Sparse Auto-Encoder Networks to Detect and Localize Structural Changes in Metallic Bridges

Abstract

The application of vibration monitoring integrated with sparse Auto-Encoder (SAE) networks is investigated in this paper with the objective of detecting and localizing structural anomalies or damages. Unlike previous studies on SAE networks, the methodology proposed is based on the definition of a single SAE model, trained with the signals simultaneously collected from several sensors. Once the SAE has been trained using measurements that represent the baseline (undamaged) condition of the structure, the network is likely to reconstruct well newly collected data if the structure maintains its intact condition. When damage or structural degradation processes start developing, an increase in the reconstruction error—defined as the residual between the original input and the reconstructed output—has to be expected, so that a deviation from the normal state is highlighted. Moreover, this rise in reconstruction errors is typically more significant near the damaged areas, allowing for precise localization of the affected zones. The performance and robustness of the proposed approach are illustrated and validated using experimental data from two real-world bridge structures.

1. Introduction

Civil Engineering structures are continually subjected to live loads as well as various natural and human-induced hazards. In addition, many structures were built decades ago using outdated design standards and construction methods. Over the years, material deterioration and aging have become major concerns, involving both safety and structural integrity. To reduce the occurrence of catastrophic events, such as collapses caused by the initiation and progression of structural issues, Structural Health Monitoring (SHM) has become a key practice in Civil Engineering, particularly for infrastructures like bridges [1] and dams [2], buildings [3] and similar systems. Consequently, maintaining the health and reliability of full-scale structures requires the use of advanced monitoring systems that can gather real-time data under actual service conditions [4]. The primary objective of continuous monitoring is to detect performance degradation and prevent structural failures.

Operational Modal Analysis (OMA) [5] remains a commonly used technique in continuous monitoring, as natural frequencies and mode shapes have proven to be reliable indicators for SHM. However, applying OMA-based SHM in practical conditions introduces well-known challenges, including: (a) inaccuracies in estimating modal parameters, and (b) the need for efficient automation of modal analysis along with consistent tracking of dynamic behavior for accurate anomaly detection.

A further significant difficulty arises from environmental and operational variability (EOV), which induces changes in the structural responses and, consequently, in the estimated modal parameters [6,7]. When the influence of EOV exceeds that of actual structural damage, particularly in the case of minor damage, accurate identification of the damage becomes problematic. This can result in false negatives, determining not negligible safety risks. Therefore, recognizing and accounting for all potential EOV factors during long-term monitoring is essential to minimize the related effects on structural responses and anomaly indicators.

In recent years, there has been a growing interest in Artificial Intelligence (AI) methods, largely driven by the increased computational capabilities enabled by Machine Learning (ML) algorithms [8]. To detect anomalies, ML methods focus on models that can recognize abnormal or outlier instances and differentiate them from normal data. Within this framework, the anomaly detector is trained exclusively on unlabeled data representing the healthy or undamaged state. Afterwards, anomaly scores or damage indicators (DIs) are computed for both training and testing samples, and these values are compared to a predefined threshold to identify possible anomalies or damage.

Within the set of deep neural networks [9], Auto-Encoders (AEs) [10] have proven to be particularly useful for anomaly detection tasks. AE networks are designed to capture the essential features or hidden structures of input data by compressing it into a lower-dimensional representation. In essence, an AE encodes the input into a concise feature space and then reconstructs the original input through a decoding phase with high fidelity. A specific variant, known as the sparse autoencoder (SAE) [11], has shown superior performance in continuous monitoring scenarios. This advantage arises from its ability to distinguish significant signal components from background noise within the input data, such as acceleration measurements [12]. By enforcing a sparsity constraint, SAEs prioritize the most informative features, thereby improving anomaly detection performance. For example, in [13], multiple SAEs—one network for each accelerometer—were applied to acceleration data to detect abnormal structural behavior. Their effectiveness was demonstrated using datasets from the Z24 Bridge [7] and the San Vittore bell tower in Italy [14], successfully identifying structural changes even when factors like temperature variations were present.

Compared to previous researches present in the literature (e.g., [10,11,12,13])—which involve designing and training an independent network for each sensor channel—a different strategy is herein introduced: the use of a single SAE model trained concurrently on dynamic data from all sensors. This specific training procedure, originally proposed in [15,16] and applied to the KW51 railway bridge monitoring, is based on the standard assumption that training is performed using time series recorded when the investigated structure is in control and exposed to typical EOV. Once training is complete, the SAE processes newly collected responses to reconstruct the corresponding signals. A close match between the original and reconstructed data suggests that the structural and environmental conditions remain consistent with those observed during training. The similarity between the original input and the reconstructed output is quantified using the Mean Absolute Error (MAE) [17]. Higher MAE values indicate a deviation from normal behavior. Furthermore, analyzing and comparing MAE values across multiple sensors not only facilitates the detection of anomalies but also aids in their localization, as sensors situated near damaged regions are expected to exhibit greater reconstruction errors.

After a brief overview of the anomaly detection and localization process based on SAE networks (Section 2), the paper presents the application of the proposed approach to two real bridges [18,19,20,21]. The first example relies on the ADA bridge [18], a steel truss structure, and demonstrates the performance of the method in the detection and localization of actual damage under nearly stable environmental conditions, as data were gathered over two consecutive days with minimal temperature variation. Previous research on the ADA bridge mainly addressed damage detection: in [19] changes in mode shapes are found to be minimal when damage was introduced asymmetrically. The present study advances those findings by identifying the induced damage directly from raw sensor data through an SAE network, eliminating any modal identification. Furthermore, in contrast to earlier investigations on the ADA bridge, the proposed technique accurately localizes all instances of damage.

In the second case study, the acceleration data was collected in the monitoring of the historic San Michele iron bridge [22], built in 1889. Previous investigations [20,21] employing OMA focused on continuous monitoring of the bridge from late 2011 to mid-2013. Specifically, by examining frequency evolution and analyzing the corresponding mode shapes, irregularities in the bridge’s structural behavior were clearly detected, with those irregularities being most likely linked to damage progression caused by corrosion. In the present work, acceleration data was directly used to train one single network, which—in turn—allows to detect structural changes and to localize the deterioration areas along the bridge.

2. SAE-Based Anomaly Detection and Localization

2.1. Theoretical Background

Typically, an AE includes three main layers (Figure 1): the encoder, the latent (or hidden), and the decoder layers. Let x_n ∈ ℜ^I denote the n-th realization of a single sensor (with I being the number of samples), the encoder compresses its dimensionality by extracting a lower-dimensional representation h_n ∈ ℜ^J (J < I) through an activation function f. Subsequently, the decoder layer reconstructs the original input x_n from the learned h_n by adopting an activation function g so that the dimensionality of the output realization y_n ∈ ℜ^I is the same as x_n.

Common choices for the activation functions f and g include the sigmoid, hyperbolic tangent, or linear functions [13]. To prevent the model from merely reproducing its input at the output layer, thereby missing deeper structural patterns, a Sparse Auto-Encoder (SAE) is employed [11]. According to this method, a sparsity constraint is applied to the hidden layer, encouraging most neurons to stay inactive during training. This mechanism facilitates learning of more latent and informative representations from the input data. Further information on the sparse AE formulation is available in [15].

2.2. Training of the SAE

In contrast to conventional methods, involving one distinct network for each data channel, the present approach develops a single network capable of processing the entire dataset X_n ∈ ℜ^M×I (see Figure 1): for each realization, a matrix consisting of M rows (corresponding to M channels) and I columns (corresponding to I time-samples) is formed and passed as input to the network. Additionally, it is crucial that the time series are sufficiently extended, to accurately represent the structural patterns and dynamic behavior under observation.

The training dataset consists of M × I matrices recorded while the structure is assumed to be in a healthy condition and exposed to typical EOV. In SAE model development, 75% of these matrices are used for training, whereas validation involves the remaining 25%. It is worth noting that the SAE development requires the optimization of several essential hyperparameters (

Table 1. List of SAE parameters’ ranges and optimal values for case studies.

Parameters	Input Range	Optimal Values
		ADA Bridge	San Michele Bridge
Number of encoder/decoder layers	1	1	1
Number of hidden neurons	10–50% of the signal length	30%	15% (P1), 30% (P2)
Encoder/decoder function	Sigmoid/linear	Sigmoid/linear	Sigmoid/linear
Max. Epochs	500–5000	500	1000 (P1), 3000 (P2)
Sparsity target value	[0.0001; 0.001; 0.01; 0.1; 0.5]	0.5	0.01
Mini-batch size	[4; 16; 32; 64]	4	16

): hyperparameter tuning is performed using a grid search approach [23], which systematically explores all possible parameter combinations within the defined search space to identify the configuration that produces the minimal reconstruction error on the validation set. In detail, the hyperparameters’ range—inspired by [24] and based also on the authors’ experience—is summarized in Table 1. A grid is thus formed by listing all possible combinations of these values: each combination is used to train the network, and its performance (in terms of reconstruction error) is evaluated using a validation set of data. The combination that results in the lowest reconstruction error is selected as the best (Table 1). The ADAM optimizer [25] is adopted to minimize the loss function Z(x_n, y_n), which measures the difference between the original input and the network’s reconstruction in an SAE model [15]. To prevent numerical instability during training, it is recommended to normalize the input data in advance [26].

2.3. Testing of the SAE

Once the training phase is completed, new data collected from unknown scenarios are fed into the SAE; for the i-th channel, the approximation error between the original input and the reconstructed output is computed by means of the MAE:

$${\mathrm{MAE}}_{\mathrm{n}}^{\left(\mathrm{i}\right)}={\displaystyle \frac{1}{\mathrm{I}}}\sum _{\mathrm{k}=1}^{\mathrm{I}}\left|x_{\mathrm{n},\mathrm{k}}^{\left(\mathrm{i}\right)}-y_{\mathrm{n},\mathrm{k}}^{\left(\mathrm{i}\right)}\right|$$

(1)

where:

• x⁽ⁱ⁾_n,k is the k-th sample of the n-th realization of input at channel i;
• y⁽ⁱ⁾_n,k is the k-th sample of the n-th realization of reconstructed output at channel i.

If the currently measured time series are collected under structural conditions similar to those present during the training phase, the network is expected to reconstruct the input with high accuracy. On the other hand, if the structural conditions have changed, the trained (optimal) SAE is likely to struggle with reconstructing the input, resulting in higher reconstruction errors. For each channel, the m-th percentile (e.g., the 95th–99th percentile) is computed from the MAE values obtained during the training phase. During the testing phase, for each channel, a data point is classified as an outlier when its reconstruction error falls beyond the computed threshold [13,15]. Although more complex methods exist in the literature for threshold determination or outlier detection (e.g., three-sigma rule, One-Class Support Vector Machine, and Support Vector Data Description), the percentile-based method is simple, based on engineering judgement and also supported by recent studies using AEs for anomaly detection [10]. It is further noticed that threshold values ranging from the 90th to 99.7th percentile (with the latter value corresponding to the three-sigma rule) are very common in SHM applications (see, e.g., [6,10]). Consequently, repeated or substantial occurrences of outliers suggest the presence of abnormal conditions.

A standard approach to evaluate experimental results against a set of known classifications (if available) involves determining the following indices: (a) normal behavior accurately recognized as such (True Negatives, TN); (b) healthy samples erroneously flagged as outliers (False Positives, FP); (c) anomalous behavior successfully detected (True Positives, TP); and (d) anomalous behavior misclassified as regular (False Negatives, FN).

Based on the above indices, the following performance metrics can be derived:

ACC = (TN + TP)/(TN + FN + TP + FP)

(2)

DR = TP/(FN + TP)

(3)

FAR = FP/(FP + TN)

(4)

where:

• Accuracy (ACC): measures the overall proportion of correctly categorized predictions across the entire dataset;
• Detection Rate (DR): represents the fraction of true anomalies successfully identified;
• False Alarm Rate (FAR): indicates the ratio of non-anomalous samples that are erroneously flagged as anomalous.

3. Application to Old ADA Bridge

3.1. Description of the Bridge and Investigated Scenarios

Vibration data were recorded at the Old ADA Bridge in Japan [18]. As illustrated in Figure 2, the simply supported steel truss bridge spans 59.2 m in length, with a deck width of 3.6 m. Having served for over 50 years, the bridge was decommissioned in 2012. Prior to its demolition, dynamic experiments were conducted on 1–2 March 2012, between 10:00 and 17:00, and during the tests human-induced damage was inflicted at two locations (Figure 2). Acceleration time series resulting from vehicle and ambient excitations were measured at a sampling frequency of 200 Hz using eight vertically oriented uniaxial accelerometers mounted on the deck (Figure 2). In this study, only the vehicle-induced responses are analyzed. The test vehicle was a two-axle Serena model (Nissan Motor Co., Ltd., Yokohama, Japan) weighing 21 kN. It should be noted that no other traffic was permitted on the bridge during testing. Additional details regarding the experimental setup can be found in [18]. Figure 3 shows the five damage scenarios that were selected for the vibration experiments:

• INT (Intact): The baseline state, where no artificial damage was introduced;
• DMG1: Involves a partial cut (half-cut) applied to one vertical truss member at midspan, with this member being placed on the same side of accelerometer A3;
• DMG2: Involves the full cut of the same truss member that was previously damaged;
• RCV (Recovery): Represents the condition following the repair of the previously cut member;
• DMG3: Consists of the total cut of one vertical member located at 5/8ths of the span, positioned in the close neighborhood of accelerometer A4.

It is important to highlight that: (a) the cuts were introduced to replicate scenarios typically resulting from corrosion or excessive loading, and (b) in the RCV condition, a jack was employed to reduce the gap in the cut member prior to welding steel components, although complete recovery of the bridge’s initial condition could not be guaranteed [18]. Each condition was tested through multiple runs: for the INT scenario [18], the vehicle speed ranged between 30 and 50 km/h. Due to slight variations in signal length between runs, time series of 40 s were consistently used for analysis.

It is further noticed that the experiments took place over two consecutive days, with a stable temperature of around 15 °C as reported in [18], so that the minimal environmental variability did not affect the dynamic characteristics of the investigated structure. Consequently, the analysis of the data collected on the ADA bridge was mainly aimed at evaluating the performance of the SAE-based approach in the detection and localization of various damage scenarios, with the EOV having a negligible impact.

3.2. Training of the SAE

A total of 26 acceleration matrices, each containing 8000 × 8 elements with columns corresponding to individual acceleration readings, were collected under the INT scenario and utilized for both model training and evaluation. Out of these, 19 matrices, representing 73% of the INT dataset, were designated for training, while 7 matrices, corresponding to 27%, served for validation. The optimal parameters (Table 1) of the SAE network were identified using a grid search strategy [23]. To improve the convergence stability of the ADAM optimizer [25], all acceleration sequences were normalized to the range [−1, +1]. The training procedure required approximately 20 min on a personal computer with 16 GB of RAM and a 2.7 GHz Intel Core i5 dual-core processor, in MATLAB 2022b framework and using the CPU exclusively.

3.3. Testing of the SAE

Once the SAE parameters have been established, the acceleration matrices from the remaining scenarios, specifically DMG1, DMG2, RCV, and DMG3, are fed into the network. The number of tested realizations was 12 for the DMG1 and 10 for the other scenarios (DMG2, RCV, DMG3), so that a total of 42 tested scenarios were used during the testing phase. As previously noted, the reconstruction performance is evaluated using the MAE, computed between the original input and the reconstructed output. For data coming from the DMG1, DMG2, and DMG3 scenarios, a worse network performance is expected in reconstruction of the acceleration sequences, leading to higher MAE values than those observed for the INT scenario. On the contrary, the MAE corresponding to the RCV scenario should closely match those of the INT condition.

Figure 4 shows the reconstructed sequences for the INT, DMG1, DMG2 and DMG3 scenarios, respectively: the figure inspection demonstrates that the trained network is capable of providing an accurate reconstruction of the data from the undamaged state (Figure 4a), whereas it fails when the input corresponds to damaged conditions (Figure 4b–d).

Figure 5 shows the evolution of the MAE, which reflects the reconstruction error, across the datasets collected by all sensors in the different scenarios. By adopting the 99th percentile of the MAE values from the training set as a threshold to differentiate between normal and anomalous reconstructions, the following insights emerge:

(a)

most of the signals corresponding to damaged conditions (specifically, the DMG1, DMG2, and DMG3 scenarios) are correctly detected;

(b)

in the damaged scenarios, MAE values tend to be higher at locations closest to the damaged strut;

(c)

more severe damage correlates with larger MAE values;

(d)

the RCV scenario introduces some ambiguity in classification due to only partial recovery toward the undamaged state [18].

The effectiveness of the anomaly localization method is further illustrated in Figure 6, which shows the mean MAE values (MAE_av) for various channels under different damage conditions. As highlighted in Figure 6, sensor A3 exhibits the highest MAE_av for damage scenario DMG2, whereas sensor A4 reaches its maximum value under DMG3. To provide a more comprehensive assessment of the anomaly detection approach,

Table 2. Performance indicators of the damage detection capability including (a) or not (b) the data measured under RCV state.

%		A1	A2	A3	A4	A5	A6	A7	A8
ACC	(a)	95.9	87.8	91.8	85.7	95.9	93.9	89.8	91.8
	(b)	97.4	100	100	97.4	97.4	100	100	100
DR	(a)	96.9	100	100	96.9	96.9	100	100	100
	(b)	96.9	100	100	96.9	96.9	100	100	100
FAR	(a)	5.9	35.3	23.5	35.3	5.9	17.6	29.4	23.5
	(b)	0	0	0	0	0	0	0	0

presents the metrics for Accuracy (ACC), Detection Rate (DR), and False Alarm Rate (FAR), calculated on the testing scenarios using the 99th percentile as the threshold value. Specifically, the metrics were calculated both including (a) and excluding (b) the 10 tests measured under the RCV condition. Notably, the trained model consistently delivers robust performance, achieving ACC and DR values above 85% and 96%, respectively. Although the FAR is not negligible when RCV data is included, it falls to 0% across all channels when the “uncertain” datasets are removed.

In addition, the MAE_av and the standard deviation (σ_MAE), evaluated for the different scenarios and sensors (

Table 3. Average (MAE_av) and standard deviation (σ_MAE) of MAE over the different scenarios and sensors.

	INT		DMG1		DMG2		RCV		DMG3
	MAEav	σMAE	MAEav	σMAE	MAEav	σMAE	MAEav	σMAE	MAEav	σMAE
A1	0.015	0.004	0.037	0.010	0.074	0.020	0.021	0.008	0.071	0.020
A2	0.014	0.003	0.045	0.010	0.097	0.023	0.025	0.009	0.087	0.022
A3	0.014	0.005	0.044	0.016	0.123	0.033	0.024	0.008	0.086	0.016
A4	0.016	0.004	0.046	0.017	0.099	0.026	0.027	0.011	0.119	0.024
A5	0.014	0.004	0.036	0.008	0.066	0.012	0.017	0.008	0.067	0.019
A6	0.012	0.003	0.036	0.005	0.073	0.021	0.017	0.008	0.080	0.024
A7	0.009	0.002	0.032	0.007	0.080	0.023	0.014	0.009	0.083	0.014
A8	0.011	0.003	0.034	0.007	0.074	0.018	0.018	0.010	0.069	0.020

), offer a clear indication of which region of the bridge is affected under various conditions (as shown in Figure 6). For instance, Table 3 enables precise identification of the damage location DMG1, situated near sensor A3. As the damage severity increases (i.e., DMG2), the effects are concentrated mainly around channel A3. In the DMG3 scenario, however, the region near channel A4 experiences greater influence, thereby demonstrating the method’s reliability in accurately locating damaged areas.

As a final remark, the advantage of the SAE-based approach is clear by comparison with previous studies. For example, the mode shapes’ variation is investigated in [19] and minor changes were observed only when the damage was applied asymmetrically. The results summarized in [19] are significantly improved herein by detecting the introduced damages directly from the raw signals using an SAE network, without the need for spectral functions or modal parameters. Moreover, unlike prior studies of the ADA bridge, the proposed approach successfully localizes all the inflicted damages.

4. Application to San Michele Bridge

4.1. Description of the Bridge and Monitoring System

The San Michele Bridge is an iron arch bridge linking the towns of Paderno and Calusco d’Adda, located roughly 50 km from Milan [22]. Completed in 1889 as part of one of Italy’s first railway routes, the bridge remains operational today, carrying both vehicular and rail traffic. As shown in Figure 7 and Figure 8, its main structural components include a parabolic iron arch, a box-shaped truss girder on the upper level, and several supporting piers. The arch extends 150 m, with a vertical rise of 37.5 m, and consists of two ribs tilting inward, spaced approximately 16 m apart at the base and 5 m at the top. The upper girder is 266 m long and rests on nine equally spaced bearings. It supports two decks: the upper deck is used for road traffic and pedestrians, while the lower deck carries a single railway track. The bridge’s structural condition has progressively worsened over the years due to difficulties in carrying out regular maintenance, especially on the arches, resulting in extensive corrosion across a large number of structural elements. As part of a bridge assessment promoted by the Province of Lecco, ambient vibration measurements were conducted on both the roadway and railway decks between June 2009 and June 2011. The preliminary results indicated a relationship between the structure’s dynamic behavior and the magnitude of the applied excitation and corresponding response [20].

In partnership with the Italian Railway Authority (RFI), the primary institutional owner of the bridge, it was decided to implement a dynamic monitoring system on the railway deck. This location was chosen because inspection and maintenance of the monitoring devices could be performed more efficiently there, with the assistance of RFI’s technical personnel. The permanent dynamic monitoring system has been fully active since 28 November 2011 [20,21], and the analysis of the data collected during the first 18 months of monitoring is presented in this study.

The monitoring setup consisted of 21 MEMS accelerometers (Figure 8), 7 data acquisition (DAQ) modules, 2 thermocouples, 2 Ethernet switches, and 1 industrial-grade PC. A distributed architecture is adopted and 7 instrumented cross-sections (Figure 8), corresponding to the bearings of the truss-box girder between the abutments, are equipped with: (a) 1 NI Ethernet DAQ unit, which is incorporated in a steel box installed between the rails and (b) 3 MEMS accelerometers, measuring the vertical accelerations on the downstream/upstream sides and the lateral acceleration. Temperature measurements were taken at the second and fifth instrumented sections. Every hour, the system generated a new binary file containing 21 acceleration time histories (sampled at 200 Hz) along with temperature readings. These files were stored locally and then sent to Politecnico di Milano for subsequent analysis.

In this study, the vertical acceleration data measured on the downstream side of the bridge (Figure 8) were used in the application of the SAE-based approach. The data, originally sampled at 200 Hz, were re-sampled at 40 Hz after being filtered with a Butterworth low-pass filter (cutoff frequency of 20 Hz). The temperature data in Figure 9 represents the average values recorded on downstream and upstream sides over the period from 28 November 2011 to 14 August 2013. Several intervals within this timeframe were characterized by snowfall events and low temperatures, most notably during the early weeks of February 2012 and, more persistently, from December 2012 through February 2013.

4.2. Training of the SAE

As previously stated, the SAE-based approach involved only the seven vertical accelerations recorded on the downstream side, with a one-minute portion being extracted from each 1 h dataset. Consequently, the data are arranged as 7 × 2400 matrices (seven channels, each containing 2400 time samples). Two distinct analyses are conducted, each based on a separate training period, denoted as P1 and P2. The selection of the training periods was constrained by the relatively limited duration of the available monitoring data and the onset of structural degradation. Specifically, progressive damage to the bridge began in February 2012 and stabilized by October 2012, as reported in previous studies [20,21]. Consequently, two specific training intervals were identified to ensure the model was trained on stable structural conditions, while also excluding time intervals with sub-zero temperatures to avoid potential non-linearities associated with freezing conditions. In details:

• Training period P1 extends from 28 November 2011 to 1 February 2012, yielding 1274 signal matrices used for training. During this interval, the average temperature (Figure 9) ranges from −2.6 °C to 17.6 °C. The coldest weeks of February 2012, which correspond to the lowest recorded temperatures, are excluded from this training set;
• Training period P2 covers the time span from 5 October 2012 to 14 August 2013, with 9860 signal matrices utilized for training. In this case, the average temperature (Figure 9) exhibits a broader range, varying between −3.6 °C and 34.7 °C, thus encompassing a wider range of thermal conditions than P1.

In both cases, roughly 75% of the matrices obtained during training were allocated for fitting the SAE model, while the remaining 25% was used for validation. The optimal SAE parameter configuration (Table 1) was identified using a grid search procedure [23]. To improve the convergence stability of the ADAM optimization algorithm [25], each acceleration signal was again normalized to the range [−1, +1]. The training process required approximately 20 min for P1 and 50 min for P2 on a computer equipped with 16 GB of RAM and a 2.7 GHz Intel Core i5 dual-core processor, in MATLAB framework and using the CPU exclusively. Compared to the 20 and 50 min required by the proposed methodology, the OMA repeated for all datasets acquired during the two training periods require 5 h and 41 h, for training periods P1 and P2, respectively.

4.3. Testing of the SAE

Figure 10 exemplifies the network’s reconstruction performance, corresponding to the P1 training phase, for both validation (Figure 10a) and testing (Figure 10b) set. The figure inspection clearly reveals that the trained network fails to accurately reproduce the test time series (Figure 10b), indicating that the test data likely contain conditions not encountered during training. To provide further evidence, Figure 11 and Figure 12 show the MAE progression for four selected sensors (A1, A3, A4, and A6 in Figure 8) across the two training intervals, P1 and P2. It is important to emphasize that:

• In both cases, the testing dataset (represented by the yellow markers in Figure 11 and Figure 12) shows reconstruction errors exceeding the control threshold, defined as the 99th percentile of the training data. Additionally, up to 50% of the samples are classified as outliers in both testing phases. As illustrated in Figure 11 and Figure 12, this effect is especially prominent in sensors A3 and A4;
• During the testing phases, reconstruction errors reach higher magnitudes and exhibit larger variability in the channels located near the arch crown, specifically, sensors A3 and A4 in Figure 11 and Figure 12. This observation is further supported by the statistical analysis of the MAE, summarized in

  Table 4. Average (MAE_av) and standard deviation (σ_MAE) of MAE in the testing periods.

  Index		A1	A2	A3	A4	A5	A6	A7
  MAEav	P1	0.493	0.493	0.531	0.530	0.467	0.410	0.355
  	P2	0.526	0.589	0.606	0.610	0.538	0.576	0.372
  σMAE	P1	0.075	0.118	0.125	0.124	0.109	0.089	0.049
  	P2	0.073	0.108	0.123	0.124	0.103	0.082	0.042

  . The mean (MAE_av) and standard deviation (σ_MAE) attain their highest values again for sensors A3 and A4, which are positioned closest to the arch crown (Figure 8). Those results fully correspond to previous observations reported in [20,21];
• The training period P1 (Figure 11), even if only 2 months long, turns out to be sufficient to develop a damage-sensitive indicator (i.e., the MAE) that effectively captures the structural deterioration occurring in the bridge;
• When the training period is extended to nearly one year (P2, Figure 12), the structural variations become more distinctly observable. This demonstrates that the environmental and operational variations were implicitly incorporated into the model during training. Indeed, the coefficients of determination (R²) between the MAE value associated to each sensor and the recorded temperature fall in the range of 0.001–0.08 (Figure 13): the hourly files used to construct the linear regression are the same as those used during the testing phase, i.e., 2947. Furthermore, for each hour, a single MAE value is calculated by the proposed algorithm (for each channel), while a single temperature value is obtained by averaging the measured values.
• Due to the unavailability of environmental data other than temperature, it is not possible to correlate reconstruction errors with additional factors such as humidity or wind speed. Furthermore, previous OMA-based investigations [20,21] have shown that the dependence of dynamic characteristics on traffic intensity (estimated via the RMS of the recorded accelerations) is significantly weaker than the dependence on temperature. For this reason, these factors were not further investigated in the present study;
• It seems to confirm the SAE capability to implicitly model the intact (healthy) structural conditions under typical EOV influence, without explicitly minimizing masking effects related to EOVs;
• The SAE-based procedure applied to the San Michele bridge demonstrates a two-fold advantage over conventional SHM techniques. Firstly, it drastically reduces the computational effort required to process extensive monitoring datasets compared to traditional OMA-based pipelines. Secondly, the SAE architecture proves capable of implicitly capturing the influence of EOVs with a training period of only two months. While traditional modal-based methods generally require 9–12 months of monitoring to account for complete seasonal cycles, the proposed methodology achieves robust anomaly detection with a significantly smaller training window, enhancing its suitability for time-effective structural health assessment.

5. Conclusions

The study introduces an unsupervised approach that employs continuous dynamic monitoring combined with SAE networks to identify and locate anomalies in Civil Engineering structures. It should be underlined that SAE networks show strong potential due to their capability to capture intricate hidden patterns within the data during training and to recognize new or unusual behaviors in subsequently gathered data.

Unlike traditional methods, where a separate network is trained for each individual data channel, the proposed framework adopts a single network trained on the dynamic responses recorded simultaneously from all available channels. Once trained, this network can accurately reproduce newly measured data, as long as the structural and environmental or operational conditions remain comparable to those of the training phase. Conversely, discrepancies between the measured and reconstructed time series across various monitoring sensors can reveal both the presence and approximate location of potential structural damage.

The first application involves artificial damage scenarios applied to the Old ADA steel truss bridge [18,19] in Japan prior to its decommissioning. For this bridge, experimental measurements were carried out under constant temperature conditions, and the scenarios varied in both the severity and location of inflicted damage, including a partial restoration to the intact state. The results indicate that the method successfully classifies damage scenarios in terms of occurrence, location, and level of stiffness reduction.

As the ADA bridge data did not exhibit significant EOV, a second case study is presented to demonstrate the SAE method’s ability to implicitly model EOV during training and detect potential structural changes. The study focused on 18 months of continuous dynamic monitoring of the San Michele bridge [20,21] and the developed SAE networks confirmed the capability of clearly localizing the areas where remarkable changes were reported [20,21] (i.e., the region near the arch crown). Furthermore, relatively short training periods (of about 2 months) turn out to ensure sufficient detection and localization capacity of the proposed methodology, as the effects of environmental and operational variability on the dynamic responses are implicitly accounted for during the training process.

It worth noting that the observed differences in MAE magnitudes between the two case studies might be attributed to the different operational conditions: while the ADA bridge tests involved single vehicle passages at controlled speeds, the San Michele bridge data reflect multiple simultaneous crossings, consistent with its significantly greater structural length.

Future developments could further investigate the influence of sensor density on the model’s performance. Although the current study was constrained by the fixed configuration of existing datasets, the SAE’s ability to learn cross-correlations between channels would be conceivably enhanced by a higher number of sensors.