Parametric Indentification For Multi-Degree-of-Freedom Nonlinear Dynamics System

In order to estimate parameters which describe the system dynamics model, nonlinear system parameter identification is appeared. According to sufficient knowledge, the dynamic equation is acquired. Then we apply identification theory to identificate some or all parameters corresponding to a variety of motion state in the dynamic equations. So system dynamics model is confirmed. Nonlinear parameter identification of nonlinear systems is a process which can be understood as the inverse of solving differential equation.In this paper, nonlinear multi-degree-of-freedom system parameter identification is analyzed. Based on the incremental harmonic balance method, the incremental harmonic balance nonlinear identification (IHBNID) is extended to high-dimensional nonlinear vibration system. Directing at periodic, almost periodic and chaotic motions of the multi-degree of freedom system, system identification equations are derived. Effectiveness of the method is verified by numerical simulation.The paper is divided into three parts.Firstly, nonlinear system identification with periodic response is researched. When the frequency of the system response Fourier series is reducible, based on incremental Harmonic Balance (IHB) method, we derive the identification equation of multi-degree-of-freedom nonlinear dynamic system. With a two degrees of freedom nonlinear system example, we carry out numerical simulation on the period-1, the period-doubling and the chaotic motions. The effect of noise on the identification parameters is analyzed. The effectiveness of the IHBNID is verified for multi-degree-of-freedom nonlinear dynamic system. The simulating results show that the proposed method has high accuracy and efficiency, and can improve the antinoise ability.Secondly, nonlinear system identification with periodic response is researched. In order to solve the nonlinear system parameter identification on the almost periodic motion, whose frequency of the system response Fourier series isn’t reducible, the identification method on account of the incremental harmonic balance nonlinear identification (IHBNID) is discussed. With a two degrees of freedom nonlinear system example, We acquire system identification equation.Thirdly, the way acquiring the estimator of dynamic equations is discussed. In order to solve the nonlinear vibration partial differential equation of the elastomer, the equation is usually discretized and blocked by Galerkin method. Then approximate simplified system kinetics equation is obtained. And the method of multiple scales is applied to the ordinary differential equation application response equation to acquire response equation. The method of multiple scales directly applied to partial differential equations in this paper to discuss the simplified Galerkin method truncation error. The derivations of frequency response equation using two methods are obtained. And the amplitude-frequency response results are compared.