A Data-Driven Approach for Linear and Nonlinear Damage Detection Using Variational Mode Decomposition and GARCH Model

TL;DR

This paper introduces a novel data-driven method combining variational mode decomposition and GARCH modeling to detect linear and nonlinear damage in structures from output responses, enhancing damage detection accuracy.

Contribution

The study develops an integrated approach using VMD and GARCH for feature extraction, combined with PCA, LDA, and supervised classifiers for improved damage detection.

Findings

Effective detection of linear and nonlinear damage demonstrated.

GARCH model proved suitable for statistical analysis of IMFs.

High classification accuracy achieved with SVM, kNN, and decision trees.

Abstract

In this article, an original data-driven approach is proposed to detect both linear and nonlinear damage in structures using output-only responses. The method deploys variational mode decomposition (VMD) and a generalised autoregressive conditional heteroscedasticity (GARCH) model for signal processing and feature extraction. To this end, VMD decomposes the response signals into intrinsic mode functions (IMFs). Afterwards, the GARCH model is utilised to represent the statistics of IMFs. The model coefficients of IMFs construct the primary feature vector. Kernel-based principal component analysis (PCA) and linear discriminant analysis (LDA) are utilised to reduce the redundancy of the primary features by mapping them to the new feature space. The informative features are then fed separately into three supervised classifiers, namely support vector machine (SVM), k-nearest neighbour (kNN), and fine tree. The performance of the proposed method is evaluated on two experimentally scaled models in terms of linear and nonlinear damage assessment. Kurtosis and ARCH tests proved the compatibility of the GARCH model.