Fractional gradient-enhanced generalized response sensitivity approach for parameter identification with applications in fractional-order systems

Fractional-order systems have found extensive applications across various fields, making the accurate and efficient estimation of their parameters a critical research focus. Addressing the challenges associated with slow convergence, insufficient precision, and noise sensitivity in fractional-order system parameter estimation, this paper introduces a generalized response sensitivity approach based on fractional-order gradients. The proposed method uniquely utilizes fractional-order operators as adaptive step-size regulators, which enhance the algorithm’s convergence performance. Through rigorous theoretical analysis, the global convergence of the method is established. Numerical experiments demonstrate that, in comparison with conventional parameter estimation approaches, the proposed algorithm improves convergence speed by a factor of 1.5 to 5, while increasing parameter estimation accuracy by 2 to 5 orders of magnitude. Furthermore, the method exhibits robust performance, maintaining stable estimation accuracy under 10% noise conditions. Particularly, in fractional-order time-delay chaotic systems, a class of highly nonlinear systems, it outperforms traditional algorithms, yielding accurate results and strong noise resistance. Specifically, the approach is successfully applied to the estimation of constitutive parameters for polymer-based viscoelastic materials. By analyzing creep experiment data, the method accurately estimates the fractional-order material parameters, offering an efficient and reliable framework for characterizing the mechanical properties of complex materials. This study provides effective methods for the modeling and parameter estimation of fractional-order systems, demonstrating both theoretical contributions and practical significance for engineering applications.