Linear and nonlinear structural identifications using the support vector regression

Abstract

Robust and efficient identification methods are necessary to study in the structural health monitoring field, especially when the I/O data are accompanied by high-level noise and the structure studied is a large-scale one. The Support vector Regression (SVR) is a promising nonlinear modeling method that has been found working very well in many fields, and has a powerful potential to be applied in system identifications. The SVR-based methods are provided in this article to make linear large-scale structural identification and nonlinear hysteretic structural identifications. The LS estimator is a cornerstone of statistics but less robust to outliers. Instead of the classical Gaussian loss function without regularization used in the LS method, a novel e-insensitive loss function is employed in the SVR. Meanwhile, the SVR adopts the 'max-margined' idea to search for an optimum hyper-plane separating the training data into two subsets by maximizing the margin between them. Therefore, the SVR-based structural identification approach is robust and accuracy even though the observation data involve different kinds and high-level noise. By means of the local strategy, the linear large-scale structural identification approach based on the SVR is first investigated. The novel SVR can identify structural parameters directly by writing structural observation equations in linear equations with respect to unknown structural parameters. Furthermore, the substrutural idea employed reduces the number of unknown parameters seriously to guarantee the SVR work in a low dimension and to focus the identification on a local arbitrary subsystem. It is crucial to make nonlinear structural identification also, because structures exhibit highly nonlinear characters under severe loads such as strong seismic excitations. The Bouc-Wen model is often utilized to describe structural nonlinear properties, the power parameter of the model however is often assumed as known even though it is unknown in the real world. In the case of unknown-power parameter, the nonlinear structural identification problem is more intricate and few approaches are dedicated to this problem. In this article, a model selection strategy is proposed to determine the unknown power parameter of the Bouc-Wen model. Meanwhile, the optimum SVR parameters are automatically selected instead of tuning manually. Based on the produced power parameter and optimum SVR parameters, the SVR is executed to identify nonlinear hysteretic structural parameters accurately and robustly. The numerical examples for two linear large-scale structures and a five-DOF nonlinear hysteretic structure provided illustrates that the proposed technique has excellent performance in robustness and accuracy for linear and nonlinear structural identifications, even when the noise exits in I/O measurements is high-level and non-Gaussion. Moreover, an incremental training algorithm utilized to solve SVR formulation in a sequential way not only significantly reduces the computation time, but also makes the structural health monitoring on-line.