trend [47, 48], and technology-related issues seem to be promising ways to reach a sustainable transportation system.Figure 3
Framework with four dimensions.


#### 2.2.2. Attribute Layer

Twelve fundamental system attributes were introduced to form the attribute layer in the proposed BNM, including “Safety,” “Accessibility,” “Reliability,” “Serviceability,” “Equity,” “Repairability,” “Low-carbon,” “Land-use resilience,” “Economic efficiency,” “Financial affordability,” “Innovation,” and “Intelligence” (Figure4). These attributes are the subdivisions of the aforementioned four dimensions and have significant contributions to general transportation system sustainability.Figure 4
The ontology structure of twelve attributes in the proposed BNM.The five attributes of “Safety,” “Accessibility,” “Reliability,” “Serviceability,” and “Equity” are crucial to the social dimension. Traffic accidents cause unacceptable damage to residents’ lives and properties, leading to social and economic losses. “Accessibility” refers to the ability to reach the destination quickly and easily by various transport services, providing a user-friendly system with lower travel impedance [49]. “Reliability” and “Serviceability” are believed to be the most significant factors of sustainable transport, which meet the basic transportation needs of residents and can bring convenience and improvement of transportation service quality for residents [50]. “Equity” directly and heavily affects social welfare and the public’s sense of gain. Indeed, life is more pleasant when mobility is efficient, accessible, and cheaper. All five attributes inevitably affect the overall quality of life.The three attributes of “Repairability,” “Low-carbon,” and “Land-use resilience” are designed to capture environmental sustainability. As a scarce resource for cities, the use of land can contribute to transportation sustainability. “Repairability” and “Low-carbon” are related to energy preservation, noise pollution prevention, toxic air contaminants, and greenhouse effect prevention, which are associated with urban livability and ecosystem health. All three attributes focus on maintaining the social-environmental balance.The essential economic dimension for sustainability includes “Economic efficiency” and “Financial supportability.” Any sustainable system must be efficient and productive to operate with minimum expense [46]. Public finance, which is directly related to the budget of the city, can nurture urban transportation and ultimately contribute to the safety, accessibility, and innovation of the transportation system.“Innovation” and “Intelligence” are designed to capture the scientific and technological dimension. The former is an inexhaustible driving force for national and social development, and the latter can make cities smarter. Rail transit systems and new energy vehicles can be regarded as the application of innovation and intelligence in the transportation system, which will continue to be an essential part of the urban mobility system in the foreseeable future. New energy vehicles, such as hybrid vehicles, and cleaner diesel vehicles can reduce carbon and toxic gas emissions; others such as tram, subways, and other rail transit systems can greatly increase transportation capacity and efficiency.


#### 2.2.3. Indicator Layer

The indicator layer acts as a microlevel bottom in the proposed BNM, which enables the application of the attribute layer. Indicators are bits of information that reflect the status of a large system from different perspectives. Although many studies have been dedicated to defining an appropriate indicator set, it remains an intangible term with great fuzziness, without any universal rule for its choice. Based on available data and research purposes, a set of indicators, including the level of municipal facilities, peak congestion coefficient, average commute speed, air pollutant emissions, traffic power consumption, and new energy vehicles, are deliberately chosen as root nodes in the BNM. During the selection, these indicators are involved in the different stages of traffic management such as design, construction, operation, maintenance, and innovation to ensure its comprehensiveness and universality. Table1 illustrates a summary of the nodes in all three layers.Table 1
Summary of all the nodes in the proposed BNM.
Dimension layerIndicator layerUnitD1: socialS1: ratio of fatalities on traffic accidentsN/AD2: environmentalA1: area of paved roads10000 Sq.mD3: economicalA2: length of paved roadskmD4: scientific and technologicA3: per capita area of paved roadsSq.mAttributes layerA4: per vehicle area of paved roadsSq.mAT1: safetyR1: congestion indexN/AAT2: accessibilityR2: average commute speedkm/hAT3: reliabilityR3: passenger capacity of urban public transport10000 personAT4: serviceabilitySE1: number of public transport operating vehicles10000 vehiclesAT5: equitySE2: length of public transport operation linekmAT6: repairabilitySE3: number of vehiclesVehicleAT7: low-carbonE1: per capita households expenditure on transportationYuanAT8: land-use resilienceE2: ratio of per capita households expenditure on transportationN/AAT9: economic efficiencyR1: toxic air contaminants emission by transportationμg/m3μg/m3AT10: financial affordabilityR2: greenhouse gases emission by transportationμg/m3AT11: innovationR3: noise pollutionDecibelAT12: intelligenceL1: electricity consumption by transportation10000 kwhLA1: area of land consumed by transportation infrastructureSq.kmEC1: GDP of the transportation industry100 million YuanF1: fiscal expenditures on transport100 million YuanF2: fixed asset investment on transportation100 million YuanI1: length of rail transit linekmI2: number of new-energy vehiclesVehicle


### 2.3. Determining the CPT of BNM Based on PCA

PCA is used to determine the CPT of the proposed BNM. For the sake of clarity, the process of determining the CPT is divided into four steps as follows.


#### 2.3.1. Normalization of Indicators

The raw data must go through normalization because they have different units, which may cause inconsistency [51]. In this study, the indicators are normalized by using the truncated normal distribution method (TNORM). This method treats the raw data as random variables and models a truncated normal distribution by calculating the mean μ, standard deviance (STD), upper bound (UB), and lower bound (LB) of the variables (Figure 5). For instance, the μ of a certain variable is a, the STD is b, UB is determined as the maximum value, LB is the minimum value, and “1” expresses the cumulative probability of the variable. Then, the TNORM is used for modeling:(2)TNORM∼μ=a,STD=b,UB=maxx,LB=minx,1.Figure 5
An illustrative example of a truncated normal distribution.In a BNM, the node variables are Boolean variables with two states of positive and negative. If an indicator is a positive-effect indicator, then its normalized value is calculated as the integral of the probability density of TNORM to [LB,X]. If an indicator is a negative-effect indicator, its normalized value is calculated as the integral of the probability density of TNORM to [X, UB]. Raw data are normalized to a range between 0 and 1 by implementing this method.


#### 2.3.2. Calculation of Subdivision Weights

The calculation of subdivision weights is demonstrated in the second step. In this step, the latent factors (j) of indicators (k) corresponding to each subdivision (s) and dimension (d) are extracted by applying PCA. NIkjsd stands for the normalized indicator value. Then, the indicators corresponding to each latent factor (j) are weighted by equation (3) and aggregated by equation (4).(3)Wkjsd=FactorLoadingkjsd2Eigenvaluejsd,k∈Ks,j∈JS,s∈Sd,d∈D,(4)CFIjsd=∑kWkjsdNIkjsd,k∈Ks,j∈Js,s∈Sd,d∈D.After calculating the composite factor indicesCFIjsd by equation (4), the weights of subdivision can be calculated by equation (5). Then, composite subdivision indices CSIsd can be aggregated by using equation (6).(5)ajsd=Eigenvaluejsd∑JSEigenvaluejsd,j∈Js,s∈Sd,d∈D,(6)CSIsd=∑jajsdCFIjsd,j∈Js,s∈Sd,d∈D.


#### 2.3.3. Calculation of Dimension Weights

The analysis process of the third step is somehow similar to that of the second step. However, the output of this step will be dimension weights. In this step,j′ is the latent factor of each dimension (d). The weights of latent factors can be calculated by equation (7), and then composite factor indices CFIj′d can be aggregated by equation (8). Then, the weights of the dimensions can be calculated by equation (9).(7)Wsj′d=FactorLoadingsj′d2Eigenvaluej′d,j′∈Jd′,s∈Sd,d∈D,(8)CFIj′d=∑sWsj′dCSIsd,j′∈Jd′,s∈Sd,d∈D,(9)aj′d=Eigenvaluej′d∑j′Eigenvaluej′d,j′∈Jd′,d∈D,(10)CDId=∑j′aj′dCFIj′d,j′∈Jd′,d∈D.


#### 2.3.4. Determining the CPT of BNM Based on the Weight System

The weights of each subdivision and each dimension were calculated by PCA in the former steps. Finally, in this step, the weight system will be applied to determine the CPT of BNM. The derivation of the equivalence relationship is as follows: taking indicatorsE1 and E2 aggregated into subdivision AT5 as an example, the relationship is(11)AT5=E1×βE1+E2×βE2βE1+βE2=1.This paper uses TNORM to normalize the raw data. As mentioned before, the node variablesE1 and E2 are Boolean variables with two states of positive and negative. Therefore, the following expressions are obtained:(12)PE1=P+PE1=N=1PE2=P+PE2=N=1.After introducing equation (12) to equation (11), we can obtain equation (10). In equation (10), the probability expression of variable AT5 with state of positive can be extended to four items, which are four possible cases of the combination of E1 and E2.(13)PAT5=P=PE1=P×βE1+PE2=P×βE2=PE1=P×PE2=P+PE2=N×βE1+PE2=P×PE1=P+PE1=N×βE2=βE1+βE2×PE1=P×PE2=P+βE1×PE1=P×PE2=N+βE2×PE1=N×PE2=P+0×PE1=N×PE2=NβE1+βE2=1.In BNM, the conditional probability relationships between a child node and its parent node can be written as follows:(14)PT=t=∑1NPT=tX1=x1,…,Xn=xn×PX1=x1,…,Xn=xn.Under the assumption that the child nodes are independent of each other, we can obtain equation (15). Equation (15) describes the conditional probability relationships between child nodes (E1, E2) and their parent node (AT5) in Bayesian network. In equation (15), the probability expression of variable AT5 with state of positive can also be extended to four items, which are four possible cases of the combination of E1 and E2.(15)PAT5=P=PAT5=P|E1=P,E2=P×PE1=P×PE2=P+PAT5=P|E1=P,E2=N×PE1=P×PE2=N+PAT5=P|E1=N,E2=P×PE1=N×PE2=P+PAT5=P|E1=N,E2=N×PE1=N×PE2=N.By comparing equations (13) and (15), it can be found that they are highly similar in mathematical structure, and the weight in equation (13) corresponds to the four items of conditional probabilities expressions in equation (15) exactly. Based on this, we determine the CPT of BNM. The detailed meaning of the determined probability table is as follows: when child nodes E1 and E2 are both in the state of positive, the parent node must be in the state as positive. When E1 is in the state of positive and E2 is in the state of negative, the probability that the parent node is in the state of positive is βE1. When E1 is in the state of negative and E2 is in the state of positive, the probability that the parent node is in the state of positive is βE2. When both child nodes are in the state of negative, the parent node must be in the state of negative, as shown in the following equation.(16)PAT5=P|E1=P,E2=P=βE1+βE2PAT5=P|E1=P,E2=N=βE1PAT5=P|E1=N,E2=P=βE2PAT5=P|E=N,E2=N=0.Therefore, we have determined the CPT of BNM.


## 2.1. Theory of Bayesian Network

A Bayesian network model (BNM), also called a Belief network model, is a combination of graph theory and probability theory [33]. It is composed of a directed acyclic graph (DAG) and a joint probability distribution (JPD) [34]. DAG, also known as the structure of the BNM, consists of nodes and arcs between nodes. Nodes represent different random variables, and arcs represent the association relationship within the variables [35, 36]. The relations represented by DAG allow JPD to be specified by the Conditional Probability Table (CPT) of each node [37]. The essence of BNM is to compute the posterior probability distribution of target variables conditioned on input variables [38–40].For the purpose of mathematically representing BNM, we letV = {X1, X2, …, Xn} be the set of variables in a given BNM, and the conditional dependence among variables is represented by the topology of the network. As shown in Figure 1, an outgoing arc from X1 to X4 indicates that X1 is the parent node of X4, and X4 is the child node of X1. In general, there are three kinds of nodes in BNM: (1) root nodes are those nodes without parent nodes, (2) leaf nodes are those nodes without child nodes, and (3) intermediate nodes are those nodes with both parent and child nodes [35]. For example, in Figure 1, the root nodes are X1, X2, and X3, the leaf node is X8, and the intermediate nodes are X4, X5, X6, and X7.Figure 1
An illustrative example of a BNM with eight variables.The association relationships among variables in BNM can be measured by their CPTs [37]. The general expression for full JPD of BNM can be written as follows:(1)PB1,B2…Bn=∏i=1nPBiParentsBi.The design of a BNM involves two steps: determining the structure and setting the CPT for the nodes. Generally, the available methods of designing a BNM can be classified into three categories [41]. The first method is to learn the structure and the CPT entirely on training data. As a data-driven approach, the prominent advantage of this method is rigorousness and objectivity. Nevertheless, it has demanding requirements on both the quantity and quality of the training data. The second method depends entirely on expert prior knowledge for both structure and the CPT. Obviously, the outcome of this method may have discrepancies with the real status due to the limitation in knowledge acquisition [37]. The third method is a combination of the first two methods as a compromise.In this paper, we consider the third method. In fact, a large strand of literature has accumulated on this theme, which can serve as effective prior knowledge for structure learning of a BNM. Moreover, PCA can be applied to determine the CPT of the proposed model. PCA is a multivariate statistical method and is commonly recognized as one of the most useful tools in sustainability studies [42]. The principles of PCA are to construct weights in the indices based on the correlation between the indicators. Owing to its data-driven nature, the subjectivity problem of weighting can be solved [15]. This hybrid method can combine the advantages of BNM and PCA to achieve a more powerful effect. In this way, the proposed BNM can increase the adaptability of the outcome while reducing the subjectivity of the BNM design as much as possible.


## 2.2. Constructing the Structure of the Model

For the structure of the BNM, we design a four-layer hierarchical topology. The top layer is the ultimate goal layer; achieving sustainability is the ultimate goal that the transportation system pursues as mentioned before. The second layer includes the four sustainability dimensions. The third layer is the attribute layer consisting of twelve system attributes related to the four dimensions, and the fourth layer is the indicator layer consisting of multiple indicators. In this proposed BNM, sustainability can be set as a “leaf node,” whose quantitative assessment can be achieved from probabilistic inference from the “root node.” The indicators act as elements of root nodes to kick off the calculation and probability propagation in the BNM (Figure2).Figure 2
Hierarchical layout of the BNM.


### 2.2.1. Dimension Layer

The purpose of the dimension layer is to establish the macrolevel dimension that directly contributes to the overall system sustainability. At this level, the reasoning process is based on established frameworks and commonly agreed-on definitions proposed in the sustainability engineering field.Many studies have proposed a sustainability framework that includes three main pillars: society, economy, and environment [43–46]. It is noteworthy that the technological dimension is added as the fourth basic dimension in this study based on the powerful momentum presented in transportation development [47, 48]. In other words, the four essential dimensions, including social, economic, environmental, and technological dimensions, outline the four essential abilities of being sustainable (Figure 3). They are generally applied in transportation systems and interpreted as follows:Social dimension: urban transportation is a public product that should satisfy the basic interests of residents in a manner that is consistent with safety and human health [2, 19]. Moreover, it should be equally beneficial for all residents at various socioeconomic levels, especially for the elderly and the disabled.Economic dimension: this dimension indicates that urban transport operates efficiently and supports a vibrant economy [43, 46]. Economic vitality is important to transport systems. The former can nurture the latter. Conversely, sustainable transportation plays a significant role in improving productivity and work opportunities, reducing economic operating costs, facilitating economic development, and finally promoting the sustainable development of the overall economy.Environmental dimension: this dimension indicates that sustainable transportation should be environmentally friendly [43, 44]. Traffic-related emissions and energy consumption should be reduced within the scope of resources and ecological carrying capacity. The negative externalities or threats to the ecological environment should be controlled as much as possible.Scientific and Technological Dimension: the aim of this dimension is to emphasize the powerful momentum of science and technology present in the sustainable development of transport system. In particular, the application of cutting-edge technology in the transportation sector is showing a booming trend [47, 48], and technology-related issues seem to be promising ways to reach a sustainable transportation system.Figure 3
Framework with four dimensions.


### 2.2.2. Attribute Layer

Twelve fundamental system attributes were introduced to form the attribute layer in the proposed BNM, including “Safety,” “Accessibility,” “Reliability,” “Serviceability,” “Equity,” “Repairability,” “Low-carbon,” “Land-use resilience,” “Economic efficiency,” “Financial affordability,” “Innovation,” and “Intelligence” (Figure4). These attributes are the subdivisions of the aforementioned four dimensions and have significant contributions to general transportation system sustainability.Figure 4
The ontology structure of twelve attributes in the proposed BNM.The five attributes of “Safety,” “Accessibility,” “Reliability,” “Serviceability,” and “Equity” are crucial to the social dimension. Traffic accidents cause unacceptable damage to residents’ lives and properties, leading to social and economic losses. “Accessibility” refers to the ability to reach the destination quickly and easily by various transport services, providing a user-friendly system with lower travel impedance [49]. “Reliability” and “Serviceability” are believed to be the most significant factors of sustainable transport, which meet the basic transportation needs of residents and can bring convenience and improvement of transportation service quality for residents [50]. “Equity” directly and heavily affects social welfare and the public’s sense of gain. Indeed, life is more pleasant when mobility is efficient, accessible, and cheaper. All five attributes inevitably affect the overall quality of life.The three attributes of “Repairability,” “Low-carbon,” and “Land-use resilience” are designed to capture environmental sustainability. As a scarce resource for cities, the use of land can contribute to transportation sustainability. “Repairability” and “Low-carbon” are related to energy preservation, noise pollution prevention, toxic air contaminants, and greenhouse effect prevention, which are associated with urban livability and ecosystem health. All three attributes focus on maintaining the social-environmental balance.The essential economic dimension for sustainability includes “Economic efficiency” and “Financial supportability.” Any sustainable system must be efficient and productive to operate with minimum expense [46]. Public finance, which is directly related to the budget of the city, can nurture urban transportation and ultimately contribute to the safety, accessibility, and innovation of the transportation system.“Innovation” and “Intelligence” are designed to capture the scientific and technological dimension. The former is an inexhaustible driving force for national and social development, and the latter can make cities smarter. Rail transit systems and new energy vehicles can be regarded as the application of innovation and intelligence in the transportation system, which will continue to be an essential part of the urban mobility system in the foreseeable future. New energy vehicles, such as hybrid vehicles, and cleaner diesel vehicles can reduce carbon and toxic gas emissions; others such as tram, subways, and other rail transit systems can greatly increase transportation capacity and efficiency.


### 2.2.3. Indicator Layer

The indicator layer acts as a microlevel bottom in the proposed BNM, which enables the application of the attribute layer. Indicators are bits of information that reflect the status of a large system from different perspectives. Although many studies have been dedicated to defining an appropriate indicator set, it remains an intangible term with great fuzziness, without any universal rule for its choice. Based on available data and research purposes, a set of indicators, including the level of municipal facilities, peak congestion coefficient, average commute speed, air pollutant emissions, traffic power consumption, and new energy vehicles, are deliberately chosen as root nodes in the BNM. During the selection, these indicators are involved in the different stages of traffic management such as design, construction, operation, maintenance, and innovation to ensure its comprehensiveness and universality. Table1 illustrates a summary of the nodes in all three layers.Table 1
Summary of all the nodes in the proposed BNM.
Dimension layerIndicator layerUnitD1: socialS1: ratio of fatalities on traffic accidentsN/AD2: environmentalA1: area of paved roads10000 Sq.mD3: economicalA2: length of paved roadskmD4: scientific and technologicA3: per capita area of paved roadsSq.mAttributes layerA4: per vehicle area of paved roadsSq.mAT1: safetyR1: congestion indexN/AAT2: accessibilityR2: average commute speedkm/hAT3: reliabilityR3: passenger capacity of urban public transport10000 personAT4: serviceabilitySE1: number of public transport operating vehicles10000 vehiclesAT5: equitySE2: length of public transport operation linekmAT6: repairabilitySE3: number of vehiclesVehicleAT7: low-carbonE1: per capita households expenditure on transportationYuanAT8: land-use resilienceE2: ratio of per capita households expenditure on transportationN/AAT9: economic efficiencyR1: toxic air contaminants emission by transportationμg/m3μg/m3AT10: financial affordabilityR2: greenhouse gases emission by transportationμg/m3AT11: innovationR3: noise pollutionDecibelAT12: intelligenceL1: electricity consumption by transportation10000 kwhLA1: area of land consumed by transportation infrastructureSq.kmEC1: GDP of the transportation industry100 million YuanF1: fiscal expenditures on transport100 million YuanF2: fixed asset investment on transportation100 million YuanI1: length of rail transit linekmI2: number of new-energy vehiclesVehicle


## 2.2.1. Dimension Layer

The purpose of the dimension layer is to establish the macrolevel dimension that directly contributes to the overall system sustainability. At this level, the reasoning process is based on established frameworks and commonly agreed-on definitions proposed in the sustainability engineering field.Many studies have proposed a sustainability framework that includes three main pillars: society, economy, and environment [43–46]. It is noteworthy that the technological dimension is added as the fourth basic dimension in this study based on the powerful momentum presented in transportation development [47, 48]. In other words, the four essential dimensions, including social, economic, environmental, and technological dimensions, outline the four essential abilities of being sustainable (Figure 3). They are generally applied in transportation systems and interpreted as follows:Social dimension: urban transportation is a public product that should satisfy the basic interests of residents in a manner that is consistent with safety and human health [2, 19]. Moreover, it should be equally beneficial for all residents at various socioeconomic levels, especially for the elderly and the disabled.Economic dimension: this dimension indicates that urban transport operates efficiently and supports a vibrant economy [43, 46]. Economic vitality is important to transport systems. The former can nurture the latter. Conversely, sustainable transportation plays a significant role in improving productivity and work opportunities, reducing economic operating costs, facilitating economic development, and finally promoting the sustainable development of the overall economy.Environmental dimension: this dimension indicates that sustainable transportation should be environmentally friendly [43, 44]. Traffic-related emissions and energy consumption should be reduced within the scope of resources and ecological carrying capacity. The negative externalities or threats to the ecological environment should be controlled as much as possible.Scientific and Technological Dimension: the aim of this dimension is to emphasize the powerful momentum of science and technology present in the sustainable development of transport system. In particular, the application of cutting-edge technology in the transportation sector is showing a booming trend [47, 48], and technology-related issues seem to be promising ways to reach a sustainable transportation system.Figure 3
Framework with four dimensions.


## 2.2.2. Attribute Layer

Twelve fundamental system attributes were introduced to form the attribute layer in the proposed BNM, including “Safety,” “Accessibility,” “Reliability,” “Serviceability,” “Equity,” “Repairability,” “Low-carbon,” “Land-use resilience,” “Economic efficiency,” “Financial affordability,” “Innovation,” and “Intelligence” (Figure4). These attributes are the subdivisions of the aforementioned four dimensions and have significant contributions to general transportation system sustainability.Figure 4
The ontology structure of twelve attributes in the proposed BNM.The five attributes of “Safety,” “Accessibility,” “Reliability,” “Serviceability,” and “Equity” are crucial to the social dimension. Traffic accidents cause unacceptable damage to residents’ lives and properties, leading to social and economic losses. “Accessibility” refers to the ability to reach the destination quickly and easily by various transport services, providing a user-friendly system with lower travel impedance [49]. “Reliability” and “Serviceability” are believed to be the most significant factors of sustainable transport, which meet the basic transportation needs of residents and can bring convenience and improvement of transportation service quality for residents [50]. “Equity” directly and heavily affects social welfare and the public’s sense of gain. Indeed, life is more pleasant when mobility is efficient, accessible, and cheaper. All five attributes inevitably affect the overall quality of life.The three attributes of “Repairability,” “Low-carbon,” and “Land-use resilience” are designed to capture environmental sustainability. As a scarce resource for cities, the use of land can contribute to transportation sustainability. “Repairability” and “Low-carbon” are related to energy preservation, noise pollution prevention, toxic air contaminants, and greenhouse effect prevention, which are associated with urban livability and ecosystem health. All three attributes focus on maintaining the social-environmental balance.The essential economic dimension for sustainability includes “Economic efficiency” and “Financial supportability.” Any sustainable system must be efficient and productive to operate with minimum expense [46]. Public finance, which is directly related to the budget of the city, can nurture urban transportation and ultimately contribute to the safety, accessibility, and innovation of the transportation system.“Innovation” and “Intelligence” are designed to capture the scientific and technological dimension. The former is an inexhaustible driving force for national and social development, and the latter can make cities smarter. Rail transit systems and new energy vehicles can be regarded as the application of innovation and intelligence in the transportation system, which will continue to be an essential part of the urban mobility system in the foreseeable future. New energy vehicles, such as hybrid vehicles, and cleaner diesel vehicles can reduce carbon and toxic gas emissions; others such as tram, subways, and other rail transit systems can greatly increase transportation capacity and efficiency.


## 2.2.3. Indicator Layer

The indicator layer acts as a microlevel bottom in the proposed BNM, which enables the application of the attribute layer. Indicators are bits of information that reflect the status of a large system from different perspectives. Although many studies have been dedicated to defining an appropriate indicator set, it remains an intangible term with great fuzziness, without any universal rule for its choice. Based on available data and research purposes, a set of indicators, including the level of municipal facilities, peak congestion coefficient, average commute speed, air pollutant emissions, traffic power consumption, and new energy vehicles, are deliberately chosen as root nodes in the BNM. During the selection, these indicators are involved in the different stages of traffic management such as design, construction, operation, maintenance, and innovation to ensure its comprehensiveness and universality. Table1 illustrates a summary of the nodes in all three layers.Table 1
Summary of all the nodes in the proposed BNM.
Dimension layerIndicator layerUnitD1: socialS1: ratio of fatalities on traffic accidentsN/AD2: environmentalA1: area of paved roads10000 Sq.mD3: economicalA2: length of paved roadskmD4: scientific and technologicA3: per capita area of paved roadsSq.mAttributes layerA4: per vehicle area of paved roadsSq.mAT1: safetyR1: congestion indexN/AAT2: accessibilityR2: average commute speedkm/hAT3: reliabilityR3: passenger capacity of urban public transport10000 personAT4: serviceabilitySE1: number of public transport operating vehicles10000 vehiclesAT5: equitySE2: length of public transport operation linekmAT6: repairabilitySE3: number of vehiclesVehicleAT7: low-carbonE1: per capita households expenditure on transportationYuanAT8: land-use resilienceE2: ratio of per capita households expenditure on transportationN/AAT9: economic efficiencyR1: toxic air contaminants emission by transportationμg/m3μg/m3AT10: financial affordabilityR2: greenhouse gases emission by transportationμg/m3AT11: innovationR3: noise pollutionDecibelAT12: intelligenceL1: electricity consumption by transportation10000 kwhLA1: area of land consumed by transportation infrastructureSq.kmEC1: GDP of the transportation industry100 million YuanF1: fiscal expenditures on transport100 million YuanF2: fixed asset investment on transportation100 million YuanI1: length of rail transit linekmI2: number of new-energy vehiclesVehicle


## 2.3. Determining the CPT of BNM Based on PCA

PCA is used to determine the CPT of the proposed BNM. For the sake of clarity, the process of determining the CPT is divided into four steps as follows.


### 2.3.1. Normalization of Indicators

The raw data must go through normalization because they have different units, which may cause inconsistency [51]. In this study, the indicators are normalized by using the truncated normal distribution method (TNORM). This method treats the raw data as random variables and models a truncated normal distribution by calculating the mean μ, standard deviance (STD), upper bound (UB), and lower bound (LB) of the variables (Figure 5). For instance, the μ of a certain variable is a, the STD is b, UB is determined as the maximum value, LB is the minimum value, and “1” expresses the cumulative probability of the variable. Then, the TNORM is used for modeling:(2)TNORM∼μ=a,STD=b,UB=maxx,LB=minx,1.Figure 5
An illustrative example of a truncated normal distribution.In a BNM, the node variables are Boolean variables with two states of positive and negative. If an indicator is a positive-effect indicator, then its normalized value is calculated as the integral of the probability density of TNORM to [LB,X]. If an indicator is a negative-effect indicator, its normalized value is calculated as the integral of the probability density of TNORM to [X, UB]. Raw data are normalized to a range between 0 and 1 by implementing this method.


### 2.3.2. Calculation of Subdivision Weights

The calculation of subdivision weights is demonstrated in the second step. In this step, the latent factors (j) of indicators (k) corresponding to each subdivision (s) and dimension (d) are extracted by applying PCA. NIkjsd stands for the normalized indicator value. Then, the indicators corresponding to each latent factor (j) are weighted by equation (3) and aggregated by equation (4).(3)Wkjsd=FactorLoadingkjsd2Eigenvaluejsd,k∈Ks,j∈JS,s∈Sd,d∈D,(4)CFIjsd=∑kWkjsdNIkjsd,k∈Ks,j∈Js,s∈Sd,d∈D.After calculating the composite factor indicesCFIjsd by equation (4), the weights of subdivision can be calculated by equation (5). Then, composite subdivision indices CSIsd can be aggregated by using equation (6).(5)ajsd=Eigenvaluejsd∑JSEigenvaluejsd,j∈Js,s∈Sd,d∈D,(6)CSIsd=∑jajsdCFIjsd,j∈Js,s∈Sd,d∈D.


### 2.3.3. Calculation of Dimension Weights

The analysis process of the third step is somehow similar to that of the second step. However, the output of this step will be dimension weights. In this step,j′ is the latent factor of each dimension (d). The weights of latent factors can be calculated by equation (7), and then composite factor indices CFIj′d can be aggregated by equation (8). Then, the weights of the dimensions can be calculated by equation (9).(7)Wsj′d=FactorLoadingsj′d2Eigenvaluej′d,j′∈Jd′,s∈Sd,d∈D,(8)CFIj′d=∑sWsj′dCSIsd,j′∈Jd′,s∈Sd,d∈D,(9)aj′d=Eigenvaluej′d∑j′Eigenvaluej′d,j′∈Jd′,d∈D,(10)CDId=∑j′aj′dCFIj′d,j′∈Jd′,d∈D.


### 2.3.4. Determining the CPT of BNM Based on the Weight System

The weights of each subdivision and each dimension were calculated by PCA in the former steps. Finally, in this step, the weight system will be applied to determine the CPT of BNM. The derivation of the equivalence relationship is as follows: taking indicatorsE1 and E2 aggregated into subdivision AT5 as an example, the relationship is(11)AT5=E1×βE1+E2×βE2βE1+βE2=1.This paper uses TNORM to normalize the raw data. As mentioned before, the node variablesE1 and E2 are Boolean variables with two states of positive and negative. Therefore, the following expressions are obtained:(12)PE1=P+PE1=N=1PE2=P+PE2=N=1.After introducing equation (12) to equation (11), we can obtain equation (10). In equation (10), the probability expression of variable AT5 with state of positive can be extended to four items, which are four possible cases of the combination of E1 and E2.(13)PAT5=P=PE1=P×βE1+PE2=P×βE2=PE1=P×PE2=P+PE2=N×βE1+PE2=P×PE1=P+PE1=N×βE2=βE1+βE2×PE1=P×PE2=P+βE1×PE1=P×PE2=N+βE2×PE1=N×PE2=P+0×PE1=N×PE2=NβE1+βE2=1.In BNM, the conditional probability relationships between a child node and its parent node can be written as follows:(14)PT=t=∑1NPT=tX1=x1,…,Xn=xn×PX1=x1,…,Xn=xn.Under the assumption that the child nodes are independent of each other, we can obtain equation (15). Equation (15) describes the conditional probability relationships between child nodes (E1, E2) and their parent node (AT5) in Bayesian network. In equation (15), the probability expression of variable AT5 with state of positive can also be extended to four items, which are four possible cases of the combination of E1 and E2.(15)PAT5=P=PAT5=P|E1=P,E2=P×PE1=P×PE2=P+PAT5=P|E1=P,E2=N×PE1=P×PE2=N+PAT5=P|E1=N,E2=P×PE1=N×PE2=P+PAT5=P|E1=N,E2=N×PE1=N×PE2=N.By comparing equations (13) and (15), it can be found that they are highly similar in mathematical structure, and the weight in equation (13) corresponds to the four items of conditional probabilities expressions in equation (15) exactly. Based on this, we determine the CPT of BNM. The detailed meaning of the determined probability table is as follows: when child nodes E1 and E2 are both in the state of positive, the parent node must be in the state as positive. When E1 is in the state of positive and E2 is in the state of negative, the probability that the parent node is in the state of positive is βE1. When E1 is in the state of negative and E2 is in the state of positive, the probability that the parent node is in the state of positive is βE2. When both child nodes are in the state of negative, the parent node must be in the state of negative, as shown in the following equation.(16)PAT5=P|E1=P,E2=P=βE1+βE2PAT5=P|E1=P,E2=N=βE1PAT5=P|E1=N,E2=P=βE2PAT5=P|E=N,E2=N=0.Therefore, we have determined the CPT of BNM.


## 2.3.1. Normalization of Indicators

The raw data must go through normalization because they have different units, which may cause inconsistency [51]. In this study, the indicators are normalized by using the truncated normal distribution method (TNORM). This method treats the raw data as random variables and models a truncated normal distribution by calculating the mean μ, standard deviance (STD), upper bound (UB), and lower bound (LB) of the variables (Figure 5). For instance, the μ of a certain variable is a, the STD is b, UB is determined as the maximum value, LB is the minimum value, and “1” expresses the cumulative probability of the variable. Then, the TNORM is used for modeling:(2)TNORM∼μ=a,STD=b,UB=maxx,LB=minx,1.Figure 5
An illustrative example of a truncated normal distribution.In a BNM, the node variables are Boolean variables with two states of positive and negative. If an indicator is a positive-effect indicator, then its normalized value is calculated as the integral of the probability density of TNORM to [LB,X]. If an indicator is a negative-effect indicator, its normalized value is calculated as the integral of the probability density of TNORM to [X, UB]. Raw data are normalized to a range between 0 and 1 by implementing this method.


## 2.3.2. Calculation of Subdivision Weights

The calculation of subdivision weights is demonstrated in the second step. In this step, the latent factors (j) of indicators (k) corresponding to each subdivision (s) and dimension (d) are extracted by applying PCA. NIkjsd stands for the normalized indicator value. Then, the indicators corresponding to each latent factor (j) are weighted by equation (3) and aggregated by equation (4).(3)Wkjsd=FactorLoadingkjsd2Eigenvaluejsd,k∈Ks,j∈JS,s∈Sd,d∈D,(4)CFIjsd=∑kWkjsdNIkjsd,k∈Ks,j∈Js,s∈Sd,d∈D.After calculating the composite factor indicesCFIjsd by equation (4), the weights of subdivision can be calculated by equation (5). Then, composite subdivision indices CSIsd can be aggregated by using equation (6).(5)ajsd=Eigenvaluejsd∑JSEigenvaluejsd,j∈Js,s∈Sd,d∈D,(6)CSIsd=∑jajsdCFIjsd,j∈Js,s∈Sd,d∈D.


## 2.3.3. Calculation of Dimension Weights

The analysis process of the third step is somehow similar to that of the second step. However, the output of this step will be dimension weights. In this step,j′ is the latent factor of each dimension (d). The weights of latent factors can be calculated by equation (7), and then composite factor indices CFIj′d can be aggregated by equation (8). Then, the weights of the dimensions can be calculated by equation (9).(7)Wsj′d=FactorLoadingsj′d2Eigenvaluej′d,j′∈Jd′,s∈Sd,d∈D,(8)CFIj′d=∑sWsj′dCSIsd,j′∈Jd′,s∈Sd,d∈D,(9)aj′d=Eigenvaluej′d∑j′Eigenvaluej′d,j′∈Jd′,d∈D,(10)CDId=∑j′aj′dCFIj′d,j′∈Jd′,d∈D.


## 2.3.4. Determining the CPT of BNM Based on the Weight System

The weights of each subdivision and each dimension were calculated by PCA in the former steps. Finally, in this step, the weight system will be applied to determine the CPT of BNM. The derivation of the equivalence relationship is as follows: taking indicatorsE1 and E2 aggregated into subdivision AT5 as an example, the relationship is(11)AT5=E1×βE1+E2×βE2βE1+βE2=1.This paper uses TNORM to normalize the raw data. As mentioned before, the node variablesE1 and E2 are Boolean variables with two states of positive and negative. Therefore, the following expressions are obtained:(12)PE1=P+PE1=N=1PE2=P+PE2=N=1.After introducing equation (12) to equation (11), we can obtain equation (10). In equation (10), the probability expression of variable AT5 with state of positive can be extended to four items, which are four possible cases of the combination of E1 and E2.(13)PAT5=P=PE1=P×βE1+PE2=P×βE2=PE1=P×PE2=P+PE2=N×βE1+PE2=P×PE1=P+PE1=N×βE2=βE1+βE2×PE1=P×PE2=P+βE1×PE1=P×PE2=N+βE2×PE1=N×PE2=P+0×PE1=N×PE2=NβE1+βE2=1.In BNM, the conditional probability relationships between a child node and its parent node can be written as follows:(14)PT=t=∑1NPT=tX1=x1,…,Xn=xn×PX1=x1,…,Xn=xn.Under the assumption that the child nodes are independent of each other, we can obtain equation (15). Equation (15) describes the conditional probability relationships between child nodes (E1, E2) and their parent node (AT5) in Bayesian network. In equation (15), the probability expression of variable AT5 with state of positive can also be extended to four items, which are four possible cases of the combination of E1 and E2.(15)PAT5=P=PAT5=P|E1=P,E2=P×PE1=P×PE2=P+PAT5=P|E1=P,E2=N×PE1=P×PE2=N+PAT5=P|E1=N,E2=P×PE1=N×PE2=P+PAT5=P|E1=N,E2=N×PE1=N×PE2=N.By comparing equations (13) and (15), it can be found that they are highly similar in mathematical structure, and the weight in equation (13) corresponds to the four items of conditional probabilities expressions in equation (15) exactly. Based on this, we determine the CPT of BNM. The detailed meaning of the determined probability table is as follows: when child nodes E1 and E2 are both in the state of positive, the parent node must be in the state as positive. When E1 is in the state of positive and E2 is in the state of negative, the probability that the parent node is in the state of positive is βE1. When E1 is in the state of negative and E2 is in the state of positive, the probability that the parent node is in the state of positive is βE2. When both child nodes are in the state of negative, the parent node must be in the state of negative, as shown in the following equation.(16)PAT5=P|E1=P,E2=P=βE1+βE2PAT5=P|E1=P,E2=N=βE1PAT5=P|E1=N,E2=P=βE2PAT5=P|E=N,E2=N=0.Therefore, we have determined the CPT of BNM.


## 3. Case Study

### 3.1. Data Description

We selected eight megacities in China as a case study, namely, Beijing, Shanghai, Guangzhou, Shenzhen, Nanjing, Tianjin, Chengdu, and Chongqing. These eight cities are ranked top in China and present top-level urban economic development in China. The multisource data between 2010 and 2019 were obtained from various sources, such as the China National Bureau of Statistics, China Statistical Yearbook, the Yearbook of China’s Urban Transportation, and Alibaba’s Amap traffic group. There were only a small number of missing data in the original dataset, and this paper used the following methods to tackle the missing data: if the data had no obvious trend, we filled the data with the mean value. Take variableR2 of Nanjing for example: the data in 2010 is missing; the figures for the remaining years have not changed much. We calculated the mean value of the variable R2 from 2011 to 2019 and then filled the missing data with the calculated mean value. If the data had an obvious trend, then the missing data could be filled with forecast data through the Grey Model Theory. The Grey Model theory was founded by the Chinese Professor Julong Deng; it has the advantage of small-sample modeling and is considered as a new method to forecast and estimate parameters through extracting valuable information from the known information. Because of its advantages, it can be applied to parameter estimation. We used this method to estimate variable E1 of Tianjin in 2015. Table 2 is a statistical summary of the collected variables in the indicator layer.Table 2
Summary of the collected variables in the indicator layer.
VariablesData collected for the variablesUnitCollection frequencyMaxMinMeanS1Ratio of fatalities on traffic accidentsN/AYearly5.290.752.43A1Area of paved roads10000 Sq.mYearly30839646014148A2Length of paved roadskmYearly1854626108075A3Per capita area of paved roadsSq.mYearly24.34.4612.69A4Per vehicle area of paved roadsSq.mYearly163.7216.4351.39R1Congestion indexN/AYearly6.141.592.30R2Average commute speedkm/hYearly34.442.0827.18R3Passenger capacity of urban public transport10000 personsYearly81584915269309167SE1Number of public transport operating vehiclesVehiclesYearly40499595216657SE2Length of public transport operation linekmYearly304140346744834SE3Number of vehicles10000 vehiclesYearly653.958.31345.48E1Per capita households expenditure on transportationYuanYearly570113843584E2Ratio of per capita households expenditure on transportN/AYearly18.647.6512.64R1Toxic air contaminants’ emission by transportμg/m3Yearly771030.17R2Greenhouse gases by transportationμg/m3Yearly71.941030.17R3Noise pollutionDecibelYearly70.965.668.34L1Electricity consumed by transportation10000 kwhYearly9930812039.96279435LA1Land consumed by transportation infrastructureSq.kmYearly485.2713.43185EC1GDP of the transportation industry100 million YuanYearly16500260743F1Fiscal expenditures on transport100 million YuanYearly104510162F2Fixed asset investment on transportation100 million YuanYearly271337667I1Length of rail transit linekmYearly704.9117.6283.31I2Number of new-energy vehiclesVehicleYearly307075042206Note that some indicators such asA4 and E2 were calculated by using a combination of multisource data. A4 can be calculated as the area of paved roads divided by vehicles.


### 3.2. Data Processing

We set binary positive and negative states of all variable nodes in the proposed BNM and then used TNORM to normalize the data from 2010 to 2019. With the fitted distribution, the probability of variableA1 being positive, P (A1 = positive) can be directly determined by obtaining the cumulative probability, and the probability of being negative, P (A1 = negative), can be simply calculated as 1 − P (A1 = positive).Table3 demonstrates the main estimated parameters of the TNORM modeling for the variables. With these parameters, one can convert data into prior probability as initial input values in the proposed BNM. As an example, Table 4 shows the converted probability values of variable A2.Table 3
Parameter estimations for truncated normal distribution modeling.
LabelVariableμSTDUBLBA1Area of paved roads14147.576228.17308396460A2Length of paved roads8074.954196.48185462610A4Per vehicle area of paved roads51.3931.75163.7216.43R1Congestion index2.3031.756.141.59SE1Number of public transport operating vehicles16657.388663.66404995952L1Electricity consumed by transportation279435.48257792.889930812039.96F2Fixed asset investment on transportation667.61455.462713.3036.57I1Length of rail transit line283.31193.78704.9117.6Table 4
Probability inputs for indicatorA2.
YearA2 = positiveBeijingShanghaiGuangzhouShenzhenNanjingTianjinChengduChongqing2010Mean = 8074.9556.45%62.39%18.86%24.88%0.85%3.90%04.63%2011STD = 4196.4860.16%58.48%96.08%39.33%1.57%5.54%3.25%6.06%2012UB = 1854660.92%60.13%97.40%35.14%1.56%9.12%12.48%7.47%2013LB = 261061.71%61.96%99.02%35.50%2.58%13.85%18.71%18.34%201464.64%61.96%99.21%37.84%6.80%20.04%19.96%20.03%201564.47%60.16%99.52%38.07%6.96%22.17%22.44%23.29%201662.84%55.33%99.63%39.94%9.75%28.82%27.95%24.78%201760.48%50.67%99.07%50.00%8.20%28.21%32.52%30.24%201860.39%48.66%99.98%48.70%9.89%38.66%40.17%38.30%201990.32%38.49%99.66%48.36%7.98%45.95%40.40%45.28%Figure6 shows the determined CPT for variable AT2—accessibility. In forward inference, the probability of AT2 can be calculated using all the inputs from A1 to A4 based on this conditional probability table.Figure 6
The determined CPT for variable AT2—accessibility.With all the variables and probability determined, we can obtain the BNM, as shown in Figure7. Then, we can carry out sustainability measurement analysis by the forward inference and sensitivity analysis in the following step. NETICA software was used to carry out BNM analysis in this study.Figure 7
The proposed BNM.


## 3.1. Data Description

We selected eight megacities in China as a case study, namely, Beijing, Shanghai, Guangzhou, Shenzhen, Nanjing, Tianjin, Chengdu, and Chongqing. These eight cities are ranked top in China and present top-level urban economic development in China. The multisource data between 2010 and 2019 were obtained from various sources, such as the China National Bureau of Statistics, China Statistical Yearbook, the Yearbook of China’s Urban Transportation, and Alibaba’s Amap traffic group. There were only a small number of missing data in the original dataset, and this paper used the following methods to tackle the missing data: if the data had no obvious trend, we filled the data with the mean value. Take variableR2 of Nanjing for example: the data in 2010 is missing; the figures for the remaining years have not changed much. We calculated the mean value of the variable R2 from 2011 to 2019 and then filled the missing data with the calculated mean value. If the data had an obvious trend, then the missing data could be filled with forecast data through the Grey Model Theory. The Grey Model theory was founded by the Chinese Professor Julong Deng; it has the advantage of small-sample modeling and is considered as a new method to forecast and estimate parameters through extracting valuable information from the known information. Because of its advantages, it can be applied to parameter estimation. We used this method to estimate variable E1 of Tianjin in 2015. Table 2 is a statistical summary of the collected variables in the indicator layer.Table 2
Summary of the collected variables in the indicator layer.
VariablesData collected for the variablesUnitCollection frequencyMaxMinMeanS1Ratio of fatalities on traffic accidentsN/AYearly5.290.752.43A1Area of paved roads10000 Sq.mYearly30839646014148A2Length of paved roadskmYearly1854626108075A3Per capita area of paved roadsSq.mYearly24.34.4612.69A4Per vehicle area of paved roadsSq.mYearly163.7216.4351.39R1Congestion indexN/AYearly6.141.592.30R2Average commute speedkm/hYearly34.442.0827.18R3Passenger capacity of urban public transport10000 personsYearly81584915269309167SE1Number of public transport operating vehiclesVehiclesYearly40499595216657SE2Length of public transport operation linekmYearly304140346744834SE3Number of vehicles10000 vehiclesYearly653.958.31345.48E1Per capita households expenditure on transportationYuanYearly570113843584E2Ratio of per capita households expenditure on transportN/AYearly18.647.6512.64R1Toxic air contaminants’ emission by transportμg/m3Yearly771030.17R2Greenhouse gases by transportationμg/m3Yearly71.941030.17R3Noise pollutionDecibelYearly70.965.668.34L1Electricity consumed by transportation10000 kwhYearly9930812039.96279435LA1Land consumed by transportation infrastructureSq.kmYearly485.2713.43185EC1GDP of the transportation industry100 million YuanYearly16500260743F1Fiscal expenditures on transport100 million YuanYearly104510162F2Fixed asset investment on transportation100 million YuanYearly271337667I1Length of rail transit linekmYearly704.9117.6283.31I2Number of new-energy vehiclesVehicleYearly307075042206Note that some indicators such asA4 and E2 were calculated by using a combination of multisource data. A4 can be calculated as the area of paved roads divided by vehicles.


## 3.2. Data Processing

We set binary positive and negative states of all variable nodes in the proposed BNM and then used TNORM to normalize the data from 2010 to 2019. With the fitted distribution, the probability of variableA1 being positive, P (A1 = positive) can be directly determined by obtaining the cumulative probability, and the probability of being negative, P (A1 = negative), can be simply calculated as 1 − P (A1 = positive).Table3 demonstrates the main estimated parameters of the TNORM modeling for the variables. With these parameters, one can convert data into prior probability as initial input values in the proposed BNM. As an example, Table 4 shows the converted probability values of variable A2.Table 3
Parameter estimations for truncated normal distribution modeling.
LabelVariableμSTDUBLBA1Area of paved roads14147.576228.17308396460A2Length of paved roads8074.954196.48185462610A4Per vehicle area of paved roads51.3931.75163.7216.43R1Congestion index2.3031.756.141.59SE1Number of public transport operating vehicles16657.388663.66404995952L1Electricity consumed by transportation279435.48257792.889930812039.96F2Fixed asset investment on transportation667.61455.462713.3036.57I1Length of rail transit line283.31193.78704.9117.6Table 4
Probability inputs for indicatorA2.
YearA2 = positiveBeijingShanghaiGuangzhouShenzhenNanjingTianjinChengduChongqing2010Mean = 8074.9556.45%62.39%18.86%24.88%0.85%3.90%04.63%2011STD = 4196.4860.16%58.48%96.08%39.33%1.57%5.54%3.25%6.06%2012UB = 1854660.92%60.13%97.40%35.14%1.56%9.12%12.48%7.47%2013LB = 261061.71%61.96%99.02%35.50%2.58%13.85%18.71%18.34%201464.64%61.96%99.21%37.84%6.80%20.04%19.96%20.03%201564.47%60.16%99.52%38.07%6.96%22.17%22.44%23.29%201662.84%55.33%99.63%39.94%9.75%28.82%27.95%24.78%201760.48%50.67%99.07%50.00%8.20%28.21%32.52%30.24%201860.39%48.66%99.98%48.70%9.89%38.66%40.17%38.30%201990.32%38.49%99.66%48.36%7.98%45.95%40.40%45.28%Figure6 shows the determined CPT for variable AT2—accessibility. In forward inference, the probability of AT2 can be calculated using all the inputs from A1 to A4 based on this conditional probability table.Figure 6
The determined CPT for variable AT2—accessibility.With all the variables and probability determined, we can obtain the BNM, as shown in Figure7. Then, we can carry out sustainability measurement analysis by the forward inference and sensitivity analysis in the following step. NETICA software was used to carry out BNM analysis in this study.Figure 7
The proposed BNM.


## 4. Results and Discussion

### 4.1. Forward Inference

The objective of the forward inference is to compute the probability of sustainability in the transportation system for the sampled cities. With input data prepared for root nodes, we can compute the probability of sustainability = positive as yearly evaluation.


#### 4.1.1. Sustainability Analysis

The yearly sustainability analysis from 2010 to 2019 is shown in Figure8. We categorize the eight cities into three groups, representing different levels of sustainability based on the values of the measurement. Values above 0.50 indicate good relative sustainability, between 0.40 and 0.50 are normal relative sustainability, and less than 0.40 are weak relative sustainability. As shown in Figure 8, most of the cities’ transportation systems are at the moderate level. Taking Nanjing and Guangzhou as examples, more than five years are labeled as normal relative sustainability, whereas those of Chengdu and Tianjin are classified as weak relative sustainability. This prominent feature indicates that the transportation system in these megacities might not be as sustainable as we had anticipated, thus requiring further improvement.Figure 8
Sustainability evaluations of transportation system.During the research period, Beijing demonstrated a growing trend throughout the 10-year observation, and the other seven cities experienced dynamic fluctuation and upward movement. Among them, Guangzhou, Shenzhen, Tianjin, and Chengdu had a rough “N” shape in the overall trend during the ten years of development, whereas Shanghai and Nanjing had a rough “bathtub” shape. Despite the year-to-year fluctuations, the mean values of sustainability from 2017 to 2019 are higher than those before 2017 in all eight cities, reflecting the gradual growing trend in the sustainability of the transportation systems. In terms of growth rate, Beijing and Shanghai had relatively higher growth rates from 2014 to 2019, whereas the growth rates of the other cities remained relatively steady during the research period.Figure9 reveals the sustainability differences among the eight cities based on the mean values of the 10-year observation. The eight cities are ranked in descending order based on the evaluated sustainability, which presents a gradient distribution pattern. The mean values of the sustainability of Beijing and Shanghai in the past 10 years are 0.57 and 0.63, respectively, showing good relative sustainability. The mean values of Shenzhen, Guangzhou, Chengdu, Nanjing, and Chongqing are 0.45, 0.44, 0.40, 0.41, and 0.49, respectively, showing medium sustainability. Tianjin’s mean score (0.38) is the lowest. In general, the great disparities among the eight cities in terms of sustainability indicate the need for improvement.Figure 9
City ranking in terms of sustainability.For more in-depth analysis, the inner reasons for the superiority can be determined. The values of Shanghai’s transportation sustainability show a drastic increase from 0.56 in 2014 to 0.73 in 2016 and is maintained around 0.75 in the following years, which may be affected by the comprehensive policies to strengthen environmental protection in Shanghai. As an indicative example, the “Shanghai Clean Air Action Plan (2013–2017)” issued by the municipal government has curbed the total emission of motor vehicle pollutants by especially taking concrete measures to eliminate high emission and older vehicles. According to rough calculations by the Shanghai Environmental Protection Department, NOX emissions can be reduced by an average of 60,000 tons per year, and the PM2.5 concentrations can be reduced by approximately 3–4 μg/m3 each year. The transportation industry is becoming more and more environmentally friendly. Thus, these factors have an obvious powerful positive effect on transport sustainability. The transport sustainability of Beijing is superior to that of the other cities, which is due to a series of research and plans on transportation during the Olympic Games. Particularly, the intelligent transportation system, rail transit system, and traffic demand management, which help residents to gain more benefits through a diversity of public transit modes and improvement of accessibility, have a significant positive impact on the sustainability of the entire traffic system.


#### 4.1.2. Sustainability-Economic Coupling Analysis

It is believed that the level of regional economic development, urban governance, and urbanization directly influence the sustainability of the transportation system. In particular, it is expected that there should be a strong and positive coupling effect between regional economic development and transport sustainability, which may not be the case. An analysis of the annual GDP development reveals that most case cities’ transport sustainability does not always positively correlate with economic growth. This can be confirmed by sustainability-economic coupling analysis (Figure10). The regression and R2 values indicate their coupling strength. A better R2 value indicates a stronger positive coupling relationship between transportation sustainability and the regional economic level, such as Shenzhen and Beijing. Moreover, a lower R2 value represents a nonlinear characteristic, such as Tianjin, whose R2 is below 0.4. The R2 values of the other cities are medium, indicating that the economic growth of these metropolises does not necessarily bring about continuous growth in transport sustainability.Figure 10
Analysis of sustainability-economic coupling effect.It is expected that economic growth will increase investment in transportation infrastructure, leading to the development of a more mature transportation network, which will enhance the overall transport sustainability. However, the development of transport sustainability is an integration involving multiple fields in which economic prosperity is merely one dimension but will not necessarily enhance it. One possible reason is that positive economic development makes the city more attractive, attracting significant resources and talents from all over the world, causing high population density and substantially increasing transportation demand, which will result in new imbalances, negative burdens, and externalities. These in turn affect the sustainability of the entire transportation system. The nonlinear relationship between economic development and transport sustainability reveals the multidimensional characteristics of sustainable development. Therefore, achieving sustainable development of urban transportation is a complex system engineering, which requires the integration of the combined effect of multiple factors and systemic consideration.


### 4.2. Sensitivity Analysis

The proposed method can compute the sensitivity index (SI) for each variable in each year, which can help to identify the good or poor performing nodes. Correspondingly, policy-makers can pay extra attention to these checkpoints when making decisions. Two tendencies of downward or upward are shown in Figure11; the former indicates that something has been tackled well and has a positive effect on traffic sustainability, and the latter indicates otherwise. Through sensitivity analysis, we can discover some of the reasons for superiority or inferiority.Figure 11
The tendencies of SI.The safety and security attributes are believed to be one of the most significant factors of transport sustainability. Due to safety management in recent years, which has been well incorporated into the entire life cycle of urban traffic systems in China, especially in megacities, these megacities have more effective enforcement of traffic safety. Moreover, many cities have started the construction of intelligent transportation, which can provide the sufficient information and diverse services to transport participants and improve the ability of traffic accident prevention and emergency disposal. Additionally, educational efforts have been paid to enhance the mutual awareness about traffic safety. China has designated December 2 as the National Traffic Safety Day. Various forms of traffic safety publicity activities have been carried out; moreover, traffic safety is an important course for Chinese primary school students. A better understanding of the standards of traffic safety, higher traffic safety awareness, and improvement of traffic safety management level have positively affected the safety, which in turn lead to a continuous downward trend in traffic accidents in recent years. This will have a positive effect on traffic sustainability, and the government should take measures to maintain this good situation.The SI of “Accessibility,” “Reliability,” and “Serviceability” has had a clear upward trend in the past ten years. These three attributes are closely related to the contradictions between traffic demand and supply, playing an increasingly important role in enhancing transport sustainability. In recent years, although the government is dedicated to increasing the supply of transportation, the demand for transportation is also increasing. The imbalance between transportation supply and demand can only be improved temporarily, and new imbalance and other associated stress appear with time, which has become hard to address and has had a negative effect on the sustainable development of transportation. The government needs to pay attention and take effective measures to tackle it.The SI of “Equity” has also experienced a continuous downward trend in the past ten years due to the low price of public transportation after the government subsidy. For example, the public transportation in many cities in China is free for the elderly and disabled; the ratio of household expenditure on transportation has been declining, and the people’s sense of satisfaction and gain in transportation has been continuously enhanced. The growing social welfare and sense of social equity have had a positive effect on urban transportation sustainability.The SI of “Reparability” and “Low carbon” has had a continuous upward trend in the past ten years. The problem of motor vehicle pollution has become increasingly prominent as the main source of air pollution. China is the largest CO2 emitter in the world, with 103.13 million tons of CO2 emissions in 2018 [3]. China’s transport-related CO2 emissions account for 25% of the total CO2 emissions, and liquid fuel consumption related to transport accounts for 65% of the total energy consumption in 2016. Moreover, the analyses of atmospheric PM2.5 sources in cities such as Beijing, Tianjin, and Shanghai indicate that almost 50% of the PM2.5 concentrations are caused by mobile sources. Therefore, issues of transport-related emission and energy consumption require more attention and action from the government.The SI of “Innovation” has had an upward trend in the past ten years. Every coin has two sides, and technology innovation is no exception. For example, the marginal effects of specific applications of new-energy vehicles may diminish with time. The increase in the number of new-energy vehicles will bring about undesirable consequences, such as tight parking space and increased road congestion, which will directly swallow up or even exceed its initial benefits. More data do not necessarily mean more useful information; it may contain ambiguous or abnormal information. Therefore, constant technological innovation is needed to cope with the problems in the development of sustainable transport. Sufficient attention should be given to it, and a combination of various policy measures should be adopted to facilitate technological innovation.


## 4.1. Forward Inference

The objective of the forward inference is to compute the probability of sustainability in the transportation system for the sampled cities. With input data prepared for root nodes, we can compute the probability of sustainability = positive as yearly evaluation.


### 4.1.1. Sustainability Analysis

The yearly sustainability analysis from 2010 to 2019 is shown in Figure8. We categorize the eight cities into three groups, representing different levels of sustainability based on the values of the measurement. Values above 0.50 indicate good relative sustainability, between 0.40 and 0.50 are normal relative sustainability, and less than 0.40 are weak relative sustainability. As shown in Figure 8, most of the cities’ transportation systems are at the moderate level. Taking Nanjing and Guangzhou as examples, more than five years are labeled as normal relative sustainability, whereas those of Chengdu and Tianjin are classified as weak relative sustainability. This prominent feature indicates that the transportation system in these megacities might not be as sustainable as we had anticipated, thus requiring further improvement.Figure 8
Sustainability evaluations of transportation system.During the research period, Beijing demonstrated a growing trend throughout the 10-year observation, and the other seven cities experienced dynamic fluctuation and upward movement. Among them, Guangzhou, Shenzhen, Tianjin, and Chengdu had a rough “N” shape in the overall trend during the ten years of development, whereas Shanghai and Nanjing had a rough “bathtub” shape. Despite the year-to-year fluctuations, the mean values of sustainability from 2017 to 2019 are higher than those before 2017 in all eight cities, reflecting the gradual growing trend in the sustainability of the transportation systems. In terms of growth rate, Beijing and Shanghai had relatively higher growth rates from 2014 to 2019, whereas the growth rates of the other cities remained relatively steady during the research period.Figure9 reveals the sustainability differences among the eight cities based on the mean values of the 10-year observation. The eight cities are ranked in descending order based on the evaluated sustainability, which presents a gradient distribution pattern. The mean values of the sustainability of Beijing and Shanghai in the past 10 years are 0.57 and 0.63, respectively, showing good relative sustainability. The mean values of Shenzhen, Guangzhou, Chengdu, Nanjing, and Chongqing are 0.45, 0.44, 0.40, 0.41, and 0.49, respectively, showing medium sustainability. Tianjin’s mean score (0.38) is the lowest. In general, the great disparities among the eight cities in terms of sustainability indicate the need for improvement.Figure 9
City ranking in terms of sustainability.For more in-depth analysis, the inner reasons for the superiority can be determined. The values of Shanghai’s transportation sustainability show a drastic increase from 0.56 in 2014 to 0.73 in 2016 and is maintained around 0.75 in the following years, which may be affected by the comprehensive policies to strengthen environmental protection in Shanghai. As an indicative example, the “Shanghai Clean Air Action Plan (2013–2017)” issued by the municipal government has curbed the total emission of motor vehicle pollutants by especially taking concrete measures to eliminate high emission and older vehicles. According to rough calculations by the Shanghai Environmental Protection Department, NOX emissions can be reduced by an average of 60,000 tons per year, and the PM2.5 concentrations can be reduced by approximately 3–4 μg/m3 each year. The transportation industry is becoming more and more environmentally friendly. Thus, these factors have an obvious powerful positive effect on transport sustainability. The transport sustainability of Beijing is superior to that of the other cities, which is due to a series of research and plans on transportation during the Olympic Games. Particularly, the intelligent transportation system, rail transit system, and traffic demand management, which help residents to gain more benefits through a diversity of public transit modes and improvement of accessibility, have a significant positive impact on the sustainability of the entire traffic system.


### 4.1.2. Sustainability-Economic Coupling Analysis

It is believed that the level of regional economic development, urban governance, and urbanization directly influence the sustainability of the transportation system. In particular, it is expected that there should be a strong and positive coupling effect between regional economic development and transport sustainability, which may not be the case. An analysis of the annual GDP development reveals that most case cities’ transport sustainability does not always positively correlate with economic growth. This can be confirmed by sustainability-economic coupling analysis (Figure10). The regression and R2 values indicate their coupling strength. A better R2 value indicates a stronger positive coupling relationship between transportation sustainability and the regional economic level, such as Shenzhen and Beijing. Moreover, a lower R2 value represents a nonlinear characteristic, such as Tianjin, whose R2 is below 0.4. The R2 values of the other cities are medium, indicating that the economic growth of these metropolises does not necessarily bring about continuous growth in transport sustainability.Figure 10
Analysis of sustainability-economic coupling effect.It is expected that economic growth will increase investment in transportation infrastructure, leading to the development of a more mature transportation network, which will enhance the overall transport sustainability. However, the development of transport sustainability is an integration involving multiple fields in which economic prosperity is merely one dimension but will not necessarily enhance it. One possible reason is that positive economic development makes the city more attractive, attracting significant resources and talents from all over the world, causing high population density and substantially increasing transportation demand, which will result in new imbalances, negative burdens, and externalities. These in turn affect the sustainability of the entire transportation system. The nonlinear relationship between economic development and transport sustainability reveals the multidimensional characteristics of sustainable development. Therefore, achieving sustainable development of urban transportation is a complex system engineering, which requires the integration of the combined effect of multiple factors and systemic consideration.


## 4.1.1. Sustainability Analysis

The yearly sustainability analysis from 2010 to 2019 is shown in Figure8. We categorize the eight cities into three groups, representing different levels of sustainability based on the values of the measurement. Values above 0.50 indicate good relative sustainability, between 0.40 and 0.50 are normal relative sustainability, and less than 0.40 are weak relative sustainability. As shown in Figure 8, most of the cities’ transportation systems are at the moderate level. Taking Nanjing and Guangzhou as examples, more than five years are labeled as normal relative sustainability, whereas those of Chengdu and Tianjin are classified as weak relative sustainability. This prominent feature indicates that the transportation system in these megacities might not be as sustainable as we had anticipated, thus requiring further improvement.Figure 8
Sustainability evaluations of transportation system.During the research period, Beijing demonstrated a growing trend throughout the 10-year observation, and the other seven cities experienced dynamic fluctuation and upward movement. Among them, Guangzhou, Shenzhen, Tianjin, and Chengdu had a rough “N” shape in the overall trend during the ten years of development, whereas Shanghai and Nanjing had a rough “bathtub” shape. Despite the year-to-year fluctuations, the mean values of sustainability from 2017 to 2019 are higher than those before 2017 in all eight cities, reflecting the gradual growing trend in the sustainability of the transportation systems. In terms of growth rate, Beijing and Shanghai had relatively higher growth rates from 2014 to 2019, whereas the growth rates of the other cities remained relatively steady during the research period.Figure9 reveals the sustainability differences among the eight cities based on the mean values of the 10-year observation. The eight cities are ranked in descending order based on the evaluated sustainability, which presents a gradient distribution pattern. The mean values of the sustainability of Beijing and Shanghai in the past 10 years are 0.57 and 0.63, respectively, showing good relative sustainability. The mean values of Shenzhen, Guangzhou, Chengdu, Nanjing, and Chongqing are 0.45, 0.44, 0.40, 0.41, and 0.49, respectively, showing medium sustainability. Tianjin’s mean score (0.38) is the lowest. In general, the great disparities among the eight cities in terms of sustainability indicate the need for improvement.Figure 9
City ranking in terms of sustainability.For more in-depth analysis, the inner reasons for the superiority can be determined. The values of Shanghai’s transportation sustainability show a drastic increase from 0.56 in 2014 to 0.73 in 2016 and is maintained around 0.75 in the following years, which may be affected by the comprehensive policies to strengthen environmental protection in Shanghai. As an indicative example, the “Shanghai Clean Air Action Plan (2013–2017)” issued by the municipal government has curbed the total emission of motor vehicle pollutants by especially taking concrete measures to eliminate high emission and older vehicles. According to rough calculations by the Shanghai Environmental Protection Department, NOX emissions can be reduced by an average of 60,000 tons per year, and the PM2.5 concentrations can be reduced by approximately 3–4 μg/m3 each year. The transportation industry is becoming more and more environmentally friendly. Thus, these factors have an obvious powerful positive effect on transport sustainability. The transport sustainability of Beijing is superior to that of the other cities, which is due to a series of research and plans on transportation during the Olympic Games. Particularly, the intelligent transportation system, rail transit system, and traffic demand management, which help residents to gain more benefits through a diversity of public transit modes and improvement of accessibility, have a significant positive impact on the sustainability of the entire traffic system.


## 4.1.2. Sustainability-Economic Coupling Analysis

It is believed that the level of regional economic development, urban governance, and urbanization directly influence the sustainability of the transportation system. In particular, it is expected that there should be a strong and positive coupling effect between regional economic development and transport sustainability, which may not be the case. An analysis of the annual GDP development reveals that most case cities’ transport sustainability does not always positively correlate with economic growth. This can be confirmed by sustainability-economic coupling analysis (Figure10). The regression and R2 values indicate their coupling strength. A better R2 value indicates a stronger positive coupling relationship between transportation sustainability and the regional economic level, such as Shenzhen and Beijing. Moreover, a lower R2 value represents a nonlinear characteristic, such as Tianjin, whose R2 is below 0.4. The R2 values of the other cities are medium, indicating that the economic growth of these metropolises does not necessarily bring about continuous growth in transport sustainability.Figure 10
Analysis of sustainability-economic coupling effect.It is expected that economic growth will increase investment in transportation infrastructure, leading to the development of a more mature transportation network, which will enhance the overall transport sustainability. However, the development of transport sustainability is an integration involving multiple fields in which economic prosperity is merely one dimension but will not necessarily enhance it. One possible reason is that positive economic development makes the city more attractive, attracting significant resources and talents from all over the world, causing high population density and substantially increasing transportation demand, which will result in new imbalances, negative burdens, and externalities. These in turn affect the sustainability of the entire transportation system. The nonlinear relationship between economic development and transport sustainability reveals the multidimensional characteristics of sustainable development. Therefore, achieving sustainable development of urban transportation is a complex system engineering, which requires the integration of the combined effect of multiple factors and systemic consideration.


## 4.2. Sensitivity Analysis

The proposed method can compute the sensitivity index (SI) for each variable in each year, which can help to identify the good or poor performing nodes. Correspondingly, policy-makers can pay extra attention to these checkpoints when making decisions. Two tendencies of downward or upward are shown in Figure11; the former indicates that something has been tackled well and has a positive effect on traffic sustainability, and the latter indicates otherwise. Through sensitivity analysis, we can discover some of the reasons for superiority or inferiority.Figure 11
The tendencies of SI.The safety and security attributes are believed to be one of the most significant factors of transport sustainability. Due to safety management in recent years, which has been well incorporated into the entire life cycle of urban traffic systems in China, especially in megacities, these megacities have more effective enforcement of traffic safety. Moreover, many cities have started the construction of intelligent transportation, which can provide the sufficient information and diverse services to transport participants and improve the ability of traffic accident prevention and emergency disposal. Additionally, educational efforts have been paid to enhance the mutual awareness about traffic safety. China has designated December 2 as the National Traffic Safety Day. Various forms of traffic safety publicity activities have been carried out; moreover, traffic safety is an important course for Chinese primary school students. A better understanding of the standards of traffic safety, higher traffic safety awareness, and improvement of traffic safety management level have positively affected the safety, which in turn lead to a continuous downward trend in traffic accidents in recent years. This will have a positive effect on traffic sustainability, and the government should take measures to maintain this good situation.The SI of “Accessibility,” “Reliability,” and “Serviceability” has had a clear upward trend in the past ten years. These three attributes are closely related to the contradictions between traffic demand and supply, playing an increasingly important role in enhancing transport sustainability. In recent years, although the government is dedicated to increasing the supply of transportation, the demand for transportation is also increasing. The imbalance between transportation supply and demand can only be improved temporarily, and new imbalance and other associated stress appear with time, which has become hard to address and has had a negative effect on the sustainable development of transportation. The government needs to pay attention and take effective measures to tackle it.The SI of “Equity” has also experienced a continuous downward trend in the past ten years due to the low price of public transportation after the government subsidy. For example, the public transportation in many cities in China is free for the elderly and disabled; the ratio of household expenditure on transportation has been declining, and the people’s sense of satisfaction and gain in transportation has been continuously enhanced. The growing social welfare and sense of social equity have had a positive effect on urban transportation sustainability.The SI of “Reparability” and “Low carbon” has had a continuous upward trend in the past ten years. The problem of motor vehicle pollution has become increasingly prominent as the main source of air pollution. China is the largest CO2 emitter in the world, with 103.13 million tons of CO2 emissions in 2018 [3]. China’s transport-related CO2 emissions account for 25% of the total CO2 emissions, and liquid fuel consumption related to transport accounts for 65% of the total energy consumption in 2016. Moreover, the analyses of atmospheric PM2.5 sources in cities such as Beijing, Tianjin, and Shanghai indicate that almost 50% of the PM2.5 concentrations are caused by mobile sources. Therefore, issues of transport-related emission and energy consumption require more attention and action from the government.The SI of “Innovation” has had an upward trend in the past ten years. Every coin has two sides, and technology innovation is no exception. For example, the marginal effects of specific applications of new-energy vehicles may diminish with time. The increase in the number of new-energy vehicles will bring about undesirable consequences, such as tight parking space and increased road congestion, which will directly swallow up or even exceed its initial benefits. More data do not necessarily mean more useful information; it may contain ambiguous or abnormal information. Therefore, constant technological innovation is needed to cope with the problems in the development of sustainable transport. Sufficient attention should be given to it, and a combination of various policy measures should be adopted to facilitate technological innovation.


## 5. Conclusion

### 5.1. Summary of Findings

This paper proposes a unique approach to quantitatively evaluate the sustainability of urban transportation systems. Eight megacities in China were used as a sample to illustrate the applicability and strength of the proposed model. Instead of finding a one-size-fits-all model for measuring transport sustainability, the ultimate purpose of this study is to introduce a new perspective on how we can interpret transport system sustainability as a multidimensional property and identify key checkpoints that should be given special attention. This study draws the following three conclusions.Firstly, the overall levels of transportation sustainability in the selected cities are moderate, revealing that the transportation system of these cities is not sustainable as we anticipated. The trend of Shenzhen, Guangzhou, and the other cities has had a rough “N” shape, whereas that of Shanghai and Nanjing has had a rough “bathtub” shape. All the cities have exhibited an increasing trend in recent years, although they have had dynamic fluctuation. Moreover, certain disparities among the eight cities in terms of sustainability indicate the need for improvement.Secondly, the sustainability-economic coupling analysis shows a nonlinear relationship between sustainability and economic level, revealing that economic growth does not necessarily lead to the enhancement of the transport sustainability.Thirdly, the results of the sensitivity analysis demonstrate the upward tendency of “Accessibility,” “Serviceability,” “Reliability,” and “Innovation,” indicating their great effect on transport sustainability. More sustainable transportation systems will be achieved after managing these relationships well.


### 5.2. Managerial Implications

Some rational managerial implications can be discussed based on the study.Firstly, systemic thinking is essential for decision-making. As previously stated, transport sustainability is a multifaceted property, which covers a vast domain, so quality of social life, economic prosperity, environmental integrity, and progressive technology should be integrated into it. Moreover, the systemic approach should not be a static consideration but should be incorporated into the entire life cycle of transportation systems, including the design, construction, and management of transportation systems. Stakeholders, including designers, constructors, operators, and managers, should closely work together.Secondly, as a type of modern sociotechnical system, more attention should be paid to the attributes that had an upward trend in the research period, such as “Accessibility,” “Serviceability,” “Reliability,” and “Innovation.” Policies that will meet the travel needs of the residents, enhance human’s environmental surroundings, and help to reduce economic costs should be implemented.


### 5.3. Limitations and Future Studies

Although the proposed BNM can satisfactorily measure the sustainability of the urban traffic system and provide insights into the effect of the indicators on sustainability, certain limitations and future extensions are worth noting. Firstly, due to the availability and quality of the data used in this study, the measurement is only four-dimensional modeling. Future research can be extended with more information, including cultural, historical, and geographical; a more comprehensive model with a wide-angle view may be required. Secondly, this study is conducted based on a finite number of microdata, the application of big data will provide good supplements for future studies, and new methods of data mining and interaction analysis may be required to enhance analysis. Thirdly, this study is limited to a relatively small group of eight metropolitan areas in China; future research can extend to a large-scale group, which would help the planner to identify the condition of regions comparatively. These extensions will be researched in our future work to provide more meaningful findings to policy-makers, scholars, and other stakeholders.


## 5.1. Summary of Findings

This paper proposes a unique approach to quantitatively evaluate the sustainability of urban transportation systems. Eight megacities in China were used as a sample to illustrate the applicability and strength of the proposed model. Instead of finding a one-size-fits-all model for measuring transport sustainability, the ultimate purpose of this study is to introduce a new perspective on how we can interpret transport system sustainability as a multidimensional property and identify key checkpoints that should be given special attention. This study draws the following three conclusions.Firstly, the overall levels of transportation sustainability in the selected cities are moderate, revealing that the transportation system of these cities is not sustainable as we anticipated. The trend of Shenzhen, Guangzhou, and the other cities has had a rough “N” shape, whereas that of Shanghai and Nanjing has had a rough “bathtub” shape. All the cities have exhibited an increasing trend in recent years, although they have had dynamic fluctuation. Moreover, certain disparities among the eight cities in terms of sustainability indicate the need for improvement.Secondly, the sustainability-economic coupling analysis shows a nonlinear relationship between sustainability and economic level, revealing that economic growth does not necessarily lead to the enhancement of the transport sustainability.Thirdly, the results of the sensitivity analysis demonstrate the upward tendency of “Accessibility,” “Serviceability,” “Reliability,” and “Innovation,” indicating their great effect on transport sustainability. More sustainable transportation systems will be achieved after managing these relationships well.


## 5.2. Managerial Implications

Some rational managerial implications can be discussed based on the study.Firstly, systemic thinking is essential for decision-making. As previously stated, transport sustainability is a multifaceted property, which covers a vast domain, so quality of social life, economic prosperity, environmental integrity, and progressive technology should be integrated into it. Moreover, the systemic approach should not be a static consideration but should be incorporated into the entire life cycle of transportation systems, including the design, construction, and management of transportation systems. Stakeholders, including designers, constructors, operators, and managers, should closely work together.Secondly, as a type of modern sociotechnical system, more attention should be paid to the attributes that had an upward trend in the research period, such as “Accessibility,” “Serviceability,” “Reliability,” and “Innovation.” Policies that will meet the travel needs of the residents, enhance human’s environmental surroundings, and help to reduce economic costs should be implemented.


## 5.3. Limitations and Future Studies

Although the proposed BNM can satisfactorily measure the sustainability of the urban traffic system and provide insights into the effect of the indicators on sustainability, certain limitations and future extensions are worth noting. Firstly, due to the availability and quality of the data used in this study, the measurement is only four-dimensional modeling. Future research can be extended with more information, including cultural, historical, and geographical; a more comprehensive model with a wide-angle view may be required. Secondly, this study is conducted based on a finite number of microdata, the application of big data will provide good supplements for future studies, and new methods of data mining and interaction analysis may be required to enhance analysis. Thirdly, this study is limited to a relatively small group of eight metropolitan areas in China; future research can extend to a large-scale group, which would help the planner to identify the condition of regions comparatively. These extensions will be researched in our future work to provide more meaningful findings to policy-makers, scholars, and other stakeholders.



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*Source: 4801336-2022-03-15.xml*