Approaches for reliability based design optimization

This thesis proposes computationally efficient and robust methodologies for reliability based design optimization (RBDO). RBDO is a hierarchical optimization problem where the constraints of the optimization problem are defined in part by a second optimization problem. Therefore, the traditional RBDO problem uses a nested algorithm to obtain the optimum solution, i.e. the constraints are evaluated at the lower level optimization problem. Several algorithms have been proposed in the past to reduce the computational effort involved in obtaining a solution to a RBDO problem. However, existing literature suggests that there is still scope for improving the computational efficiency and robustness of RBDO algorithms. In this dissertation, several approaches are proposed to address these two issues in the context of three different kinds of problems, namely reliability estimation, reliability based design optimization, and reliability based topology optimization (RBTO).;The first part of the thesis addresses the reliability estimation problem where an approach based on importance sampling is suggested to improve the efficiency and robustness of simulation based reliability estimation. In this approach, a new algorithm for reliability estimation based on cross entropy and low discrepancy sampling is proposed.;In the second part of the thesis, four algorithms are proposed for solving the RBDO problem to reduce the number of function evaluations of limit state function and to improve the convergence characteristics. In the first approach, the Jacobian and Hessian computation involved in the computation of sensitivity of most probable point of failure with respect to design variables in a decoupled RBDO algorithm has been improved through the implementation of automatic differentiation techniques. In the second approach, the robustness of a reformulated uni-level RBDO based on Karush-Kuhn Tucker conditions is improved by employing a cross entropy and exterior penalty method. In the third and fourth approaches, a progressive surrogate model is developed using kriging and moving least squares technique respectively, to estimate the sensitivity of most probable point of failure with respect to design variables. The progressive surrogate model is developed using Halton sequences, which evolve through the iterations and help to achieve faster convergence to the optimum of a RBDO problem.;In the third part of the thesis, an efficient algorithm is proposed to solve a RBTO problem using the constitutive relationship of a linear elastic problem in structural mechanics. The efficiency of the proposed algorithm to obtain a solution to the RBTO problem is the same as that of a deterministic topology optimization problem.;Finally, computational efficiency and robustness of proposed approaches are demonstrated through a number of examples presented in each chapter.