157 research outputs found

    Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

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    This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

    Gradient-based iterative parameter estimation for bilinear-in-parameter systems using the model decomposition technique

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    The parameter estimation issues of a block-oriented non-linear system that is bilinear in the parameters are studied, i.e. the bilinear-in-parameter system. Using the model decomposition technique, the bilinear-in-parameter model is decomposed into two fictitious submodels: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear dynamic one and the noise model. Then a gradient-based iterative algorithm is proposed to estimate all the unknown parameters by formulating and minimising two criterion functions. The stochastic gradient algorithms are provided for comparison. The simulation results indicate that the proposed iterative algorithm can give higher parameter estimation accuracy than the stochastic gradient algorithms

    Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation

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    This paper considers the parameter identification problems of the input nonlinear output-error (IN-OE) systems, that is the Hammerstein output-error systems. In order to overcome the excessive calculation amount of the over-parameterization method of the IN-OE systems. Through applying the hierarchial identification principle and decomposing the IN-OE system into three subsystems with a smaller number of parameters, we present the key term separation auxiliary model hierarchical gradient-based iterative algorithm and the key term separation auxiliary model hierarchical least squares-based iterative algorithm, which are called the key term separation auxiliary model three-stage gradient-based iterative algorithm and the key term separation auxiliary model three-stage least squares-based iterative algorithm. The comparison of the calculation amount and the simulation analysis indicate that the proposed algorithms are effective. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

    Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems

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    This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods

    Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

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    By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

    Parameter and State Estimator for State Space Models

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    This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective

    Adaptive filtering-based multi-innovation gradient algorithm for input nonlinear systems with autoregressive noise

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    In this paper, by means of the adaptive filtering technique and the multi-innovation identification theory, an adaptive filtering-based multi-innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi-innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering-based multi-innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm

    Parameter estimation algorithm for multivariable controlled autoregressive autoregressive moving average systems

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    This paper investigates parameter estimation problems for multivariable controlled autoregressive autoregressive moving average (M-CARARMA) systems. In order to improve the performance of the standard multivariable generalized extended stochastic gradient (M-GESG) algorithm, we derive a partially coupled generalized extended stochastic gradient algorithm by using the auxiliary model. In particular, we divide the identification model into several subsystems based on the hierarchical identification principle and estimate the parameters using the coupled relationship between these subsystems. The simulation results show that the new algorithm can give more accurate parameter estimates of the M-CARARMA system than the M-GESG algorithm

    Identification of continuous-time model of hammerstein system using modified multi-verse optimizer

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    his thesis implements a novel nature-inspired metaheuristic optimization algorithm, namely the modified Multi-Verse Optimizer (mMVO) algorithm, to identify the continuous-time model of Hammerstein system. Multi-Verse Optimizer (MVO) is one of the most recent robust nature-inspired metaheuristic algorithm. It has been successfully implemented and used in various areas such as machine learning applications, engineering applications, network applications, parameter control, and other similar applications to solve optimization problems. However, such metaheuristics had some limitations, such as local optima problem, low searching capability and imbalance between exploration and exploitation. By considering these limitations, two modifications were made upon the conventional MVO in our proposed mMVO algorithm. Our first modification was an average design parameter updating mechanism to solve the local optima issue of the traditional MVO. The essential feature of the average design parameter updating mechanism is that it helps any trapped design parameter jump out from the local optima region and continue a new search track. The second modification is the hybridization of MVO with the Sine Cosine Algorithm (SCA) to improve the low searching capability of the conventional MVO. Hybridization aims to combine MVO and SCA algorithms advantages and minimize the disadvantages, such as low searching capability and imbalance between exploration and exploitation. In particular, the search capacity of the MVO algorithm has been improved using the sine and cosine functions of the Sine Cosine Algorithm (SCA) that will be able to balance the processes of exploration and exploitation. The mMVO based method is then used for identifying the parameters of linear and nonlinear subsystems in the Hammerstein model using the given input and output data. Note that the structure of the linear and nonlinear subsystems is assumed to be known. Moreover, a continuous-time linear subsystem is considered in this study, while there are a few methods that utilize such models. Two numerical examples and one real-world application, such as the Twin Rotor System (TRS) are used to illustrate the efficiency of the mMVO-based method. Various nonlinear subsystems such as quadratic and hyperbolic functions (sine and tangent) are used in those experiments. Numerical and experimental results are analyzed to focus on the convergence curve of the fitness function, the parameter variation index, frequency and time domain response and the Wilcoxon rank test. For the numerical identifications, three different levels of white noise variances were taken. The statistical analysis value (mean) was taken from the parameter deviation index to see how much our proposed algorithm has improved. For Example 1, the improvements are 29%, 33.15% and 36.68%, and for the noise variances, 0.01, 0.25, and 1.0 improvements can be found. For Example 2, the improvements are 39.36%, 39.61% and 66.18%, and for noise variances, the improvements are by 0.01, 0.25 and 1.0, respectively. Finally, for the real TRS application, the improvement is 7%. The numerical and experimental results also showed that both Hammerstein model subsystems are defined effectively using the mMVO-based method, particularly in quadratic output estimation error and a differentiation parameter index. The results further confirmed that the proposed mMVObased method provided better solutions than other optimization techniques, such as PSO, GWO, ALO, MVO and SCA

    Bubble size distribution measurement, modeling and control in a laboratory flotation column

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    Ce travail de recherche vise à mesurer et à contrôler la distribution du diamètre des bulles (DDB) dans une colonne de flottation. L'objectif se décompose en trois parties. La première phase vise à estimer correctement la taille des bulles grâce à des algorithmes de traitement d'images prises par une caméra. La DDB obtenue est ensuite modélisée par une distribution log-normale qui est définie par deux paramètres, la moyenne et l'écart type. Deuxièmement, grâce au nouveau système de mesure et à la représentation log-normale, un modèle dynamique à gains non linéaires (structure de Wiener) dont les sorties sont la moyenne et l'écart-type de la DDB est estimé. Une bonne concordance entre la réponse du système expérimental et celle du modèle identié est observée. Finalement, une stratégie de commande prédictive contrainte basée sur le modèle de Wiener est conçue afin de réguler la BSD. Les résultats de laboratoire obtenus sont très satisfaisants
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