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The mathematical modelling and optimization of nonlinear problems arising in diversified engineering applications is an area of great interest. The Hammerstein structure is widely used in the modelling of various nonlinear processes found in a range of applications. This study investigates the parameter optimization of the nonlinear Hammerstein model using the abilities of the marine predator algorithm (MPA) and the key term separation technique. MPA is a population-based metaheuristic inspired by the behavior of predators for catching prey, and utilizes Brownian/Levy movement for predicting the optimal interaction between predator and prey. A detailed analysis of MPA is conducted to verify the accurate and robust behavior of the optimization scheme for nonlinear Hammerstein model identification. [ABSTRACT FROM AUTHOR]

In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification. [ABSTRACT FROM AUTHOR]

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness. [ABSTRACT FROM AUTHOR]