Enhanced single-loop method for efficient reliability-based design optimization with complex constraints

Keshtegar, Behrooz; Hao, Peng

doi:10.1007/s00158-017-1842-x

Cited by 58 publications

(22 citation statements)

References 48 publications

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“…In addition, researches show that θ k is not beneficial to improve computation efficiency in CGA. Therefore, θ k is changed into (14) in MCGA, and the iterative approach of the MCGA is formulated by…”

Section: B Existing Reliability Analysis Tools In Rbdomentioning

confidence: 99%

“…In FORM, the HL-RF method is often used in engineering practice because of its simple and efficient characteristics. However, iterative oscillation and low efficiency could be caused for a performance function with a high nonlinearity [12]- [14]. In RBDO, the PMA of the double loop method transforms the probability constraint problem into an optimization problem with the constraint function of target reliability index, then the minimum performance target point (MPTP) can be obtained through continuously searching in PMA.…”

Section: Introductionmentioning

confidence: 99%

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A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

2020

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To improve the efficiency of structural reliability-based design optimization (RBDO) based on the performance measure approach (PMA), a modified conjugate gradient approach (MCGA) is proposed for RBDO with nonlinear performance function. In PMA, the advanced mean value (AMV) approach is widely used in engineering because its simplicity and efficiency. However, the AMV method shows the inefficient and unstable results for structural performance function with high nonlinearity in RBDO. To overcome this shortcoming, the proposed MCGA method improves the efficiency of solution by modifying the relevant parameters of conjugate gradient approach (CGA) and the direction of conjugate gradient algorithm for searching the optimal design point. Finally, three numerical examples with highly nonlinear performance function and an optimization design example of speed reducer are presented. Compared with different methods, the results show that the MCGA method exhibited the better efficiency and robustness in structural reliability and RBDO analyses. INDEX TERMS Reliability-based design optimization, modified conjugate gradient approach, advanced mean value, performance measure approach, reliability analysis.

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Section: B Existing Reliability Analysis Tools In Rbdomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

2020

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“…[41][42][43] To improve the robustness of single-loop methods in highly nonlinear problems, some enhanced single-loop methods have been developed. 44,45 For HRBDO-RI, Du et al 46 develop a decoupled method, where the inverse reliability analysis and optimization procedure are separately performed. To avoid the interval-constrained optimization in HRBDO-RI, Xia et al 47 develop a hybrid perturbation inverse mapping method to estimate the reliability of constraints.…”

Section: Introductionmentioning

confidence: 99%

A new hybrid reliability‐based design optimization method under random and interval uncertainties

Zhang

Gao

Xiao

2020

Numerical Meth Engineering

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Summary This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI.

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“…Commonly used uncertainty optimization frameworks are derived from the FORM and the SORM. Based on the coupling between the uncertainty analysis and the optimization process, the methods can be divided into three groups: double loop approach (Keshtegar and Hao 2017;Meng et al 2015;Youn et al 2005), single loop approach (Keshtegar and Hao 2016;Keshtegar and Hao 2018) and decoupled approach (Du and Chen 2004;Meng et al 2016). The framework based on gradient-based optimization has attracted attention in recent years (Keshavarzzadeh et al 2017;Keshavarzzadeh et al 2016;Torii et al 2017).…”

Section: Introductionmentioning

confidence: 99%

A gradient-based uncertainty optimization framework utilizing dimensional adaptive polynomial chaos expansion

Fang

Gong

et al. 2018

Struct Multidisc Optim

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To improve the efficiency of solving uncertainty design optimization problems, a gradient-based optimization framework is herein proposed, which combines the dimension adaptive polynomial chaos expansion (PCE) and sensitivity analysis. The dimensional adaptive PCE is used to quantify the quantities of interest (e.g. reliability, robustness metrics) and the sensitivity. The dimensional adaptive property is inherited from the dimension adaptive sparse grid, which is used to evaluate the PCE coefficients. Robustness metrics, referred to as statistical moments, and their gradients with respect to design variables are easily derived from the PCE, whereas the evaluation of the reliability and its gradient require integrations. To quantify the reliability, the framework uses the Heaviside step function to eliminate the failure domain and calculates the integration by Monte Carlo Simulation with the function replaced by PCE. The PCE is further combined with Taylor's expansion and the finite difference to compute the reliability sensitivity. Since the design vector may affect the sample set determined by dimension adaptive sparse grid, the update of the sample set is controlled by the norm variations of the design vector. The optimization framework is formed by combining reliability, robustness quantification and sensitivity analysis and the optimization module. The accuracy and efficiency of the reliability quantification, as well as the reliability sensitivity, are verified through a mathematical example, a system of springs, and a cantilever beam. The effectiveness of the framework in solving optimization problems is validated by multiple limit states example, a truss optimization example, an airfoil optimization example and an ONERA M6 wing optimization problem. The results demonstrate that the framework can obtain accurate solutions at the expense of a manageable computational cost.

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Enhanced single-loop method for efficient reliability-based design optimization with complex constraints

Cited by 58 publications

References 48 publications

A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

A Modified Conjugate Gradient Approach for Reliability-Based Design Optimization

A new hybrid reliability‐based design optimization method under random and interval uncertainties

A gradient-based uncertainty optimization framework utilizing dimensional adaptive polynomial chaos expansion

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