Blade Arrangement Optimization for Mistuned Bladed Disk Based on Gaussian Process Regression and Genetic Algorithm

Mistuning phenomena exist in the bladed disk due to the inevitable deviations among blades' properties, e.g., stiffness, mass, geometry, etc., leading to localization and response amplification. The dynamic performance of mistuned bladed disk is sensitive to the arrangement of blades. The blade arrangement optimization aims to obtain the optimal arrangement that minimizes the influence of mistuning. In this paper, a framework of high efficiency is raised to deal with the challenge of high computational cost this optimization. It comprehensively utilizes mixed-dimensional finite element model (MDFEM), Gaussian process (GP) regression, and genetic algorithm (GA). The MDFEM can perform mistuned modal analysis efficiently and provides the training set of GP regression rapidly. The GP model, as a surrogate model, predicts the desired dynamic performance directly without calculating the numerical model and can function as fitness function in optimization. GA has the capability to deal with combinatorial problems and is a good option for problems with large search domains and several local maxima/minima. The techniques and processes of three methods are illustrated in detail. Case studies, based on a real turbine, are concretely presented in a gradually progressive manner to test and verify the effectiveness, accuracy, and efficiency of methods and entire framework step by step. The results show the satisfactory optimal arrangement for a randomly chosen set of mistuned blades, and the influence of mistuning is reduced indeed. The time cost of the optimization has been reduced several orders of magnitude. This framework can be a promising approach for the blade arrangement optimization problem.