Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine

•A LS-SVM based estimator of modal parameters of time-varying structures.•A Gamma-test-based non-parametric approach for estimation of regularization factor.•Wendland's function based compactly supported basis function for sparsity.•Robustness to overestimation and less sensitive to change of order of AR model.•A series of numerical examples and a group of experiments validate the estimator.

Identification of time-varying modal parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based modal parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland's compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed modal parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.