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A novel reliability-based robust design optimization method integrating a multivariate quality loss function and advanced finite step length

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ENGINEERING optimization 2025年

作者： Zhang, Duo Li, Yonghua Zhang, Xu Zhang, Dong Xu Dalian Jiao Tong Univ Sch Locomot & Rolling Stock Engn Dalian Peoples R China Shandong Univ Sch Mech Engn Key Lab High Efficiency & Clean Mech Manufacture M Natl Demonstrat Ctr Expt Mech Engn Jinan Peoples R China

To enhance the robustness of mechanical structures and reduce fluctuations in reliability, a novel reliability-based robust design optimization method combining a multivariate quality loss function (MQLF) and advanced finite step length (AFSL) is proposed. Gaussian process regression is used to formulate an MQLF for mechanical structures, integrating multiple quality characteristic deviations, predicted quality and robustness. An AFSL method for structural reliability analysis is proposed, effectively enhancing the efficiency and accuracy of reliability calculations through conjugate gradient search and an adaptive step length adjustment formula, while also solving the reliability sensitivity using the AFSL method. A multi-objective reliability-based robust optimization model is established with the objective of the MQLF and reliability sensitivity, considering structural reliability and design variable tolerances as constraints. Practical examples demonstrate that the proposed method achieves an optimal equilibrium solution, accounting for both quality loss and reliability sensitivity, in contrast to the traditional approach.

关键词： reliability-based robust design optimization multivariate quality loss function Gaussian process regression reliability sensitivity finite step length method

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reliability-based robust design optimization with the reliability Index Approach applied to composite laminate structures

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COMPOSITE STRUCTURES 2019年 209卷 844-855页

作者： Carneiro, Goncalo das Neves Antonio, Carlos Conceicao Univ Porto Fac Engn INEGI LAETA Porto Portugal

In this paper a new approach to the reliability-based robust design optimization (RBRDO) of angle-ply composite laminate structures is presented. The problem is defined as a bi-objective robust design optimization (RDO) problem, with deterministic and probabilistic constraints. design optimization is considered as the minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix of the response functionals of the system (robustness). reliability assessment is executed by the reliability Index Approach (RIA), as an inner cycle. The key concept of this methodology is the exclusive use of evolutionary algorithms with elitist strategy, allowing for global convergence in the two optimization cycles. The RIA problem was reformulated and a set of new evolutionary operators were developed. A numerical example is presented and the results compared with other RBRDO and RDO formulations. Results show that deterministic and probabilistic structural integrity measures are quite sensitive to uncertainty, for multi-component composite structures.

关键词： Uncertainty reliability-based robust design optimization Multi-objective optimization Composite structures

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reliability-based robust design optimization: A general methodology using genetic algorithm

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期74卷 199-207页

作者： Shahraki, Ameneh Forouzandeh Noorossana, Rassoul Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

In this paper, we present an improved general methodology including four stages to design robust and reliable products under uncertainties. First, as the formulation stage, we consider reliability and robustness simultaneously to propose the new formulation of reliability-based robust design optimization (RBRDO) problems. In order to generate reliable and robust Pareto-optimal solutions, the combination of genetic algorithm with reliability assessment loop based on the performance measure approach is applied as the second stage. Next, we develop two criteria to select a solution from obtained Pareto-optimal set to achieve the best possible implementation. Finally, the result verification is performed with Monte Carlo Simulations and also the quality improvement during manufacturing process is considered by identifying and controlling the critical variables. The effectiveness and applicability of this new proposed methodology is demonstrated through a case study. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： reliability-based robust design optimization Multi-objective optimization Genetic algorithm Process capability index Most probable point

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reliability-based robust design optimization for torque ripple reduction considering manufacturing uncertainty of interior permanent magnet synchronous motor

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2020年第3期34卷 1249-1256页

作者： Jang, Gyeong Uk Kim, Chang-Wan Bae, Daesung Cho, Younghoon Lee, Jeong-Jong Cho, Seunghyeon Konkuk Univ Grad Sch Mech Design Prod Engn Seoul 05029 South Korea Konkuk Univ Sch Mech Engn Seoul 05029 South Korea Hanyang Univ Sch Mech Engn Ansan 15588 South Korea Konkuk Univ Dept Elect Engn Seoul 05029 South Korea Korea Elect Technol Inst Intelligent Mechatron Res Ctr Puchon 14502 South Korea

This study performed reliability-based robust design optimization (RBRDO) of stator and rotor shape of the IPM type electric motor to reduce the torque ripple considering uncertainties. A metamodel based on the design of experiments results, which was calculated by using 2-D electromagnetic finite element analysis, was used to calculate manufacturing uncertainties and material property distribution. As a result, the mean torque ripple of the optimum electric motor design was reduced by 56.4 % and the robustness was increased by 61.8 % compared with the initial design. The RBRDO design was compared with the designs of deterministic design optimization and reliability-based design optimization, and it was shown that, by using the RBRDO method, the optimum IPMSM can be designed to satisfying not only the minimum torque ripple but also the robustness and the reliability of output torque and torque ripple.

关键词： Interior permanent magnet synchronous motor Manufacturing uncertainty Torque ripple reliability Metamodel reliability-based robust design optimization

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reliability-based robust design optimization using anchored ANOVA expansion and truncated Edgeworth series approximation

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART E-JOURNAL OF PROCESS MECHANICAL ENGINEERING 2018年第4期232卷 408-417页

作者： Lu, Hao Zhu, Zhencai China Univ Min & Technol Coll Mech & Elect Engn Xuzhou 221116 Peoples R China China Univ Min & Technol Jiangsu Key Lab Mine Mech & Elect Equipment Xuzhou Peoples R China

based on the basic concept of reliability-based design optimization and robust design optimization, a reliability-based robust design optimization is achieved with the moment method in this work. At the first step, two methods, i.e. the anchored ANOVA expansion and truncated Edgeworth series approximation, are combined to solve the reliability constraints in the optimization procedure. The computational effort of the reliability analysis involved in the reliability-based design optimization is then reduced by the moment method. The reliability-based robust design optimization is then formulated by introducing the reliability sensitivity into the reliability-based design optimization as a sub-objective function, which is derived based on the truncated Edgeworth series expansion. The numerical examples illustrate the effectiveness and applicability of the proposed methodology and that the moment-based reliability-based robust design optimization satisfies (1) the reliability target of each constraint and (2) the minimum reliability sensitivity with respect to the mean value of the input random variables. The proposed reliability-based robust design optimization procedure could be applied to the product design under uncertain environment.

关键词： Moment method sensitivity analysis reliability-based robust design optimization Edgeworth series ANOVA expansion

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Efficient reliability-based robust design optimization of structures under extreme wind in dual response surface framework

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2020年第5期62卷 2711-2730页

作者： Datta, Gaurav Bhattacharjya, Soumya Chakraborty, Subrata Indian Inst Engn Sci & Technol Dept Civil Engn Sibpur 711103 Howrah India

This paper deals with an efficient reliability-based robust design optimization (RBRDO) of structures under extreme wind excitation. To solve such problems in the direct Monte Carlo simulation (MCS) framework, extensive computational time is required. To circumvent this, a new CDF-based RBRDO approach is proposed using the dual response surface method (RSM) framework. In the proposed approach, once the response surfaces are obtained by the dual RSM, the direct MCS can be fully avoided during optimization. Thereby, the approach evades several repetitive executions of finite element analyses code inside the optimization loop. Generally, RSM uses least squares method (LSM) which is reported to be a major source of error in few recent studies. Thus, the proposed approach utilizes the adaptive nature of moving least squares method (MLSM) for construction of response surfaces. The RBRDO is performed by using a two-criterion equivalent optimization problem, where the mean value of the cost of a structure and its standard deviation are optimized-ensuring constraint feasibility under parameter uncertainty. The dynamic response of structures necessary to define constraint functions is obtained using a random wind field model, which considers the effect of coherence and wind directionality. Two illustrative examples are presented to demonstrate the efficiency of the proposed RBRDO approach. When benchmarked through direct MCS results, the proposed MLSM-based RBRDO approach yields more accurate and robust solutions compared with that of the conventional LSM-based approach.

关键词： reliability-based robust design optimization Extreme wind load Dual response surface method Moving least squares method Parameter uncertainty

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An improved reliability-based robust design optimization method using Bayesian seemingly unrelated regression and multivariate loss function

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2022年第2期65卷 1-16页

作者： Wan, Liangqi Ouyang, Linhan Zhou, Tianyu Chen, Yuejian Nanjing Univ Finance & Econ Sch Management Sci & Engn Nanjing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Econ & Management Nanjing Peoples R China Univ Alberta Dept Mech Engn Edmonton AB Canada Tongji Univ Inst Rail Transit Shanghai Peoples R China

At present, loss function-based reliability-based robust design optimization (RBRDO) methods have been widely used to ensure reliable and robust product designs. However, conventional methods suffer from a problem that they did not consider the variance-covariance structure of responses in the loss function-based optimization strategy, which leads to an undesirable design. To address the problem, this paper proposes an improved loss function-based RBRDO method. First, the proposed method adopts Bayesian inference for the seemingly unrelated regression (SUR) model. Bayesian SUR models are applied to construct accurate response models when responses are correlated and model parameters are under uncertainty. Second, the proposed method integrates Bayesian SUR models and multivariate loss function approach into the loss function-based optimization strategy to consider the variance-covariance structure of responses. Thus, the three properties (i.e., bias, robustness, and quality of predictions) are simultaneously considered for objective functions in the loss function-based optimization strategy, in which the expected responses optimized to be close to their design targets, and the variances of both the observed and the predicted responses to be small at an optimal design. The proposed method was applied to the design of a bridge-type amplification mechanism to demonstrate its effectiveness. Results revealed that the proposed method provides a better solution than existing methods in terms of optimal design.

关键词： reliability-based robust design optimization Loss function Seemingly unrelated regression Metamodeling

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A response band-based method for time-dependent reliability-based robust design optimization

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND reliability 2024年第3期238卷 559-577页

作者： Lu, Li Wu, Yizhong Zhang, Qi Xia, Zhehao Qiao, Ping Huazhong Univ Sci & Technol Natl Intelligent Design & CNC Technol Innovat Ctr 1037 Luoyu Rd Wuhan 430074 Peoples R China Suzhou Univ Sci & Technol Sch Mech Engn Suzhou Peoples R China

In this paper, a response band-based method for time-dependent reliability-based robust design optimization is proposed. The proposed method provides a novel alternative framework, consist of a two-step transformation stage and a solving stage, to solve the time-dependent reliability-based robust design optimization problem. The original time-dependent reliability-based robust design optimization problem is transformed into an equivalent deterministic robust design optimization problem in the transformation stage, and the equivalent problem is settled in the solving stage. In the transformation stage, the dynamic modal decomposition technique and the kriging technique are combined to overcome the problem that there is no standard for both time division and observation sampling in the commonly used transformation methods. In the solving stage, an approach for constructing the response band of the objective function is presented, which significantly reduces the computational consumption of the variation evaluation of the objective function. Five cases are employed to verify the effectiveness of the proposed method.

关键词： reliability-based robust design optimization time-dependent reliability response band dynamic mode decomposition

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An efficient procedure for structural reliability-based robust design optimization

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2016年第3期54卷 511-530页

作者： Motta, Renato de S. Afonso, Silvana M. B. Univ Fed Pernambuco Dept Civil Engn Rua Acad Helio Ramos S-N Recife PE Brazil

This paper focuses on the development of an optimization tool with the aim to obtain robust and reliable designs in short computational time. The robustness measures considered here are the expected value and standard deviation of the performance function involved in the optimization problem. When using these robustness measures combined, the search of optimal design appears as a robust multiobjective optimization (RMO) problem. Reliable design addresses uncertainties to restrict the structural probability of failure. The mathematical formulation for the reliability based robust design optimization (RBRDO) problem is obtained by adding a reliability based constraint into the RMO problem. As both, statistics calculations and the reliability analysis could be very costly, approximation technique based on reduced-order modeling (ROM) is also incorporated in our procedure. The selected ROM is the proper orthogonal decomposition (POD) method, with the aim to produce fast outputs considering structural non-linear behavior. Moreover, to obtain RBRDO designs with reduced CPU time we propose others developments to be added in the integrated tool. They are: Probabilistic Collocation Method (PCM) to evaluate the statistics of the structural responses and, also, an approximated reliability constraints procedure based on the Performance Measure Approach (PMA) for reliability constraint assessment. Finally, Normal-Boundary Intersection (NBI) or Normalized Normal-Constraint (NNC) multiobjective optimization techniques are employed to obtain fast and even spread Pareto robust designs. To illustrate the application of the proposed tool, optimization studies are conducted for a linear (benchmark) and nonlinear trusses problems. The nonlinear example consider different loads level, exploring the material plasticity. The integrated tool prove to be very effective reducing the computational time by up to five orders of magnitude, when compared to the solutions obtained via classical sta

关键词： robust optimization Probabilistic collocation method reliability-based robust design optimization Multiobjective optimization Reduced-order modelling Proper orthogonal decomposition

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A general methodology for reliability-based robust design optimization of computation-intensive engineering problems

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JOURNAL OF COMPUTATIONAL design AND ENGINEERING 2022年第5期9卷 2151-2169页

作者： Lai, Xiongming Huang, Ju Zhang, Yong Wang, Cheng Zhang, Xiaodong Huaqiao Univ Coll Mech Engn & Automat Xiamen 361021 Peoples R China Huaqiao Univ Coll Comp Sci & Technol Xiamen 361021 Peoples R China

As for complex engineering structures, their single deterministic solutions need to be calculated with the help of computation-intensive finite element software, and the corresponding computation time always lasts very long. When referring to robust design optimization of complex engineering structures, the above expensive job should be repeatedly carried out for a considerable amount of time during the full optimization process. Hence, such repetitive jobs may be difficult to complete for most engineering applications. Aiming at this problem, the paper proposes a general methodology for reliability-based robust design optimization (RBRDO). Firstly, the improved formulation of the RBRDO problem is proposed based on the conventional RBRDO form, and the original probabilistic constraint functions in the improved formulation are changed into the deterministic ones by means of employing the performance measure approach (PMA). Secondly, the above-mentioned improved RBRDO problem is approximately replaced by a new sequence of approximate suboptimizations. For each suboptimization, its original PMA functions are replaced by the approximate explicit form only concerning the deterministic design variables rather than random variables. In this way, each suboptimization is deterministic. Furthermore, the trust-region method is adopted to ensure that the new sequence of suboptimization converge to the original improved RBRDO problem. Lastly, a test problem and three applications are adopted to demonstrate the effectiveness and efficiency of the above-proposed methods. PACS(optional, as per journal): 75.40.-s;***

关键词： reliability-based robust design optimization performance measure approach trust region double-loop optimizations

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