Reliability-Based Design Optimization
The solution of reliability-based design optimization problems by using reduced-order models is considered in this chapter. Specifically, problems involving high-dimensional stochastic dynamical systems are analyzed. The design process is formulated in te
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Reliability-Based Design Optimization
Abstract The solution of reliability-based design optimization problems by using reduced-order models is considered in this chapter. Specifically, problems involving high-dimensional stochastic dynamical systems are analyzed. The design process is formulated in terms of a constrained nonlinear optimization problem, which is solved by a class of interior point algorithms based on feasible directions. Search directions are estimated in an efficient manner as a by-product of reliability analyses. The design process generates a sequence of steadily-improved feasible designs. Three numerical examples are presented to evaluate the performance of the interior point algorithm and the effectiveness of reduced-order models in the context of complex reliability-based optimization problems. High speedup values can be obtained for the design process without changing the accuracy of the final designs.
6.1 Motivation Structural optimization by means of deterministic mathematical programming techniques has been widely accepted as a viable tool for engineering design [2, 17]. However, in many structural engineering applications response predictions are based on models whose parameters are uncertain. This is due to a lack of information about the value of system parameters either external to the structure, such as environmental loads, or internal, such as system behavior. Although traditional approaches have been used successfully in many practical applications, a proper design procedure must explicitly consider the effects of uncertainties as they may cause significant changes in the global performance of final designs [12, 15, 31]. Under uncertain conditions, probabilistic approaches such as reliability-based formulations provide a realistic and rational framework for structural optimization, which explicitly accounts for the uncertainties [13, 28, 32, 41]. In this chapter, a reliability-based formulation characterized in terms of the minimization of an objective function subject to multiple design requirements, including standard deterministic constraints and reliability constraints, is considered.
© Springer Nature Switzerland AG 2019 H. Jensen and C. Papadimitriou, Sub-structure Coupling for Dynamic Analysis, Lecture Notes in Applied and Computational Mechanics 89, https://doi.org/10.1007/978-3-030-12819-7_6
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6 Reliability-Based Design Optimization
6.2 Optimization Problem Formulation A reliability-based design optimization problem can be characterized as a constrained nonlinear optimization problem of the form
Minx c(x) s.t. gi (x) ≤ 0 i = 1, . . . , n c si (x) ≤ 0 i = 1, . . . , n f (6.1) where x(xi , i = 1, . . . , n d ) is the vector of deterministic design variables, c(x) is the objective function, gi (x) ≤ 0, i = 1, . . . , n c , are standard constraints, and si (x) ≤ 0 , i = 1, . . . , n f , are reliability constraints. The side constraints are defined as x ∈ X , xi ∈ X i = {xi |xil ≤ xi ≤ xiu } , i = 1, . . . , n d
(6.2)
where xil and xiu are the lower and upper li
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