Normalized SPSA for Hammerstein model identification of twin rotor and electro-mechanical positioning systems

Abstract

A wide range of optimization methodologies have been introduced for identifying Hammerstein model systems, but existing approaches often face challenges such as convergence instability, computational inefficiency, and over-parameterization. These issues necessitate research into fast, stable, and precise identification methods. This study proposes the normalized simultaneous perturbation stochastic approximation (N-SPSA) to address the challenges mentioned earlier. The N-SPSA mitigates unstable convergence and excessive parameter growth of the conventional SPSA by normalizing objective functions to their highest value, ensuring stable convergence while maintaining the same number of coefficients. The effectiveness of the proposed method was validated by modeling the actual systems, which included the twin-rotor system (TRS) and the electro-mechanical positioning system (EMPS). Performance metrics such as the objective functions statistics, the number of function evaluations (NFE), and time- and frequency-domain responses were used for evaluation. For the TRS, the N-SPSA improved the mean objective function by 18.09 % compared to the average multi-verse optimizer sine-cosine algorithm (AMVO-SCA) and 3.42 % compared to the norm-limited (NL-SPSA), while reducing the computational load by 60 % compared to the AMVO-SCA. Similarly, for the EMPS, the N-SPSA improved the mean objective function by 71.19 % over the NL-SPSA and 25.18 % over the AMVO-SCA, achieving a 50 % reduction in computational effort compared to the AMVO-SCA. Additionally, Wilcoxon’s rank-sum test results for both the TRS and EMPS confirmed the statistical superiority of the N-SPSA over the NL-SPSA. These findings demonstrate that the N-SPSA provides a fast and precise solution for the identification of continuous-time Hammerstein systems, overcoming the limitations of existing methods.