scholarly journals An Improved Method for Stochastic Nonlinear System’s Identification Using Fuzzy-Type Output-Error Autoregressive Hammerstein–Wiener Model Based on Gradient Algorithm, Multi-Innovation, and Data Filtering Techniques

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-29
Author(s):  
Donia Ben Halima Abid ◽  
Saif Eddine Abouda ◽  
Hanane Medhaffar ◽  
Mohamed Chtourou
Keyword(s):  
Stochastic Systems ◽  
Parametric Estimation ◽  
Gradient Algorithm ◽  
Data Filtering ◽  
Estimation Algorithms ◽  
Output Error ◽  
Proposed Model ◽  
Identification Approach ◽  
Identification Techniques ◽  
Intermediate Variables

This paper proposes an innovative identification approach of nonlinear stochastic systems using Hammerstein–Wiener (HW) model with output-error autoregressive (OEA) noise. Two fuzzy systems are suggested for the identification of the input and output nonlinear blocks of a proposed model from given input-output data measurements. In this work, the need for the commonly used assumptions including well-known structure of input and/or output nonlinearities and/or reversible nonlinear output is eliminated by replacing the intermediate variables and noise with their estimates. Four parametric estimation algorithms to identify the proposed fuzzy-type stochastic output-error autoregressive HW (FSOEAHW) model are derived based on backpropagation algorithm and multi-innovation and data filtering identification techniques. The proposed algorithms are improved backpropagation gradient (IBPG) algorithm, multi-innovation IBPG (MIIBPG) algorithm, a data filtering IBPG (FIBPG) algorithm, and a multi-innovation-based FIBPG (MIFIBPG) algorithm. The convergence of the parameter estimation algorithms is studied. The effectiveness of the proposed algorithms is shown by a given simulation example.

scholarly journals DATA FILTERING BASED STOCHASTIC GRADIENT ALGORITHMS FOR MULTIVARIABLE CARAR-LIKE SYSTEMS

2013 ◽  
Vol 18 (3) ◽  
pp. 374-385 ◽  
Author(s):  
Dongqing Wang ◽  
Tong Shan ◽  
Rui Ding
Keyword(s):  
Colored Noise ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Data Filtering ◽  
Gradient Estimation ◽  
Identification Problems ◽  
Hierarchical Identification ◽  
Estimation Algorithms ◽  
Stochastic Gradient Algorithm ◽  
Gradient Algorithms

This paper considers identification problems for a multivariable controlled autoregressive system with autoregressive noises. A hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm are presented to estimate the parameter vectors and parameter matrix of such multivariable colored noise systems, by using the hierarchical identification principle. The simulation results show that the proposed hierarchical gradient estimation algorithms are effective.

scholarly journals Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2254
Author(s):  
Huafeng Xia ◽  
Feiyan Chen
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Systems ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Parameter Estimates ◽  
Data Filtering ◽  
Model Decomposition ◽  
Stochastic Gradient Algorithm ◽  
Equation Error ◽  
Identification Theory

This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.

Gradient approach for recursive estimation and control in finite Markov chains

1981 ◽  
Vol 13 (04) ◽  
pp. 778-803 ◽  
Author(s):  
Yousri M. El-Fattah
Keyword(s):  
Likelihood Function ◽  
Transition Probabilities ◽  
Control Policy ◽  
Recursive Estimation ◽  
Gradient Algorithm ◽  
Expansion Formula ◽  
Estimation Algorithms ◽  
Stochastic Gradient Algorithm ◽  
Long Run ◽  
Estimation And Control

The problem studied is that of controlling a finite Markov chain so as to maximize the long-run expected reward per unit time. The chain's transition probabilities depend upon an unknown parameter taking values in a subset [ a, b ] of Rn . A control policy is defined as the probability of selecting a control action for each state of the chain. Derived is a Taylor-like expansion formula for the expected reward in terms of policy variations. Based on that result, a recursive stochastic gradient algorithm is presented for the adaptation of the control policy at consecutive times. The gradient depends on the estimated transition parameter which is also recursively updated using the gradient of the likelihood function. Convergence with probability 1 is proved for the control and estimation algorithms.

scholarly journals An adaptive model combining a total variation filter and a fractional-order filter for image restoration

2019 ◽  
Vol 13 ◽  
pp. 174830181983305 ◽  
Author(s):  
Yafeng Yang ◽  
Donghong Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Gradient Algorithm ◽  
Remarkable Effect ◽  
Order Filter ◽  
Model Combining ◽  
Proposed Model ◽  
Primal Dual ◽  
Image Edges

In this paper, we propose a model that combines a total variation filter with a fractional-order filter, which can unite the advantages of the two filters, and has a remarkable effect in the protection of image edges and texture details; simultaneously, the proposed model can eliminate the staircase effect. In addition, the model improves the PSNR compared with the total variation filter and the fractional-order filter when removing noise. Zhu and Chan presented the primal-dual hybrid gradient algorithm and proved that it is effective for the total variation filter. On the basis of their work, we employ the primal-dual hybrid gradient algorithm to solve the combined model in this article. The final experimental results show that the new model and algorithm are effective for image restoration.

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