Identification of continuous-time Hammerstein model using improved Archimedes optimization algorithm

Although various optimization algorithms have been widely employed in multiple applications, the traditional Archimedes optimization algorithm (AOA) has presented imbalanced exploration with exploitation phases and the propensity for local optima entrapment. Therefore, this article identified various continuous-time Hammerstein models based on an improved Archimedes optimization algorithm (IAOA) to address these concerns. The proposed algorithm employed two principal modifications to mitigate these issues and enhance identification accuracy: (i) exploration and exploitation phase recalibrations using a revised density decreasing factor and (ii) local optima entrapment alleviation utilizing safe experimentation dynamics. Various advantages were observed with this proposed algorithm, including a lower number of coefficient criteria, improved accuracy in Hammerstein model identification, and diminished processing demands by reducing gain redundancy between nonlinear and linear subsystems. This proposed algorithm also discerned linear and nonlinear subsystem variables within a continuous-time Hammerstein model utilizing input and output data. The process was evaluated using a numerical example and two practical experiments [twin-rotor system (TRS) and electro-mechanical positioning system (EMPS)]. Several parameters were then analyzed, such as the convergence curve of the fitness function, frequency and time domain-related responses, variable deviation index, and Wilcoxon's rank-sum test. Consequently, the proposed algorithm reliably determined the most optimal design variables during numerical trials, demonstrating 54.74 % mean fitness function and 75.34 % variable deviation indices enchantments compared to the traditional AOA. Improved mean fitness function values were also revealed in the TRS (11.63 %) and EMPS (69.63 %) assessments, surpassing the conventional algorithm. This proposed algorithm produced solutions with superior accuracy and consistency compared to various established metaheuristic strategies, including particle swarm optimizer, grey wolf optimizer, multi-verse optimizer, AOA, and a hybrid optimizer (average multi-verse optimizer-sine-cosine algorithm).