scholarly journals Two Identification Methods for a Nonlinear Membership Function

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yuejiang Ji ◽  
Lixin Lv
Keyword(s):  
Parameter Identification ◽  
Iterative Algorithm ◽  
Membership Function ◽  
Nonlinear Function ◽  
Gradient Algorithm ◽  
Unknown Parameters ◽  
Identification Methods ◽  
Stochastic Gradient Algorithm ◽  
Gradient Based ◽  
Two Parameter

This paper proposes two parameter identification methods for a nonlinear membership function. An equation converted method is introduced to turn the nonlinear function into a concise model. Then a stochastic gradient algorithm and a gradient-based iterative algorithm are provided to estimate the unknown parameters of the nonlinear function. The numerical example shows that the proposed algorithms are effective.

An improved nonlinear innovation-based parameter identification algorithm for ship models

2021 ◽  
pp. 1-9
Author(s):  
Baigang Zhao ◽  
Xianku Zhang
Keyword(s):  
Parameter Identification ◽  
Test Data ◽  
Stochastic Gradient ◽  
Least Square ◽  
Gradient Algorithm ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Process Innovations ◽  
Stochastic Gradient Algorithm ◽  
Tangent Function

Abstract To solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

Identification of Hammerstein Systems with Two-Segment Preload Nonlinearity Based on the Gradient Search

2014 ◽  
Vol 651-653 ◽  
pp. 2314-2317 ◽  
Author(s):  
Hong Fen Zou
Keyword(s):  
Convergence Rate ◽  
Special Form ◽  
Approximation Theorem ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Gradient Search ◽  
Unknown Parameters ◽  
Hammerstein System ◽  
Hammerstein Systems ◽  
Stochastic Gradient Algorithm

This paper deals with the parameter identication problem for Hammerstein systems with two-segment preload nonlinearity. Taking into account the complexity of Hammerstein systems, we use theWeierstrass approximation theorem to convert a Hammerstein system into a special form that has linear-in-parameters, and propose a stochastic gradient algorithm to estimate all unknown parameters of Hammerstein systems. Furthermore, a modified stochastic gradient algorithm is given to improve the convergence rate. The applicability of the approach is illustrated by a simulation example.

scholarly journals Improved parameter identification algorithm for ship model based on nonlinear innovation decorated by sigmoid function

2021 ◽  
Author(s):  
Xianku Zhang ◽  
Baigang Zhao ◽  
Guoqing Zhang
Keyword(s):  
Parameter Identification ◽  
Least Squares ◽  
Test Data ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Identification Algorithm ◽  
Sigmoid Function ◽  
Stochastic Gradient Algorithm ◽  
Identification Test ◽  
Small Test

Abstract This paper investigates the problem of parameter identification for ship nonlinear Nomoto model with small test data, a nonlinear innovation-based identification algorithm is presented by embedding sigmoid function in the stochastic gradient algorithm. To demonstrate the validity of the algorithm, an identification test is carried out on the ship ‘SWAN’ with only 26 sets of test data. Furthermore, the identification effects of the least squares algorithm, original stochastic gradient algorithm and the improved stochastic gradient algorithm based on nonlinear innovation are compared. Generally, the stochastic gradient algorithm is not suitable for the condition of small test data. The simulation results indicate that the improved stochastic gradient algorithm with sigmoid function greatly increases its accuracy of parameter identification and has 14.2% up compared with the least squares algorithm. Then the effectiveness of the algorithm is verified by another identification test on the ship ‘Galaxy’, the accuracy of parameter identification can reach more than 95% which can be used in ship motion simulation and controller design. The proposed algorithm has advantages of the small test data, fast speed and high accuracy of identification, which can be extended to other parameter identification systems with less sample data.

Nonlinear innovation identification of ship response model via the hyperbolic tangent function

2020 ◽  
pp. 095965182095653
Author(s):  
Chunyu Song ◽  
Xianku Zhang ◽  
Guoqing Zhang
Keyword(s):  
Parameter Identification ◽  
Stochastic Gradient ◽  
Least Square ◽  
Gradient Algorithm ◽  
Response Model ◽  
Hyperbolic Tangent ◽  
Hyperbolic Tangent Function ◽  
Original Algorithm ◽  
Stochastic Gradient Algorithm ◽  
Tangent Function

This research is concerned with the problem of parameter identification for ship response model. A novel nonlinear innovation–based algorithm is proposed by use of the hyperbolic tangent function and the stochastic gradient algorithm. In order to demonstrate the validity of the algorithm, two identification experiments are adopted by the “Galaxy” ship and the “Yupeng” ship. Furthermore, the comparison experiment is illustrated to verify the effectiveness of the proposed algorithm, including the least square algorithm, the traditional stochastic gradient algorithm and the improved nonlinear innovation–based stochastic gradient algorithm. The identification results indicate that the improved stochastic gradient algorithm is with higher accuracy by 95.2% than the original algorithm and 11.75% than the least square algorithm. In addition, the proposed algorithm is with advantages of fast speed and high accuracy of identification. That can be extended to other parameter identification systems with the limited test data.

Modified Stochastic Gradient Algorithm for Hammerstein Systems

2013 ◽  
Vol 336-338 ◽  
pp. 2320-2323
Author(s):  
Li Xing Lv ◽  
Jing Chen
Keyword(s):  
Approximation Theorem ◽  
Stochastic Gradient ◽  
Gradient Algorithm ◽  
Identification Algorithm ◽  
Unknown Parameters ◽  
Hammerstein Systems ◽  
Stochastic Gradient Algorithm ◽  
Weierstrass Approximation Theorem ◽  
Identification Model

This paper proposes a modified stochastic gradient algorithm for Hammerstein systems. By the Weierstrass approximation theorem, the model of the nonlinear Hammerstein systems be changed to an identification model, then based on the derived model, a modified stochastic gradient identification algorithm is used to estimate all the unknown parameters of the systems. An example is provided to show the effectiveness of the proposed algorithm.

scholarly journals Iterative Parameter Identification for Fractional-Order Block-Oriented Nonlinear Systems with Application to a Battery Model

2021 ◽  
Author(s):  
Yan Ji ◽  
Junwei Wang ◽  
Xiangxiang Meng
Keyword(s):  
Nonlinear Systems ◽  
Parameter Identification ◽  
Iterative Algorithm ◽  
Fractional Order ◽  
Two Stage ◽  
Hierarchical Identification ◽  
Battery Model ◽  
Block System ◽  
Gradient Based ◽  
Simulation Results

Abstract This paper investigates parameter and order identification of a class of block-oriented nonlinear systems. By using the hierarchical identification principle, the system is divided into two subsystems, which are a linear block system and a nonlinear block system. For the purpose of solving the difficulty of estimating two sets of parameter vectors, the over-parameterization method and the key item separation technique are used, respectively. Therefore, a two-stage over-parameterization gradient-based iterative algorithm and a key term separation two-stage gradient-based iterative algorithm are derived. The simulation results indicate that the proposed algorithms are effective. Finally, the proposed method is evaluated through a battery model. The results show well agreement with the real system outputs.

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