Design of Flow Direction Optimization Paradigm for Fractional Nonlinear Hammerstein Output Error System Identification With Shifted Asymmetric Laplace Distribution Noise

Abstract In this paper, the flow direction optimization algorithm (FDOA) is exploited for the parameter estimation of the fractional nonlinear Hammerstein output error (FNHOE) system under shifted asymmetric Laplace distribution (SALD) noise. The Grünwald Letnikov finite difference fractional derivative converts the classical nonlinear Hammerstein output error system to FNHOE. The initialization phase of the FDOA refers to the iterative optimization of a specific parameter estimation process with a directional flow methodology, which is the search direction of this algorithm, and rotates the direction according to how the system reacts to SALD noise. The FDOA takes advantage of the system's flexibility by effectively identifying its parameters, which no longer pose a significant challenge to the system due to the designed stiffness. An objective function based on mean square is developed to assess the algorithm's performance, focusing on its robustness, accuracy, and convergence speed. Experimental outcomes demonstrate the superior performance of the FDOA, in terms of parameter estimation accuracy and its ability to handle noisy environments, outperforms counterpart algorithms such as the African vulture optimization algorithm, gazelle optimization algorithm, mountain gazelle optimization algorithm, and triangulation topology optimization algorithm.