Accounting for non-normal distribution of input variables and their correlations in robust optimization
Tóm tắt
In this work, metamodel-based robust optimization is performed using measured scatter of noise variables. Principal component analysis is used to describe the input noise using linearly uncorrelated principal components. Some of these principal components follow a normal probability distribution, others however deviate from a normal probability distribution. In that case, for more accurate description of material scatter, a multimodal distribution is used. An analytical method is implemented to propagate the noise distribution via metamodel and to calculate the statistics of the response accurately and efficiently. The robust optimization criterion as well as the constraints evaluation are adjusted to properly deal with multimodal response. Two problems are presented to show the effectiveness of the proposed approach and to validate the method. A basketball free throw in windy weather condition and forming of B-pillar component are presented. The significance of accounting for non-normal distribution of input variables using multimodal distributions is investigated. Moreover, analytical calculation of response statistics, and adjustment of the robust optimization problem are presented and discussed.
Tài liệu tham khảo
Abspoel M, Neelis BM, van Liempt P (2016) Constitutive behaviour under hot stamping conditions. J Mater Process Technol 228:34–42
Abspoel M, Scholting ME, Lansbergen M, An Y, Vegter H (2017) A new method for predicting advanced yield criteria input parameters from mechanical properties. J Mater Process Technol 248:161–177
Atzema E, Abspoel M, Kömmelt P, Lambriks M (2009) Towards robust simulations in sheet metal forming. Int J Mater Form 2(1):351
Barchiesi D, Kessentini S, Grosges T (2011) Uncertainty analysis of nanoparticles for cancer photothermal therapy. In: Advances in safety, reliability and risk management: ESREL 2011, p 353
Ben-Tal A, Nemirovski A (2002) Robust optimization—methodology and applications. Math Program 92(3):453–480
Bonte MHA, van den Boogaard AH, Huétink J (2008) An optimisation strategy for industrial metal forming processes. Struct Multidiscip Optim 35(6):571–586
Brancazio PJ (1981) Physics of basketball. Am J Phys 49(4):356–365
Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127(5):875–886
Cohen AC (1967) Estimation in mixtures of two normal distributions. Technometrics 9(1):15–28
Cui J, Wang D, Vlahopoulos N (2014) Containership structural design and optimization based on knowledge-based engineering and Gaussian process. J Shanghai Jiaotong Univ (Sci) 19(2):205–218
de Souza T, Rolfe BF (2010) Characterising material and process variation effects on springback robustness for a semi-cylindrical sheet metal forming process. Int J Mech Sci 52(12):1756–1766
Dettinger MD, Wilson JL (1981) First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development. Water Resour Res 17(1):149–161
Du X, Guo J, Beeram H (2008) Sequential optimization and reliability assessment for multidisciplinary systems design. Struct Multidiscip Optim 35(2):117–130
Eisenberger I (1964) Genesis of bimodal distributions. Technometrics 6(4):357–363
Enevoldsen I, Sorensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196
Gao L, Zhang Z (2008) Robust optimization for managing pavement maintenance and rehabilitation. Transp Res Rec J Transp Res Board 2084:55–61
Goedel V, Merklein M (2011) Variation of deep drawing steel grades’ properties in dependency of the stress state and its impact on FEA. Int J Mater Form 4(2):183–192
Gomes C, Onipede O, Lovell M (2005) Investigation of springback in high strength anisotropic steels. J Mater Process Technol 159(1):91–98
Hora P, Heingartner J, Manopulo N, Tong L, Hortig D, Neumann A, Roll K (2011) On the way from an ideal virtual process to the modelling of the real stochastic. Form Technol Forum 2011:04
https://data.knmi.nl/datasets
Jurecka F, Ganser M, Bletzinger K-U (2007) Update scheme for sequential spatial correlation approximations in robust design optimisation. Comput Struct 85(10):606–614
Kang J, Lee T, Lee D (2012) Robust optimization for engineering design. Eng Optim 44(2):175–194
Kann A, Weyant JP (2000) Approaches for performing uncertainty analysis in large-scale energy/economic policy models. Environ Model Assess 5(1):29–46
Koch PN, Yang RJ, Gu L (2004) Design for six sigma through robust optimization. Struct Multidiscip Optim 26(3):235–248
Marretta L, Di Lorenzo R (2010) Influence of material properties variability on springback and thinning in sheet stamping processes: a stochastic analysis. Int J Adv Manuf Technol 51(1):117–134
Myklebust O (2013) Zero defect manufacturing: a product and plant oriented lifecycle approach. Procedia CIRP 12:246–251 (Eighth CIRP Conference on intelligent computation in manufacturing engineering)
Nejadseyfi O, Geijselaers HJM, van den Boogaard AH (2019a) Robust optimization based on analytical evaluation of uncertainty propagation. Eng Optim 51(9):1581–1603
Nejadseyfi O, Geijselaers HJM, van den Boogaard AH (2019b) Evaluation and assessment of non-normal output during robust optimization. Struct Multidiscip Optim 59(6):2063–2076
Palmer TN (2000) Predicting uncertainty in forecasts of weather and climate. Rep Prog Phys 63(2):71
Prates PA, Adaixo AS, Oliveira MC, Fernandes JV (2018) Numerical study on the effect of mechanical properties variability in sheet metal forming processes. Int J Adv Manuf Technol 96(1–4):561–580
Putko MM, Taylor AC, Newman PA, Green LL (2002) Approach for input uncertainty propagation and robust design in CFD using sensitivity derivatives. J Fluids Eng 124(1):60–69
ur Rehman S, Langelaar M (2017) Expected improvement based infill sampling for global robust optimization of constrained problems. Optim Eng 18(3):723–753
Vegter H, van den Boogaard AH (2006) A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states. Int J Plast 22(3):557–580
Wiebenga JH, van den Boogaard AH, Klaseboer G (2012) Sequential robust optimization of a V-bending process using numerical simulations. Struct Multidiscip Optim 46(1):137–153
Wiebenga JH, Atzema EH, An YG, Vegter H, van den Boogaard AH (2014) Effect of material scatter on the plastic behavior and stretchability in sheet metal forming. J Mater Process Technol 214(2):238–252
Wurm A, Bestle D (2016) Robust design optimization for improving automotive shift quality. Optim Eng 17(2):421–436
Zhao H, Yue Z, Liu Y, Gao Z, Zhang Y (2015) An efficient reliability method combining adaptive importance sampling and Kriging metamodel. Appl Math Model 39(7):1853–1866
Zhou Q, Jiang P, Huang X, Zhang F, Zhou T (2018a) A multi-objective robust optimization approach based on Gaussian process model. Struct Multidiscip Optim 57(1):213–233
Zhou Q, Wang Y, Choi S, Cao L, Gao Z (2018b) Robust optimization for reducing welding-induced angular distortion in fiber laser keyhole welding under process parameter uncertainty. Appl Therm Eng 129:893–906