Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring

We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offline-online decomposition. A synthetic dataset is constructed offline by solving a parametric time-dependent partial differential equation for multiple input parameters, sampled from their probability distributions of natural variation. The collected time-signals, extracted at sensor locations, are used to train classifiers at such sensor locations, thus constructing multiple databases of healthy configurations. These datasets are then used to train one class Support Vector Machines (OC-SVMs) to detect anomalies. During the online stage, a new measurement, possibly obtained from a damaged configuration, is evaluated using the classifiers. Information on damage is provided in a hierarchical manner: first, using a binary feedback, the entire structure response is either classified as inlier (healthy) or outlier (damaged). Then, for the outliers, we exploit the outputs of multiple classifiers to retrieve information both on the severity and the spatial location of the damages. Because of the large number of signals needed to construct the datasets offline, a model order reduction strategy is implemented to reduce the computational burden. We apply this strategy to both 2D and 3D problems to mimic the vibrational behavior of complex structures under the effect of an active source and show the effectiveness of the approach for detecting and localizing cracks.

MATHICSE Technical Report: Simulation-Based Anomaly Detection and Damage Localization: an Application to Structural Health Monitoring

Caterina Bigoni, Jan Sickmann Hesthaven

We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offine-online decomposition. A synthetic dataset is constructed offine by solving a parametric time-dependent partial differential equation for multiple input parameters, sampled from their probability distributions of natural variation. The collected time-signals, extracted at sensor locations, are used to train classiffiers at such sensor locations, thus constructing multiple databases of healthy configurations. These datasets are then used to train one class Support Vector Machines (OC-SVMs) to detect anomalies. During the online stage, a new measurement, possibly obtained from a damaged configuration, is evaluated using the classiffiers. Information on damage is provided in a hierarchical manner: first, using a binary feedback, the entire structure response is either classifiied as inlier (healthy) or outlier (damaged). Then, for the outliers, we exploit the outputs of multiple classiffiers to retrieve information both on the severity and the spatial location of the damages. Because of the large number of signals needed to construct the datasets offline, a model order reduction strategy is implemented to reduce the computational burden. We apply this strategy to both 2D and 3D problems to mimic the vibrational behavior of complex structures under the effect of an active source and show the effectiveness of the approach for detecting and localizing cracks.

MATHICSE2019

Towards goal-driven deep neural network models to elucidate human arm proprioception

Pranav Mamidanna, Alexander Mathis

Proprioceptive signals are a critical component of our ability to perform complex movements, identify our posture and adapt to environmental changes. Our movements are generated by a large number of muscles and are sensed via a myriad of different receptor types. Even the most important ones, muscle spindles, carry highly multiplexed information. For instance, arm movements are sensed via distributed and individually ambiguous activity patterns of muscle spindles, which depend on relative joint configurations rather than the absolute hand position. This high dimensional input (~50 muscles for a human arm) of distributed information poses a challenging decoding problem for the nervous system. Given the diversity in muscle activity, what are the necessary computations that the proprioceptive system needs to perform to sense our movements? Here we studied a proprioceptive variant of the handwritten character recognition task to gain insight into potential computations that the proprioceptive system needs to perform. We focussed on handwritten character classification of muscle length configuration patterns that were required to draw that character. We started from a dataset comprising of pen-tip trajectory data recorded while subjects were writing individual single-stroke characters of the Latin alphabet (Williams et al. ICANN 2006), and employed a musculoskeletal model of the human upper limb to generate muscle length configurations corresponding to drawing the pen-tip trajectories in multiple horizontal and vertical planes. Using this model we created a large, scalable dataset of muscle length configurations corresponding to handwritten characters of varying sizes, locations and orientations (n > 105 samples). To determine the difficulty of this problem, we trained support vector machines (SVM) to solve a binary one-vs-all classification task on the dataset, which achieves an accuracy of 0.89 ± 0.08 (mean ± s.e.m). Contrary to naive expectation, reading out the character at the level of muscles is much easier whereas SVMs trained on the same task using pen-tip coordinates performed relatively poorly: 0.75 ± 0.14. This suggests that the musculoskeletal system itself serves as a non-linear projection to a higher dimensional space, which simplifies character recognition. Next we focussed on goal-driven deep neural network architectures to achieve higher accuracy. Training deep neural networks requires a large, diverse datasets and challenging tasks. We found that the scalable dataset for character recognition we generated is large enough to constrain deep convolutional architectures. We are currently exploring the performance of different deeplearning architectures in solving the handwritten character classification task to investigate which representations are learned and what computations are most efficient. We found that convolutional neural networks factoring out temporal and inter-muscle ('spatial') information achieve almost perfect accuracy for the multi-class problem. These preliminary results suggest that neural networks can learn pose-invariant character recognition from muscle configurations.

2018

Towards goal-driven deep neural network models to elucidate human arm proprioception

Pranav Mamidanna, Alexander Mathis

2018