CAJ | 학술논문

基于时间相关矩阵分式多项式传递函数模型，给出线性时变结构时频域参数化模型。以时频域参数化模型为基础，将现有广泛用于时不变结构模态参数辨识的最小二乘复指数法拓展到时频域，提出基于矩阵分式多项式模型的时频域线性时变结构模态参数最小二乘辨识方法；针对时频域最小二乘对计算资源庞大需求问题，给出基于缩减正则方程的最小二乘问题求解方法。通过对两质量连续变化三自由度时变结构仿真算例，说明最小二乘中待估参数约束对模态参数辨识影响，阐述所提线性时变结构模态参数辨识方法特点，说明方法的有效性及潜在实用性。
기우시간상관구진분식다항식전체함수모형，급출선성시변결구시빈역삼수화모형。이시빈역삼수화모형위기출，장현유엄범용우시불변결구모태삼수변식적최소이승복지수법탁전도시빈역，제출기우구진분식다항식모형적시빈역선성시변결구모태삼수최소이승변식방법；침대시빈역최소이승대계산자원방대수구문제，급출기우축감정칙방정적최소이승문제구해방법。통과대량질량련속변화삼자유도시변결구방진산례，설명최소이승중대고삼수약속대모태삼수변식영향，천술소제선성시변결구모태삼수변식방법특점，설명방법적유효성급잠재실용성。
Based on the time-dependent matrix fraction polynomial model of transfer functions,the time-frequency-domain parametric model of linear time-varying structures was presented.Furthermore,based on the time-frequency-domain parametric model,through introducing the conventional least square complex frequency-domain method for modal parameter estimation of linear time-invariant structures into time-frequency domain,a matrix fraction polynomial model-based least square estimation method of modal parameters for linear time-varying structures in time-frequency domain was provided.In addition, to reduce the unacceptable computational consumption in the time-frequency least squares calculation,a reduced normal equation-based solution for the least square problem was proposed.Two 3-DOF simulation examples with varying mass were presented to illustrate the influence of constraints on the estimation results of unknown parameters.The characteristics of the proposed method were discussed,its effectiveness was validated and its potential applications were pointed out.