Subspace-based identification of Hammerstein-Wiener systems utilising OGPSO-LGSA algorithm

This paper proposes an identification algorithm for nonlinear dynamic systems based on the Hammerstein-Wiener model. For the initial static nonlinear block, a multi-layer perceptron (MLP) neural network is employed to represent the system. To train the MLP parameters, a novel linear variable-weight Levenberg-Marquardt Quasi-Newton (LVW-LM-QN) algorithm is introduced. The intermediate linear dynamic subsystem is identified using the subspace method, specifically the Numerical Algorithms for Subspace State Space System Identification (N4SID) algorithm. For the subsequent static nonlinear block, an MLP trained with a hybrid optimiser combining Oscillating Gradient Particle Swarm Optimization (OGPSO) and Lévy-flight Gravitational Search Algorithm (LGSA) is adopted, termed OGPSO-LGSA. The effectiveness of the proposed method is validated through simulation studies and practical application examples.