基于模态空间时域精细积分的结构动力学参数辨识方法  

A Structural Dynamics Parameter Identification Method Based on the Modal Space Time-Domain Precise Integration

作　　者：潘耀宗 赵岩[1,2] PAN Yaozong;ZHAO Yan(State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,School of Mechanics and Aerospace Engineering,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China;Ningbo Institute of Dalian University of Technology,Ningbo,Zhejiang 315016,P.R.China)

机构地区：[1]大连理工大学力学与航空航天学院工业装备结构分析优化与CAE软件全国重点实验室,辽宁大连116024 [2]大连理工大学宁波研究院,浙江宁波315016

出　　处：《应用数学和力学》2025年第1期29-39,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11772084,U1906233);国家重点研发计划(2017YFC0307203)。

摘　　要：提出了一种基于模态空间时域精细积分的动力学参数辨识方法.首先,基于时域测量信号和理论预测模型构造辨识方程,在模态空间内,由时域精细积分方法构造了理论预测模型;其次,通过矩阵、向量的Kronecker积运算法则推导了辨识模态的无约束向量的二次型函数,解析地给出了辨识振型的数学表达;最后,通过对辨识优化问题进行数学变换,仅需要辨识结构动力学特性的谱参数(频率和阻尼比),极大地降低了辨识参数的维度.数值算例中,进行了三自由度弹簧质量系统和高速受电弓的动力学参数辨识,辨识得到的固有频率、阻尼比与理论值相比,误差在8%以内;辨识振型与理论振型之间的夹角的余弦接近1,验证了辨识结果的准确性.该文提出的方法能够有效地实现辨识谱参数(频率、阻尼)和空间参数(振型)的分离,具有非常好的求解效率和应用前景.Based on the modal space time-domain precise integration,a dynamic parameter identification method was proposed.Firstly,an identification model was constructed based on the time-domain measurement signals and the theoretical prediction model with the time-domain precise integration method in the modal space.Secondly,the quadratic function of the unconstrained vector was derived through the Kronecker product of matrices,and the mathematical expressions of the mode shapes were analyzed and given.Finally,through mathematical transformations of the identification optimization problem,only the dynamics spectrum parameters(frequencies and damping ratios)need be identified,to greatly reduce the dimensionality of the identification parameters.In numerical examples,the dynamic parameter identification for the spring-mass system and the high-speed pantograph system were studied.The identified natural frequencies and damping ratios have errors less than 8%compared to the theoretical values.The cosine of the angle between the identified and the theoretical mode shapes is close to 1,which verifies the accuracy of the identification results.The proposed method can effectively achieve the separation of dynamic spectral parameters(frequencies,damping ratios)and spatial parameters(modal shapes),and has better solving efficiency and application prospects.

关 键 词：动力学参数辨识 时域精细积分法 最小二乘法 自振特性 动力学优化 

分 类 号：O32[理学—一般力学与力学基础]