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robust design optimization of dynamic and static manufacturing processes using the stochastic frontier model

MECHANICS & INDUSTRY 2025年 26卷

作者： Trabelsi, Ali Rezgui, Mohamed-Ali Amdouni, Marwan Dokkar, Atef Jmal, Hamdi Univ Tunis Higher Natl Engn Sch Tunis Lab Mech Prod & Energet LR18ES01 5 Av Taha HusseinBP 56 Bab Manara Tunis 1008 Tunisia Univ Strasbourg Mech Dept ICube Lab UMR CNRS 7357 F-67000 Strasbourg France

The paper discusses a novel method, which addresses robust design optimization of dynamic and static multi-objective processes. For a dynamic process, the optimal setting of the graded signal and input parameters are sought so that it is least sensitive to internal and external noises. In addition to addressing planned and unplanned experiments (cross-sectional and panel data), the method estimates the random and nonrandom variance components variably (i.e., returns a non-constant uncertainty at each combination level or treatment). The stochastic frontier model is utilized to ensure this purpose. For dynamic processes, the method operates in three main steps, (i) data preparation by transforming the outputs to maximization functions, (ii) estimate of the composed variation (random and non-random error components), (iii) and, composition of the process uncertainty array for each output across the signal levels. The robust design optimization solution corresponds to the levels combination of the signal and the input factors, which adds up to the lowest global uncertainty score. The applicability of the approach is then illustrated with a case study that uses one signal factor at two levels and four input factors (x1, x2, x3, and x4) at three levels each. The process responses, Y1, Y2, and Y3 are of types Dynamic Larger the Best (DLB), Dynamic Nominal the Best (DNB), and Dynamic Smaller the Best (DSB), respectively.

关键词： robust design optimization dynamic and static systems/processes Taguchi method stochastic frontier model multi-objective processes external and internal noises

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robust design optimization with limited data for char combustion

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2025年第3期68卷 1-18页

作者： Guo, Yulin Lee, Dongjin Kramer, Boris Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Hanyang Univ Dept Automot Engn Seoul South Korea

This work presents a robust design optimization approach for a char combustion process in a limited-data setting, where simulations of the fluid-solid coupled system are computationally expensive. We integrate a polynomial dimensional decomposition (PDD) surrogate model into the design optimization and induce computational efficiency in three key areas. First, we transform the input random variables to have fixed probability measures, which eliminates the need to recalculate the PDD's basis functions associated with these probability quantities. Second, using the limited data available from a physics-based high-fidelity solver, we estimate the PDD coefficients via sparsity-promoting diffeomorphic modulation under observable response-preserving homotopy regression. Third, we propose a single-pass surrogate model training that avoids the need to generate new training data and update the PDD coefficients during the derivative-free optimization. The results provide insights for optimizing process parameters to ensure consistently high energy production from char combustion.

关键词： robust design optimization Surrogate modeling Sparsity-promoting D-MORPH regression Polynomial dimensional decomposition Char combustion

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robust design optimization of gas-lubricated herringbone grooved journal bearings: Surrogate modeling and experimental validation

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TRIBOLOGY INTERNATIONAL 2025年 204卷

作者： Massoudi, Soheyl Bush, Cameron Schiffmann, Jurg Ecole Polytech Fed Lausanne Lab Appl Mech Design Lausanne Switzerland

This study experimentally validates robust designs for herringbone grooved journal bearings (HGJBs) in micro-turbocompressors, addressing manufacturing deviations that lead to rotor instabilities. Experiments on a Pelton-driven rotor system focused on maximizing the hypervolume (HV) of the feasible operational region and the signal-to-noise ratio (S/N), considering deviations in groove depths and bearing clearances. robustness was tested at 15 points using various rotor and bushing combinations, compared with non-robust control points emphasizing stability, load capacity, and loss minimization. Results showed strong alignment between surrogate model predictions and experimental data, confirming the model's effectiveness. The successful validation highlights the potential of surrogate model-assisted robust design optimization to enhance HGJB robustness in practical applications.

关键词： Herringbone grooved journal bearings Gas-lubricated bearings robust design optimization Surrogate modeling Experimental validation Manufacturing tolerances Rotordynamics

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robust design optimization for a Hairpin Winding Permanent Magnet Motor Considering Permanent Magnet Inconsistency and Manufacturing Uncertainty

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2024年第3期39卷 1601-1612页

作者： Ding, Ling Cheng, Yuan Zhao, Tianxu Cui, Shumei Yang, Mingliang Gao, Bo Li, Yukuan Harbin Inst Technol Sch Elect Engn & Automat Harbin 150001 Peoples R China Harbin Inst Technol Zhengzhou Res Inst Harbin 450000 Henan Peoples R China Harbin Inst Technol Chongqing Res Inst Chongqing 401151 Peoples R China China FAW Grp Co LTD New Energy Dev Inst Changchun 130011 Peoples R China

This article presents an effort to develop an effective method for the robust design optimization of a hairpin winding permanent magnet motor. The comprehensive influence of variable uncertainties due to PM property inconsistency and manufacturing uncertainties is considered. During the implementation of robust design optimization of the hairpin winding permanent magnet motor by using an evolution-based multi-objective optimization algorithm, one major obstacle is the huge computation cost, especially for the robust analysis process. Therefore, a two-level solution strategy, an adaptive least square support vector regression model, and a novel dominant judging condition are skillfully employed to realize the tradeoff between the computation cost and accuracy of the robust design optimization algorithm. To verify the effectiveness of the proposed method, the fluctuation and distribution of electromagnetic performance of the robust motor design are analyzed and compared with those of a deterministic motor design. Finally, a prototype of the hairpin winding permanent magnet motor is manufactured and tested to further confirm the validity of the proposed method.

关键词： Uncertainty Permanent magnet motors design optimization Torque Traction motors Reluctance motors Manufacturing robust design optimization hairpin winding permanent magnet motor manufacturing uncertainty permanent magnet inconsistency computation cost

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robust design optimization of a multi-body system with aleatory and epistemic uncertainty

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2024年 245卷

作者： Ma, Yuan-Zhuo Li, Chen-Xu Wang, You-Yu Zhang, Zhi-Yong Li, Hong-Shuang Ding, A. -Nai Rui, Xiao-Ting Hohai Univ Coll Renewable Energy 1915 Hohai Ave Changzhou 213200 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Energy & Power Engn Nanjing 210094 Peoples R China Tianjin Univ Sch Mech Engn Tianjin 300350 Peoples R China Tianjin Key Lab Nonlinear Dynam & Control Tianjin 300350 Peoples R China Nanjing Univ Sci & technol Inst Launch Dynam Nanjing 210094 Peoples R China Natl Key Lab Complex Multibody Syst Dynam Nanjing 210094 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn 29 Yudao St Nanjing 210016 Jiangsu Peoples R China

There are several issues in robust design optimization of the multi-body system with aleatory and epistemic uncertainty, such as the difficulty in the multi-source uncertainty characterization and low efficiency in dynamic modeling, analysis and the corresponding solving strategy for its robust design optimization. To address these problems, this paper firstly constructs a unified analysis framework for aleatory and epistemic uncertainty for the multi-body system based on probability theory and evidence theory. Taking a multi-body system of a shipborne artillery model as an example, the transfer matrix method is next employed to rapidly calculate the dynamic response of the muzzle. The results are compared with those by the finite element method to verify the accuracy and efficiency of the transfer matrix method. A decision model of the robust design optimization with both aleatory and epistemic uncertainty is proposed. Based on the polynomial chaos expansion-Kriging model, subset simulation optimization method and a weighted single-objective solving strategy, the multi-objective robust design optimization problem involving aleatory and epistemic uncertainty is then transformed into a singleobjective optimization one. Finally, results of both the multi-objective and weighted single-objective robust design optimization methods for the shipborne artillery model are compared to demonstrate the performance of the proposed method.

关键词： Multi-source uncertainty robust design optimization Uncertain multi-body system Subset simulation optimization Weighted single-objective method

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A gradient-assisted learning strategy of Kriging model for robust design optimization

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2024年 244卷

作者： Nan, Hang Liang, Hao Di, Haoyuan Li, Hongshuang Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn Nanjing 210016 Peoples R China China Shipbuilding Grp Res Inst 705 Xian 710077 Peoples R China

robust design optimization (RDO) is a remarkable technique for improving product quality in an uncertain environment. The double-loop structure of RDO involves uncertainty quantification which leads to a prohibitive computational issue. Kriging is used to approximate response statistics to decouple the double-loop structure of RDO. Multimodal and highly nonlinear characteristics of response statistics impede the Kriging assisted RDO from obtaining an accurate optimal solution. This paper presents a gradient-assisted (GA) learning function composed of gradient, uncertainty, and distance terms to cope with such issues. The gradient term serves as the key basis for the proposed learning function to reflect the global trend and local optimum. The uncertainty term represents the prediction credibility of candidate samples and the distance term is used to avoid the cluster of training samples. These three terms collaborate in the proposed learning function to identify the updating samples to train the Kriging model of objective function. In order to terminate the training process efficiently, a new stopping criterion based on the gradient direction is proposed. Based on the trained Kriging model, genetic algorithm is utilized to search the robust optimal solution. Three examples were used to demonstrate the advantages of the proposed method.

关键词： robust design optimization Kriging model Learning function Stopping criterion Genetic algorithm

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Analytical robust design optimization for hybrid design variables: An active-learning methodology based on polynomial chaos Kriging

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2024年 250卷

作者： Song, Chaolin Shafieezadeh, Abdollah Xiao, Rucheng Sun, Bin Tongji Univ Dept Bridge Engn Shanghai 200092 Peoples R China Ohio State Univ Dept Civil Environm & Geodet Engn Risk Assessment & Management Struct & Infrastructu Columbus OH 43210 USA

In robust design optimization, statistical moments of performance are widely adopted in formulating robustness metrics. To address the high computational costs stemming from the many-query nature of such optimizations with respect to robustness metrics, analytical formulas of the statistical moments have been developed based on surrogate models. However, existing methods consider random variables as the sole model input, which excludes, from the application scope, problems that also involve deterministic design variables. To remedy this issue, this paper proposes a new Polynomial Chaos Kriging-based methodology for efficient and accurate analytical robust design optimization. The analytical solutions for the statistical moments of performance are developed considering that the Polynomial Chaos Kriging model is established in the augmented space of the deterministic design and random variables. This is achieved by systematically decoupling associations with deterministic input from random input, providing effective solutions even when the orthonormality of the basis function is not applicable in the augmented space. This work also presents an active-learning framework enabling seamless implementation of various numerical optimization methods. Several numerical examples and a practical application illustrate the performance and superiority of the proposed method.

关键词： robust design optimization Polynomial Chaos Kriging Analytical formula robustness Hybrid random and deterministic design variables

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Sensitivity analysis and multi-objective robust design optimization of compact aero-engine nacelles

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ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS 2025年第1期19卷

作者： Tao, Guocheng Liu, Yang Ye, Zhouteng Fan, Chengwei Gong, Yanzhao Yan, Yan Cui, Jiahuan Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou 310027 Peoples R China Zhejiang Univ ZJU UIUC Inst Haining 314400 Peoples R China Beihang Univ Hangzhou Int Innovat Inst Hangzhou Peoples R China Xian Jiaotong Liverpool Univ Sch Adv Technol Suzhou Peoples R China

Future civil aero-engines are expected to feature larger bypass ratios and fan diameters to reduce specific thrust and improve propulsive efficiency, thereby lowering specific fuel consumption. These new configurations introduce design challenges, as the traditional scaling will result in the increase of nacelle drag, weight and the integration effects of aircraft. For this reason, compact nacelles are preferred for integration with next-generation civil turbofan engines. Moreover, designing and optimizing compact aero-engine nacelles is particularly challenging due to the non-linear nature of transonic aerodynamics and the diverse operating conditions experienced across the flight envelope. This work first establishes a mapping relationship between geometric parameters and the nacelle drag coefficient through surrogate models across various operating conditions. Then, sensitivity analyses are performed by applying the Sobol sequence sampling method and variance-based sensitivity analysis within the design bounds. To investigate the impact of compactness on the uncertainty of the drag coefficient, compact nacelles with various length-to-highlight radius ratios are examined. The Sobol-based sensitivity analysis reveals that the ratio $ {\boldsymbol{r}_{\boldsymbol{max}}}/{\boldsymbol{r}_{\boldsymbol{hi}}} $ rmax/rhi dominates the first-order effects, with its total-effect Sobol index remaining above 85% across all configurations. The optimized design shows significantly smaller absolute changes compared to the baseline, particularly in the nacelle cruise drag coefficient $ {\boldsymbol{C}_{\boldsymbol{D} - \boldsymbol{cruise}}} $ CD-cruise at mid-cruise condition, with the variation reduced from 0.0017 to 0.0004, indicating that the optimized nacelle design is more geometric robust and less sensitive to parameter variations. The novelty of this work lies in applying Sobol-based sensitivity analysis to quantify geometric parameter impacts on nacelle drag under uncerta

关键词： Sensitivity analysis robust design optimization nacelle surrogate model transonic

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A Heuristic robust design optimization Approach for Batch Production Permanent Magnet Actuator Consider Various Uncertainties and Life-Cycle Quality Loss

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2024年第2期39卷 805-816页

作者： Tan, Jun Chen, Hao Ye, Xuerong Zhai, Guofu Yan, Jihong Harbin Inst Technol Dept Elect Engn & Automat Harbin 150001 Peoples R China Harbin Inst Technol Sch Mechatron Engn Harbin 150001 Peoples R China

The design optimization of a robust, low-cost, and high-quality permanent magnet actuator (PMA) that meets the requirements of industrial applications presents numerous challenges. In particular, uncertainties arising from fabrication, assembly, and degradation are omnipresent and can produce erratic or infeasible solutions, complicating the robust design optimization (RDO) for PMAs. State-of-art RDO approaches treat these uncertainties as fixed contribution margins while disregarding the changes in the contribution margin, manufacturing cost, and life-cycle quality loss resulting from variations in uncertainty range and time-variant degradation. To address these issues, we propose a heuristic RDO approach for the batch production of PMAs that considers the manufacturing cost, life-cycle quality loss, and adaptive iterative step size to address these issues. Firstly, a unified manufacturing cost model is innovated to assess the complex component morphologies. Subsequently, a life-cycle dynamic quality loss model considering the time-variant degradation is established by applying the modified quality loss function, which can effectively track the losses caused by fluctuations in life-cycle quality. Based on the manufacturing cost and life-cycle quality loss models, a heuristic RDO approach with an adaptive iterative step size model is proposed, which automatically assigns the maximum bound of uncertainties and reduces the quality variation without significantly increasing manufacturing cost. Finally, a case study on a latching rotary PMA is used to illustrate the effectiveness of the proposed approach through simulation and experiment. This method achieves a 35.8% increase in robustness for batch-produced PMAs along with a 100% reduction in life-cycle quality losses at only a marginal increase of 5.9% in manufacturing costs.

关键词： Permanent magnet actuator robustness cost function life-cycle quality loss robust design optimization

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How does a resilient, flexible ammonia process look? robust design optimization of a Haber-Bosch process with optimal dynamic control powered by wind

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PROCEEDINGS OF THE COMBUSTION INSTITUTE 2023年第4期39卷 5511-5520页

作者： Verleysen, Kevin Parente, Alessandro Contino, Francesco Vrije Univ Brussel VUB Thermo & Fluid Dynam FLOW Brussels Belgium Univ Libre Bruxelles ULB Aerothermomech Dept ATM Brussels Belgium Vrije Univ Brussel VUB Brussels Inst Thermal Fluid Syst & Clean Energy BR Brussels Belgium Univ Libre Bruxelles ULB Brussels Belgium Univ Catholique Louvain UCLouvain Inst Mech Mat & Civil Engn iMMC Louvain La Neuve Belgium

Ammonia can be an essential energy vector for storing excess renewable energy during the year and release this energy when demand is high. This storage during the year provides an essential part in the energy sector for moments when there is not enough wind and sun to cover the demand. Although the Haber-Bosch is a very mature process to synthesize hydrogen and nitrogen to ammonia, it is not flexible enough to match the erratic nature of renewables. This mismatch creates the need for large intermediate hydrogen buffer tanks. To reduce the capacity of the hydrogen storage tank, we need to optimize the dynamic power-to-ammonia process in a minute time scale while considering the uncertainties linked to renewables. Therefore, we coupled a stochastic wind power process to a dynamic Power-to-Ammonia process and performed a design optimization under uncertainties, i.e. a robust design optimization, for a three-hour wind scenario while considering optimal dy-namic control. The robust design optimization showed significant trade-offs between the most productive, the most flexible, the most resilient, and robust power-to-ammonia plant designs. For the flexible and produc-tive designs, the bypass fraction and buffer feed have essential roles in achieving these designs. In the future, we will use a stochastic process to consider the uncertainty of renewable power over more extended periods (days, weeks and months) coupled with the robust design optimization of the dynamic power-to-ammonia process and investigate its effect on the intermediate hydrogen buffer size and the plant's cost. & COPY;2022 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

关键词： Ammonia synthesis Dynamic Haber-Bosch robust design optimization Stochastic process

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