Frequency-domain nonlinear model updating based on analytical sensitivity and the Multi-Harmonic balance method

• Published in: Mechanical systems and signal processing 2022-01, Vol.163, p.108169, Article 108169
• Main Authors: Zhu, Tianxu, Zhang, Genbei, Zang, Chaoping
• Format: Article
• Language: English
• Subjects: Analytical sensitivity; Dynamic response; Frequency domain; Frequency domain analysis; Harmonic balance method; Iterative methods; Mathematical models; Model updating; Multi-harmonic balance method; Nonlinear model updating; Nonlinear parameters; Nonlinearity; Numerical methods; Optimization; Parameters; Sensitivity analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2021.108169

•A frequency-domain nonlinear model updating procedure is proposed.•Analytical sensitivity and multi harmonic balance method is developed for nonlinear model updating.•The Gamma matrix based DFT-AFT procedure is developed for analytical sensitivity.•The analytical sensitivity-based updating method is much more efficient and effective than the numerical sensitivity-based approach. The predicted dynamic response of the structure with nonlinearity can be in some difference from the experimental one due to the discrepancies of nonlinear parameters between the constructed model and the real structure. The gradient-based nonlinear model updating procedures is an effective tool to reduce the difference. However, the computational costs for the sensitivity matrix could be too expensive. In this paper, a novel approach of the frequency-domain nonlinear model updating using the analytical sensitivity and the Multi-Harmonic Balance Method (MHBM) is proposed. The analytical sensitivity, directly derived from the frequency domain algebraic function obtained by the MHBM and Gamma matrix-based DFT-AFT methods, can significantly reduce the iteration time in model updating process. The proposed nonlinear model updating procedure is easily carried out and also considered as the FRF-based model updating framework. To illustrate the method, a simulated 3DOF nonlinear structure is utilized and differences between the updated nonlinear parameters and the original ones are reduced below 0.4% after updating. Besides, the proposed updating procedure has the best performance compared with the numerical method and the Nelder-Mead optimization. The simulation shows that the proposed analytical sensitivity calculation is generally above 4 times faster than the numerical one. Finally, the updating process of a real 3DOF nonlinear lumped parameter structure is described in detail. After the updating, the overlay of the prediction responses and the experimental ones is in a good agreement. Results indicate the efficiency and superiority of the proposed method to update nonlinear structures.