A Noise Correction Embedded Identification Approach for Delays and Parameters in Nonlinear Delay Systems

To identify unknown parameters from the noise-polluted measurement in time-delayed systems, this paper proposes the incremental harmonic balance based approach. By assuming that the steady response is periodic and the noise pollution does not change the periodicity of the measured response, this approach expands the ideal and measured response into the form of Fourier series. With this process, the noise correction can be parameterized as the harmonic increments of the measured response so that the noise correction can be determined by the same process of the identification of the unknown parameters. Numerical examples are given to verify the efficiency of the proposed approach. In comparison with the identified parameters without noise correction, the results show that the accuracy of the ones with noise correction is significantly improved. This achievement also implies that the proposed approach is reliable in similar cases of engineering applications.