Efficient sampling techniques for stochastic simulation of structural systems

• Autorzy: Stocki R. , Tauzowski P. , Kleiber M.
• Języki publikacji: EN

Abstrakty

EN

One of the main obstacles in making stochastic simulation a standard design tool is its high computational cost. However, this problem can be significantly reduced by using efficient sampling techniques like optimal Latin hypercube (OLH) sampling. The paper advocates this kind of approach for scatter analysis of structural responses. After explaining the idea of the OLH sampling the principal component analysis method (PCA) is briefly described. Next, on numerical examples it is shown how this technique of statistical postprocessing of simulation results can be used in the design process. Important improvements of the estimation quality offered by OLH design of experiments are illustrated on two numerical examples, one simple truss problem and one involving finite element analysis of elastic plate. Based on numerical experiments an attempt is made to propose the sample size which for a given number of random variables provides an acceptable estimation accuracy of statistical moments of system responses and which enables more advanced statistical post-processing.

Słowa kluczowe

EN

stochastic simulation; structural system

PL

symulacja stochastyczna; system strukturalny

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2007
• Tom: Vol. 14, No. 1
• Strony: 127--140
• Opis fizyczny: Bibliogr. 12 poz., rys., tab., wykr.

Twórcy

autor

Stocki R.

autor

Tauzowski P.

autor

Kleiber M.

• Polish Academy of Science [Polska Akademia Nauk], Institute of Fundamental Technological Research, Świetokrzyska 21, 00-049 Warsaw

Bibliografia

• [1] P. Audze, V. Eglais. New approach to planning out of experiments (in Russian). In: Problems of Dynamics and Strength, vol. 35, pp. 104-107, 1977.
• [2] M.A. Crisfield. Non-linear Finite Element Analysis of Solids and Structures, vol. 1. Wiley, 1991.
• [3] A. Der Kiureghian, J.-B. Ke. The stochastic finite element method in structural reliability. Probabilistic Engineering Mechanics, 3: 83-91, 1988.
• [4] I. Doltsinis. Stochastic Analysis of Multivariate Systems in Computational Mechanics and Engineering. CIMNE, Barcelona, Spain, 1999.
• [5] M. Liefvendahl, R. Stocki. A study on algorithms for optimization of Latin hypercubes. Journal of StatisticalPlanning and Inference, 136: 3231-3247, 2006.
• [6] T.J. Mitchell. Computer construction of d-optimal first-order designs. Technometrics, 16: 211-220, 1974.
• [7] A. Nataf. Determination des distribution dont les marges sont donnees. Comptes Rendus de VAcademie desSciences, 1962.
• [8] J.-S. Park. Optimal Latin-hypercube designs for computer experiments. Journal of Statistical Planning and Inference, 39: 95-111, 1994.
• [9] M. Rosenblatt. Remarks on multivariate transformation. The Annals of Mathematical Statistics, 23: 470-472, 1952.
• [10] T.W. Simpson. A Concept Exploration Method for Product Family Design. PhD thesis, Georgia Institute of Technology, 1998.
• [11] B. Sudret, A. Der Kiureghian. Stochastic finite element and reliability. A state-of-the-art report. Technical report, Department of Civil and Environmental Engineering, University of California, Berkeley, 2000.
• [12] K.Q. Ye, W. Li, A. Sudjianto. Algorithmic construction of optimal symmetric Latin hypercubes. Journal of Statistical Planning and Inference, 90: 145-159, 2000.