Auxiliary Model-Based Multi-Innovation Fractional Stochastic Gradient Algorithm for Hammerstein Output-Error Systems

This paper focuses on the nonlinear system identification problem, which is a basic premise of control and fault diagnosis. For Hammerstein output-error nonlinear systems, we propose an auxiliary model-based multi-innovation fractional stochastic gradient method. The scalar innovation is extended to the innovation vector for increasing the data use based on the multi-innovation identification theory. By establishing appropriate auxiliary models, the unknown variables are estimated and the improvement in the performance of parameter estimation is achieved owing to the fractional-order calculus theory. Compared with the conventional multi-innovation stochastic gradient algorithm, the proposed method is validated to obtain better estimation accuracy by the simulation results.

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

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.

Two Identification Methods for a Nonlinear Membership Function

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

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.

Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

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.