Response Surface Method for Time-Variant Reliability Analysis

Abstract

13.'Type of Report So; Period Covered 1-1-93 to 6-30-93 "14. l~.n efficient, approximate n1ethod for computing the structural reliability of uncertain systems subjected to time -varying loads is presented in this study. The method uses response surface methodology and the fast integration scheme developed by \Ven and Chen (1987). The mean and coc:f~id~nt of v~riation of the . D13Xlmum response of the structure are rn.odeled by second order polynoffiIais fItted usmg central composite designs applied to data from response time histories. The structural failure probability conditional upon the uncertain system parameter values is assumed to fol1o\v an extreme value distribution, the parameters of which are fitted by the response surface n10dels. The fast integration scheme provides a fonnulation of a limit state function which incorporates this infonnation. The failure probability over a specified time interval can then be evaluated using Monte Carlo simulation. Four numerical examples are solved by the proposed approach, with results compared against approximate solutions by existing methods. i\n empirical measure is introduced to nfovide information on the goodness-of-fit of the response surface models. The proposed method is shown to be particularly effic.ient~when used for analyzing the sensitivity of the failure probability to the distribution parameters of the uncertain systenl parameters. give civil engineers better tools to use in so1ving problen1s. In spite of this, it is still necessary to Iin1it or decrease the size and/or scope of ITl0S! realistic probJen1s to sOIllething which can be solved in a reasonable an10unt of tirne and with a practical allocation of resources; i.e., structural ITIodels often are but pale shadovvs of the reality \vhich they atternpt to portray. This is especially true in the area of safety and reliability, \vhere incorporation of eleI1Jents of uncertainty 'within the structure or load 1110dels can greatly COD1plicate the solution or Illake it inl,nractical to find \vithout further sin1DEfication. !vIanv recent advances in structural Application of Fast Integration to Create the Limit Statereliability thus seenl geared to\vard reducing the arnount of cOlnputation required. It is in1portant, ho\vever, to linlit the level of approxin1atioll so that the answer generated is a D1eaningful one.\Vith inlproved abilities to handle more con1plex structural reliability problenls, eivil engineers \"vere able to solve more difficult prob1cn1s. For instance~ SOITIe studies (e.g.~ Kin1 and \Yen, 1988; Rojiani and Bailey, 1981) have sho\vn that existing design codes fail to give consistent levels of safety benveen that required for structural cOD1ponents and the level of reliability required for the overall structure. One solution to this problern is reliability-based structural optimization which requires accurate Inethods for determining the structural reliability under a \vide array of circUD1stances. \Vhile it is a long -tenn goal to find such a The proposed method is presente...

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