Estimation Of Time-varying Parameters Research Articles

Nonlinear systems time-varying parameter estimation: Application to induction motors

In this paper, an algorithm for time-varying parameter estimation for a large class of nonlinear systems is presented. The proof of the convergence of the estimates to their true values is achieved using Lyapunov theories and does not require that the classical persistent excitation condition be satisfied by the input signal. Since the induction motor (IM) is widely used in several industrial sectors, the algorithm developed is potentially useful for adjusting the controller parameters of variable speed drives. The method proposed is simple and easily implementable in real-time. The application of this approach to on-line estimation of the rotor resistance of IM shows a rapidly converging estimate in spite of measurement noise, discretization effects, parameter uncertainties (e.g. inaccuracies on motor inductance values) and modeling inaccuracies. The robustness analysis for this IM application also revealed that the proposed scheme is insensitive to the stator resistance variations within a wide range. The merits of the proposed algorithm in the case of on-line time-varying rotor resistance estimation are demonstrated via experimental results in various operating conditions of the induction motor. The experimental results obtained demonstrate that the application of the proposed algorithm to update on-line the parameters of an adaptive controller (e.g. IM and synchronous machines adaptive control) can improve the efficiency of the industrial process. The other interesting features of the proposed method include fault detection/estimation and adaptive control of IM and synchronous machines.

Visual motion and structure estimation using sliding mode observers

The problem of estimating motion and structure from a sequence of images has been a major research theme in machine vision for many years and remains one of the most challenging ones. In this work, we use sliding mode observers to estimate the motion and the structure of a moving body with the aid of a change-coupled device (CCD) camera. We consider a variety of dynamical systems which arise in machine vision applications and develop a novel identification procedure for the estimation of both constant and time-varying parameters. The basic procedure introduced for parameter estimation is to recast image feature dynamics linearly in terms of unknown parameters and construct a sliding mode observer to produce asymptotically correct estimates of the observed image features, and then use the observer input to compute parameters. Much of our analysis has been substantiated by computer simulations and real experiments.

Adaptive control of the airflow of a PEM fuel cell system

An appropriate oxygen excess ratio could improve the net power of a fuel cell system and reduce the potential of oxygen starvation. Due to nonlinear and time-varying characteristics, it is a difficult task to maintain the oxygen excess ratio within an ideal range particularly during transients. An adaptive control algorithm is therefore proposed to dynamically stabilize the oxygen excess ratio around an optimal level. The application of the algorithm inevitably involves the estimation of time-varying parameters and the pole assignment of the closed-loop system. The proposed adaptive control is evaluated on a test bench, and its application to overcome the time-varying problem is demonstrated.

Estimation of Time-Varying Vibration Parameters by the Segmental Use of the Harmonic Wavelet

Estimation of Time-Varying Vibration Parameters by the Segmental Use of the Harmonic Wavelet

A blind separation method of overlapped multi-components based on time varying AR model

A method utilizing single channel recordings to blindly separate the multicomponents overlapped in time and frequency domains is proposed in this paper. Based on the time varying AR model, the instantaneous frequency and amplitude of each signal component are estimated respectively, thus the signal component separation is achieved. By using prolate spheroidal sequence as basis functions to expand the time varying parameters of the AR model, the method turns the problem of linear time varying parameters estimation to a linear time invariant parameter estimation problem, then the parameters are estimated by a recursive algorithm. The computation of this method is simple, and no prior knowledge of the signals is needed. Simulation results demonstrate validity and excellent performance of this method.

Recursive Estimation and Identification of Time-Varying Long-Term Fading Channels

This paper is concerned with modeling of time-varying wireless long-term fading channels, parameter estimation, and identification from received signal strength data. Wireless channels are represented by stochastic differential equations, whose parameters and state variables are estimated using the expectation maximization algorithm and Kalman filtering, respectively. The latter are carried out solely from received signal strength data. These algorithms estimate the channel path loss and identify the channel parameters recursively. Numerical results showing the viability of the proposed channel estimation and identification algorithms are presented.

Adaptive Estimation of Time-Varying Parameters in Linearly Parametrized Systems

Abstract Adaptive estimation of time-varying parameters in linearly parametrized systems is considered. The estimation time is divided into small intervals; in each interval the time-varying parameter is approximated by a time polynomial with unknown coefficients. A condition for resetting of the parameter estimate at the beginning of each interval is derived; the condition guarantees that the estimate of the time-varying parameter is continuous and also allows for the coefficients of the polynomial to be different in various time intervals. A modified version of the least-squares algorithm is provided to estimate the time-varying parameters. Stability of the proposed algorithm is shown and discussed. Simulation results on an example are given to validate the proposed method.

Nonlinear estimation methods for parameter tracking in power plants

This paper presents parameter estimation of physical time-varying parameters for combined-cycle power plant models. Four different variants of the Kalman filter are compared extensively on models of different complexities. The first filter is the well-known extended Kalman filter. The second and third filters are recent (2000 and 2001) developments of unscented versions of the Kalman filter. The fourth filter is a new (2000) and compact version of the adaptive sensitivity-based Kalman filter. The four different approaches have different complexities, behaviour and advantages that are surveyed in this paper.

Particle filters for state and parameter estimation in batch processes

In process engineering, on-line state and parameter estimation is a key component in the modelling of batch processes. However, when state and/or measurement functions are highly non-linear and the posterior probability of the state is non-Gaussian, conventional filters, such as the extended Kalman filter, do not provide satisfactory results. This paper proposes an alternative approach whereby particle filters based on the sequential Monte Carlo method are used for the estimation task. Particle filters are initially described prior to discussing some implementation issues, including degeneracy, the selection of the importance density and the number of particles. A kernel smoothing approach is introduced for the robust estimation of unknown and time-varying model parameters. The effectiveness of particle filters is demonstrated through application to a benchmark batch polymerization process and the results are compared with the extended Kalman filter.

A VARIANCE-ADAPTIVE PARTICLE FILTER WITH APPLICATION TO TIME-VARYING PARAMETER ESTIMATION

Particle filtering, as a new method to solve dynamic system filtering problems, has been applied with great success to many scientific and engineering fields. Particle filters have the ability to perform state estimation in nonlinear and non-Gaussian state space models. However, the standard particle filter algorithm is not applicable for time-varying parameter estimation problems, especially incompetent for abrupt parameters. In this paper, a variance-adaptive particle filter (VAPF) algorithm is proposed, and is applied to time-varying parameter estimation. A simulation example is also presented to demonstrate this method.

IDENTIFICATION OF TIME-VARYING MODAL MODELS

Modal, decoupled models of linear systems have easily interpreted parameters: gains and poles for independent rate processes, hence time constants and damping ratios. Time-varying modal models can fit a wide range of time-invariant, non-linear systems, and the time variation shows the effects of non-linearity. Modal parameters can be estimated via an ARMAX model, but the calculation is ill conditioned, so direct estimation of time-varying modal parameters is examined. The modal components of the output cannot be observed so must be estimated along with the parameters, a nonlinear estimation problem. It is treated as state estimation, using the extended Kalman filter (EKF) and optimal smoothing. The capabilities and limitations of the EKF are investigated by simulation. With care, good results can be obtained even in difficult cases, e.g. with abrupt change in an input or output offset.

Comparison of Different Kalman Filters for Tracking Nonlinear Transmission Torques

This paper presents parameter estimation of physical time-varying parameters for a mechanical system with a nonlinear gear-box transmission torque. Four different variants of the Kalman filter are compared extensively on models of different complexities. The first filter is the well-known Extended Kalman filter. The second and third filters are recent (2000 and 2001) developments of unscented versions of the Kalman filter. The fourth filter is a new (2000) and compact version of the adaptive sensitivity-based Kalman filter. The four different approaches have different complexities, behaviour and advantages that are surveyed in this paper. The paper shows that some of the filters are able to successfully track a rapidly changing transmission torque.

A finite-horizon adaptive Kalman filter for linear systems with unknown disturbances

In this paper, a class of linear systems subject to process disturbances and structured measurement disturbances with unknown time-varying covariances is considered. First, we construct a finite-horizon filter structure to recursively obtain a suit of positive definite matrices and propose the sufficient conditions to ensure the above positive definite matrices to be upper bounds of the unknown covariances of the state estimation errors, filtering residuals and state prediction errors. Then some parameters are directly determined through simultaneously minimizing such upper bounds, while the other parameters are obtained via optimization through minimizing the upper bound of the covariances of filtering residuals. Furthermore, the parameter optimization is transformed into a convex optimization problem, which can be effectively solved by use of linear matrix inequality (LMI). Hence a finite-horizon adaptive Kalman filter (FHAKF) is proposed. The simulation study is about the joint time-varying time delay and parameter estimation of a nonlinear stochastic system with sensors subject to disturbances with unknown covariances, which shows that the proposed FHAKF has excellent performance and reveals the robustness of the FHAKF against the a priori filter parameters.

Motion parameters estimation by new propagation approach and time–frequency representations

Estimation of time-varying motion parameters of moving objects is considered. The motion parameters are mapped into the instantaneous frequency (IF) of a frequency modulated signal. The IF estimation is obtained by using the Wigner distribution. Generalization in the case of multiple objects and reduced interference distributions is given. A new propagation approach is proposed for joint estimation of velocity and position of objects in a video-sequence. This approach produces better accuracy than the variable μ -propagation-based one.

A novel variable‐length sliding window blockwise least‐squares algorithm for on‐line estimation of time‐varying parameters

AbstractMotivated by the advances in computer technology and the fact that the batch/block least‐squares (LS) produces more accurate parameter estimates than its recursive counterparts, several important issues associated with the block LS have been re‐examined in the framework of on‐line identification of systems with abrupt/gradual change parameters in this paper. It is no surprise that the standard block LS performs unsatisfactorily in such a situation. To overcome this deficiency, a novel variable‐length sliding window‐based LS algorithm, known as variable‐length sliding window blockwise least squares, is developed. The algorithm consists of a change detection scheme and a data window with adjustable length. The window length adjustment is triggered by the change detection scheme. Whenever a change in system parameters is detected, the window is shortened to discount ‘old’ data and place more weight on the latest measurements. Several strategies for window length adjustment have been considered. The performance of the proposed algorithm has been evaluated through numerical studies. In comparison with the recursive least squares (RLS) with forgetting factors, superior results have been obtained consistently for the proposed algorithm. Robustness analysis of the algorithm to measurement noise have also been carried out. The significance of the work reported herein is that this algorithm offers a viable alternative to traditional RLS for on‐line parameter estimation by trading off the computational complexity of block LS for improved performance over RLS, because the computational complexity becomes less and less an issue with the rapid advance in computer technologies. Copyright © 2004 John Wiley & Sons, Ltd.

Measuring time-varying capital mobility in East Asia

This paper examines the dynamic capital mobility in East Asia's newly industrialized economies (NIEs). We propose an alternative measure of capital mobility based on an intertemporal current account model that is developed by Shitaba and Shintani [J. Int. Money Financ. 17 (1998) 741]. We present the time-varying parameter estimates to illustrate the different processes of financial liberalization in these developing countries. The results indicate that capital is much more mobile over time, corresponding to the liberalization policies. Our findings are sharply in contrast to the previous studies, which show the lower degree of capital mobility either in developed or in developing countries.

On‐line identification and damage detection in non‐linear structural systems using a variable forgetting factor approach

AbstractThis paper presents an adaptive on‐line identification algorithm based on a newly defined variable forgetting factor approach. At each time step, the proposed methodology, a recursive least‐square (Kalman filter) based algorithm, upgrades the adaptation gain matrix using an adaptive forgetting factor that is expressed as the ratio between the minimum value of the diagonal elements of the adaptation gain matrix and a set of pre‐defined threshold values. This approach requires only acceleration measurements and is particularly robust to the integration errors introduced in determining velocities and displacements. Such an algorithm has been implemented for both parametric and non‐parametric identification studies. For the case of no a priori information on the type of the structural model, an analytical method based on a power series of multivariable polynomial expansions has been introduced. The effectiveness and robustness of the proposed approach has been shown in various numerical simulations, considering the effects of excitation amplitude, of measurement noise, of a priori mass estimation error, and of exact‐, under‐, and over‐parameterization of the structural model. General polynomial‐type non‐linear models such as Duffing and Van der Pole oscillators and Bouc–Wen hysteretic model have been analyzed using the proposed modeling process. The methodology presented in this paper leads to a more accurate and controllable on‐line identification either for the estimation of time‐invariant or time‐varying structural parameters (for damage detection purposes) or for the prediction of the future structural response to dynamic loading. Copyright © 2003 John Wiley & Sons, Ltd.

Estimation of Time-Varying Parameters in Rule Systems for Music Performance

In studies of music performance, rule systems have been used to model the expressive deviations introduced by musicians. In this work we present a methodology for the estimation of the rule parameters to reproduce a given human performance as closely as possible. To achieve best fit, a least square algorithm was used. The estimation can be carried out on different time scales to improve the fit when the performer used different expressive strategies during the piece. The method has been tested on different pieces, recorded both in a controlled experiment, and also in ecological settings. Results confirm this methodology, and allow an objective comparison of parameter sets already studied in literature. The model can also be used to compare different rule systems, both from a numerical point of view, and also by listening the synthesized performances obtained using the estimated values.

Estimation of time-varying time delay and parameters of a class of jump Markov nonlinear stochastic systems

It is a challenging problem to estimate time-varying time delay and parameters, especially for systems subject to disturbances with unknown statistics in measurements. The desirable filter should be sensitive to unmodeled dynamics caused by random changes in time delay and parameters, and also be robust to disturbances. Recently, we proposed a finite-horizon robust Kalman filter (RKF) through designing and simultaneously minimizing the upper bounds of unknown covariances of prediction errors, filtering residuals and estimation errors. Unfortunately, unmodeled dynamics and disturbances must be hypothesized to be zero-mean white noises in the RKF. To cope with more general unmodeled dynamics and/or disturbances, a class of jump Markov stochastic systems (JMSS) subject to unmodeled dynamics and disturbances is considered in this article so that a priori system information, such as the value range of unknown and/or randomly changing parameters, can be introduced. Through combining the RKF with the interacting multiple model (IMM) estimation technique, a RKF/IMM algorithm is proposed for such JMSS. Then it is applied to estimate time-varying time delay and parameters of a continuous stirred tank reactor (CSTR) with sensors subject to Gaussian disturbances with unknown means and/or covariances. The RKF/IMM algorithm is compared with the extended Kalman filter (EKF), the strong tracking filter (STF) and the RKF through computer simulations. The results show that, in the case that measurement disturbances are zero-mean noise with unknown covariances, the RKF/IMM and RKF achieve almost the same accurate estimates, which are superior to those of the STF and EKF; in the case that such disturbances have unknown covariances and time-varying means, only the RKF/IMM remains the ability to estimate time-varying time delay and parameters. Furthermore the RKF/IMM has unique ability to identify the disturbance mean no matter whether it is constant or time-varying. Moreover, the RKF/IMM algorithm is shown having strong robustness against the a priori filter parameters, this may be attractive in practical applications.

A magnitude/phase-locked loop approach to parameter estimation of periodic signals

Presents a parameter estimator that is designed to estimate the frequencies, magnitudes, and phases of the components of a periodic signal. The structure of the algorithm is reminiscent of a phase-locked loop, although significant differences can be observed. The performance of the estimator is analyzed, and useful design guidelines are provided. A version of the algorithm is presented that combines different components of the signal and/or signals from multiple sensors in order to estimate the fundamental frequency. In this manner, the algorithm is able to maintain tracking of the fundamental frequency despite changes in signal characteristics. The results are verified in simulations and the algorithms are found to be simple and effective for estimation and tracking of time-varying parameters. Experimental results are reported where periodic signals are collected from an active noise control testbed.