Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform

Abstract

The response of a nonlinear oscillator is characterized by its instantaneous amplitude (IA) and instantaneous frequency (IF) features, which can be significantly affected by the physical properties of the system. Accordingly, the system properties could be inferred from the IA and IF of its response if both instantaneous features can be identified accurately. To fulfill such an idea, a nonlinear system parameter identification method is proposed in this paper with the aid of polynomial chirplet transform (PCT), which has been proved a powerful tool for processing nonstationary signals. First, the PCT is used to extract the instantaneous characteristics, i.e., IA and IF, from nonlinear system responses. Second, instantaneous modal parameters estimation was adopted to extract backbone and damping curves, which characterize the inherent nonlinearities of the system. Third, the physical property parameters of the system were estimated through fitting the identified average nonlinear characteristic curves. Finally, the proposed nonlinear identification method is experimentally validated through comparing with two Hilbert transform (HT) based methods.

Kernel Regression Residual Decomposition-Based Polynomial Frequency Modulation Integral Algorithm to Identify Physical Parameters of Time-Varying Systems under Random Excitation

“…In essence, PCT is still WT and supports signal reconstruction. In addition, the first derivative and the second derivative basis functions satisfy the admissible condition and decay condition [35], which are given as follows:…”

“…Meanwhile, the optimized method was applied to field seismic data, and the tight sandstone gas reservoirs can be effectively identified. Deng et al [35] compared PCT with two parameter identification methods based on the Hilbert transform and verified the parameter identification performance of PCT by experiments. However, PCT is not suitable for multi-modal compound signals.…”

A Robust Process Identification Method under Deterministic Disturbance

“…Among the array of techniques developed, parametric identification methods such as subspace, prediction error, and instrumental variable Processes 2024, 12, 986 2 of 14 methods stand out for their efficacy and widespread application [30][31][32][33][34][35][36][37]. Furthermore, the advent of parametric identification techniques utilizing various weight functions and integral transforms represents an advancement in the identification of continuous-time processes [38][39][40][41][42]. In parallel, the development of nonparametric identification methods has introduced a new dimension of flexibility and robustness [43][44][45][46][47][48].…”

An Adaptive Parameterized Domain Mapping Method and Its Application in Wheel–Rail Coupled Fault Diagnosis for Rail Vehicles

“…This method showed superior performance in feature extraction accuracy compared to other traditional TFA methods and has good application prospects for parameter identification and fault diagnosis. Deng et al [ 35 ] proposed a parameter identification method for nonlinear systems based on the polynomial Chirplet transform, which is a powerful tool for handling nonstationary signals. Chen et al [ 36 ] proposed an algorithm called Chirplet path fusion for analyzing nonstationary signals with time-varying frequencies that had better IF extraction capability in a noisy environment and could be applied to situations with short time signals.…”