  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.
