A Robust Hammerstein-Wiener Model Identification Method for Highly Nonlinear Systems

Sun, Lijie; Hou, Jie; Chuan-jun, Xing; Fang, Zhewei

doi:10.3390/pr10122664

Cited by 40 publications

(11 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the above analysis, it can be seen that the CGS method uses the square of BCG polynomial, and the GCGS method has been extended on this basis. Using the product of BCG polynomials and approximate BCG polynomials, the GCGS method does not have quasi-minimal residuals [33,34]. Terefore, quasiminimal residuals are introduced into the GCGS method, and the QMRGCGS method is derived [35,36].…”

Section: Qmrgcgs Methodmentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

View full text Add to dashboard Cite

The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. Open linear algebraic equations can be divided into symmetric linear equations and asymmetric linear equations. The former is based on 2 × 2. The latter is preprocessed by the improved QMRGCGS method, and the applications of the two methods are analyzed, respectively. The experimental results show that when the step is 500, the pretreatment time of quasi-minimal residual generalized conjugate gradient square 2 method is 34.23 s, that of conjugate gradient square 2 method is 35.14 s, and that of conjugate gradient square method is 45.20 s, providing a new reference method and idea for solving and preprocessing non-closed linear algebraic equations.

show abstract

Section: Qmrgcgs Methodmentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Most models explored and analyzed under the FC framework use the Caputo operator. Momani and Shawagfeh provide several basic works of fractional calculus on various aspects [1]: Podlubny [2], Jafari and Seifi [3,4], Kiryakova [5], Oldham and Spanier [6], Miller and Ross [7], Diethelm et al [8], Trujillo [9], Kilbas and Kemple and Beyer [10] and so on [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

et al. 2023

View full text Add to dashboard Cite

In this paper, we investigate the fractional-order Klein–Fock–Gordon equations on quantum dynamics using a new iterative method and residual power series method based on the Caputo operator. The fractional-order Klein–Fock–Gordon equation is a generalization of the traditional Klein–Fock–Gordon equation that allows for non-integer orders of differentiation. This equation has been used in the study of quantum dynamics to model the behavior of particles with fractional spin. The Laplace transform is employed to transform the equations into a simpler form, and the resulting equations are then solved using the proposed methods. The accuracy and efficiency of the method are demonstrated through numerical simulations, which show that the method is superior to existing numerical methods in terms of accuracy and computational time. The proposed method is applicable to a wide range of fractional-order differential equations, and it is expected to find applications in various areas of science and engineering.

show abstract

“…They used to mimic complex relationships and interactions between variables, allowing for the modeling of a wide range of phenomena. These equations are essential in fields such as fluid dynamics, quantum mechanics, mathematical biology, and materials science [1][2][3][4][5][6][7][8]. Analytical methods for PDEs aim to find exact solutions that satisfy the equation for all values of the independent variables.…”

Section: Introductionmentioning

confidence: 99%

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Shehab,

El‐Sheikh,

Ahmed

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.

show abstract

A Robust Hammerstein-Wiener Model Identification Method for Highly Nonlinear Systems

Cited by 40 publications

References 17 publications

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Investigating the Impact of Fractional Non-Linearity in the Klein–Fock–Gordon Equation on Quantum Dynamics

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Contact Info

Product

Resources

About