An Efficient Interior Point Algorithm for Stochastic Optimization of Dynamical Systems

Abstract eng:
Structural optimization is concerned with achieving an optimal design while satisfying certain constraints. In most structural engineering applications response predictions are based on models whose parameters are uncertain. Under uncertain conditions the field of reliability-based optimization provides a realistic and rational framework for structural design which explicitly accounts for the uncertainties. Due to uncertain conditions reliability-based formulations are considerable more involved that their deterministic counterpart. This difference is especially critical when dealing with design problems involving dynamical systems under uncertain loadings characterized by stochastic processes. In general such characterization requires numerically involved models described by a large number of uncertain parameters. In this context, the optimization scheme may require the evaluation of costly objective and constraint functions during the optimization process. In this work an efficient feasible direction interior point algorithm is implemented for solving reliability-based optimization problems of high dimensional stochastic dynamical systems. The reliability based optimization problem is formulated as the minimization of an objective function subject to deterministic and reliability constraints (Jensen et al. 2009). The algorithm consists of fixed point iterations to solve the Karush-Kuhn-Tucker first-order optimality conditions. For this purpose, a quasi-Newton iteration is used to solve the corresponding nonlinear system of equations (Herskovits and Santos 1997). At each iteration a feasible descent direction is defined by solving a couple of linear systems. To determine a new point, an inexact line search along the feasible descent direction is carried out. A numerical example is presented to illustrate the effectiveness of the proposed methodology. The example problem and additional numerical validations showed that the proposed algorithm converges in a relatively small number of iterations. This in turn implies that only a moderate number of reliability estimates has to be performed during the entire optimization process.

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