Article

Leon Vale Lobo; Renato Máximo Sátiro

DOI: 10.22167/2675-6528-202602550

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the Revista E&S with the support of the ResumeAI tool, an artificial intelligence solution developed by the Pecege Institute for textual synthesis and organization.

Summary

Structural health monitoring of bridges has become increasingly relevant due to the aging of infrastructure and the intensification of extreme events associated with climate change. In this context, data-driven approaches have emerged as promising alternatives for anomaly detection. The study aimed to develop and evaluate a machine learning-based approach for anomaly detection in structural acceleration time series. The adopted methodology consisted of using autoencoders trained exclusively with data representative of the intact condition, allowing the model to learn patterns associated with the structure’s healthy state; subsequently, the reconstruction error, quantified by the mean squared error (MSE), was used as a criterion for identifying deviations from this condition. The analyzed dataset comprised 1767 time series of 1000 points each, belonging to two classes: intact (normal) and anomalous (damaged). The results obtained demonstrated that the proposed model exhibited a high capacity for detecting the anomalous class, with a detection rate exceeding 90%, and satisfactory overall performance, with an area under the ROC curve (AUC) close to 0.78, indicating good discriminative ability and reinforcing the potential of the approach for structural monitoring applications.

Keywords: Autoencoders; Anomaly Detection; Bridge Monitoring; Neural Networks.

1. Introduction

Structural Health Monitoring (SHM) has become crucial given the aging of infrastructures and the growing occurrence of extreme events associated with climate change (NUMAN, 2024). Its purpose is to detect damages or anomalies early, such as cracks, corrosion, displacements, or unexpected vibrations, aiming to prevent catastrophic failures, extend the service life of structures, optimize maintenance, and reduce costs. This monitoring involves the use of various sensors for real-time data collection and periodic inspections (ALAHAKOON et al., 2009), requiring the modeling of structural behavior under normal and damaged conditions to identify deviations.

With the advancement in data acquisition capabilities, the need for automatic methods to process and diagnose useful information has become evident (FAVARELLI and GIORGETTI, 2020). In this scenario, Machine Learning (ML) and, in particular, neural networks, emerge as essential tools for analyzing large volumes of monitoring data (GIORGETTI, 2020).

Recent applications demonstrate the effectiveness of ML in detecting and locating cracks in structures using sensor data (SHAH MANSOURI et al., 2024). Semi-supervised approaches, which combine variational autoencoders with one-class support vector machines, have been employed to detect structural damage, training models with normal condition data to identify anomalies (SHANG et al., 2021). Neural networks are particularly promising, as they can model nonlinear relationships between sensor signals and structural state, enabling automatic anomaly detection without relying on constant human inspection (ZHANG and LEI, 2021; KATAM et al., 2023).

In addition to the intrinsic challenges of monitoring, climate change intensifies the variability and intensity of extreme events, such as heavy rainfall, floods, and abrupt temperature variations, which directly impact the structural integrity of bridges and other infrastructures (PALIN et al., 2021). The construction of resilient infrastructures, capable of withstanding and rapidly recovering from these events (SEAGER et al., 2017), requires that planning, monitoring, and maintenance consider climate risks (OECD, 2024).

Despite advances, there is still a gap in the ability to continuously and directly identify damage in operational structures, especially under variable environmental and loading conditions, and in the absence of purely mechanical-physical approaches that provide real-time diagnostics. The scarcity of labeled damage data also limits the application of supervised methods. Given this, data-driven methods, such as the one proposed in this work, become a viable alternative and, in many contexts, the only practical approach for anomaly detection, justifying the importance of maximizing the correct identification of damaged states to mitigate risks and ensure safety.

Thus, this study is justified by the need to improve anomaly detection in critical infrastructures, and aims to develop an anomaly detection model in bridge acceleration signals that will allow the automatic identification of dynamic changes associated with the occurrence of structural damage, contributing to the prevention of failures, optimization of maintenance, and increased resilience of critical infrastructures in scenarios characterized by extreme events, natural disasters, and climate change, through the development of a machine learning-based approach, aiming to increase the resilience of critical infrastructures and support decision-making in smart city contexts.

2. Material and Methods

This research was characterized by a quantitative, applied approach, with the objective of developing and evaluating a model for detecting anomalies in bridge acceleration signals. The methodological strategy focused on the use of unsupervised machine learning techniques, specifically autoencoders, trained to recognize patterns associated with the intact condition of a structure and identify deviations that could indicate the presence of damage.

The empirical object of the study was the Z24 bridge, a full-scale prestressed concrete road structure, located in Switzerland, near the cities of Koppigen and Utzenstorf (MAECK and ROECK, 2003). The bridge, built in the early 1960s and demolished in 1998, consisted of a two-cell box girder with a main span of approximately 30 meters and two side spans of about 14 meters, supported by reinforced concrete piers and abutments.

The data used were from the public domain, originating from the Z24 bridge benchmark, made available by the Department of Civil Engineering at KU Leuven, Belgium. The original records, stored in .txt format files, were imported into the Python environment for processing. Data collection occurred over approximately one month, during which multiple damage scenarios were sequentially introduced into the structure.

Structural response signals were acquired using a vertical R3V sensor, positioned in the middle of the bridge span, with an acquisition rate of 100 Hz. For the study, data from three representative days of different structural conditions were selected: August 20 (undamaged condition), August 25 (level one damage condition), and August 26 (level two damage condition).

Each monitoring day corresponded to a continuous signal of approximately 11 minutes, which was segmented into temporal windows of 1000 points. This procedure resulted in 589 samples per day. The concatenation of data from the three analyzed days originated a final set with 1767 time series, organized for later use in the model’s training and evaluation.

The data preprocessing included segmenting the long signals into windows of 1000 samples, following the approach by SHANG et al. (2022), applied identically to both signals corresponding to the intact structural condition (label zero) and the damaged condition (label one). Subsequently, the segments from both conditions were combined into a single dataset, with associated binary labels.

As a final preprocessing step, z-score normalization was applied to the data (CURTIS et al., 2016). The mean and standard deviation were estimated exclusively from the training set, and subsequently used to normalize both the training and testing data, thus avoiding information leakage between the sets and promoting algorithm convergence.

The anomaly detection model was based on a fully connected autoencoder, composed of an encoder and a decoder. The encoder was responsible for mapping the input signals, represented by temporal segments of 1000 samples, to a lower-dimensional latent space, with a dimension equal to 64.

The encoder architecture consisted of a sequence of three dense layers with 512, 256, and 128 neurons, respectively, followed by the compression layer. All encoder layers used the ReLU activation function. The decoder, symmetric to the encoder, performed the inverse mapping, reconstructing the original signal from the latent representation, with dense layers of 128, 256, and 512 neurons, and an output layer with 1000 neurons and a linear activation function.

The definition of the model architecture was preceded by an automatic hyperparameter search process, using the Optuna library (AKIBA et al., 2019). This procedure sought to identify the best combination of parameters, such as the number of layers for the encoder/decoder, the number of neurons in the input layer and in the latent space.

The autoencoder training was performed using exclusively data corresponding to the intact structural condition, allowing the model to learn the representation of the bridge’s normal behavior. The model was trained for up to 200 epochs, with a batch size of 128, using the input signals themselves as the reconstruction target and a validation set composed of intact data not used in training.

The complete model was trained by minimizing the reconstruction error between the input signal and the reconstructed signal, using the mean squared error (MSE) loss function. Optimization was performed using the Adam algorithm. To prevent overfitting, an early stopping criterion was adopted based on monitoring the loss on the validation set, interrupting training if there was no improvement in the loss function after two consecutive epochs.

The performance evaluation of the damage detection method was carried out by analyzing the reconstruction error of the autoencoder, quantified by the mean squared error (MSE), which expresses the difference between the input data and its reconstruction by the model (PALUBINSKAS, 2017; ZHANG et al., 2023). Signals with an error above a determined threshold were classified as potential indicators of structural damage.

For the objective choice of the decision threshold, the Youden index (FLUSS et al., 2005) was used, which simultaneously maximizes the true positive rate and minimizes the false positive rate. Additionally, to evaluate the model’s discriminative capacity, the Receiver Operating Characteristic (ROC) curve and the Area Under the Curve (AUC) metric (JAMES et al., 2006), as well as the confusion matrix, were used.

3. Results and Discussion

The research results demonstrate the effectiveness of the autoencoder-based approach for anomaly recognition in structural acceleration time series of bridges, aligning with the objective of developing a model capable of automatically identifying damage-associated dynamic changes. The employed methodology, focusing on exclusive training with data from the intact condition, allowed the model to learn the structure’s healthy behavior patterns, using reconstruction error as a robust indicator for deviations. The detailed analysis of the findings, from data preprocessing to model performance evaluation, offers an in-depth understanding of the proposed approach’s discriminative capability. Preprocessing

The data preprocessing step was a fundamental stage for enabling the training and evaluation of the anomaly detection model. Initially, the structural response signals, acquired in long time series with approximately 589,824 points per sensor, were segmented into windows of 1000 samples. This segmentation, as highlighted by Shang et al. (2022), is crucial for generating multiple independent realizations of the structure’s dynamic behavior, preserving its statistical and spectral characteristics, while simultaneously expanding the dataset available for analysis.

Segmentation was applied consistently to signals corresponding to the intact structural condition, labeled as zero, as well as to signals from the damaged condition, labeled as one. This uniformity in data representation is essential to ensure the validity of comparisons and the robustness of model training. After segmentation, segments from both conditions were combined into a single dataset, to which binary labels indicating the intact or damaged structural states were assigned, preparing the dataset for subsequent study phases.

As a final preprocessing step, z-score normalization was applied to the data. This procedure involves transforming each observation by subtracting the mean and dividing by the standard deviation of the variable, resulting in data with a null mean and unit variance (Curtis et al., 2016). It is important to note that the mean and standard deviation were estimated exclusively from the training set, avoiding any information leakage between the training and testing datasets. This normalization contributes significantly to the numerical stability and convergence of neural network-based algorithms, ensuring that all variables operate on the same scale and with a standardized distribution. Model Creation and Training

The definition of the autoencoder architecture was preceded by an automatic hyperparameter search process, employing the Optuna library (Akiba et al., 2019). This procedure aimed to identify a neural network configuration that offered an optimal balance between representation capacity, training stability, and performance in reconstructing structural signals. The optimized hyperparameters included the number of layers for the encoder and decoder, the number of neurons in each input layer and in the latent space, seeking the best configuration for the model.

The autoencoder architecture was implemented with a sequence of three dense layers in the encoder, containing 512, 256, and 128 neurons, respectively, followed by a compression layer that defines the latent code with a dimension of 64. All encoder layers utilized the ReLU activation function, which is known for favoring the modeling of non-linear relationships and optimizing computational efficiency. The model consists of a fully connected autoencoder, where the encoder maps the input signals, represented by temporal segments of 1000 samples, to a lower-dimensional latent space.

The decoder, in turn, performs the inverse mapping, reconstructing the original signal from the latent representation. Its architecture is symmetrical to that of the encoder, composed of dense layers with 128, 256, and 512 neurons, also with a ReLU activation function, and concludes with an output layer that has a number of neurons equal to the length of the input segment. The final layer employs a linear activation function, suitable for reconstructing continuous signals, ensuring the fidelity of the reconstructed signal to the original.

The full model training was conducted with the objective of minimizing the reconstruction error between the input signal and the reconstructed signal, using the mean squared error (MSE) loss function. Optimization was performed using the Adam algorithm, widely recognized in deep neural networks for its robustness and rapid convergence. To mitigate the risk of overfitting and ensure better generalization, an early stopping criterion was implemented, monitoring the loss on the validation set and interrupting training if there was no improvement in the loss function after two consecutive epochs, which contributed to the computational efficiency and stability of the learning process.

The autoencoder was trained exclusively with data corresponding to the intact structural condition, allowing the model to learn the representation of the bridge’s normal behavior. The training was performed for up to 200 epochs, with a batch size of 128, using the input signals themselves as the reconstruction target and a validation set composed of intact data not used in training. The evolution of the loss function demonstrated that the learning process converged around epoch 25, with a significant reduction in reconstruction error, from initial values around 0.5 to approximately 0.1. After this point, the validation loss remained stable, while the training loss reached an almost null plateau, indicating that the model achieved an adequate representation of normal structural behavior without evidence of overfitting. Performance evaluation

The initial evaluation of the model was performed through direct comparison between the input time series and those reconstructed by the autoencoder. For the intact structural condition, the model demonstrated a high capacity to reproduce the signal with high fidelity, presenting a smoothed reconstruction with significant noise reduction. This behavior suggests that the autoencoder learned the dominant characteristics of the structure’s normal dynamic behavior, implicitly acting as a filter, which is a positive indicator of its representation capability.

In contrast, when the model was applied to signals from the damaged condition, which were not included in the training, the reconstruction showed significantly lower quality. It was observed that operational and environmental variations strongly influenced the reconstruction, resulting in greater discrepancies between the original and reconstructed signal. This pronounced difference in reconstruction quality highlights the autoencoder’s ability to effectively distinguish between patterns associated with the healthy condition and those related to anomalous states, establishing the basis for damage detection through reconstruction error analysis.

The quantitative evaluation of the damage detection method’s performance was carried out by analyzing the autoencoder’s reconstruction error and classic classification metrics, such as the confusion matrix. This matrix provided a direct view of the model’s ability to differentiate between intact and damaged structural states. It was found that 92.4% of the segments corresponding to the damaged condition were correctly identified as anomalous, demonstrating a high sensitivity of the method to the presence of structural damage.

This result is particularly relevant for structural health monitoring, as maximizing the hit rate for the anomalous class is directly linked to mitigating real risks. Failures in damage identification, known as false negatives, can lead to the undetected progression of structural pathologies, with the potential to result in collapses or severe service disruptions. Therefore, prioritizing model sensitivity is more critical than simple global accuracy, as it directly aligns with preventing high-impact events and ensuring infrastructure safety.

On the other hand, approximately 7.6% of the damaged signals were classified as normal, constituting false negatives. Although undesirable, these cases can be attributed to the partial overlap between structural response patterns under mild damage and operational or environmental variations. Regarding the intact condition, 66.1% of the segments were correctly classified as normal, while 33.9% were incorrectly identified as anomalous, characterizing false positives.

This result is associated with the deliberately conservative nature of the method, which uses reconstruction error as a decision criterion. Natural variations in structural behavior, measurement noise, and environmental influences can increase reconstruction error even in the absence of damage, leading to the classification of some intact signals as anomalous. However, this approach increases the model’s sensitivity to detect relevant structural changes, which is an acceptable trade-off in practical structural health monitoring applications, where the balance between damage detection and false alarms must be evaluated according to the safety and risk requirements of the infrastructure.

The definition of the decision threshold to separate normal and anomalous states is a central aspect of the methodology. The threshold was determined based on the Youden index (Fluss et al., 2005), which simultaneously maximizes the true positive rate and minimizes the false positive rate. This criterion offers an objective choice of threshold, balancing sensitivity and specificity and avoiding arbitrary decisions based solely on visual inspection, which is fundamental for the robustness of the detection system.

The analysis of the reconstruction error of the intact data through a histogram allowed visualizing the distribution of error values for the normal and damaged conditions. A clear separation was observed between the distributions, although with a region of overlap, a common characteristic in real-world Structural Health Monitoring (SHM) problems. This overlap indicates the complexity of perfectly distinguishing between slight damage conditions and normal variations, reinforcing the need for robust methods such as the autoencoder.

The analysis through the Receiver Operating Characteristic (ROC) curve complemented the evaluation of the method’s overall performance. The ROC curve describes the classifier’s behavior for different threshold values, relating the true positive rate to the false positive rate. The area under the curve (AUC) value was approximately 0.78, indicating a good discriminative capacity of the model, significantly superior to random performance. This result confirms that the reconstruction error learned by the autoencoder contains relevant information about the bridge’s structural state, allowing for robust distinction between intact and damaged conditions, even in the presence of operational and environmental variability.

Taken together, the obtained results indicate that the autoencoder, trained exclusively with data from the intact condition, is capable of learning a consistent representation of the pattern associated with the normal state and of identifying deviations related to damage by increasing the reconstruction error. Although the AUC of 0.78 suggests that there is still room for improvement in the global discrimination capacity between intact and anomalous states, the model presents high performance in identifying the anomalous class, with an accuracy rate exceeding 90%. This aspect is particularly relevant to the problem at hand, where the correct identification of damage has greater practical importance than the classification of the intact condition, as errors in this context are directly associated with risks to infrastructure safety.

Thus, the autoencoder-based approach proves to be a robust and promising alternative to traditional inspection methods and supervised techniques, especially in contexts where labeled damage data is scarce or non-existent. The method has the potential for application in continuous monitoring systems, contributing to condition-based maintenance strategies and to increasing the resilience of critical infrastructures against aging scenarios and climate change. The ability to early identify structural changes is essential for the safety and optimization of bridges’ lifespan, aligning directly with the central objective of this study.

4. Conclusion

The present study aimed to develop and evaluate a machine learning-based approach for anomaly recognition in structural acceleration time series of bridges. It was found that the autoencoder, trained exclusively with data representative of the intact condition, demonstrated the ability to learn the patterns of healthy structural behavior. The analysis of reconstruction error, quantified by mean squared error (MSE), allowed for the identification of deviations from this condition, with an anomalous class detection rate exceeding 90%. Satisfactory overall performance was observed, with an area under the ROC curve (AUC) close to 0.78, indicating the robustness of the approach in distinguishing between intact and damaged conditions, even in the face of operational and environmental variability. Prioritizing sensitivity in damage detection proved crucial for risk mitigation in critical infrastructures.

The main contribution of this work lies in offering a robust and promising alternative to traditional inspection methods and supervised techniques, especially in scenarios with scarcity of labeled damage data. The developed model has the potential for application in continuous monitoring systems, optimizing condition-based maintenance strategies and increasing the resilience of critical infrastructures against aging and climate change. However, the partial overlap between structural response patterns under light damage and operational or environmental variations, which resulted in false positives and an AUC of 0.78, indicates that there is still room for improvement in the overall discrimination capability. It is suggested that future studies explore model optimization to reduce the false positive rate without compromising the high sensitivity in anomaly detection, and investigate the integration of environmental data to refine the distinction between normal variations and actual damage.

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Article originating from the Course Conclusion Work of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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