基于增量谐波平衡的参激系统非线性识别法

Nonlinearity system identification method with parametric excitation based on the incremental harmonic balance method

摘要: 将增量谐波平衡法应用到非线性系统的建模和参数识别中，针对Mathieu-Duffing方程，推导了利用增量谐波平衡原理识别参数激励非线性系统参数的方法. 该方法改进了增量谐波平衡方法的推导过程，通过数值模拟对比研究了谐波平衡非线性识别(harmonic balance nonlinearity identification, HBNID)和增量谐波平衡非线性识别(incremental harmonic balance nonlinearity identification, IHBNID)的效果，验证了增量谐波平衡非线性识别的有效性. 结果表明，增量谐波平衡非线性识别的计算效率较高，计算精度和抗噪能力都优于谐波平衡非线性识别.

Abstract: In this paper, the incremental harmonic balance for nonlinearityidentification (IHBNID) is presented for the modeling and parametricidentification of nonlinear systems. The effects of harmonic balancenonlinearity identification (HBNID) and IHBNID are also studied and comparedby using the numerical simulation. Considering the Mathieu-Duffing equationas an example, the effectiveness of the IHBNID can be verified. With the aidof the new method, the derivation procedures of the incremental harmonicbalance method are simplified. The results show that the IHBNID is highlyefficient for computation, and its performances excel in those of the HBNID,such as the computation accuracy and the noise resistance.