This paper reports on some advanced computational techniques for probabilistic analysis of turbomachinery. A description of the requirements for probabilistic analysis and several solution methods are summarized. The traditional probabilistic analysis method, Monte Carlo simulation, and two advanced techniques, the Advanced Mean Value (AMV) method and importance sampling, are discussed.
The performance of the Monte Carlo, AMV, and importance sampling methods is explored through a forced response analysis of a two degree-of-freedom Jeffcott rotor model. Variations in rotor weight, shaft length, shaft diameter, Young’s modulus, foundation stiffness, bearing clearance, viscosity, and length are considered. The cumulative distribution function of transmitted force is computed using Monte Carlo simulation and AMV at several RPM. Also, importance sampling is used to compute the probability of transmitted force exceeding a specified limit at several RPM. In both cases, the AMV and importance sampling methods are shown to give accurate solutions with far fewer number of simulations than the Monte Carlo method. These methods enable the engineer to perform accurate and efficient probabilistic analysis of realistic complex rotor dynamic models.