Output-only Modal Parameter Recursive Estimation For Linear Time-varying Structures

With the development of aerospace engineering applications,more and more time-varying structures are being used and their intrinsic time-varying characteristics are increasingly inevitable,which brings us many problems on time-varying structural dynamics.Due to the complexity of the problem,it is usually difficult to build the explicit model of a structure by exclusively using mechanism analysis,and there is also no guarantee that the model will accurately represent its time-varying dynamic characteristics.Therefore,time-varying system identification,in a way that takes time variation explicitly into account,is worth more attention and investigation.As an inverse problem,experimental modal analysis is able to obtain the dynamic characteristics at a system level of a structure under its operating conditions.However,experimental modal analysis of time-varying structures has not yet been well developed,and the core issue lies in the lack of modal parameter estimation methods for time-varying structures.This thesis focuses on the problem of output-only modal parameter recursive estimation for linear time-varying structures.The main contents of this work are followed by:(1)The research background of time-varying structural dynamics and the motivation of modal parameter estimation for time-varying structures are introduced.By reviewing the history and investigating state-of-the-art of modal parameter estimation methods for time-varying structures,the need for output-only modal parameter recursive estimation is presented.(2)The frozen-time assumption is summarized in the frequency domain and the time domain,and different definitions of modal parameters of linear time-varying systems are subsequently discussed.The TARMA model adopted in this work and the procedure to obtain its frozen-time modal parameters are presented,which provides the theoretical basis for the subsequent research on TARMA model parameter recursive estimation methods.(3)Based on an improved recursive pseudo-linear form of TARMA model proposed in this work,recursive pseudo-linear regression,Kalman filter,ridge regression,and Bayesian linear regression are respectively applied to the TARMA model parameter recursive estimation to improve the unstructured parameter evolution methods in terms of lower computational complexity,extended application scope,and reduced overfitting.Numerical results demonstrate the effectiveness of the above improved methods.(4)The kernelized TARMA model,between the unstructured and the deterministic structured TARMA model,is proposed based on the reproducing kernel Hilbert space.A kernel ridge regression TARMA model parameter estimation method and a Gaussian process regression TARMA model parameter estimation method are respectively proposed by using ridge regression and Bayesian linear regression in the high-dimensional feature space.Numerical results demonstrate the superior achievable accuracy and the enhanced tracking capabilities of the proposed kernelized parameter evolution methods by comparing with their unstructured parameter evolution counterparts.(5)By using the oscillating memory mechanism to forget past data,a kernel ridge regression functional series TARMA model parameter estimation method with superior achievable accuracy and enhanced tracking capabilities is proposed.By approximating the TARMA model parameter trajectory by a linear combination of the proposed adaptive compactly supported radial basis functions,a recursive pseudo-linear regression adaptable functional series TARMA model parameter estimation method with enhanced local tracking capabilities is proposed.Numerical results demonstrate the superior achievable accuracy and the enhanced tracking capabilities of the proposed deterministic parameter evolution methods by comparing with their unstructured and kernelized parameter evolution counterparts.(6)The above TARMA model parameter recursive estimation methods are experimentally validated by setting up an experimental system consisting of a simply supported beam and a moving mass sliding on it.The dynamic model of the coupled moving-mass and beam time-varying system is first built and the corresponding numerical simulation is subsequently carried out.The modal testing under the frozen-time assumption is carried out to obtain the frozen-time modal parameters of the experimental system,which will be used as the baseline of the subsequent time-varying case.The time-varying experiment of the experimental system is conducted with the moving mass sliding on the beam,and acceleration of the beam is measured.The proposed TARMA model parameter recursive estimation methods are finally tested based on the measured non-stationary acceleration signals.