Structural optimization considering dynamic reliability constraints via probability density evolution method and change
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RESEARCH PAPER
Structural optimization considering dynamic reliability constraints via probability density evolution method and change of probability measure Jianbing Chen 1
&
Jiashu Yang 1 & Hector Jensen 2
Received: 24 December 2019 / Revised: 22 March 2020 / Accepted: 26 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The present paper presents a framework for solving dynamic reliability–based design optimization (DRBDO) problems. The proposed approach is based on a sequential approximate programming technique, where the solution of the original design problem is obtained by converting it into a sequence of sub-optimization problems with a simple explicit algebraic structure. The technique is combined with the probability density evolution method (PDEM) for the purpose of estimating the reliability and/or the failure probability at the different designs in an efficient manner. The change of probability measure (COM), a strategy based on the Radon-Nikodym derivative, is employed to estimate the sensitivity information required by the optimization scheme. Based on this strategy, the sensitivity information can be obtained without any additional function evaluation. Thus, the numerical efforts associated with the reliability assessment and sensitivity analysis can be considerably reduced. The results of the numerical examples indicate that the proposed method is an effective and efficient tool for solving a class of DRBDO problems. Keywords Change of probability measure . Dynamic reliability . Probability density evolution method . Reliability-based design optimization . Sensitivity
1 Introduction Structural optimization has long been recognized as a powerful design tool for engineering structures (Haftka and Gürdal 1992). It provides a rational approach to design structures which can economically fulfill the prescribed constraints on serviceability and safety. Nevertheless, uncertainties in material properties, geometrical properties, and loadings are Responsible Editor: Jianbin Du * Jianbing Chen [email protected] Jiashu Yang [email protected] Hector Jensen [email protected] 1
State Key Laboratory of Disaster Reduction in Civil Engineering & College of Civil Engineering, Tongji University, Shanghai 200092, People’s Republic of China
2
Department of Civil Engineering, Santa Maria University, Valparaiso, Chile
usually inevitable (Ang and Tang 2006; Melchers and Beck 2018). Such uncertainties could affect the structural performance in a significant manner. Therefore, taking into account the uncertainties in structural optimization is an imperative task for the engineering practice. In this regard, reliabilitybased design optimization (RBDO) is an appropriate framework to explicitly combine uncertainties and structural optimization. The investigations on RBDO can be dated back to the 1960s. A number of methods have been developed in the past. Among them, the Karush-Kuhn-Tucker (KKT) condition– based single loop method (Agarwal et al. 2007; Kuschel and Rackwitz 1
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