A novel stochastic collocation method for uncertainty propagation in complex mechanical systems

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• 作者：WuChao Qi ; SuMei Tian ; ZhiPing Qiu
• 关键词：uncertainty propagation ; stochastic collocation method ; equivalent weak form ; guided surface ; statistics ; 024601
• 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：58
• 期：2
• 页码：1-8
• 全文大小：525 KB
• 参考文献：1. Jonas C, Sven OH, Fred N. Generalizing the safety factor approach. Reliab Eng Syst Safety, 2006, 91(8): 964-73 CrossRef
  2. Gerhart IS, Adriano C, Sebastiaan H J A F, et al. Uncertainty analysis of a large-scale satellite finite element model. J Spacecraft Rockets, 2009, 46(1): 191-02 CrossRef
  3. Stéphane T, Zheng W X, Marion G, et al. Unifying some higher-order statistic-based methods for errors-in-variables model identification. Automatica, 2009, 45(8): 1937-942 CrossRef
  4. M’hamed B, Driss A. Higher-order statistics based blind estimation of non-Gaussian bidimensional moving average models. Signal Processing, 2006, 86(10): 3031-042 CrossRef
  5. Yu S N, Chen Y H. Noise-tolerant electrocardiogram beat classification based on higher order statistics of subband components. Artif Intell Med, 2009, 46(2): 165-78 CrossRef
  6. Cho H K, Rhee J. Vibration in a satellite structure with a laminate composite hybrid sandwich panel. Composite Struct, 2011, 93(10): 2566-574 CrossRef
  7. Hong S K, Bogdan I E, Matthew P C, et al. Parametric reduced-order models for predicting the vibration response of complex structures with component damage and uncertainties. J Sound Vib, 2011, 330(6): 1091-110 CrossRef
  8. Qiu Z Q, Xia Y Y, Yang J L. The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem. Comput Methods Appl Mech Eng, 2007, 196(49-2): 4965-984 CrossRef
  9. Knio O M, Maitre O P L. Uncertainty propagation in CFD using polynomial chaos decomposition. Fluid Dyn Res, 2006, 38(9): 616-40 CrossRef
  10. Loeven G J A, Witteveen J A S, Bijl H. Efficient uncertainty quantification in computational fluid-structure interactions. AIAA Paper, 2006, AIAA-2006-1634
  11. Wang X J, Qiu Z P. Nonprobabilistic interval reliability analysis of wing flutter. AIAA J, 2009, 47(3): 743-48 CrossRef
  12. Rippel M, Choi S K. Alternatives to Taylor series approximation for the variance estimation in robust design. AIAA Paper, 2010, AIAA-2010-9083
  13. Qi W C, Qiu Z P. A collocation interval analysis method for interval structural parameters and stochastic excitation. Sci China-Phys Mech Astron, 2012, 55(1): 66-7 CrossRef
  14. Christos E P, Hoi Y. Uncertainty estimation and Monte Carlo simulation method. Flow Meas Instrum, 2001, 12(4): 291-98 CrossRef
  15. Herrador M A, Gonzalez A G. Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation. Talanta, 2004, 64(2): 415-22 CrossRef
  16. Kamran S, Pooneh N. A new optimized uncertainty evaluation applied to the Monte-Carlo simulation in platinum resistance thermometer calibration. Measurement, 2010, 43(7): 901-11 CrossRef
  17. Kaveh M, Jay R L. A Monte-Carlo game theoretic approach for multi-criteria decision making under uncertainty. Adv Water Resour, 2011, 34(5): 607-16 CrossRef
  18. Abhishek H, Raktim B. Beyond Monte Carlo: A computational framework for uncertainty propagation in planetary entry, descent and landing. AIAA Paper, 2010, AIAA-2010-8029
  19. Lu Z M, Zhang D X. On importance s
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Chinese Library of Science
  Mechanics, Fluids and Thermodynamics
  Physics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1927

文摘

This paper presents a novel stochastic collocation method based on the equivalent weak form of multivariate function integral to quantify and manage uncertainties in complex mechanical systems. The proposed method, which combines the advantages of the response surface method and the traditional stochastic collocation method, only sets integral points at the guide lines of the response surface. The statistics, in an engineering problem with many uncertain parameters, are then transformed into a linear combination of simple functions-statistics. Furthermore, the issue of determining a simple method to solve the weight-factor sets is discussed in detail. The weight-factor sets of two commonly used probabilistic distribution types are given in table form. Studies on the computational accuracy and efforts show that a good balance in computer capacity is achieved at present. It should be noted that it’s a non-gradient and non-intrusive algorithm with strong portability. For the sake of validating the procedure, three numerical examples concerning a mathematical function with analytical expression, structural design of a straight wing, and flutter analysis of a composite wing are used to show the effectiveness of the guided stochastic collocation method.