A sensitivity based heuristic for optimal blade arrangement in a linear mistuned rotor

This paper investigates methodologies for finding optimal or near-optimal blade arrangements in a bladed disk with inserted blades for minimizing or maximizing blade response amplification due to mistuning in material properties of the blades. The mistuning in the blades is considered to be known, and only their arrangement is modifiable. Hence, this is a problem in discrete optimization, particularly combinatorial optimization where the objective of response amplification is a nonlinear function of the blade arrangement. Previous studies have treated mistuning as a continuous parameter to analyze its effects on the response amplification. Sensitivity metrics have proven to be an important tool in quantifying the effects of mistuning. One such sensitivity metric is used here to formulate an iterative heuristic approach to solve the optimization problem. A component mode mistuning reduced order model is used for fast evaluations of the dynamic responses of a bladed disk with a given blade arrangement. At any iteration the sensitivity of the maximum response of the current rotor design to changes in blade stiffnesses due to changes in the blade arrangement is used to predict the arrangement for the following iteration. In addition to the proposed sensitivity-based approach, we use genetic algorithms to find optimal arrangements and compare results with the heuristic approach.