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3rd International Conference on Engineering Design and Optimization (ICEDO 2012)

作者： Zhang, Siliang Zhu, Ping Chen, Wei Shanghai Jiao Tong Univ Shanghai Key Lab Digital Autobody Engn Shanghai 200240 Peoples R China

ISBN: (纸本)9783037854822

Metamodeling techniques are commonly used to replace expensive computer simulations in complex engineering optimization problems. Due to the discrepancy between the simulation model and metamodel, the prediction error in predicted responses may lead to a wrong solution. To balance the predicted mean and prediction error, the efficient global optimization (EGO) algorithm using Kriging predictor can be used to explore the design space and find next sample to adaptively improve the fitting accuracy of the predicted responses. However in conventional EGO algorithm, adding one point per iteration may be not efficient for the complex engineering problems. In this paper, a new multi-point sequential sampling method is proposed to include multiple points per iteration. To validate the benefits of the proposed multi-point sequential sampling method, a mathematical example and a highly-nonlinear automotive crashworthiness design example are illustrated. Results show that the proposed method can efficiently mitigate the prediction error and find the global optimum using fewer iterations.

关键词： sequential sampling method Multi-point Expected improvement criterion Automotive lightweight design

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EXTENDED OBJECTIVE-ORIENTED sequential sampling method FOR ROBUST DESIGN OF COMPLEX SYSTEMS AGAINST DESIGN UNCERTAINTY

EXTENDED OBJECTIVE-ORIENTED SEQUENTIAL SAMPLING METHOD FOR R...

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ASME International Design Engineering Technical Conferences/Computers Information in Engineering Conference

作者： Zhang, Siliang Zhu, Ping Arendt, Paul D. Chen, Wei Shanghai Jiao Tong Univ State Key Lab Mech Syst & Vibrat Shanghai 200030 Peoples R China NW Univ Dept Mech Engn Evanston IL USA

ISBN: (纸本)9780791845011

In robust design of complex systems, metamodeling techniques are commonly used to replace expensive computer simulations. To improve the sampling efficiency, efforts have been made towards developing objective-oriented sequential sampling methods for deterministic problems. In this paper, an extended objective-oriented sequential sampling method is proposed for robust design, with an emphasis on those problems with uncertainty in design variables. The method involves quantitative assessment of the effects of metamodeling uncertainty on the robust responses, as well as a sequential strategy of choosing samples to adaptively improve the predicted robust response. To validate the benefits of the sequential strategy, two mathematical examples are illustrated first. This is followed by an automotive crashworthiness design example, a highly expensive and non-linear problem. Results show that the proposed method can mitigate the effect of both metamodeling uncertainty and design uncertainty, and more efficiently identify the robust solution compared to the one-stage sampling approach that is commonly used in practice.

关键词： Objective-oriented sequential sampling method Kriging robust design crashworthiness design

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A New sequential sampling method for Surrogate Modeling Based on a Hybrid Metric

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JOURNAL OF MECHANICAL DESIGN 2024年第6期146卷 061705-061705页

作者： Hu, Weifei Zhao, Feng Deng, Xiaoyu Cong, Feiyun Wu, Jianwei Liu, Zhenyu Tan, Jianrong Zhejiang Univ State Key Lab Fluid Power & Mechatron Syst Hangzhou 310058 Peoples R China Zhejiang Univ Sch Mech Engn Hangzhou 310058 Peoples R China

sequential sampling methods have gained significant attention due to their ability to iteratively construct surrogate models by sequentially inserting new samples based on existing ones. However, efficiently and accurately creating surrogate models for high-dimensional, nonlinear, and multimodal problems is still a challenging task. This paper proposes a new sequential sampling method for surrogate modeling based on a hybrid metric, specifically making the following three contributions: (1) a hybrid metric is developed by integrating the leave-one-out cross-validation error, the local nonlinearity, and the relative size of Voronoi regions using the entropy weights, which well considers both the global exploration and local exploitation of existing samples;(2) a Pareto-TOPSIS strategy is proposed to first filter out unnecessary regions and then efficiently identify the sensitive region within the remaining regions, thereby improving the efficiency of sensitive region identification;and (3) a prediction-error-and-variance (PE&V) learning function is proposed based on the prediction error and variance of the intermediate surrogate models to identify the new sample to be inserted in the sensitive region, ultimately improving the efficiency of the sequential sampling process and the accuracy of the final surrogate model. The proposed sequential sampling method is compared with four state-of-the-art sequential sampling methods for creating Kriging surrogate models in seven numerical cases and one real-world engineering case of a cutterhead of a tunnel boring machine. The results show that compared with the other four methods, the proposed sequential sampling method can more quickly and robustly create an accurate surrogate model using a smaller number of samples.

关键词： sequential sampling method surrogate model hybrid metric Pareto-TOPSIS strategy learning function design of experiments Kriging design optimization design theory metamodeling multidisciplinary design and optimization product design simulation-based design

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Response Surface method Using sequential sampling for Reliability-Based Design Optimization

Response Surface Method Using Sequential Sampling for Reliab...

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ASME International Design Engineering Technical Conferences/Computers and Information in Engineering Conference

作者： Zhao, Liang Choi, K. K. Lee, Ikjin Du, Liu Univ Iowa Coll Engn Dept Mech & Ind Engn Iowa City IA 52242 USA

ISBN: (纸本)9780791849026

Traditional RBDO requires the sensitivity for both the most probable point (MPP) search in inverse reliability analysis and design optimization. However, the sensitivity is often unavailable or difficult to compute in complex multi-physics or multidisciplinary engineering applications. Hence, the response surface method (RSM) is often used to calculate both function evaluations and sensitivity effectively. Researchers have been developing the RSM for decades, and yet are still searching for an approach with an efficient sampling method for fast convergence while meeting the accuracy criteria. This paper proposes a new adaptive sequential sampling method to be integrated with the Kriging method for RBDO. By using the bandwidth of the prediction interval from the Kriging method, a new sampling strategy and a new local response surface accuracy criteria are proposed. In this sequential sampling method, the response surface is initiated using very few samples. An additional sampling point will then be determined by finding the point that has the largest absolute ratio between the bandwidth of the prediction interval and the predicted response within a neighboring area of current point of interest. The insertion of additional sampling will continue until the accuracy criterion of the response surface in the neighborhood of the current point of interest is achieved. Case studies show this proposed adaptive sequential sampling technique yields better result in terms of convergence speed compared with other sampling methods, such as the Latin hypercube sampling and the grid sampling, when the same sample size is used. Both a highly nonlinear mathematical example and a vehicle durability engineering example show that the proposed RSM yields accurate RBDO results that are comparable to the sensitivity-based RBDO results, as well as significant savings in computational time for function evaluation and sensitivity computation.

关键词： sequential sampling method Response Surface method (RSM) Kriging method Gaussian Stochastic Process Prediction Interval Reliability-Based Design Optimization (RBDO)

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Robust Expected Violation Criterion for Constrained Robust Design Problems and Its Application in Automotive Lightweight Design

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Journal of Shanghai Jiaotong university(Science) 2013年第3期18卷 257-263页

作者： ZHANG Si-liang ZHU Ping CHEN Wei Shanghai Key Laboratory of Digital Autobody Engineering Shanghai Jiaotong University Shanghai 200240 China Department of Mechanical Engineering Northwestern University Evanston IL 60201 USA

Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.

关键词： robust design robust expected violation (REV) sequential sampling method automotive lightweight design

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