Matrix fraction polynomial model-based least square estimation of modal parameters for linear time-varying structures

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.