Assessment of probabilistic methods for mistuned bladed disk vibration

In this paper, the accuracy and efficiency of various probabilistic methods are assessed for the vibration analysis of a mistuned bladed disk system with small, random blade-to-blade differences. A quantity of primary engineering interest is examined, namely the maximum resonant response amplitude of any blade in the assembly over a given frequency range. For the purpose of comparing the probabilistic methods, the response amplitude of a specific blade at a given resonant frequency is also considered. Initially, the following methods are applied to analyze the effects of small blade stiffness uncertainties for a lumped-parameter model of a 29-blade rotor: (1) a first-order reliability method (FORM), (2) a second-order reliability method (SORM), (3) an advanced mean value (AMV+) method, (4) a response surface method (RSM) using a moving least squares approach, and (5) a radius-based importance sampling method. In general, these methods do well in predicting the response statistics of a given blade at a given frequency, at least in limited ranges of uncertainties. However, all of these reliability-based methods fail to capture the statistics of the maximum resonant response across the blade assembly, regardless of the range of uncertainties. To circumvent this shortcoming, an accelerated Monte Carlo simulation (MCS) approach is also considered, which involves a combination of a small-sample MCS and a Weibull probability distribution fit. This method is found to predict the statistics of the largest resonant blade response over the blade assembly with great accuracy and efficiency. It is thus better suited to the analysis of bladed disk response statistics than the class of reliability-based probabilistic methods.