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A surrogate modeling approach for reliability analysis of a multidisciplinary system with spatio-temporal output

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Abstract

Reliability analysis of a multidisciplinary system is computationally intensive due to the involvement of multiple disciplinary models and coupling between the individual models. When the system inputs and outputs are varying over time and space, the reliability analysis is even more challenging. This paper proposes a surrogate model-based method for the reliability analysis of a multidisciplinary system with spatio-temporal output. The transient characteristics of the multidisciplinary system output under time-dependent variability are analyzed first. Based on the transient analysis, surrogate models are built for individual disciplinary analyses instead of a single surrogate model for the fully coupled analysis. To address the challenge introduced by the high-dimensionality of spatially varying inter-disciplinary coupling variables, a data compression method is first employed to convert the high-dimensional coupling variables into low-dimensional latent space. Kriging surrogate modeling is then used to build surrogates for the individual disciplinary models in the latent space. Based on the individual disciplinary surrogate models, reliability analysis of the coupled multidisciplinary system under time-dependent uncertainty is investigated. Further, epistemic uncertainty sources, such as data uncertainty and model uncertainty, lead to uncertainty in the reliability estimate. Therefore, an auxiliary variable approach is used to efficiently include the epistemic uncertainty sources within the reliability analysis. An aircraft panel subjected to hypersonic flow conditions is used to demonstrate the proposed method. The analysis involves four interacting disciplinary models, namely, aerodynamics, aerothermal analysis, heat transfer, and structural analysis. The results show that the proposed method is able to effectively perform reliability analysis of a multidisciplinary system with spatio-temporal output.

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References

  1. Ahn J, Kwon J (2004) Sequential approach to reliability analysis of multidisciplinary analysis systems. Struct Multidiscip Optim 28(6):397–406

  2. Amaral S, Allaire D, Willcox K (2014) A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems. Int J Numer Methods Eng 100(13):982–1005

  3. Andrieu-Renaud C, Sudret B, Lemaire M (2004) The PHI2 method: a way to compute time-variant reliability. Reliab Eng Syst Saf 84(1):75–86

  4. Bichon BJ, Eldred MS, Swiler LP, Mahadevan S, McFarland JM (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468

  5. Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78(7):808–817

  6. Cho S-g, Jang J, Kim S, Park S, Lee TH, Lee M, Choi J-S, Kim H-W, Hong S (2016) Nonparametric approach for uncertainty-based multidisciplinary design optimization considering limited data. Struct Multidiscip Optim 54(6):1671–1688

  7. Culler AJ, McNamara JJ (2011) Impact of fluid-thermal-structural coupling on response prediction of hypersonic skin panels. AIAA J 49(11):2393–2406

  8. DeCarlo EC, Mahadevan S, Smarslok BP (2014) Bayesian Calibration of Coupled Aerothermal Models Using Time-Dependent Data. In: Proc. 16th AIAA Non-Deterministic Approaches Conference, p 0123

  9. DeCarlo EC, Smarslok BP, Mahadevan S (2016) Segmented Bayesian calibration of multidisciplinary models. AIAA J 54:3727–3741

  10. Du X, Chen W (2002) Efficient uncertainty analysis methods for multidisciplinary robust design. AIAA J 40(3):545–552

  11. Du X, Chen W (2005) Collaborative reliability analysis under the framework of multidisciplinary systems design. Optim Eng 6(1):63–84

  12. Dubreuil S, Bartoli N, Gogu C, Lefebvre T (2016) Propagation of modeling uncertainty by polynomial chaos expansion in multidisciplinary analysis. J Mech Des 138(11):111411

  13. Espig M, Hackbusch W, Litvinenko A, Matthies HG, Zander E (2012) Efficient analysis of high dimensional data in tensor formats. Sparse Grids and Applications, Springer, pp 31–56

  14. Felippa CA, Park K, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Methods Appl Mech Eng 190(24):3247–3270

  15. Golub GH, Van Loan CF (2012) Matrix computations, JHU Press. Baltimore, Maryland, United States

  16. Guo J, Du X (2010) Reliability analysis for multidisciplinary systems with random and interval variables. AIAA J 48(1):82–91

  17. Higdon D, Nakhleh C, Gattiker J, Williams B (2008a) A Bayesian calibration approach to the thermal problem. Comput Methods Appl Mech Eng 197(29):2431–2441

  18. Higdon D, Gattiker J, Williams B, Rightley M (2008b) Computer model calibration using high-dimensional output. J Am Stat Assoc 103(482):570–583

  19. Hombal V, Mahadevan S (2011) Bias minimization in Gaussian process surrogate modeling for uncertainty quantification. Int J Uncertain Quantif 1(4):321–349

  20. Hu Z, Du X (2013) Time-dependent reliability analysis with joint upcrossing rates. Struct Multidiscip Optim 48(5):893–907

  21. Hu Z, Du X (2015) Mixed efficient global optimization for time-dependent reliability analysis. J Mech Des 137(5):051401

  22. Hu Z, Mahadevan S (2015) Time-dependent system reliability analysis using random field discretization. J Mech Des 137(10):101404

  23. Hu Z, Mahadevan S (2016a) A single-loop Kriging surrogate modeling for time-dependent reliability analysis. J Mech Des 138(6):061406

  24. Hu Z, Mahadevan S (2016b) Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis. Struct Multidiscip Optim 53(3):501–521

  25. Hu Z, Mahadevan S (2017) Adaptive Surrogate Modeling for Time-Dependent Multidisciplinary Reliability Analysis. J Mech Des, under review

  26. Hu Z, Du X, Kolekar NS, Banerjee A (2014) Robust design with imprecise random variables and its application in hydrokinetic turbine optimization. Eng Optim 46(3):393–419

  27. Hu Z, Mahadevan S, Du X (2016) Uncertainty quantification in time-dependent reliability analysis in the presence of parametric uncertainty. ASCE-ASME Journal of risk and uncertainty in Engineering systems, Part B: Mechanical Engineering 2(3):031005

  28. Kolekar N, Hu Z, Banerjee A, Du X (2013) Hydrodynamic design and optimization of hydro-kinetic turbines using a robust design method. In: Proc. Proceedings of the 1st Marine Energy Technology Symposium. METS13, Washington, DC

  29. Kumar NC, Subramaniyan AK, Wang L, Wiggs G (2013) Calibrating transient models with multiple responses using Bayesian inverse techniques. In: Proc. ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, American Society of Mechanical Engineers, pp V07AT28A007–V007AT028A007

  30. Li C, Mahadevan S (2016) Role of calibration, validation, and relevance in multi-level uncertainty integration. Reliab Eng Syst Saf 148:32–43

  31. Liang C, Mahadevan S (2016) Stochastic multidisciplinary analysis with high-dimensional coupling. AIAA J 54(2):1209–1219

  32. Liang C, Mahadevan S, Sankararaman S (2015) Stochastic multidisciplinary analysis under epistemic uncertainty. J Mech Des 137(2):021404

  33. Litvinenko A, Matthies H (2010) Sparse data formats and efficient numerical methods for uncertainties quantification in numerical aerodynamics. ECCM IV: Solids, Structures and Coupled Problems in Engineering

  34. Litvinenko A, Matthies HG (2013) Numerical methods for uncertainty quantification and Bayesian update in aerodynamics. Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics, Springer, pp 265–282

  35. Litvinenko A, Matthies HG, El-Moselhy TA (2013) Sampling and low-rank tensor approximation of the response surface. Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer, pp 535–551

  36. Long Q, Motamed M, Tempone R (2015) Fast Bayesian optimal experimental design for seismic source inversion. Comput Methods Appl Mech Eng 291:123–145

  37. Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE-A Matlab Kriging toolbox, version 2.0. Technical University of Denmark, technical report no. IMM-TR-2002-12

  38. Mahadevan S, Smith N (2006) Efficient first-order reliability analysis of multidisciplinary systems. Int J Reliab Saf 1(1–2):137–154

  39. Michler C, Hulshoff S, Van Brummelen E, De Borst R (2004) A monolithic approach to fluid–structure interaction. Comput Fluids 33(5):839–848

  40. Nannapaneni S, Mahadevan S (2016) Reliability analysis under epistemic uncertainty. Reliab Eng Syst Saf 155:9–20

  41. Nannapaneni S, Hu Z, Mahadevan S (2016) Uncertainty quantification in reliability estimation with limit state surrogates. Struct Multidiscip Optim 54(6):1509–1526

  42. Ong YS, Nair PB, Keane AJ (2003) Evolutionary optimization of computationally expensive problems via surrogate modeling. AIAA J 41(4):687–696

  43. Park KC, Felippa CA, DeRuntz JA (1977) Stabilization of staggered solution procedures for fluid-structure interaction analysis. Computational methods for fluid-structure interaction problems 1(1):95–124

  44. Rangavajhala S, Sura VS, Hombal VK, Mahadevan S (2011) Discretization error estimation in multidisciplinary simulations. AIAA J 49(12):2673–2683

  45. Rasmussen CE (2006) Gaussian processes for machine learning. The MIT Press, ISBN 0-262-18253-X

  46. Sankararaman S, Mahadevan S (2012) Likelihood-based approach to multidisciplinary analysis under uncertainty. J Mech Des 134(3):031008

  47. Sankararaman S, Mahadevan S (2013) Separating the contributions of variability and parameter uncertainty in probability distributions. Reliab Eng Syst Saf 112:187–199

  48. Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Springer Science & Business Media, New York

  49. Singh A, Mourelatos ZP, Li J (2010) Design for lifecycle cost using time-dependent reliability. J Mech Des 132(9):091008

  50. Singh A, Mourelatos Z, Nikolaidis E (2011) Time-dependent reliability of random dynamic systems using time-series modeling and importance sampling. SAE International Journal of Materials and Manufacturing 4(2011-01-0728):929–946

  51. Smarslok B, Culler A, Mahadevan S (2012) Error quantification and confidence assessment of aerothermal model predictions for hypersonic aircraft. Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials, pp 2012–1817

  52. Steinfeldt BA, Braun RD (2014) Using dynamical systems concepts in multidisciplinary design. AIAA J 52(6):1265–1279

  53. Wang Z, Wang P (2012) A nested extreme response surface approach for time-dependent reliability-based design optimization. J Mech Des 134(12):121007

  54. Wang Z, Wang P (2013) A new approach for reliability analysis with time-variant performance characteristics. Reliab Eng Syst Saf 115:70–81

  55. Wang Z, Zhang X, Huang H-Z, Mourelatos ZP (2016) A simulation method to estimate two types of time-varying failure rate of dynamic systems. J Mech Des 138(12):121404

  56. Zhang X, Mahadevan S, Deng X (2017) Reliability analysis with linguistic data: an evidential network approach. Reliab Eng Syst Saf 162:111–121

  57. Zhu Z, Hu Z, Du X (2015) Reliability Analysis for Multidisciplinary Systems Involving Stationary Stochastic Processes. In: Proc. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, pp V02BT03A050–V002BT003A050

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Acknowledgements

The research reported in this paper was supported by the Air Force Office of Scientific Research (Grant No. FA9550-15-1-0018, Program Manager: Dr. David Stargel). The support is gratefully acknowledged. The authors also thank Erin DeCarlo at Vanderbilt University for helping with the simulations.

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Correspondence to Sankaran Mahadevan.

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Hu, Z., Mahadevan, S. A surrogate modeling approach for reliability analysis of a multidisciplinary system with spatio-temporal output. Struct Multidisc Optim 56, 553–569 (2017). https://doi.org/10.1007/s00158-017-1737-x

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Keywords

  • Reliability
  • Multidisciplinary system
  • Spatial response
  • Steady state
  • Transient response