Flexible fractional wavelet neural network for non-linear system identification

Dadashzadeh, Hasan; Ahmadi, Ghasem; Edrisi Tabrizi, Yousef; Rezaei, Behrooz

doi:10.22034/cmde.2025.64339.2915

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	Flexible fractional wavelet neural network for non-linear system identification
Computational Methods for Differential Equations
مقاله 17، دوره 14، شماره 3، مهر 2026، صفحه 1280-1300 اصل مقاله (529.17 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64339.2915
نویسندگان
Hasan Dadashzadeh^* ¹؛ Ghasem Ahmadi^* ¹؛ Yousef Edrisi Tabrizi¹؛ Behrooz Rezaei²
¹Department of Mathematics, Payame Noor University, Tehran, Iran.
²Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol, Iran.
چکیده
This paper presents a novel neural network architecture called the flexible fractional wavelet neural network (FFrWNN), which enhances traditional wavelet networks by introducing two additional fractional wavelet parameters. These fractional parameters, along with the translation and scale parameters, are dynamically adjusted during the learning process, offering greater flexibility and improved approximation power. The network is trained using a stochastic gradient descent algorithm, and iterative online training formulas are developed for optimizing both the wavelet parameters and network weights. The stability of the network is proven through the Lyapunov stability approach, ensuring reliable convergence. The proposed FFrWNN is evaluated in the context of both one-dimensional and multi-dimensional dynamic system identification. Results demonstrate that the fractional wavelet parameters significantly improve the network’s accuracy and efficiency. Compared to conventional neural networks, the FFrWNN shows superior performance in terms of precision and learning capability, making it a powerful tool for complex system modeling and signal processing applications.
کلیدواژه‌ها
Fractional wavelet neural network؛ Stochastic gradient descent؛ Fractional order wavelets theory؛ System identification

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Flexible fractional wavelet neural network for non-linear system identification