基于Bouc-Wen模型的非线性实时混合模拟稳定性分析  

Stability analysis of nonlinear real-time hybrid simulation based on Bouc-Wen model

作　　者：卜逸凡 黄亮[1,2] 汤志伟 PU Yifan;HUANG Liang;TANG Zhiwei(School of Civil and Hydraulic Engineering,Hefei University of Technology,Hefei 230009,China;Anhui Key Laboratory of Civil Engineering Structures and Materials,Hefei 230009,China)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009 [2]土木工程结构与材料安徽省重点实验室,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2024年第8期1141-1147,共7页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(52008145);中央高校基本科研业务费专项资金资助项目(PA2021GDSK0080)。

摘　　要：实时混合模拟(real-time hybrid simulation,RTHS)中不可避免的作动器响应延迟会影响试验系统稳定性。为研究同时含非线性构件和作动器时滞的复杂试验系统稳定性,文章采用分段线性方法将非线性模型近似简化为多个线性状态的叠加,基于T-S模糊模型理论建立试验系统运动方程,通过Lyapunov稳定理论分析其近似稳定性,获得线性矩阵不等式(linear matrix inequality,LMI)形式的稳定性判据。数值分析和试验结果验证在外荷载输入下,简化模型高度近似于原模型,表明该近似方法具有良好的计算精度。对于具有刚度软化特性的Bouc-Wen模型,最大刚度决定试验系统稳定性。当试验系统时滞小于临界时滞,处于渐近稳定状态时,结构的动力响应逐步收敛;而当试验系统时滞大于临界时滞处于失稳状态时,系统仍能通过材料屈服耗能保持能量平衡。而在线性系统中,能量则不断积累,导致试验系统响应无限增加,是线性与非线性试验系统的最大差异。The inevitable actuator response delay in real-time hybrid simulation(RTHS) will affect the stability of the test system.In order to study the stability of complex test systems with both nonlinear components and actuator delays,this paper adopts piecewise linear method to approximately simplify the nonlinear model to the superposition of multiple linear states,establishes the motion equation of the test system based on T-S fuzzy model theory,and analyzes its approximate stability through Lyapunov stability theory.The stability criterion of linear matrix inequality(LMI) form is obtained.Numerical analysis and experimental results verify that the simplified model is highly approximate to the original model under external load input,indicating that the approximate method has good computational accuracy.For the Bouc-Wen model with stiffness softening characteristics,the maximum stiffness determines the stability of the test system.When the time delay of the test system is less than the critical time delay and is in the asymptotically stable state,the dynamic response of the structure gradually converges.When the time delay of the test system is greater than the critical time delay and is in the unstable state,the system can still maintain the energy balance through the yielding energy dissipation.In linear systems,energy accumulates continuously,resulting in an infinite increase in the response of the test system,which is the biggest difference between linear and nonlinear test systems.

关 键 词：实时混合模拟(RTHS) 非线性 BOUC-WEN模型 T-S模糊模型 稳定性 

分 类 号：TU317.2[建筑科学—结构工程]