Parameter identification of systems with multiple disproportional local nonlinearities

Abstract

Identification of nonlinear systems, especially with multiple local nonlinearities exhibiting disproportional ratios of the degree of nonlinearity and present at a single or multiple spatial locations, is a highly challenging inverse problem. Identification of such complex nonlinear systems cannot be handled easily by the existing conventional restoring force or describing function methods. Further, noise-corrupted measured time history responses make the parameter identification process much more difficult. Keeping this in view, we propose a new meta support vector machine (meta-SVM) model to precisely identify the type, spatial location(s) and also the nonlinear parameters present in disproportionate levels using the noisy measurements. Apart from the conventional SVM model, we also explore the effectiveness of the non-batch processing models like incremental learning for lesser computational cost and increased efficiency. Both incremental and conventional support vector regression models are explored to precisely identify the nonlinear parameters. A numerically simulated multi-degree of freedom spring-mass system with limited multiple local nonlinearities at a few selected spatial locations is considered to illustrate the proposed meta-SVM model for nonlinear parametric identification. However, the extension of the proposed meta-SVM model is rather straightforward to include all types of nonlinearities and cases with the simultaneous existence of multiple numbers of same or different nonlinearities (i.e. combined nonlinearities) at single or multiple locations. It is also clearly established from the numerical simulation studies that the proposed incremental meta-SVM model paves way for online real-time identification of nonlinear parameters which is not yet been addressed in the existing literature.