Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the Lilleb{\ae}lt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.
Population-based structural health monitoring (PBSHM), aims to share information between members of a population. An offshore wind (OW) farm could be considered as a population of nominally-identical wind-turbine structures. However, benign variations exist among members, such as geometry, sea-bed conditions and temperature differences. These factors could influence structural properties and therefore the dynamic response, making it more difficult to detect structural problems via traditional SHM techniques. This paper explores the use of a Bayesian hierarchical model as a means of multitask learning, to infer foundation stiffness distribution parameters at both population and local levels. To do this, observations of natural frequency from populations of structures were first generated from both numerical and experimental models. These observations were then used in a partially-pooled Bayesian hierarchical model in tandem with surrogate FE models of the structures to infer foundation stiffness parameters. Finally, it is demonstrated how the learned parameters may be used as a basis to perform more robust anomaly detection (as compared to a no-pooling approach) e.g. as a result of scour.
Structural Health Monitoring (SHM) is a critical task for ensuring the safety and reliability of civil infrastructures, typically realized on bridges and viaducts by means of vibration monitoring. In this paper, we propose for the first time the use of Transformer neural networks, with a Masked Auto-Encoder architecture, as Foundation Models for SHM. We demonstrate the ability of these models to learn generalizable representations from multiple large datasets through self-supervised pre-training, which, coupled with task-specific fine-tuning, allows them to outperform state-of-the-art traditional methods on diverse tasks, including Anomaly Detection (AD) and Traffic Load Estimation (TLE). We then extensively explore model size versus accuracy trade-offs and experiment with Knowledge Distillation (KD) to improve the performance of smaller Transformers, enabling their embedding directly into the SHM edge nodes. We showcase the effectiveness of our foundation models using data from three operational viaducts. For AD, we achieve a near-perfect 99.9% accuracy with a monitoring time span of just 15 windows. In contrast, a state-of-the-art method based on Principal Component Analysis (PCA) obtains its first good result (95.03% accuracy) only considering 120 windows. On two different TLE tasks, our models obtain state-of-the-art performance on multiple evaluation metrics (R$^2$ score, MAE% and MSE%). On the first benchmark, we achieve an R$^2$ score of 0.97 and 0.85 for light and heavy vehicle traffic, respectively, while the best previous approach stops at 0.91 and 0.84. On the second one, we achieve an R$^2$ score of 0.54 versus the 0.10 of the best existing method.
Contemporary deep learning models have demonstrated promising results across various applications within seismology and earthquake engineering. These models rely primarily on utilizing ground motion records for tasks such as earthquake event classification, localization, earthquake early warning systems, and structural health monitoring. However, the extent to which these models truly extract meaningful patterns from these complex time-series signals remains underexplored. In this study, our objective is to evaluate the degree to which auxiliary information, such as seismic phase arrival times or seismic station distribution within a network, dominates the process of deep learning from ground motion records, potentially hindering its effectiveness. Our experimental results reveal a strong dependence on the highly correlated Primary (P) and Secondary (S) phase arrival times. These findings expose a critical gap in the current research landscape, highlighting the lack of robust methodologies for deep learning from single-station ground motion recordings that do not rely on auxiliary inputs.
Classification of damages in honeycomb composite sandwich structure (HCSS) is important to decide remedial actions. However, previous studies have only detected damages using deviations of monitoring signal from healthy (baseline) using a guided wave (GW) based structural health monitoring system. Classification between various types of damages has not been reported for challenging cases. We show that using careful feature engineering and machine learning it is possible to classify between various types of damages such as core crush (CC), high density core (HDC), lost film adhesive (LFA) and teflon release film (TRF). We believe that we are the first to report numerical models for four types of damages in HCSS, which is followed up with experimental validation. We found that two out of four damages affect the GW signal in a particularly similar manner. We extracted and evaluated multiple features from time as well as frequency domains, and also experimented with features relative to as baseline as well as those that were baseline-free. Using Pearson's correlation coefficient based filtering, redundant features were eliminated. Finally, using an optimal feature set determined using feature elimination, high accuracy was achieved with a random forest classifier on held-out signals. For evaluating performance of the proposed method for different damage sizes, we used simulated data obtained from extensive parametric studies and got an accuracy of 77.89%. Interpretability studies to determine importance of various features showed that features computed using the baseline signal prove more effective as compared to baseline-free features.
Machine learning models trained with structural health monitoring data have become a powerful tool for system identification. This paper presents a physics-informed Gaussian process (GP) model for Timoshenko beam elements. The model is constructed as a multi-output GP with covariance and cross-covariance kernels analytically derived based on the differential equations for deflections, rotations, strains, bending moments, shear forces and applied loads. Stiffness identification is performed in a Bayesian format by maximising a posterior model through a Markov chain Monte Carlo method, yielding a stochastic model for the structural parameters. The optimised GP model is further employed for probabilistic predictions of unobserved responses. Additionally, an entropy-based method for physics-informed sensor placement optimisation is presented, exploiting heterogeneous sensor position information and structural boundary conditions built into the GP model. Results demonstrate that the proposed approach is effective at identifying structural parameters and is capable of fusing data from heterogeneous and multi-fidelity sensors. Probabilistic predictions of structural responses and internal forces are in closer agreement with measured data. We validate our model with an experimental setup and discuss the quality and uncertainty of the obtained results. The proposed approach has potential applications in the field of structural health monitoring (SHM) for both mechanical and structural systems.
Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design. However, fatigue often involves entangled complexities of material microstructures and service conditions, making diagnosis and prognosis of fatigue damage challenging. We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties. Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations. Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth. Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events. The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns. The end-to-end approach is validated by representative examples with fatigue cracks in plates, which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making.
This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit (https://github.com/rohdelab/PyTransKit).
With the rising demands for robust structural health monitoring procedures for aerospace structures, the scope of intelligent algorithms and learning techniques is expanding. Supervised algorithms have shown promising results in the field provided a large, balanced, and labeled amount of data for training. For some applications like aerospace, the data collection process is cumbersome, time-taking, and costly. Also, generating possible damage scenarios in a laboratory setup is challenging because of the complexity of the damage initiation and failure mechanism. Besides this, the uncertainties of the real-time operation restrict the online prediction accuracy with supervised learning. In this paper, deep generative models are proposed for unsupervised delamination prediction as an anomaly detection problem. In this one-class-based model, the deep learning network is trained to learn the distribution of baseline signals. In the testing phase, damage signals and unseen baseline signals are fed into the trained network to predict the state of the structure, i.e., healthy or unhealthy (delamination). It is seen that the proposed method can successfully predict the delamination with high accuracy.
Structural Health Monitoring (SHM) describes a process for inferring quantifiable metrics of structural condition, which can serve as input to support decisions on the operation and maintenance of infrastructure assets. Given the long lifespan of critical structures, this problem can be cast as a sequential decision making problem over prescribed horizons. Partially Observable Markov Decision Processes (POMDPs) offer a formal framework to solve the underlying optimal planning task. However, two issues can undermine the POMDP solutions. Firstly, the need for a model that can adequately describe the evolution of the structural condition under deterioration or corrective actions and, secondly, the non-trivial task of recovery of the observation process parameters from available monitoring data. Despite these potential challenges, the adopted POMDP models do not typically account for uncertainty on model parameters, leading to solutions which can be unrealistically confident. In this work, we address both key issues. We present a framework to estimate POMDP transition and observation model parameters directly from available data, via Markov Chain Monte Carlo (MCMC) sampling of a Hidden Markov Model (HMM) conditioned on actions. The MCMC inference estimates distributions of the involved model parameters. We then form and solve the POMDP problem by exploiting the inferred distributions, to derive solutions that are robust to model uncertainty. We successfully apply our approach on maintenance planning for railway track assets on the basis of a "fractal value" indicator, which is computed from actual railway monitoring data.
Gathering properly labelled, adequately rich, and case-specific data for successfully training a data-driven or hybrid model for structural health monitoring (SHM) applications is a challenging task. We posit that a Transfer Learning (TL) method that utilizes available data in any relevant source domain and directly applies to the target domain through domain adaptation can provide substantial remedies to address this issue. Accordingly, we present a novel TL method that differentiates between the source's no-damage and damage cases and utilizes a domain adaptation (DA) technique. The DA module transfers the accumulated knowledge in contrasting no-damage and damage cases in the source domain to the target domain, given only the target's no-damage case. High-dimensional features allow employing signal processing domain knowledge to devise a generalizable DA approach. The Generative Adversarial Network (GAN) architecture is adopted for learning since its optimization process accommodates high-dimensional inputs in a zero-shot setting. At the same time, its training objective conforms seamlessly with the case of no-damage and damage data in SHM since its discriminator network differentiates between real (no damage) and fake (possibly unseen damage) data. An extensive set of experimental results demonstrates the method's success in transferring knowledge on differences between no-damage and damage cases across three strongly heterogeneous independent target structures. The area under the Receiver Operating Characteristics curves (Area Under the Curve - AUC) is used to evaluate the differentiation between no-damage and damage cases in the target domain, reaching values as high as 0.95. With no-damage and damage cases discerned from each other, zero-shot structural damage detection is carried out. The mean F1 scores for all damages in the three independent datasets are 0.978, 0.992, and 0.975.
Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable Extended Kalman Filter (EKF), named the Neural Extended Kalman Filter (Neural EKF) throughout this paper, for learning the latent evolution dynamics of complex physical systems. The Neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. In this work, we show that the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the efficacy of the framework on both simulated and real-world structural monitoring datasets, with the results indicating significant predictive capabilities of the proposed scheme.
Nowadays, more and more datasets are published towards research and development of systems and models, enabling direct comparisons, continuous improvement of solutions, and researchers engagement with experimental, real life data. However, especially in the Structural Health Monitoring (SHM) domain, there are plenty of cases where new research projects have a unique combination of structure design and implementation, sensor selection and technological enablers that does not fit with the configuration of relevant individual studies in the literature. Thus, we share the data from our case study to the research community as we did not find any relevant repository available. More specifically, in this paper, we present a novel time-series dataset for impact detection and localization on a plastic thin-plate, towards Structural Health Monitoring applications, using ceramic piezoelectric transducers (PZTs) connected to an Internet of Things (IoT) device. The dataset was collected from an experimental procedure of low-velocity, low-energy impact events that includes at least 3 repetitions for each unique experiment, while the input measurements come from 4 PZT sensors placed at the corners of the plate. For each repetition and sensor, 5000 values are stored with 100 KHz sampling rate. The system is excited with a steel ball, and the height from which it is released varies from 10 cm to 20 cm. The dataset is available in GitHub (https://github.com/Smart-Objects/Impact-Events-Dataset).
Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For example, the lack of accurate baseline models, high dimensionality, and complex multivariate partial differential equations (PDEs) pose significant difficulties in training and learning conventional data-driven algorithms. This paper explores a new framework, dubbed NeuralSI, for structural identification by augmenting PDEs that govern structural dynamics with neural networks. Our approach seeks to estimate nonlinear parameters from governing equations. We consider the vibration of nonlinear beams with two unknown parameters, one that represents geometric and material variations, and another that captures energy losses in the system mainly through damping. The data for parameter estimation is obtained from a limited set of measurements, which is conducive to applications in structural health monitoring where the exact state of an existing structure is typically unknown and only a limited amount of data samples can be collected in the field. The trained model can also be extrapolated under both standard and extreme conditions using the identified structural parameters. We compare with pure data-driven Neural Networks and other classical Physics-Informed Neural Networks (PINNs). Our approach reduces both interpolation and extrapolation errors in displacement distribution by two to five orders of magnitude over the baselines. Code is available at https://github.com/human-analysis/neural-structural-identification
The practical application of structural health monitoring (SHM) is often limited by the availability of labelled data. Transfer learning - specifically in the form of domain adaptation (DA) - gives rise to the possibility of leveraging information from a population of physical or numerical structures, by inferring a mapping that aligns the feature spaces. Typical DA methods rely on nonparametric distance metrics, which require sufficient data to perform density estimation. In addition, these methods can be prone to performance degradation under class imbalance. To address these issues, statistic alignment (SA) is discussed, with a demonstration of how these methods can be made robust to class imbalance, including a special case of class imbalance called a partial DA scenario. SA is demonstrated to facilitate damage localisation with no target labels in a numerical case study, outperforming other state-of-the-art DA methods. It is then shown to be capable of aligning the feature spaces of a real heterogeneous population, the Z24 and KW51 bridges, with only 220 samples used from the KW51 bridge. Finally, in scenarios where more complex mappings are required for knowledge transfer, SA is shown to be a vital pre-processing tool, increasing the performance of established DA methods.
Modern real-time Structural Health Monitoring systems can generate a considerable amount of information that must be processed and evaluated for detecting early anomalies and generating prompt warnings and alarms about the civil infrastructure conditions. The current cloud-based solutions cannot scale if the raw data has to be collected from thousands of buildings. This paper presents a full-stack deployment of an efficient and scalable anomaly detection pipeline for SHM systems which does not require sending raw data to the cloud but relies on edge computation. First, we benchmark three algorithmic approaches of anomaly detection, i.e., Principal Component Analysis (PCA), Fully-Connected AutoEncoder (FC-AE), and Convolutional AutoEncoder (C-AE). Then, we deploy them on an edge-sensor, the STM32L4, with limited computing capabilities. Our approach decreases network traffic by $\approx8\cdot10^5\times$ , from 780KB/hour to less than 10 Bytes/hour for a single installation and minimize network and cloud resource utilization, enabling the scaling of the monitoring infrastructure. A real-life case study, a highway bridge in Italy, demonstrates that combining near-sensor computation of anomaly detection algorithms, smart pre-processing, and low-power wide-area network protocols (LPWAN) we can greatly reduce data communication and cloud computing costs, while anomaly detection accuracy is not adversely affected.
Feature selection refers to the process of selecting useful features for machine learning tasks, and it is also a key step for structural health monitoring (SHM). This paper proposes a fast feature selection algorithm by efficiently computing the sum of squared canonical correlation coefficients between monitored features and target variables of interest in greedy search. The proposed algorithm is applied to both synthetic and real datasets to illustrate its advantages in terms of computational speed, general classification and regression tasks, as well as damage-sensitive feature selection tasks. Furthermore, the performance of the proposed algorithm is evaluated under varying environmental conditions and on an edge computing device to investigate its applicability in real-world SHM scenarios. The results show that the proposed algorithm can successfully select useful features with extraordinarily fast computational speed, which implies that the proposed algorithm has great potential where features need to be selected and updated online frequently, or where devices have limited computing capability.
In modern building infrastructures, the chance to devise adaptive and unsupervised data-driven health monitoring systems is gaining in popularity due to the large availability of big data from low-cost sensors with communication capabilities and advanced modeling tools such as Deep Learning. The main purpose of this paper is to combine deep neural networks with Bidirectional Long Short Term Memory and advanced statistical analysis involving Instantaneous Frequency and Spectral Kurtosis to develop an accurate classification tool for tensile, shear and mixed modes originated from acoustic emission events (cracks). We investigated on effective event descriptors to capture the unique characteristics from the different types of modes. Tests on experimental results confirm that this method achieves promising classification among different crack events and can impact on the design of future on structural health monitoring (SHM) technologies. This approach is effective to classify incipient damages with 92% of accuracy, which is advantageous to plan maintenance.