# Ambient vibration prediction of a cable-stayed bridge by Artificial Neural Network

Melissa de Iuliis, Cecilia Rinaldi, Francesco Potenza, Vincenzo Gattulli, Thibaud Toullier, Jean Dumoulin

► To cite this version:

Melissa de Iuliis, Cecilia Rinaldi, Francesco Potenza, Vincenzo Gattulli, Thibaud Toullier, et al. Ambient vibration prediction of a cable-stayed bridge by Artificial Neural Network. Data Driven Methods for Civil Structural Health Monitoring and Resilience, CRC Press, pp.1-16, 2023, 9781003306924. 10.1201/9781003306924. hal-04302882

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# Ambient vibration prediction of a cable-stayed bridge by Artificial Neural Network

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Melissa De Iuliis¹, Cecilia Rinaldi¹, Francesco Potenza², Vincenzo Gattulli¹, Thibaud Toullier³, Jean Dumoulin³

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¹Department of Structural and Geotechnical Engineering, University of Rome, via Eudossiana 19, Rome 00167, Italy; Email: melissa.deiuliis@uniroma1.it, cecilia.rinaldi@uniroma1.it, vincenzo.gattulli@uniroma1.it

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²Department of Engineering and Geology, University of Chieti-Pescara, viale Pindaro, 42 65127 Pescara, Italy; Email: francesco.potenza@unich.it

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³Université Gustave Eiffel, Inria, COSYS-SII, I4S Teram, F-44344 Bouguenais, France; Email: thibaud.toullier@univ-eiffel.fr, jean.dumoulin@univ-eiffel.fr

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## Abstract

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Large-scale civil infrastructures play a vital role in society as they ensure smooth transportation and improve the quality of people's daily life. However, they are exposed to several and continuous external dynamic actions such as wind loads, vehicular loads, and environmental changes. Interaction assessment between external actions and civil structures is become more challenging due to the rapid development of transportation. Data-driven models have lately emerged as a viable alternative to traditional model-based techniques. They provide different advantages: timely damage detection, structural behaviors prediction and suggestions for optimal maintenance strategies. The chapter aims to describe the advantages and the characteristics of data-driven techniques to predict the dynamic behavior of civil structures through Artificial Neural Network (ANN). The applicability and effectiveness of the proposed approach are supported by the results achieved processing the measurements coming from a monitoring system installed on a cable-stayed bridge (Tabarly, Nantes). Accelerations recorded by a network of sixteen mono-axial accelerometers and Nantes Airport weather data acquired with the observation platform of the METAR (METeorological Terminal Aviation Routine Weather Report) Station Network have been used as training to predict the structural response and to statistically characterize the behavior through a Nonlinear AutoRegressive (NAR) prediction network. The performance has been evaluated through statistical analysis of the error between the measured and predicted values also related to both environmental conditions and number of the signals. The results show that the forecast network could be useful to detect the trigger of anomalies, hidden in the dynamic response of the bridge, at a low computational cost.

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**Keywords:** Data-driven approaches, Nonlinear AutoRegressive network, Structural Health Monitoring, Civil Infrastructures, Accelerometric Sensors
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# 1 Introduction

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Engineering structures and infrastructures, such as bridges, gradually suffer from aging because of different loads and environmental conditions. Proper and periodic assessment operations are paramount for structural safety to prevent the effects of environmental hazards, reduce maintenance costs, and to improve the level of safety of bridges. Therefore, structural identification has become an increasingly intensive research topic for Structural Health Monitoring (SHM), damage evaluation, and safety assessment of existing engineering structures. [1-7]. A significant number of studies of SHM systems focusing on damage detection of bridges can be found in the literature [8, 9]. For instance, Dutta and Talukdar [10] proposed a modal-based approach in finite element framework for damage detection of complex structures like bridges. Magalhães et al. [8] presented a statistically-based damage detection ability through short-term vibration monitoring data sets. Liu et al. [11] evaluated the structural performance of existing bridges using a strain-based monitoring system and a condition assessment of structural components. A strain-based monitoring system was integrated into a structural performance assessment of a steel girder bridge by Orcesi and Frangopol [12], who used the monitoring data to carry out a structural reliability analysis of critical sections. A load rating of a bridge was evaluated through diagnostic load testing based on a strain-based SHM system by Phares et al. [13].

Although many studies have been conducted on SHM systems to predict the behavior of engineering structures, traditional techniques are mostly based on dynamical models of the structure. The performance of conventional approaches strictly depends on the accuracy of the analytical and numerical dynamical models that are, in most cases, very challenging to derive [14, 15]. Furthermore, the development of such models and the definition of the parameters required to represent the behavior of structures may be time-consuming and computationally intensive. With the recent development in computer technology for communication, data acquisition, signal processing and analysis, an alternative solution to structural identification can be data-driven models [16]. Unlike the traditional physics-based SHM models, data-driven models exploit patterns arising from spatial and temporal correlations in measurements and offer bottom-up solutions that include damage detection, remaining life estimation and also structural control [17, 18]. In addition, data-driven techniques require a training dataset comprising measurements that represent baseline conditions of a bridge [19]. Consequently, data-driven models have recently drawn considerable attention in civil engineering community. Artificial Neural Networks
(ANN) are amongst the most common machine learning techniques employed for structural system identification and model updating [20]. Barai and Pandey [21] presented an ANN based approach for damage identification in steel bridges. A model updating scheme with an adaptive neural network was proposed by Chang et al. [22] for structural health assessment methodologies and control strategies. In their work, the model updating, and network training were repeated until achieving a good agreement between the calculated and measured modal responses of the bridge. In Fang et al. [23], ANNs were employed to study the identification of structural damage in beams. A cantilever beam was divided into a given number of elements, and the damage was associated with loss of stiffness in one or more elements. Bakhary et al. [24] detected simulated damage in a numerical steel portal frame model through ANNs accounting also for uncertainties derived from the model and the measured vibration data. A methodological framework for predicting the dynamic responses of the vehicle-bridge interaction system using ANNs was illustrated by Li et al. [25]. Further, de Oliveira Dias Prudente dos Santos et al. [26] presented a Neural Network (NN) to simulate and predict the structural behavior of a bridge using the air temperature as an input to the network. Taking into account the changes of the environmental conditions (e.g., climate, traffic load, and degradation mechanisms) is paramount in the structural health monitoring process and development of fault detection methods. Yun-Lai and Wahab [27] employed an auto-associative neural network combined with transmissibility to identify damage location in a ten-floor structure. Furthermore, in their study the effect of noise on natural frequencies was evaluated. A back propagation algorithm in ANN was used to apply the change of static properties (i.e., strains and displacements) for damage detection in a cantilever beam [28]. Cascardi et al. [29] employed artificial neural networks to estimate the strength of FRP-confined concrete showing that the proposed model could provide a good agreement with measurements. A novel data-driven measurement approach to predict traffic-induced and thermal response of bridges was presented by Kromanis and Kripakaran [19]. In their work, prediction error signals are created and then interpreted with anomaly detection techniques. Wang et al. [30] developed a long short-term memory (LSTM) approach for condition assessment of bridges to provide an early warning protocol through the analysis of the time-series measured data of deflection and temperature.

Among different types of recurrent neural networks, time delays neural networks (TDNN) [31, 32], layer recurrent networks [31], and Nonlinear AutoRegressive (NAR) networks [33, 34] have been widely used in time series forecasting. TDNN is a straightforward dynamic network consisting of a feed-forward network
with a tapped delay line at the input layer. NAR is a dynamic recurrent network with feedback connections including different layers of the network. In [35] hybrid approaches on time series data using ARMA with TDNN or ARMA with NAR are compared and results presented showed that NAR trends to perform well in providing more precise result for multi-step ahead prediction [35].

In the framing of the research field presented above, this study is concerned with investigation and implementation of ANNs for dynamic behavior prediction of bridges. A SHM system, installed in a cable-stayed bridge (Tabarly, Nantes, France) is used as a case study to demonstrate and verify the method. First, accelerations recorded by sixteen sensors and the Nantes airport METAR (Meteorological Terminal Aviation Routine Weather Report) weather measurements station data are used as training to predict the structural response and to statistically characterize the behavior through a Nonlinear AutoRegressive (NAR) prediction network. Statistical analysis of the error between measured and predicted values is performed. It is shown that the proposed network could constitute a useful tool to detect the presence of anomalies in the dynamic response of a bridge at a reasonable computational cost. The chapter is organized as follows: Section 2 briefly introduces ANNs and their underlying computational methodologies. Section 3 describes the geometrical and structural features of the cable-stayed bridge used as case study. Furthermore, the characteristics of a vibration based SHM system installed on the bridge are illustrated. Section 4 discusses the results obtained by the application of the data-driven approach. Finally, conclusions and future developments are drawn.

## 2 Artificial Neural Network (ANNs): basic principles

Artificial Neural Networks (ANNs) have been developed to model complex relationships where explicit formulae are difficult to carry out [22]. ANNs are defined as nonlinear nonparametric systems consisting of three main components: architecture, learning algorithm, and activation functions. Multi-layered feed-forward neural networks are most widely used network models in structural engineering applications. A typical neural network comprises an input layer, an output layer, and one or more hidden layers of neurons (computational units) that are interconnected through weighted connections. Figure 1 schematizes the architecture of a neural network along with the layers (i.e., input and output layers) and neuron numbers [36, 37].
<figure><img src="image_2.png" /><figcaption>Figure 1. Artificial Neural Network architecture (adapted from [36])</figcaption></figure>

Let consider a neuron *j* with *n*<sub>*i*</sub> inputs, as illustrated in Figure 2. If neuron *j* is in the first layer, all its inputs would be connected to the inputs of the network. If connections across layers are allowed, its inputs can be connected to outputs of other neurons or to network inputs. Node *y* can have two indices (*y*<sub>*j*,*i*</sub>) as the *i*-th input of neuron *j* or it can be implemented as *y*<sub>*j*</sub> to define the output of neuron *j* (with one index).

<figure><img src="image_3.png" /><figcaption>Figure 2. Connection of a neuron *j* with the rest of the network (extracted from [38])</figcaption></figure>

The output node of neuron *j* is computed as:

$$y_j = f_j(net_j) \tag{1}$$

where $f_j$ is the activation function of neuron *j* and net value $net_j$ is the sum of weighted input nodes of neuron *j*:

$$net_j = \sum_{i=1}^{n} w_{j,i} y_{j,i} + w_{j,0} \tag{2}$$

where $y_{j,i}$ is the *i*-th input node of neuron *j*, weighted by $w_{j,i}$, and $w_{j,0}$ is the bias weight of neuron *j*.
Activation functions are linear and non-linear components of neural networks. They are responsible for mapping between input and target values. The S-shaped sigmoidal functions such as tangent-sigmoid and logistic-sigmoid functions are widely used as activation functions as their non-linear mapping ability within the hidden layer of the network. Usually, output layer contains linear activation functions such as step and purelin functions [36]. The activation function in Neural Networks takes the input $y_{j,i}$ multiplied by its weight $w_{j,i}$. Bias allows to shift the activation function by adding a constant to the input and it has the effect of shifting the activation function by a constant amount ($w_{j,0}$). A complex nonlinear relationship between the output node $y_j$ of a hidden neuron $j$ and network output $o_m$ can be defined:

$$o_m = F_{m,j}(y_j) \qquad (3)$$

where $o_m$ is the m-th output of the network. The complexity of the mentioned nonlinear function $F_{m,j}(y_j)$ depends on the number of neurons between neuron $j$ and network output $m$.

## 2.1 Training Algorithms

The training of a network is performed to adjust the weight connections between the considered neurons. During the training process the input data is given to the network and the estimated output of the network is computed by using the current value set of weight coefficients and it is compared with the desired output. Then, the error between the estimated and desired output of the network is calculated and it is used to adjust the weight coefficients (initially set based on Nguyen-Widrow initialization method [39, 40]). In Neural Network, the learning algorithm is the component of training process which makes neural networks learn from data lags. Learning algorithms of neural networks are basically back propagation algorithms that use error functions derivatives as gradients. To evaluate the training process for all training patterns and network outputs, the Sum Square Error (SSE) is implemented as:

$$E(x, w) = \frac{1}{2} \sum_{p=1}^{P} \sum_{m=1}^{M} e_{p,m}^2 \qquad (4)$$

where $p$ is the index of patterns ranging from 1 to $P$ (i.e., number of patterns), $m$ is the index of outputs ranging from 1 to $M$ (i.e., number of outputs), $x$ is the input vector, $w$ is the weight vector, and $e_{p,m}$ is the training error at output $m$ when applying pattern $p$, and it is defined as:

$$e_{p,m} = d_{p,m} - o_{p,m} \qquad (5)$$
153 where *d* is the desired output vector and *o* is the output vector from the model.

154 A suitable algorithm for training small- and medium-sized problem in the artificial neural-networks field is
155 Levenberg-Marquardt backpropagation which provides a numerical solution to the problem of minimizing a
156 nonlinear function which, in this case, is the error function *E*. This function uses the Jacobian for calculations,
157 which assumes that performance is a mean or sum of squared errors. Therefore, networks trained with this
158 function must use either the MSE (Mean Squared Error) or SSE (Sum Square Error) performance function.

159 The Levenberg-Marquardt algorithm combines two algorithms for the training process: around the area with
160 complex curvature, it shifts to the steepest descent algorithm; when the local curvature becomes suitable for a
161 quadratic approximation it converts to the Gauss-Newton algorithm, which can significantly accelerate
162 convergence [38, 41].

163 The prediction performance of a network strictly depends on the network parameters, training process, and
164 quality of the training data set. Generally, extensive parametric studies performed on different networks are
165 necessary to get the best performance. Further details on ANNs as well as their implementation steps are
166 provided in [42-47].

167 2.2 Neural network time-series prediction

168 Dynamic neural networks are generally employed to forecast future values of a time series *y*(*t*) only from past
169 values of the actual time series. Time series prediction using neural network approach is non-parametric,
170 therefore it is not necessary to know any information about the process that generates the signal [33, 48, 49].

171 This form of prediction is known as Nonlinear AutoRegressive (NAR) model. The NAR network is a feed
172 forward neural network with three layers, namely input, hidden, and output layers. The NAR neural network
173 is trained in a series-parallel configuration. In the training phase, the true output is provided, and it is used as
174 the input to the network. In the testing phase, the computer output is fed back to the network to estimate the
175 next value of the output in a parallel configuration.

176 The NAR network consists of feedback connections, layers, and it is determined by the following equation:

$$
177 \qquad \hat{y}(t) = f(y(t-1) + y(t-2) + \cdots + y(t-d)) \qquad (6)
$$
where *f* is a nonlinear function, where the future values depend only on regressed *d* earlier values of the output signal. Since the network performs only a one-step ahead prediction after the training in the NAR network, it is necessary to use the closed loop network to perform a multi-step ahead prediction. Subsequent time steps can be predicted in a sequence through closed loop forecasting by using the previous predictions as input.

## 3 Monitoring system of a cable-stayed bridge

The Éric Tabarly bridge in Nantes (France) is a 210m long cable-stated road bridge crossing the Loire River. It is composed of a 27m wide steel deck divided into two spans by a 57m high steel pylon, being the main span 143m long (Figure 3).

<figure><img src="image_4.png" /><figcaption>Figure 3. Photo (a) and BIM model (b) of the Tabarly bridge in Nantes</figcaption></figure>

In 2016 the instrumentation has been installed for monitoring the vibrational behavior of the bridge. That is, 16 single-axis accelerometers have been installed onto the bridge with 2 different acquisition zones: 8 accelerometers in the deck and 8 accelerometers in the pylon. Data are acquired through a PEGASE generation 2 acquisition card marketed by A3IP company under IFSTTAR (now University Gustave Eiffel) license for each of the two zones. Each acquisition card exports voltage measurements at a sampling frequency of 100 Hz. Silicon Designs 2210 accelerometers, which can collect acceleration from -10G to 10G and usable with a 700 Hz acquisition frequency, were used. Figure 4 depicts the locations of the accelerometers (red dots) and details of the deck and pylon. In the deck, each slot contains two single-axis accelerometers, with one along Y-direction (vertical) and one along Z-direction (horizontal-transversal). Two accelerometers along Y-direction are placed in X3 (see Figure 4a). In the pylon (see Figure 4b), three of the eight accelerometers follow
198 the Z-direction, while the others are along the X-direction. The directions of the different accelerometers along
199 with the sensitivities of the sensors are listed in Table 1 and Table 2.

<figure><img src="image_5.png" /><figcaption>Figure 4. Layout of the accelerometric sensors placement for deck (a) and pylon (b)</figcaption></figure>

<table><caption>Table 1. Direction and sensitivities of the deck accelerometers</caption><thead><tr><th colspan="5">Deck</th></tr><tr><th>Location</th><th>Channel</th><th>Serial Number</th><th>Direction</th><th>Sensitivity (mV/g)</th></tr></thead><tbody><tr><td rowspan="2">X1</td><td>1</td><td>26188</td><td>Y&#773;</td><td>2009</td></tr><tr><td>2</td><td>26192</td><td>Z&#773;</td><td>2009</td></tr><tr><td rowspan="2">X2</td><td>3</td><td>26187</td><td>-Y&#773;</td><td>2013</td></tr><tr><td>4</td><td>26193</td><td>Z&#773;</td><td>2012</td></tr><tr><td rowspan="2">X3</td><td>5</td><td>26182</td><td>-Y&#773;(west)</td><td>2004</td></tr><tr><td>6</td><td>26184</td><td>-Y&#773;(east)</td><td>2012</td></tr><tr><td rowspan="2">X4</td><td>7</td><td>26197</td><td>-Y&#773;</td><td>2010</td></tr><tr><td>8</td><td>26190</td><td>Z&#773;</td><td>2012</td></tr></tbody></table>

<table><caption>Table 2. Direction and sensitivities of the pylon accelerometers</caption><thead><tr><th colspan="5">Pylon</th></tr><tr><th>Location</th><th>Channel</th><th>Serial Number</th><th>Direction</th><th>Sensitivity (mV/g)</th></tr></thead><tbody><tr><td rowspan="3">Y1</td><td>1</td><td>26183</td><td>-X&#773;</td><td>2013</td></tr><tr><td>2</td><td>26189</td><td>-Z&#773;</td><td>2008</td></tr><tr><td>3</td><td>23435</td><td>-X&#773;</td><td>2000</td></tr><tr><td rowspan="3">Y2</td><td>4</td><td>26194</td><td>Z&#773;</td><td>2013</td></tr><tr><td>5</td><td>26191</td><td>-X&#773;</td><td>2010</td></tr><tr><td>6</td><td>26185</td><td>-X&#773;</td><td>2008</td></tr><tr><td rowspan="2">Y3</td><td>7</td><td>26186</td><td>Z&#773;</td><td>2008</td></tr><tr><td>8</td><td>26195</td><td>X&#773;</td><td>2009</td></tr></tbody></table>
A global schematic view of the monitoring system and its connection to a cloud database solution is presented in Figure 4. As shown, the fully system is connected to a cloud database through a 3G/UMTS modem. Due to few bandwidth limitations induced by some communication components of the first monitoring system solution, only data issued from accelerometers were feeding the database. All accelerometers were integrated in a designed cube accessory connected to the structure.

## 4 Application of the NAR algorithm to the monitored data

In this study, a NAR network model is employed to predict the dynamic response of a cable-stayed bridge induced by ambient vibration through the measurements recorded by the SHM system previously described. The data-driven processing has been carried out through the Neural Network Time Series, that is a specific tool implemented in MATLAB. The accelerations elaborated by the algorithm were recorded on July 17, 2017, at 11:00 a.m. The registration has a total length of almost ten minutes, and it is composed of 59991 samples since the rate was 100 Hz. A first simulation has been performed by selecting different parameters: the training function "trainlm" that updates weight and bias values according to Levenberg-Marquardt optimization (among the fastest ones), and the network parameters (number of *hidden layers* and *time delay*) [38, 41]. Furthermore, the neural network modeling approach requires the determination of the percentages proportion of the data which are divided into a training dataset, validation dataset, and a test dataset. More specifically, the properties of the neural network are the following: (a) a Levenberg-Marquardt backpropagation algorithm, (b) the hidden layers were equal to 10, (c) the selected number of delays was equivalent to 10, (d) the network training set ratio was equal to 70%, the validation set was equal to 15%, and the network test ratio was equivalent to 15%. The neural network's performance results are presented in Figure 5 in terms of real (black line) and simulated (red line) acceleration time series related to location X2 (Deck) and channel 3 (Y-direction). Results show that the simulated time series is slightly higher than the real time series, resulting in a good match between them. Furthermore, a comparison between frequencies has been performed in the training dataset (the first 70% of the recorded samples) and test dataset (the last 15%) (see Figure 5b and Figure 5c). From the figures we observe a good agreement of the frequencies and higher amplitudes between the experimental and the simulated results by the network (red line). Figure 6 depicts different zoom (ranging
232 1 second) of the analyzed results. The ranges have been selected in areas with relatively high and small amplitudes. Results show a better agreement for the higher amplitudes (see Figure 6a, and Figure 6c).
233

<figure><img src="image_6.png" /><figcaption>Figure 5. Time (a) and frequency (b, c) comparison between recorded and simulated acceleration trained by NAR algorithm. Training (70%), validation (15%), test (15%). Hidden layers:10 and time delay:10</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6. Zoom of the comparison reported in Figure 5: range of relatively high (a, c) and low (b, d) amplitudes.</figcaption></figure>

239 A parametric analysis has been conducted by changing the *hidden layers* and *time delay* network parameters.

240 Specifically, the hidden layers have been set to 10 and 20, while for the time delay, six different values have

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been chosen (i.e., 10, 20, 50, 100, 1000, and 2000). Results, listed in Table 3 and Table 4, have been compared in terms of Standard Deviation (Std), Root-Mean-Squared-Error (RMSE), and Coefficient of Determination (R-squared, R²). From the results, it can be claimed that Std show a low variability when *hidden layers* and *time delays* are equal to 10 and to 1000 and 2000, respectively. RMSE and R² are substantially the same in all cases. However, it is right to highlight that while the simulations for the *time delays* 10, 20, 50 and 100 the computation time is up to few minutes, for *time delays* 1000 and 2000 the computation time is over ten hours.

<table><caption>Table 3. Performance of the ANN algorithm: hidden layers 10.</caption><thead><tr><td>Time delay [sample]</td><td>StD real [g]</td><td>StD simulated [g]</td><td>StD Difference (%)</td><td>RMSE</td><td>R<sup>2</sup></td></tr></thead><tbody><tr><td>10</td><td>0.00092</td><td>0.00081</td><td>13.58</td><td>0.00060</td><td>0.57</td></tr><tr><td>20</td><td>0.00092</td><td>0.00084</td><td>9.52</td><td>0.00061</td><td>0.56</td></tr><tr><td>50</td><td>0.00092</td><td>0.00083</td><td>10.84</td><td>0.00060</td><td>0.57</td></tr><tr><td>100</td><td>0.00092</td><td>0.00086</td><td>6.98</td><td>0.00059</td><td>0.59</td></tr><tr><td>1000</td><td>0.00092</td><td>0.00087</td><td>5.75</td><td>0.00060</td><td>0.58</td></tr><tr><td>2000</td><td>0.00092</td><td>0.00087</td><td>5.75</td><td>0.00061</td><td>0.56</td></tr></tbody></table>

<table><caption>Table 4. Performance of the ANN algorithm: hidden layers 20.</caption><thead><tr><td>Time delay [sample]</td><td>StD real [g]</td><td>StD simulated [g]</td><td>StD Difference (%)</td><td>RMSE</td><td>R<sup>2</sup></td></tr></thead><tbody><tr><td>10</td><td>0.00092</td><td>0.00083</td><td>10.84</td><td>0.00061</td><td>0.56</td></tr><tr><td>20</td><td>0.00092</td><td>0.00083</td><td>10.84</td><td>0.00061</td><td>0.56</td></tr><tr><td>50</td><td>0.00092</td><td>0.00084</td><td>9.52</td><td>0.00060</td><td>0.57</td></tr><tr><td>100</td><td>0.00092</td><td>0.00086</td><td>6.98</td><td>0.00059</td><td>0.59</td></tr><tr><td>1000</td><td>0.00092</td><td>0.00084</td><td>9.52</td><td>0.00059</td><td>0.60</td></tr><tr><td>2000</td><td>0.00092</td><td>0.00086</td><td>6.98</td><td>0.00060</td><td>0.58</td></tr></tbody></table>

Conclusions

Recently, artificial neural networks have been implemented in time series forecasting applications due to their nonlinear modeling capability. In this context, the chapter aims at evaluating the performance of an ANN in the prediction of the dynamic response of a cable-stayed bridge induced by ambient vibration. The proposed network was formulated to be capable of efficiently predicting relevant dynamic responses associated with the bridge. Accelerations recorded by a SHM system installed in the Tabarly bridge (Nantes, France) has been used as case study. Such measurements have been processed by a script generated by the Neural Time Series tool included in the toolbox of MATLAB. The Levenberg-Marquardt solution algorithm was preferred as it is
found to attain faster convergence without compromising the quality of the final network. After the training of NAR, MATLAB software can predict future value of one-time step ahead. The results, even if not completely satisfactory (for example the maximum value achieved of R² is equal to 0.60), are promising and with margins of improvement. Indeed, they could be useful as an adjunct tool to detect the trigger of possible anomalies related to the structural health.

Future attempts, including different variables to address missing parameters, such as temperature, that explain the predicted error, would likely attain a higher degree of accuracy. Finally, Deep Learning models for time series forecasting could be applied to improve the results.

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**Acknowledgments:** The research leading to these results has received funding by project DESDEMONA - *DEtection of Steel Defects by Enhanced MONitoring and Automated procedure for self-inspection and maintenance* (grant agreement number RFCS-2018_800687) supported by EU Call RFCS-2017.

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