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.