A data-driven approach for linear and nonlinear damage detection using variational mode decomposition and GARCH model

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 generalized autoregressive conditional heteroscedasticity (GARCH) model for signal processing and feature extraction. To this end, VMD decomposes the response signals that are first decomposed to intrinsic mode functions (IMFs), and then, GARCH model is utilized 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 utilized to reduce the redundancy from the primary features by mapping them to the new feature space. The informative features are then fed separately into three supervised classifiers: support vector machine (SVM), k-nearest neighbor (kNN), and fine tree. The performance of the proposed method is evaluated on two experimental scaled models in terms of linear and nonlinear damage assessment. Kurtosis and ARCH tests proved the compatibility of GARCH model. The results demonstrate that the proposed technique reaches the accuracy of 100% and 98.82% in classifying linear and nonlinear damage, respectively. Also, its accuracy is higher than 80% in the presence of noise with a signal-to-noise ratio (SNR) of more than 10 dB.