协方差分析描述函数法的通用化数值算法  

Generalized Numerical Algorithm for the Covariance Analysis Description Function Technique

作　　者：王汉平[1] 柳洋鑫 张宝振 WANG Hanping;LIU Yangxin;ZHANG Baozhen(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Beijing Institute of Electronic System Engineering,Beijing 100854,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]北京电子工程总体研究所,北京100854

出　　处：《北京理工大学学报》2024年第5期439-446,共8页Transactions of Beijing Institute of Technology

基　　金：科技部重点研发计划基金资助项目(2018YFF0300804)。

摘　　要：协方差分析描述函数法(covariance analysis describing function technique,CADET)在处理系统的随机响应问题上具有求解迅速、仿真精度高等优点.但对于复杂系统,其理论推导过程、求解系统解析响应方程较为复杂繁琐.为进一步推广CADET的应用,依托高斯–埃尔米特积分法,提出了一种通用化的CADET数值算法.作为算法验证,以车辆行驶过程中的随机振动为例,建立了几种不同非线性悬架车辆的二自由度动力学模型,并将CADET通用化数值算法与传统CADET算法及蒙特卡罗法进行了对比分析.仿真结果表明,CADET的通用化数值算法可以达到满足应用要求的计算精度,这验证了所提数值算法的有效性,且具有更强的泛化应用于复杂非线性动力系统的价值.Covariance analysis describing function technique(CADET)has the advantages of fast solution and high simulation accuracy in dealing with random responses of systems.However,for complex systems,the theoretical derivation process and the solving of the analytical response equation of the system are more complicated and cumbersome.In order to further promote the application of CADET,a generalized CADET numerical algorithm was proposed based on the Gauss-Hermitian integral method.As an algorithm verification,taking random vibrations during vehicle driving as an example,the two-degree-of-freedom dynamic models of several nonlinear suspension vehicles were established,and the CADET generalized numerical algorithm was compared with the traditional CADET algorithm and Monte Carlo method.The simulation results show that the generalized numerical algorithm of CADET can achieve the calculation accuracy that meets the application requirements,which verifies the effectiveness of the proposed numerical algorithm and has a stronger value of generalized application in complex nonlinear dynamical systems.

关 键 词：车辆悬架系统 协方差分析描述函数法 随机振动 数值算法 非线性系统 

分 类 号：TJ762.4[兵器科学与技术—武器系统与运用工程]