Multidisciplinary Optimization of a Mixed-Flow Impeller With 140 Parameters and Its Shapley Additive Explanations

In recent years, we have made several improvements to the geometric parameterization method, the surrogate model method, and the sampling method, with the goal of making the traditional surrogate model-based optimization method applicable to aerodynamic optimization of hundreds of parameters with reasonable computational cost. However, increasing the number of control parameters raises two additional issues. First, the impeller geometry becomes too complex to ensure the required mechanical performance. Second, the optimization mechanism becomes difficult to understand with too many parameters. To address the first issue, this paper builds a multidisciplinary optimization platform to achieve the optimization of a large flow coefficient mixed-flow impeller under 140 control parameters, resulting in a significant improvement in both aerodynamic and mechanical performance. To address the latter, a novel machine learning interpretation tool, Shapley additive explanations (SHAP), is introduced in this paper. Using this methodology, the contribution of all 140 parameter values in the final optimal impeller to each aspect of the performance improvement is presented in this paper, providing the first in-depth understanding of the intricate mechanisms involved in the multidisciplinary optimization of hundreds of control parameters.