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In this article, an original data-driven approach is proposed to detect bothlinear and nonlinear damage in structures using output-only responses. Themethod deploys variational mode decomposition (VMD) and a generalisedautoregressive conditional heteroscedasticity (GARCH) model for signalprocessing and feature extraction. To this end, VMD decomposes the responsesignals into intrinsic mode functions (IMFs). Afterwards, the GARCH model isutilised to represent the statistics of IMFs. The model coefficients of IMFsconstruct the primary feature vector. Kernel-based principal component analysis(PCA) and linear discriminant analysis (LDA) are utilised to reduce theredundancy of the primary features by mapping them to the new feature space.The informative features are then fed separately into three supervisedclassifiers, namely support vector machine (SVM), k-nearest neighbour (kNN),and fine tree. The performance of the proposed method is evaluated on twoexperimentally scaled models in terms of linear and nonlinear damageassessment. Kurtosis and ARCH tests proved the compatibility of the GARCHmodel.

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