WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis between Complexity and Accuracy

Several approaches have been presented to identify Wiener-Hammerstein models, most of them starting from a linear dynamic model whose poles and zeros are distributed around the static non-linearity. To achieve good precision in the estimation, the Best Linear Approximation (BLA) has usually been used to represent the linear dynamics, while static non-linearity has been arbitrarily parameterised without considering model complexity. In this paper, identification of Wiener, Hammerstein or Wiener-Hammerstein models is stated as a multiobjective optimisation problem (MOP), with a trade-off between accuracy and model complexity. Precision is quantified with the Mean-Absolute-Error (MAE) between the real and estimated output, while complexity is based on the number of poles, zeros and points of the static non-linearity. To solve the MOP, WH-MOEA, a new multiobjective evolutionary algorithm (MOEA) is proposed. From a linear structure, WH-MOEA will generate a set of optimal models considering a static non-linearity with a variable number of points. Using WH-MOEA, a procedure is also proposed to analyse various linear structures with different numbers of poles and zeros (known as design concepts). A comparison of the Pareto fronts of each design concept allows a more in-depth analysis to select the most appropriate model according to the user's needs. Finally, a complex numerical example and a real thermal process based on a Peltier cell are identified, showing the procedure's goodness. The results show that it can be useful to consider the simultaneously precision and complexity of a block-oriented model (Wiener, Hammerstein or Wiener-Hammerstein) in a non-linear process identification.