A new approach for parameter identification of time-varying systems via generalized orthogonal polynomials

Time-varying parameter identification is essential for structural health monitoring and performance evaluation. In this paper, a combined method based on the variational mode decomposition and generalized Morse wavelet is proposed to identify the structural time-varying parameters. Based on the sparse property of structural response signals in wavelet domain, a fast iterative shrinkage-thresholding algorithm is adopted to reduce the noise. Then the de-noised signal is decomposed into multi- modes by the variational mode decomposition, and the generalized Morse wavelet is performed to identify the instantaneous frequency. To validate the proposed method, a numerical example including different frequency variations is studied. Experimental validations of a moving vehicle across a bridge and a time-varying cable system considering two patterns of cable tension variations in the laboratory are carried out to investigate the capability of the proposed approach. It is confirmed that the proposed approach can effectively perform the signal decomposition, while identifying the instantaneous frequencies of the time-varying systems accurately.

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A New Approach for Control of Periodically Time Varying Systems with Application to Spacecraft Momentum Unloading

AIAA Guidance, Navigation, and Control Conference and Exhibit ◽

10.2514/6.2006-6355 ◽

2006 ◽

Cited By ~ 1

Author(s):

Serkan Kalender ◽

Henryk Flashner

Keyword(s):

Time Varying ◽

New Approach ◽

Time Varying Systems

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Application of Generalized Orthogonal Polynomials to Parameter Estimation of Time-Invariant and Bilinear Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3143824 ◽

1987 ◽

Vol 109 (1) ◽

pp. 7-13 ◽

Cited By ~ 3

Author(s):

Maw-Ling Wang ◽

Shwu-Yien Yang ◽

Rong-Yeu Chang

Keyword(s):

Parameter Estimation ◽

Orthogonal Polynomial ◽

Orthogonal Polynomials ◽

Computational Algorithm ◽

State Equation ◽

Dynamic State ◽

Generalized Orthogonal Polynomials ◽

Generalized Orthogonal ◽

Time Invariant ◽

Estimation Of Time

Generalized orthogonal polynomials (GOP) which can represent all types of orthogonal polynomials and nonorthogonal Taylor series are first introduced to estimate the parameters of a dynamic state equation. The integration operation matrix (IOP) and the differentiation operation matrix (DOP) of the GOP are derived. The key idea of deriving IOP and DOP of these polynomials is that any orthogonal polynomial can be expressed by a power series and vice versa. By employing the IOP approach to the identification of time invariant systems, algorithms for computation which are effective, simple and straightforward compared to other orthogonal polynomial approximations can be obtained. The main advantage of using the differentiation operation matrix is that the parameter estimation can be carried out starting at an arbitrary time of interest. In addition, the computational algorithm is even simpler than that of the integral operation matrix. Illustrative examples for using IOP and DOP approaches are given. Very satisfactory results are obtained.

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