Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain. (1st February 2017)

• Record Type: Journal Article
• Authors: Zhang, B.; Billings, S.A.
• Is Part Of: Mechanical systems and signal processing. Volume 84:Part A(2017)
• Page Start: 39
• Page End: 57
• Publication Date: 2017-02-01
• Subjects: Orthogonal least squares -- Volterra series -- Generalised frequency response function -- Nonlinear systems; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2016.07.008
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case. Highlights: A novel complex-valued orthogonal least squares algorithm is developed. The algorithm truncates Volterra series and estimates the kernel at one time. The algorithm can also indicate the divergence of Volterra series. Comparing the simulation results with the analytical ones validates the algorithm.