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By Seung-Kyum Choi

This publication presents readers with an realizing of the basics and functions of structural reliability, stochastic finite point process, reliability research through stochastic growth, and optimization less than uncertainty. It examines using stochastic expansions, together with polynomial chaos growth and Karhunen-Loeve enlargement for the reliability research of useful engineering difficulties.

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In the transformation procedure, the design vector X is transformed into the vector of standardized, independent Gaussian variables, U. 2. Because it makes the most significant contribution to the nominal failure probability Pf ) ( E ) , this design point is called the Most Probable failure Point (MPP).

14a). Thus, to ensure accurate analysis results, the engineer should consider the stochastic and modeling complexities of the problem before determining the size and number of elements. 2 Covariance Function The degree of correlation between the random process at nearby points can be specified by covariance functions. If the variability of the random field is entirely random, the covariance function will decay asymptotically to zero. The points close together yield high correlation, and the lag points, vice versa.

19, (3), 1997, pp. 283-336. , Introduction to Linear Regression Analysis, Wiley, New York, 1992. , Probability, Random Variables, and Stochastic Processes, Third Edition. McGraw-Hill, New York, 1991. , Detection, Estimation, and Modulation Theory Part I, Wiley, New York, 1971. , 1983. , Schuëller, G. , “Random Fields and Stochastic Finite Elements,” Journal of Structural Safety, Special Issue, No. 3, 1986, pp. 143-166. 3 Probabilistic Analysis This chapter presents several probabilistic analysis methods, including the firstand second-order reliability methods, Monte Carlo simulation, Importance sampling, Latin Hypercube sampling, and stochastic expansions.

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