Detecting structural anomalies using fast simulations in the absence of damage scenarios

Significance 

Structural health monitoring (SHM) refers to the automated procedure involving the implementation of a damage detection and characterization strategy for engineering structures. Timely detection of various forms of failures in structures has the potential to greatly reduce the maintenance cost over the lifetime of a structure and may help prevent catastrophic events. At present, the combined advent of low-cost sensor technologies and digital twins, i.e., accurate virtual representations of complex heavy industry assets, have helped in the transition from classical time-based maintenance with scheduled periodic inspections to condition-based maintenance for large-scale structural systems. In general, the combination of parametrized mathematical models with experimental data is crucial to guarantee reliable monitoring of the lifecycle phases of a structure. The inspiration to this work is to circumvent the shortfalls of previous approaches (particularly model-based methodology), which focus on estimating the parameters that minimize the difference between the model response and the new sensor measurements. Ideally, such a methodology presents an inverse-problem approach which is often ill-posed and requires many online model solves and therefore not suitable for real-time damage assessment.

A reliable alternative is provided by data-driven methodologies, where predictions on the state of damage of a structure of interest are achieved by comparing the outcome of physics-based models with new experimental observations using machine learning techniques. To this end, Dr. Caterina Bigoni and Professor Jan S. Hesthaven from the Federal Institute of Technology in Lausanne (EPFL) in Switzerland proposed an anomaly detection approach by adopting mathematical numerical models that can approximate the propagation of acoustic-elastic waves in a structure excited by an active source.  Specifically, their goal was to compare the measurements of a network of sensors, placed on the structure, with equivalent quantities of interests obtained from numerical simulations to discriminate between healthy and damaged scenarios. Their work is currently published in the research journal, Computer Methods in Applied Mechanics and Engineering.

In their approach, the authors focused on applications where the physical system can be modeled by parametric partial differential equations (pPDEs). To begin with, the two scholars constructed an offline synthetic dataset aiming at describing all possible healthy environmental and operational configurations by repeatedly solving a time-dependent pPDE for multiple input parameters, sampled from their probability distributions of natural variation. The collected time signals, extracted at sensor locations, were used to construct multiple databases of healthy configurations. These datasets were then used to train one class Support Vector Machines (oc-SVMs) at such sensor locations to detect anomalies. During the online stage, a new measurement, possibly obtained from a damaged configuration, was evaluated using the classifiers, which ultimately assigned a class label (damaged or undamaged) to each measurement.

The authors observed that using an anomaly detection strategy based on multiple sensor-based synthetic datasets, generated using guided wave non-destructive evaluation scheme with active sources, detection and localization of damages was possible provided that damages were sufficiently far from the source. Moreover, they reported that the offline–online decoupling of tasks, leveraging model order reduction techniques to overcome the computational bottleneck associated with the many query context, allowed them to compute the sensor response under different operational and environmental conditions in a fast and inexpensive manner.

In summary, the study conducted by Bigoni and Hesthaven presented a data-driven approach for structural health monitoring which leverages the physics-based representation of the structure of interest. In the presented approach, damage detection and localization were carried out on a sensor-by-sensor basis by constructing synthetic training data emulating the sensor response of the structure under the effect of an active source. The results showed that the approach is successful in detecting, localizing, and estimating the severity of damages for 2D and 3D digital twins test problems. In a statement to Advances in Engineering, the authors highlighted that their findings can be applied to other examples; nonetheless, more realistic experiments ought to be carried out within a laboratory environment to further validate their approach.

Detecting structural anomalies using fast simulations in the absence of damage scenarios - Advances in Engineering
Flowchart for the offline and online phases of simulation-based SHM procedure for a known sensor network of size n_s.
Detecting structural anomalies using fast simulations in the absence of damage scenarios - Advances in Engineering
Flowchart to summarize the decision-level fusion approach for the semi-supervised damage detection strategy with multi-dimensional training data captured by n_s sensors.
Detecting structural anomalies using fast simulations in the absence of damage scenarios - Advances in Engineering
One-class SVMs classification average results on test data for nine 2D damaged configurations. For each configuration, each one of the 15 sensors is classified either as strong outlier, i.e., with an average anomaly score s_i(xi)\ ≥2 (red filled squares), mild outlier, i.e., with an average anomaly score s_i(xi)[1,2[ (red asterisks), or inlier, i.e., with an average anomaly score s_i(xi)<1 (blue empty circles). For all types of damages we can identify at least one sensor classified as an outlier. With the exception of damage (b), a clear proximity between the location of the damages and the sensors classified as outliers can be observed. For major damages (a, c, d), 3 to 4 sensors are classified as strong outliers and at most 1 as as mild outlier with a maximum total of 5 sensors classified as outliers. For minor damages (e, f, g, h), from 1 to 3 sensors are classified as outliers. For the combined damage (i) 7 sensors are classified as strong outliers and 1 as mild outlier. The location of the center of the active source is the same for the nine damaged geometries in the test phase and the undamaged configuration in the training phase, which corresponds to S = [0.54, 0.125] (black triangle).
Detecting structural anomalies using fast simulations in the absence of damage scenarios - Advances in Engineering
One-class SVMs classification average results on test data for one healthy and three damaged configurations in 3D. For each configuration, each one of the 46 sensors is classified either as strong outlier, i.e., with an average anomaly score s_i(xi)\ ≥2 (red squares), mild outlier, i.e., with an average anomaly score s_i(xi)[1,2[ (red circles), or inlier, i.e., with an average anomaly score s_i(xi)<1 (blue circles). The left and right plots show the front (z = 0) and rear (z = 0.1) of the 3D configurations. For the damaged configurations, a correlation between sensors classified as outliers and location of damage can be identified. A low false positive error is observed for both the healthy and damaged configurations: 1 sensor is misclassified in the healthy configuration (a) and few sensors, far from the damages, are mistakenly classified as mild outliers, especially for the damaged configuration (d). The location of the center of the active source is the same for the three damaged geometries and the undamaged configuration, which corresponds to S = [0.51, 0.06 0] (large green semi-sphere).

About the author

Jan S Hesthaven
Professor of Mathematics
Chair of Computational Mathematics and Simulation Science
EPFL, Lausanne, CH

After receiving his PhD in 1995 from the Technical University of Denmark, Professor Hesthaven joined Brown University, USA where he became Professor of Applied Mathematics in 2005. In 2013 he joined EPFL as Chair of Computational Mathematics and Simulation Science and since 2017 as Dean of the School of Basic Sciences. His research interests focus on the development, analysis, and application of high-order accurate methods for the solution of complex time-dependent problems, often requiring high-performance computing. A particular focus of his research has been on the development of computational methods for problems of linear and non-linear wave problems and the development of reduced basis methods, recently with an emphasis on combining traditional methods with machine learning and neural networks with broad applications, including structural health monitoring.

He has received several awards for both his research and his teaching, and has published 4 monographs and more than 150 research papers. He is on the editorial board of 8 journals and serves as Editor-in-Chief of SIAM J. Scientific Computing.

About the author

Caterina Bigoni received her MSc degree in Computational Science and Engineering in 2015 and her PhD in Mathematics in 2020 from the Swiss Federal Institute of Technology in Lausanne (EPFL) under the supervision of Professor Jan S. Hesthaven. Prior to this, she obtained a BSc degree in Mathematical Engineering from Politecnico di Milano, Italy in 2013 and she spent one semester at the Grenoble Institute of Technology (INP), France thanks to the Erasmus exchange program. In 2014, she also did a summer internship at ABB in Vittuone, Italy, where she worked on computational electromagnetism.

Her current research projects focus on numerical methods for structural anomaly detection and her expertise includes numerical approximation of time-dependent PDEs, model order reduction, uncertainty quantification, and machine learning techniques. She strives to combine mathematical modeling and scientific computing with innovative technologies to make a positive impact on our society.

Reference

Caterina Bigoni, Jan S. Hesthaven. Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring. Computer Methods in Applied Mechanics and Engineering Volume 363, 112896.

Go To Computer Methods in Applied Mechanics and Engineering

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