Robust design approach to the minimization of functional performance variations of products and systems

Abstract

Functional performance variations of products and systems are often used to measure the qualities of products and systems considering the changes in the design parameter values caused by uncertainties. A robust design approach has been developed in this research to minimize the functional performance variations considering the design parameter uncertainties by identifying the boundaries of the functional performance variations through optimization. In this work, a mathematical model is developed to describe the relationships among functional performance, design configurations and parameters, and design parameter uncertainties. A multi-level optimization model is established to identify: (1) The optimal design configuration, (2) the optimal values of design parameters, and (3) the boundaries of functional performance variations. Sensitivity analysis considering the impact of parameter uncertainties on functional performance variation boundaries has also been conducted. A case study on the design of a truss system has been conducted. Case study results show that the sensitivities of functional performance variation boundaries to the design parameter uncertainties can be reduced significantly using the new robust design approach.

Graphical abstract

Keywords

product design / robust design / design optimization / uncertainties

References

[1] Pahl G, Beitz W. Engineering Design: A Systematic Approach.Berlin: Springer, 1988

[2] Xue D, Cheing S Y, Gu P. Configuration design considering the impact of design changes on downstream processes based upon the axiomatic design approach. Journal of Engineering Design, 2006, 17(6): 487–508

[3] Taguchi G. Taguchi on Robust Technology Development: Bringing Quality Engineering Upstream. New York: ASME Press, 1993

[4] Gu P, Lu B, Spiewak S. A new approach for robust design of mechanical systems. CIRP Annals, 2004, 53(1): 129–133

[5] Zhan J, Luo Y. Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model. Frontiers of Mechanical Engineering, 2019, 14(2): 201–212

[6] Zang C, Friswell M I, Mottershead J E. A review of robust optimal design and its application in dynamics. Computers & Structures, 2005, 83(4–5): 315–326

[7] Zhang Y. Principle of maximum entropy for reliability analysis in design of machine components. Frontiers of Mechanical Engineering, 2019, 14(1): 21–32

[8] Zhang J, Li S, Bao N, A robust design approach to determination of tolerance of mechanical products. CIRP Annals, 2010, 59(1):195–198

[9] Jia X, Jiang C, Fu C, Uncertainty propagation analysis by an extended sparse grid technique. Frontiers of Mechanical Engineering, 2019, 14(1): 33–46

[10] Zhang J, Wu M, Peng Q, Design for interface stiffness of mechanical products using integrated simulation and optimization under uncertainty. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2020, 6(2): 021006

[11] Taguchi G. Performance analysis design. International Journal of Production Research, 1978, 16(6): 521–530

[12] Murphy T, Tsui K, Allen J. A review of robust design methods for multiple response. Research in Engineering Design, 2005, 15(4): 201–215

[13] Beyer H G, Sendhoff B. Robust optimization—A comprehensive survey. Computer Methods in Applied Mechanics and Engineering, 2007, 196(33–34): 3190–3218

[14] Zhang Y. Reliability-based robust design optimization of vehicle components, Part I: Theory. Frontiers of Mechanical Engineering, 2015, 10(2): 138–144

[15] Hasenkamp T, Arvidsson M, Gremyr I. A review of practices for robust design methodology. Journal of Engineering Design, 2009, 20(6): 645–657

[16] Zhou X, Ruan X, Gosling P. Robust design optimization of variable angle tow composite plates for maximum buckling load in the presence of uncertainties. Composite Structures, 2019, 223: 110985

[17] Parkinson A, Sorensen C, Pourhassan N. A general approach for robust optimal design. Journal of Mechanical Design, 1993, 115(1): 74–80

[18] Huang B, Du X. Analytical robustness assessment for robust design. Structural and Multidisciplinary Optimization, 2007, 34(2): 123–137

[19] Fonseca J R, Friswell M I, Lees A W. Efficient robust design via Monte Carlo sample reweighting. International Journal for Numerical Methods in Engineering, 2007, 69(11): 2279–2301

[20] Wang H, Gong Z, Huang H Z, System reliability based design optimization with Monte Carlo simulation. In: Proceedings of the International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. Chengdu: IEEE, 2012, 1143–1147

[21] Du X, Chen W. Towards a better understanding of modeling feasibility robustness in engineering design. Journal of Mechanical Design, 2000, 122(4): 385–394

[22] Mayda M, Choi S K. A reliability-based design framework for early stages of design process. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39(6): 2105–2120

[23] Mayda M. An efficient simulation-based search method for reliability-based robust design optimization of mechanical components. Mechanika, 2017, 23(5): 696–702

[24] Zhang X, He D. A reliability-based robust design method for the sealing of slipper-swash plate friction pair in hydraulic piston pump. IEEE Transactions on Reliability, 2018, 67(2): 459–469

[25] Wu J. A robust optimization for the frequency and decoupling ratio of a powertrain mounting system based on interval analysis. International Journal of Automotive Technology, 2012, 13(3): 409–422

[26] Do D, Gao W, Song C, Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters. International Journal for Numerical Methods in Engineering, 2016, 108(10): 1198–1229

[27] Li W, Xiao M, Yi Y, Maximum variation analysis based analytical target cascading for multidisciplinary robust design optimization under interval uncertainty. Advanced Engineering Informatics, 2019, 40: 81–92

[28] Gao W. Interval finite element analysis using interval factor method. Computational Mechanics, 2007, 39(6): 709–717

[29] Ouyang L, Ma Y, Byun J, An interval approach to robust design with parameter uncertainty. International Journal of Production Research, 2016, 54(11): 3201–3215

[30] Sun W, Dong R, Xu H. A novel non-probabilistic approach using interval analysis for robust design optimization. Journal of Mechanical Science and Technology, 2009, 23(12): 3199–3208

[31] Yoo D, Lee I. Sampling-based approach for design optimization in the presence of interval variables. Structural and Multidisciplinary Optimization, 2014, 49(2): 253–266

[32] Wu J, Gao J, Luo Z, Robust topology optimization for structures under interval uncertainty. Advances in Engineering Software, 2016, 99: 36–48

[33] Xia B, Lu H, Yu D, Reliability-based design optimization of structural systems under hybrid probabilistic and interval model. Computers & Structures, 2015, 160: 126–134

[34] Jiang C, Zheng J, Han X. Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: A review. Structural and Multidisciplinary Optimization, 2018, 57(6): 2485–2502

[35] Xia T, Li M. A sequential approach for robust multidisciplinary design optimization under mixed interval and probabilistic uncertainties. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2019, 5(2): 020905

[36] Zhang J, Chen Y, Xue D, Robust design of configurations and parameters of adaptable products. Frontiers of Mechanical Engineering, 2014, 9(1): 1–14

[37] Zhang J, Xue D, Gu P. Adaptable design of open architecture products with robust performance. Journal of Engineering Design, 2015, 26(1–3): 1–23

[38] Hong G, Hu L, Xue D, Identification of the optimal product configuration and parameters based on individual customer requirements on performance and costs in one-of-a-kind production. International Journal of Production Research, 2008, 46(12): 3297–3326

[39] Long Y, Bao S H, Yuan S. Structural Mechanics.Beijing: Higher Education Press, 2012

RIGHTS & PERMISSIONS

Higher Education Press