A Comprehensive Procedure to Estimate the Probability of Extreme Vibration Levels Due to Mistuning

A new procedure is developed to find the probabilities of extremely high amplification factors in mistuned bladed disk vibration levels, typical of events which occur rarely. While a rough estimate can be made by curve-fitting the distribution function generated in a Monte Carlo simulation, the procedure presented here can determine a much more accurate upper bound and the probabilities of amplification factors near to that bound. The procedure comprises an optimization analysis based on the conjugate gradient method and a stochastic simulation using the importance sampling method. Two examples are provided to illustrate the efficiency of the procedure, which can be 2 or 3 orders of magnitude more efficient than Monte Carlo simulations.