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Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Lasota R., Stocki R., Tauzowski P., Szolc T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 2

413--422

The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for an accurate representation of the probability density functions with an exponential behavior, which appears to be characteristic for the investigated rotor-shaft responses. Performing multiple numerical tests for a range of sample sizes it was found that the sparse polynomial chaos method provides the best balance between the accuracy and computational effectiveness in estimating the unknown probability distribution of the maximal vibration amplitude.

Scatter assessment of rotating system vibrations due to uncertain residual unbalances and bearing properties

Stocki R., Lasota R., Tauzowski P., Szolc T.

Computer Assisted Methods in Engineering and Science

2012

Vol. 19, no. 2

95-120

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for e?cient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the eight-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration responses is the inherently random nature of residual unbalances as well as stiffeness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based on Taylor series expansion in most of the analyzed cases fail to approximate the rotor-shaft response statistics.