Reliability analysis and reliability-based optimal design of linear structures subjected to stochastic excitations

In this thesis reliability analysis and reliability-based optimal design of linear structures subjected to stochastic excitations are investigated.;In the first part, the problem of calculating the probability that the responses of a wind-excited structure exceed specified thresholds within a given time interval is considered. The failure domain of the problem can be expressed as a union of elementary failure domains whose boundaries are of quadratic form. The Domain Decomposition Method (DDM) is employed, after being appropriately extended, to solve this problem. The probability estimate of the overall failure domain is given by the sum of the probabilities of the elementary failure domains multiplied by a reduction factor accounting for the overlapping degree of the different elementary failure domains. The DDM is extended with the help of Line Sampling (LS), from its original presentation where the boundaries of the elementary failure domains are of linear form, to the current case involving quadratic elementary failure domains. An example involving an along-wind excited steel building shows the accuracy and efficiency of the proposed methodology as compared with that obtained using standard Monte Carlo simulations (MCS).;In the second part, the problem of reliability-based optimal design of linear structures subjected to stochastic excitations is considered. The global optimization method based on simulated annealing is used to address the problem, where the optimization problem is converted into the task of generating sample points (designs) according to a probability density function (PDF) suitably constructed on the feasible space of designs satisfying all the constraints. The constructed PDF ensures that the PDF value is larger at the design with smaller cost, which is desired in the optimization process, and thus the optimal design is the sample point having the largest PDF value. Transitional Markov chain Monte Carlo (TMCMC) is used for generating sample points, in order to get higher convergence rate of the stationary distribution of the Markov chain states to the constructed PDF. The generation of sample points uniformly distributed in the feasible space, which is required at the initial stage of TMCMC, is achieved by using subset simulation. To apply subset simulation and TMCMC in the concerned reliability-based optimization problem, the task of judging whether the failure probability at a design exceeds a specified threshold has to be undertaken. The DDM is utilized to perform this task. Based on the statistical properties of the failure probability estimator given by DDM, a 'minimum' computational effort, in terms of providing a reliable judgment on the relationship between the failure probability at the given design and the specified threshold, is defined so that a further reduction in the computational cost can be achieved in our proposed reliability-based optimization (RBO) algorithm. Illustrative examples are presented to show the application and the advantages of our proposed global RBO algorithm.