Skip to main content
SpringerLink
Log in

A conservative multi-fidelity surrogate model-based robust optimization method for simulation-based optimization

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Multi-fidelity (MF) surrogate model-based robust optimization has been used to deal with engineering design and optimization problems that have uncertainty in their inputs. However, the MF surrogate model constructed by a limited number of samples ineluctable has prediction uncertainty, which often leads to the optimal solutions becoming infeasible. In this paper, a MF surrogate model-assisted semi-nested variable adjustment robust optimization (CMF-SN-VARO) method is proposed to address the impact of prediction uncertainty of the MF surrogate model during the optimization process. A piecewise conservative MF surrogate modeling method is proposed to replace the objective functions and constraints, in which the safety margin is calculated by different error metrics according to their performance in problems with different dimensions. The variable adjustment robust optimization (VARO) framework is adopted to solve the robust optimization problem by adjusting the preexisting design. A switch criterion is utilized to adaptively determine when to use surrogate models or inner optimization problems to evaluate the robustness index of design alternatives. The performance of the proposed method is illustrated with an analytical example, a torque arm design problem, and a micro aerial vehicle fuselage design problem. Results show that the proposed method achieves better optimal design solutions that are both objective robust and feasibility robust.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32

Similar content being viewed by others

References

  • Acar P, Sundararaghavan V (2019) Stochastic design optimization of microstructural features using linear programming for robust design. AIAA J 57:448–455

    Article  Google Scholar 

  • Alinejad F, Botto D (2019) Innovative adaptive penalty in surrogate-assisted robust optimization of blade attachments. Acta Mech 230:2735–2750

    Article  Google Scholar 

  • Chatterjee T, Chakraborty S, Chowdhury R (2019) A critical review of surrogate assisted robust design optimization. Archives of Computational Methods in Engineering 26:245–274

    Article  MathSciNet  Google Scholar 

  • Chunna L, Hai F, Chunlin G (2020) Development of an efficient global optimization method based on adaptive infilling for structure optimization. Struct Multidisc Optim 62, 3383–3412. https://doi.org/10.1007/s00158-020-02716-y

  • Dasari SK, Cheddad A, Andersson P (2020) Predictive modelling to support sensitivity analysis for robust design in aerospace engineering. Struct Multidisc Optim 61, 2177–2192. https://doi.org/10.1007/s00158-019-02467-5

  • Dourado ADP, Lobato FS, Ap Cavalini A, Steffen V (2019) Fuzzy reliability-based optimization for engineering system design. Int J Fuzzy Syst 21:1418–1429

    Article  Google Scholar 

  • Ghosh S, Kristensen J, Zhang Y, Subber W, Wang L (2019). A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty. Proceedings of the ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2B: 45th Design Automation Conference. Anaheim, California, USA. https://doi.org/10.1115/DETC2019-98418

  • Giorgetti S, Coppitters D, Contino F, Paepe WD, Bricteux L, Aversano G, Parente A (2020) Surrogate-assisted modeling and robust optimization of a micro gas turbine plant with carbon capture. J Eng Gas Turbines Power 142:011010

    Article  Google Scholar 

  • Hu J, Yang Y, Zhou Q, Jiang P, Shao X, Shu L, Zhang Y (2018) Comparative studies of error metrics in variable fidelity model uncertainty quantification. J Eng Des 29:512–538

    Article  Google Scholar 

  • Hu Z, Hu C, Mourelatos ZP, Mahadevan S (2019) Model discrepancy quantification in simulation-based design of dynamical systems. J Mech Des 141:011401

    Article  Google Scholar 

  • Huan Z, Zhenghong G, Fang X, Yidian Z (2019) Review of robust aerodynamic design optimization for air vehicles. Arch Comput Meth Eng 26:685–732

    Article  MathSciNet  Google Scholar 

  • Jiang P, Cheng J, Zhou Q, Shu L, Hu J (2019) Variable-fidelity lower confidence bounding approach for engineering optimization problems with expensive simulations. AIAA J 57:5416–5430

    Article  Google Scholar 

  • Li M (2011) An improved kriging-assisted multi-objective genetic algorithm. J Mech Des 133:071008

    Article  Google Scholar 

  • Li M, Wang Z (2018) Confidence-driven design optimization using Gaussian process metamodeling with insufficient data. J Mech Des 140:121405

    Article  Google Scholar 

  • Li M, Wang Z (2019) Surrogate model uncertainty quantification for reliability-based design optimization. Reliab Eng Syst Saf 192:106432

    Article  Google Scholar 

  • Li X, Qiu H, Jiang Z, Gao L, Shao X (2017) A VF-SLP framework using least squares hybrid scaling for RBDO. Struct Multidiscip Optim 55:1629–1640

    Article  MathSciNet  Google Scholar 

  • Li M, Sadoughi M, Hu C, Hu Z, Eshghi AT, Lee S (2019) High-dimensional reliability-based design optimization involving highly nonlinear constraints and computationally expensive simulations. J Mech Des 141:051402

    Article  Google Scholar 

  • Meng Z, Zhang Z, Zhou H, Chen H, Yu B (2020) Robust design optimization of imperfect stiffened shells using an active learning method and a hybrid surrogate model. Eng Optim 52(12):2044–2061

    Article  MathSciNet  Google Scholar 

  • Mohammadi MS, Naghash A (2019) Robust optimization of impulsive orbit transfers under actuation uncertainties. Aerosp Sci Technol 85:246–258

    Article  Google Scholar 

  • Nguyen J, Park S-i, Rosen D (2013) Heuristic optimization method for cellular structure design of light weight components. Int J Precis Eng Manuf 14:1071–1078

    Article  Google Scholar 

  • Ouyang Q, Lu W, Lin J, Deng W, Cheng W (2017) Conservative strategy-based ensemble surrogate model for optimal groundwater remediation design at DNAPLs-contaminated sites. J Contam Hydrol 203:1–8

    Article  Google Scholar 

  • Padron AS, Alonso JJ, Eldred MS (2016) Multi-fidelity methods in aerodynamic robust optimization. In 18th AIAA non-deterministic approaches conference (p. 0680). https://doi.org/10.2514/6.2016-0680

  • Qiu N, Gao Y, Fang J, Sun G, Li Q, Kim NH (2018) Crashworthiness optimization with uncertainty from surrogate model and numerical error. Thin-Walled Struct 129:457–472

    Article  Google Scholar 

  • Rafiee V, Faiz J (2019) Robust design of an outer rotor permanent magnet motor through six-sigma methodology using response surface surrogate model. IEEE Trans Magn 55:1–10

    Article  Google Scholar 

  • Ribaud M, Blanchet-Scalliet C, Helbert C, Gillot F (2020) Robust optimization: a kriging-based multi-objective optimization approach. RRELIAB ENG SYST SAFE, 200, 106913. https://doi.org/10.1016/j.ress.2020.106913

  • Shah H, Hosder S, Koziel S, Tesfahunegn YA, Leifsson L (2015) Multi-fidelity robust aerodynamic design optimization under mixed uncertainty. Aerosp Sci Technol 45:17–29

    Article  Google Scholar 

  • Shi M, Lv L, Sun W, Song X (2020) A multi-fidelity surrogate model based on support vector regression. Struct Multidiscip Optim 61:2363–2375

    Article  MathSciNet  Google Scholar 

  • Shu L, Jiang P, Song X, Zhou Q (2019) Novel approach for selecting low-fidelity scale factor in multifidelity metamodeling. AIAA J 57:5320–5330

    Article  Google Scholar 

  • Sjöstedt-de Luna S, Young A (2003) The bootstrap and kriging prediction intervals. Scand J Stat 30:175–192

    Article  MathSciNet  Google Scholar 

  • Song J, Yang Y, Chen G, Sun X, Lin J, Wu J, Wu J (2019) Surrogate assisted multi-objective robust optimization for groundwater monitoring network design. J Hydrol 577:123994

    Article  Google Scholar 

  • Suprayitno, Yu J-C (2019) Evolutionary reliable regional Kriging surrogate for expensive optimization. Eng Optim 51:247–264

    Article  MathSciNet  Google Scholar 

  • Tao J, Sun G (2019) Application of deep learning based multi-fidelity surrogate model to robust aerodynamic design optimization. Aerosp Sci Technol 92:722–737

    Article  Google Scholar 

  • Viana FA, Picheny V, Haftka RT (2010) Using cross validation to design conservative surrogates. AIAA J 48:2286–2298

    Article  Google Scholar 

  • Wang D, Wu Z, Fei Y, Zhang W (2014) Structural design employing a sequential approximation optimization approach. Comput Struct 134:75–87

    Article  Google Scholar 

  • Wang F, Xiong F, Chen S, Song J (2019) Multi-fidelity uncertainty propagation using polynomial chaos and Gaussian process modeling. Struct Multidiscip Optim 60:1583–1604

    Article  Google Scholar 

  • Wu Y, Hu J, Zhou Q, Wang S, Jin P (2020) An active learning multi-fidelity metamodeling method based on the bootstrap estimator. Aerosp Sci Technol 106:106116

    Article  Google Scholar 

  • Xu Y, Song X, Zhang C (2021) Hierarchical regression framework for multi-fidelity modeling. Knowledge-Based Systems, 212, 106587. https://doi.org/10.1016/j.knosys.2020.106587

  • Yang J, Sun D, Hu N, Ning H, Zhang J, Ye W, Wu J (2019a) Multi-objective robust design optimization of a two-dimensional tri-axial braided hollow pillar using an evolutionary algorithm. Compos Struct 220:105–113

    Article  Google Scholar 

  • Yang Q, Meng S, Jin H, Xie W, Zhang X (2019b) Multi-fidelity uncertainty quantification method with application to nonlinear structural response analysis. Appl Math Model 75:853–864

    Article  MathSciNet  Google Scholar 

  • Yoo K, Bacarreza O, Aliabadi MF (2020) A novel multi-fidelity modelling-based framework for reliability-based design optimisation of composite structures. Eng Comput doi: https://doi.org/10.1007/s00366-020-01084-x

  • Zhao L (2011) Reliability-based design optimization using surrogate model with assessment of confidence level (Order No. 3473264). Available from ProQuest Dissertations & Theses Global. (894769536). Retrieved from https://www.proquest.com/dissertations-theses/reliability-based-design-optimization-using/docview/894769536/se-2?accountid=11524

  • Zhao L, Choi KK, Lee I, Gorsich D (2013) Conservative surrogate model using weighted Kriging variance for sampling-based RBDO. J Mech Des 135:091003

    Article  Google Scholar 

  • Zhou Q, Shao X, Jiang P, Zhou H, Cao L, Zhang L (2015) A deterministic robust optimisation method under interval uncertainty based on the reverse model. J Eng Des 26:416–444

    Article  Google Scholar 

  • Zhou Q, Wang Y, Choi S-K, Jiang P, Shao X, Hu J (2017a) A sequential multi-fidelity metamodeling approach for data regression. Knowl-Based Syst 134:199–212

    Article  Google Scholar 

  • Zhou Q, Yang Y, Jiang P, Shao X, Cao L, Hu J, Gao Z, Wang C (2017b) A multi-fidelity information fusion metamodeling assisted laser beam welding process parameter optimization approach. Adv Eng Softw 110:85–97

    Article  Google Scholar 

  • Zhou Q, Wang Y, Choi S-K, Jiang P, Shao X, Hu J, Shu L (2018a) A robust optimization approach based on multi-fidelity metamodel. Struct Multidiscip Optim 57:775–797

    Article  Google Scholar 

  • Zhou H, Zhou Q, Liu C, Zhou T (2018b) A kriging metamodel-assisted robust optimization method based on a reverse model. Eng Optim 50:253–272

    Article  Google Scholar 

  • Zhou Q, Shao X, Jiang P, Xie T, Hu J, Shu L, Cao L, Gao Z (2018c) A multi-objective robust optimization approach for engineering design under interval uncertainty. Eng Comput 35:580–603

    Article  Google Scholar 

Download references

Funding

This research has been supported by the National Natural Science Foundation of China (NSFC) under Grant nos. 51805179 and 51721092, the China Postdoctoral Science Foundation under Grant no. 2020M682396, the National Defense Innovation Program under Grant no. 18-163-00-TS-004-033-01, and the Research Funds of the Maritime Defense Technologies Innovation under Grant no. YT19201901.

Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Huazhong University of Science & Technology, 430074, Wuhan, People’s Republic of China

    Jiexiang Hu, Quan Lin, Qi Zhou & Huaping Liu

  2. School of Mechanical Science and Engineering, Huazhong University of Science & Technology, 430074, Wuhan, People’s Republic of China

    Lili Zhang & Meng Cheng

Authors
  1. Jiexiang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lili Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Quan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Meng Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Huaping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaping Liu.

Ethics declarations

Competing of interest

The authors declare that they have no conflict of interest.

Replication of results

The results provided in this paper are generated by MATLAB codes developed by the authors. The codes can be available upon request by contacting the corresponding author via email.

Additional information

Responsible Editor: Xiaoping Du

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, J., Zhang, L., Lin, Q. et al. A conservative multi-fidelity surrogate model-based robust optimization method for simulation-based optimization. Struct Multidisc Optim 64, 2525–2551 (2021). https://doi.org/10.1007/s00158-021-03007-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-021-03007-w

Keywords

Search

Navigation