Data-driven damage localization is a demanding process for vibration-based structural health monitoring (SHM) strategies. The ability to locate single and multiple damage states featuring different severity levels, particularly the smaller ones, plays a prominent role in establishing an effective and robust method for damage assessment. The statistical pattern recognition paradigm based on feature extraction and statistical decision-making can be a successful framework for this process [1,2]. In case of data gathered by dense sensor networks, which provide vibration datasets of high dimensionality and large volume, this framework may be time-consuming or complex; it also results questionable whether existing order selection techniques are able to provide a low-order feature extraction approach [1]. Furthermore, a fast decision-making process within an unsupervised learning strategy can help overcome the main obstacles experienced in the accurate localization of damage, if large volumes of damage-sensitive features are extracted from high-dimensional samples gathered by the mentioned dense sensor networks. In this study, we propose an efficient unsupervised learning method for feature extraction by an iterative approach based on order reduction in AutoRegressive (AR) modelling [3], and for damage localization through a statistical distance method termed Kullback-Leibler Divergence with Empirical Probability Measure (KLDEPM). The proposed iterative feature extraction approach mainly aims at model order reduction. In the training phase, this is accomplished simultaneously with parameter estimation and residual extraction; in the following monitoring phase, the low-order AR model is adopted to only extract the new residuals. With this approach, correlated residual samples of the AR model are adopted as a new time series dataset to reduce the model order at each iteration. This strategy is shown to effectively and efficiently reduce the order of the AR model necessary for feature extraction. Selecting a reduced AR order that guarantees model sufficiency and accuracy by generating uncorrelated residuals is therefore the main strength of the proposed order selection method; in case of an inadequate order selection, the model may not be able to capture the underlying dynamics of the structure, and lead to the extraction of features insensitive to damage. The proposed KLDEPM, which is an enhancement of the classical KLD technique, next exploits a segmentation technique to subdivide the handled random data (i.e. the AR model residuals relevant to the virgin and damaged conditions) into independent segments, and compute a distance between the features relevant to the training stage and those relevant to the monitoring stage, based on the theory of empirical probability measure. This procedure provides an effective distance approach for damage identification and a fast tool for decision-making. To establish an unsupervised learning strategy, a threshold limit is determined by computing the mean of the 95% confidence intervals of distance quantities obtained from the virgin conditions in the training phase. The sensor location(s) associated with the KLDEPM value(s) greater than the threshold limit is (are) identified as the damaged area(s) of the structure. Numerical concrete beam and IASC-ASCE experimental benchmarks are considered to assess the accuracy of the proposed SHM method, and the improvement in the performance (in terms of feature extraction and damage localization) against alternative approaches available in the literature. More specifically, the proposed order selection method aimed at reducing the model order is compared with the state-of-the-art Bayesian Information Criterion technique, and with a conventional residual-based feature extraction approach. Furthermore, the method is benchmarked by the classical KLD technique and the Kolmogorov–Smirnov test. Results demonstrate that both the iterative feature extraction technique and the KDLEPM method are superior to their counterparts, and provide fast unsupervised learning strategies to extract reliable damage-sensitive features and locate single and multiple damages of different severities. References [1] C.R. Farrar, K. Worden, Structural Health Monitoring: A Machine Learning Perspective, John Wiley & Sons Ltd, 2013. [2] F. Kopsaftopoulos, S. Fassois, Vibration based health monitoring for a lightweight truss structure: experimental assessment of several statistical time series methods, Mechanical Systems and Signal Processing, 24:1977-1997, 2010. [3] G.E. Box, G.M. Jenkins, G.C. Reinsel, G.M. Ljung, Time series analysis: forecasting and control, Fifth ed., John Wiley & Sons, 2015.

Low-order feature extraction technique and unsupervised learning for SHM under high-dimensional data

ENTEZAMI, ALIREZA;S. Mariani
2019-01-01

Abstract

Data-driven damage localization is a demanding process for vibration-based structural health monitoring (SHM) strategies. The ability to locate single and multiple damage states featuring different severity levels, particularly the smaller ones, plays a prominent role in establishing an effective and robust method for damage assessment. The statistical pattern recognition paradigm based on feature extraction and statistical decision-making can be a successful framework for this process [1,2]. In case of data gathered by dense sensor networks, which provide vibration datasets of high dimensionality and large volume, this framework may be time-consuming or complex; it also results questionable whether existing order selection techniques are able to provide a low-order feature extraction approach [1]. Furthermore, a fast decision-making process within an unsupervised learning strategy can help overcome the main obstacles experienced in the accurate localization of damage, if large volumes of damage-sensitive features are extracted from high-dimensional samples gathered by the mentioned dense sensor networks. In this study, we propose an efficient unsupervised learning method for feature extraction by an iterative approach based on order reduction in AutoRegressive (AR) modelling [3], and for damage localization through a statistical distance method termed Kullback-Leibler Divergence with Empirical Probability Measure (KLDEPM). The proposed iterative feature extraction approach mainly aims at model order reduction. In the training phase, this is accomplished simultaneously with parameter estimation and residual extraction; in the following monitoring phase, the low-order AR model is adopted to only extract the new residuals. With this approach, correlated residual samples of the AR model are adopted as a new time series dataset to reduce the model order at each iteration. This strategy is shown to effectively and efficiently reduce the order of the AR model necessary for feature extraction. Selecting a reduced AR order that guarantees model sufficiency and accuracy by generating uncorrelated residuals is therefore the main strength of the proposed order selection method; in case of an inadequate order selection, the model may not be able to capture the underlying dynamics of the structure, and lead to the extraction of features insensitive to damage. The proposed KLDEPM, which is an enhancement of the classical KLD technique, next exploits a segmentation technique to subdivide the handled random data (i.e. the AR model residuals relevant to the virgin and damaged conditions) into independent segments, and compute a distance between the features relevant to the training stage and those relevant to the monitoring stage, based on the theory of empirical probability measure. This procedure provides an effective distance approach for damage identification and a fast tool for decision-making. To establish an unsupervised learning strategy, a threshold limit is determined by computing the mean of the 95% confidence intervals of distance quantities obtained from the virgin conditions in the training phase. The sensor location(s) associated with the KLDEPM value(s) greater than the threshold limit is (are) identified as the damaged area(s) of the structure. Numerical concrete beam and IASC-ASCE experimental benchmarks are considered to assess the accuracy of the proposed SHM method, and the improvement in the performance (in terms of feature extraction and damage localization) against alternative approaches available in the literature. More specifically, the proposed order selection method aimed at reducing the model order is compared with the state-of-the-art Bayesian Information Criterion technique, and with a conventional residual-based feature extraction approach. Furthermore, the method is benchmarked by the classical KLD technique and the Kolmogorov–Smirnov test. Results demonstrate that both the iterative feature extraction technique and the KDLEPM method are superior to their counterparts, and provide fast unsupervised learning strategies to extract reliable damage-sensitive features and locate single and multiple damages of different severities. References [1] C.R. Farrar, K. Worden, Structural Health Monitoring: A Machine Learning Perspective, John Wiley & Sons Ltd, 2013. [2] F. Kopsaftopoulos, S. Fassois, Vibration based health monitoring for a lightweight truss structure: experimental assessment of several statistical time series methods, Mechanical Systems and Signal Processing, 24:1977-1997, 2010. [3] G.E. Box, G.M. Jenkins, G.C. Reinsel, G.M. Ljung, Time series analysis: forecasting and control, Fifth ed., John Wiley & Sons, 2015.
2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1119841
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