Convergence of polynomial chaos expansion based estimates of acoustic field and array beam response probability density functions.

2011 ◽  
Vol 129 (4) ◽  
pp. 2601-2601
Author(s):  
Thomas J. Hayward ◽  
Roger M. Oba
Keyword(s):  
Probability Density ◽  
Acoustic Field ◽  
Polynomial Chaos ◽  
Response Probability ◽  
Polynomial Chaos Expansion ◽  
Probability Density Functions ◽  
Density Functions ◽  
Chaos Expansion

The Rapid Uncertainty Prediction of the Ocean-Acoustic Coupled Model

2020 ◽  
Author(s):  
Baolong Cui ◽  
Wuhong Guo
Keyword(s):  
Computational Complexity ◽  
Acoustic Field ◽  
Sound Speed ◽  
Polynomial Chaos ◽  
Coupled Model ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Uncertainty Distribution ◽  
Uncertainty Prediction ◽  
Sound Speed Structure

<p>Focusing on the rapid prediction of acoustic field uncertainty in environment with temporal and spatial sound speed perturbation, evolvement of sound speed structure over time is predicted based on the ocean-acoustic coupled model to obtain the uncertainty distribution of the vertical structure of sound speed. Further, a method combining  the arbitrary polynomial chaos expansion with the empirical orthogonal function is proposed to reduce the dimensionality of uncertain parameters and to obtain the uncertainty distribution of the acoustic field. Simulations have shown that the computational complexity can be reduced by 2 orders of magnitude compared to the conventional polynomial chaos expansion while ensures the same precision. Moreover, the computational complexity is not influenced by the complexity of the sound speed profile. The acoustic field and uncertainty predicted in uncertain environment by proposed method also have been tested with the experimental data.</p>

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

2015 ◽  
Vol 63 (2) ◽  
pp. 413-422 ◽  
Author(s):  
R. Lasota ◽  
R. Stocki ◽  
P. Tauzowski ◽  
T. Szolc
Keyword(s):  
Probability Distribution ◽  
Probability Density ◽  
Vibration Amplitude ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Robust Design Optimization ◽  
Chaos Expansion ◽  
Rotor Shaft ◽  
Sparse Polynomial

Abstract 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

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