Analyzing the Nearly Optimal Solutions in a Multi-Objective Optimization Approach for the Multivariable Nonlinear Identification of a PEM Fuel Cell Cooling System

In this work, the parametric identification of a cooling system in a PEM (proton exchange membrane) fuel cell is carried out. This system is multivariable and nonlinear. In this type of system there are different objectives and the unmodeled dynamics cause conflicting objectives (prediction errors in each output). For this reason, resolution is proposed using a multi-objective optimization approach. Nearly optimal alternatives can exist in any optimization problem. Among them, the nearly optimal solutions that are significantly different (that we call nearly optimal solutions nondominated in their neighborhood) are potentially useful solutions. In identification problems, two situations arise for consideration: 1) aggregation in the design objectives (when considering the prediction error throughout the identification test). When an aggregation occurs in the design objectives, interesting non-neighboring (significantly different) multimodal and nearly optimal alternatives appear. These alternatives have different trade-offs in the aggregated objectives; 2) new objectives in decision making appear. Some models can, with similar performance in the design objectives, obtain a significant improvement in new objectives not included in the optimization phase. A typical case of additional objectives are the validation objectives. In these situations, nearly optimal solutions nondominated in their neighborhood play a key role. These alternatives allow the designer to make the final decision with more valuable information. Therefore, this work highlights, as a novelty, the relevance of considering nearly optimal models nondominated in their neighborhood in problems of parametric identification of multivariable nonlinear systems and shows an application in a complex problem.