Parameter Identification of Time Varying System Using Basic Function Expansion

Time-varying parameters identification in linear system is considered, which can be changed into time-invariant coefficient polynomials after Taylor expansion. Using response data to establish the time-varying autoregressive moving average (TV-ARMA) model, then utilizing least-square algorithm to obtain time-invariant coefficients of time-varying parameters. According to error analysis, to reduce errors and improve accuracy, the estimation time is divided into small internals and the above method is used in each interval. Simulation shows that, under certain error condition, the time-varying parameters obtained by the method have good agreement with the theoretical values; the measures taken have strong anti-interference and high efficiency.

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An Extended Time Series Algorithm for Modal Identification from Nonstationary Ambient Response Data Only

Mathematical Problems in Engineering ◽

10.1155/2014/391815 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Chang-Sheng Lin ◽

Dar-Yun Chiang ◽

Tse-Chuan Tseng

Keyword(s):

Time Series ◽

Arma Model ◽

Identification Problem ◽

Nonstationary Time Series ◽

Modal Identification ◽

Ambient Vibration ◽

Time Varying ◽

Varying Parameters ◽

Response Data ◽

Time Varying Parameters

Modal Identification is considered from response data of structural systems under nonstationary ambient vibration. The conventional autoregressive moving average (ARMA) algorithm is applicable to perform modal identification, however, only for stationary-process vibration. The ergodicity postulate which has been conventionally employed for stationary processes is no longer valid in the case of nonstationary analysis. The objective of this paper is therefore to develop modal-identification techniques based on the nonstationary time series for linear systems subjected to nonstationary ambient excitation. Nonstationary ARMA model with time-varying parameters is considered because of its capability of resolving general nonstationary problems. The parameters of moving averaging (MA) model in the nonstationary time-series algorithm are treated as functions of time and may be represented by a linear combination of base functions and therefore can be used to solve the identification problem of time-varying parameters. Numerical simulations confirm the validity of the proposed modal-identification method from nonstationary ambient response data.

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Numerical Study on Identification of Time Varying Parameters of Vibration Systems

Shock and Vibration ◽

10.1155/1997/495860 ◽

1997 ◽

Vol 4 (1) ◽

pp. 69-76

Author(s):

Yanchun Liang ◽

Qiang Zhen ◽

Zaishen Wang

Keyword(s):

Linear Model ◽

Nonlinear Term ◽

Numerical Study ◽

Time Varying ◽

Linear Vibration ◽

Factors Affecting ◽

Varying Parameters ◽

Time Varying Parameters ◽

On Line ◽

Time Invariant

An on-line least squares algorithm has previously been successfully applied to linear vibration systems in order to identify time varying parameters. In this article the limitations of the approach and the factors affecting the identification are further examined. The existence of the nonlinear term is determined by means of the time varying characteristics of the estimated linear parameters using the linear model and the data from a time invariant nonlinear system. The identification of the time varying linear parameters is also examined in accordance with the linear model by using the data with nonlinear elements.

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Control of Dynamic Systems With Nonlinearities and Time Varying Parameters

14th Biennial Conference on Mechanical Vibration and Noise: Dynamics and Vibration of Time-Varying Systems and Structures ◽

10.1115/detc1993-0114 ◽

1993 ◽

Author(s):

Dirk Söffker ◽

Peter C. Müller

Keyword(s):

Dynamic Systems ◽

Disturbance Rejection ◽

Linear Time ◽

Time Varying ◽

Varying Parameters ◽

Linear Time Invariant ◽

Time Variance ◽

Disturbance Rejection Control ◽

Time Varying Parameters ◽

Time Invariant

Abstract The well-known theory of disturbance rejection control and the experience of using a generalized technique with universal fault model for building observers and regulators for the estimation and compensation of disturbances and unmodeled or uncertain effects as well, could be used for controlling dynamic systems with time varying parameters and nonlinearities. Based on a linear time-invariant model the effects of non-linearities and unmodeled dynamics are estimated by an extended observer scheme. Using this information these dynamic effects will be compensated by the developed compensation scheme. Here also different compensation techniques of disturbance rejection control are discussed, compared, and modified. The simulation example of an inverted flexible pendulum shows the efficiency of the method controlling an unstable mechanical system without exact knowledge of structure and parameters of nonlinearity and time-variance.

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A Bayesian analysis of moving average processes with time-varying parameters

Computational Statistics & Data Analysis ◽

10.1016/j.csda.2007.04.001 ◽

2007 ◽

Vol 52 (2) ◽

pp. 1025-1046 ◽

Cited By ~ 5

Author(s):

K. Triantafyllopoulos ◽

G.P. Nason

Keyword(s):

Bayesian Analysis ◽

Moving Average ◽

Time Varying ◽

Varying Parameters ◽

Time Varying Parameters ◽

Moving Average Processes

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Modeling of adaptations to physical training by using a recursive least squares algorithm

Journal of Applied Physiology ◽

10.1152/jappl.1997.82.5.1685 ◽

1997 ◽

Vol 82 (5) ◽

pp. 1685-1693 ◽

Cited By ~ 42

Author(s):

Thierry Busso ◽

Christian Denis ◽

Régis Bonnefoy ◽

André Geyssant ◽

Jean-René Lacour

Keyword(s):

Least Squares ◽

Physical Training ◽

Recursive Least Squares ◽

Model Parameters ◽

Time Varying ◽

Varying Parameters ◽

Recursive Least Squares Algorithm ◽

Time Varying Parameters ◽

Least Squares Algorithm ◽

Time Invariant

Busso, Thierry, Christian Denis, Régis Bonnefoy, André Geyssant, and Jean-René Lacour. Modeling of adaptations to physical training by using a recursive least squares algorithm. J. Appl. Physiol. 82(5): 1685–1693, 1997.—The present study assesses the usefulness of a systems model with time-varying parameters for describing the responses of physical performance to training. Data for two subjects who undertook a 14-wk training on a cycle ergometer were used to test the proposed model, and the results were compared with a model with time-invariant parameters. Two 4-wk periods of intensive training were separated by a 2-wk period of reduced training and followed by a 4-wk period of reduced training. The systems input ascribed to the training doses was made up of interval exercises and computed in arbitrary units. The systems output was evaluated one to five times per week by using the endurance time at a constant workload. The time-invariant parameters were fitted from actual performances by using the least squares method. The time-varying parameters were fitted by using a recursive least squares algorithm. The coefficients of determination r 2 were 0.875 and 0.879 for the two subjects using the time-varying model, higher than the values of 0.682 and 0.666, respectively, obtained with the time-invariant model. The variations over time in the model parameters resulting from the expected reduction in the residuals appeared generally to account for changes in responses to training. Such a model would be useful for investigating the underlying mechanisms of adaptation and fatigue.

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