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Erschienen in: Structural and Multidisciplinary Optimization 1/2018

28.07.2017 | RESEARCH PAPER

Local maximum-entropy based surrogate model and its application to structural reliability analysis

verfasst von: Jiang Fan, Huming Liao, Hao Wang, Junheng Hu, Zhiying Chen, Jian Lu, Bo Li

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 1/2018

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Abstract

A novel surrogate model based on the Local Maximum-Entropy (LME) approximation is proposed in this paper. By varying the degrees of locality, the LME-based surrogate model is constructed according to the local behavior of the response function at the prediction points. The proposed method combines the advantages of both local and global approximation schemes. The robustness and effectiveness of the model are systematically investigated by comparing with the conventional surrogate models (such as Polynomial regression, Radial basis function, and Kriging model) in three types of test problems. In addition, the performance of the LME-based surrogate model is evaluated by an industry case of turbine disk reliability analysis (TDRA) involving random geometric parameters. In TDRA, two LME-based surrogate models are built including a 1 s t surrogate model employed in the sensitivity analysis to determine the key random variables and a 2 n d surrogate model utilized in Monte-Carlo Simulations (MCS) to predict the Low Cycle Fatigue (LCF) life of turbine disks. Finally, a model-based Uncertainty Quantification (UQ) analysis is performed to rigorously quantify the uncertainties of the physical system and fidelity of surrogate model predictions simultaneously. Results show that the LME-based surrogate model can achieve a desirable level of accuracy and robustness with reduced number of sample points, which indicates the proposed method possess the potential for approximating highly nonlinear limit state functions and applicable for structural reliability analysis.

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Literatur
Zurück zum Zitat Adams M, Lashgari A, Li B, McKerns M, Mihaly J, Ortiz M, Owhadi H, Rosakis A, Stalzer M, Sullivan T (2012) Rigorous model-based uncertainty quantification with application to terminal ballistics—part ii. systems with uncontrollable inputs and large scatter. J Mech Phys Solids 60(5):1002–1019CrossRef Adams M, Lashgari A, Li B, McKerns M, Mihaly J, Ortiz M, Owhadi H, Rosakis A, Stalzer M, Sullivan T (2012) Rigorous model-based uncertainty quantification with application to terminal ballistics—part ii. systems with uncontrollable inputs and large scatter. J Mech Phys Solids 60(5):1002–1019CrossRef
Zurück zum Zitat Arroyo M, Ortiz M (2006) Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Int J Numer Methods Eng 65(13):2167–2202MathSciNetCrossRefMATH Arroyo M, Ortiz M (2006) Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Int J Numer Methods Eng 65(13):2167–2202MathSciNetCrossRefMATH
Zurück zum Zitat Barton RR (1992) Metamodels for simulation input-output relations Proceedings of the 24th conference on Winter simulation. ACM, pp 289–299 Barton RR (1992) Metamodels for simulation input-output relations Proceedings of the 24th conference on Winter simulation. ACM, pp 289–299
Zurück zum Zitat Birnbaum ZW (1952) Numerical tabulation of the distribution of Kolmogorov’s statistic for finite sample size. J Am Stat Assoc 47(259):425–441MathSciNetCrossRefMATH Birnbaum ZW (1952) Numerical tabulation of the distribution of Kolmogorov’s statistic for finite sample size. J Am Stat Assoc 47(259):425–441MathSciNetCrossRefMATH
Zurück zum Zitat Bucher CG, Bourgund U (1990) A fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57–66CrossRef Bucher CG, Bourgund U (1990) A fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57–66CrossRef
Zurück zum Zitat Das PK, Zheng Y (2000) Cumulative formation of response surface and its use in reliability analysis. Probab Eng Mech 15(4):309–315CrossRef Das PK, Zheng Y (2000) Cumulative formation of response surface and its use in reliability analysis. Probab Eng Mech 15(4):309–315CrossRef
Zurück zum Zitat Elhewy AH, Mesbahi E, Pu Y (2006) Reliability analysis of structures using neural network method. Probab Eng Mech 21(1):44–53CrossRef Elhewy AH, Mesbahi E, Pu Y (2006) Reliability analysis of structures using neural network method. Probab Eng Mech 21(1):44–53CrossRef
Zurück zum Zitat Fan J, Liao H, Li D, Wang R, Hu D (2017) Probabilistic analysis of turbine disk fatigue life considering geometric uncertainties. J Aerosp Pow 32(1):66–74 Fan J, Liao H, Li D, Wang R, Hu D (2017) Probabilistic analysis of turbine disk fatigue life considering geometric uncertainties. J Aerosp Pow 32(1):66–74
Zurück zum Zitat Golub GH, Van Loan CF (2012) Matrix computations, vol 3. JHU Press Golub GH, Van Loan CF (2012) Matrix computations, vol 3. JHU Press
Zurück zum Zitat Guan XL, Melchers RE (2001) Effect of response surface parameter variation on structural reliability estimates. Struct Saf 23(4):429–444CrossRef Guan XL, Melchers RE (2001) Effect of response surface parameter variation on structural reliability estimates. Struct Saf 23(4):429–444CrossRef
Zurück zum Zitat Guo Z, Bai G (2009) Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut 22(2):160–166CrossRef Guo Z, Bai G (2009) Application of least squares support vector machine for regression to reliability analysis. Chin J Aeronaut 22(2):160–166CrossRef
Zurück zum Zitat Habib M, McDiarmid C, Ramirez-Alfonsin J, Reed B (2013) Probabilistic methods for algorithmic discrete mathematics, vol 16. Springer Science & Business Media Habib M, McDiarmid C, Ramirez-Alfonsin J, Reed B (2013) Probabilistic methods for algorithmic discrete mathematics, vol 16. Springer Science & Business Media
Zurück zum Zitat Hock W, Schittkowski K (1980) Test examples for nonlinear programming codes. J Optim Theory Appl 30 (1):127–129CrossRefMATH Hock W, Schittkowski K (1980) Test examples for nonlinear programming codes. J Optim Theory Appl 30 (1):127–129CrossRefMATH
Zurück zum Zitat Hurtado JE, Alvarez DA (2001) Neural-network-based reliability analysis: a comparative study. Comput Methods Appl Mech Eng 191(1):113–132CrossRefMATH Hurtado JE, Alvarez DA (2001) Neural-network-based reliability analysis: a comparative study. Comput Methods Appl Mech Eng 191(1):113–132CrossRefMATH
Zurück zum Zitat Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Optim 23(1):1–13CrossRef Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Optim 23(1):1–13CrossRef
Zurück zum Zitat Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press
Zurück zum Zitat Kaymaz I, McMahon CA (2005) A response surface method based on weighted regression for structural reliability analysis. Probab Eng Mech 20(1):11–17CrossRef Kaymaz I, McMahon CA (2005) A response surface method based on weighted regression for structural reliability analysis. Probab Eng Mech 20(1):11–17CrossRef
Zurück zum Zitat Kidane A, Lashgari A, Li B, McKerns M, Ortiz M, Owhadi H, Ravichandran G, Stalzer M, Sullivan TJ (2012) Rigorous model-based uncertainty quantification with application to terminal ballistics, part i: Systems with controllable inputs and small scatter 60(5):983–1001. doi:10.1016/j.jmps.2011.12.001 Kidane A, Lashgari A, Li B, McKerns M, Ortiz M, Owhadi H, Ravichandran G, Stalzer M, Sullivan TJ (2012) Rigorous model-based uncertainty quantification with application to terminal ballistics, part i: Systems with controllable inputs and small scatter 60(5):983–1001. doi:10.​1016/​j.​jmps.​2011.​12.​001
Zurück zum Zitat Kim SH, Na SW (1997) Response surface method using vector projected sampling points. Struct Saf 19 (1):3–19CrossRef Kim SH, Na SW (1997) Response surface method using vector projected sampling points. Struct Saf 19 (1):3–19CrossRef
Zurück zum Zitat Koziel S, Ciaurri DE, Leifsson L (2011) Surrogate-based methods. In: Koziel S, Yang XS (eds) Computational optimization, methods and algorithms, no. 356 in studies in computational intelligence. doi:10.1007/978-3-642-20859-1_3. Springer Berlin Heidelberg, pp 33–59 Koziel S, Ciaurri DE, Leifsson L (2011) Surrogate-based methods. In: Koziel S, Yang XS (eds) Computational optimization, methods and algorithms, no. 356 in studies in computational intelligence. doi:10.​1007/​978-3-642-20859-1_​3. Springer Berlin Heidelberg, pp 33–59
Zurück zum Zitat Li B, Habbal F, Ortiz M (2010) Optimal transportation meshfree approximation schemes for fluid and plastic flows. Int J Numer Methods Eng 83(12):1541–1579MathSciNetCrossRefMATH Li B, Habbal F, Ortiz M (2010) Optimal transportation meshfree approximation schemes for fluid and plastic flows. Int J Numer Methods Eng 83(12):1541–1579MathSciNetCrossRefMATH
Zurück zum Zitat Li J, Wang H, Kim NH (2012) Doubly weighted moving least squares and its application to structural reliability analysis. Struct Multidiscip Optim 46(1):69–82CrossRef Li J, Wang H, Kim NH (2012) Doubly weighted moving least squares and its application to structural reliability analysis. Struct Multidiscip Optim 46(1):69–82CrossRef
Zurück zum Zitat Lilliefors HW (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62(318):399–402CrossRef Lilliefors HW (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62(318):399–402CrossRef
Zurück zum Zitat Liu YW, Moses F (1994) A sequential response surface method and its application in the reliability analysis of aircraft structural systems. Struct Saf 16(1-2):39–46CrossRef Liu YW, Moses F (1994) A sequential response surface method and its application in the reliability analysis of aircraft structural systems. Struct Saf 16(1-2):39–46CrossRef
Zurück zum Zitat Lucas LJ, Owhadi H, Ortiz M (2008) Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities. Comput Methods Appl Mech Eng 197(51):4591–4609MathSciNetCrossRefMATH Lucas LJ, Owhadi H, Ortiz M (2008) Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities. Comput Methods Appl Mech Eng 197(51):4591–4609MathSciNetCrossRefMATH
Zurück zum Zitat Most T (2007) An adaptive response surface approach for structural reliability analyses based on support vector machines Proceedings of the eleventh international conference on civil, structural and environmental engineering computing, BHV Topping Most T (2007) An adaptive response surface approach for structural reliability analyses based on support vector machines Proceedings of the eleventh international conference on civil, structural and environmental engineering computing, BHV Topping
Zurück zum Zitat Nguyen XS, Sellier A, Duprat F, Pons G (2009) Adaptive response surface method based on a double weighted regression technique. Probab Eng Mech 24(2):135–143CrossRef Nguyen XS, Sellier A, Duprat F, Pons G (2009) Adaptive response surface method based on a double weighted regression technique. Probab Eng Mech 24(2):135–143CrossRef
Zurück zum Zitat Panda SS, Manohar CS (2008) Applications of meta-models in finite element based reliability analysis of engineering structures. Comput Model Eng Sci 28:161–184 Panda SS, Manohar CS (2008) Applications of meta-models in finite element based reliability analysis of engineering structures. Comput Model Eng Sci 28:161–184
Zurück zum Zitat Papadrakakis M, Papadopoulos V, Lagaros ND (1996) Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 136(1):145–163CrossRefMATH Papadrakakis M, Papadopoulos V, Lagaros ND (1996) Structural reliability analyis of elastic-plastic structures using neural networks and Monte Carlo simulation. Comput Methods Appl Mech Eng 136(1):145–163CrossRefMATH
Zurück zum Zitat Preparata SM, Franco P (1985) Computational geometry - an introduction | Franco P. Preparata | Springer Preparata SM, Franco P (1985) Computational geometry - an introduction | Franco P. Preparata | Springer
Zurück zum Zitat Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220CrossRef Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220CrossRef
Zurück zum Zitat Simpson TW, Lin DK, Chen W (2001) Sampling strategies for computer experiments: design and analysis. Int J Reliability Appl 2(3):209–240 Simpson TW, Lin DK, Chen W (2001) Sampling strategies for computer experiments: design and analysis. Int J Reliability Appl 2(3):209–240
Zurück zum Zitat Song H, Choi KK, Lee I, Zhao L, Lamb D (2013) Adaptive virtual support vector machine for reliability analysis of high-dimensional problems. Struct Multidiscip Optim 47(4):479–491MathSciNetCrossRefMATH Song H, Choi KK, Lee I, Zhao L, Lamb D (2013) Adaptive virtual support vector machine for reliability analysis of high-dimensional problems. Struct Multidiscip Optim 47(4):479–491MathSciNetCrossRefMATH
Zurück zum Zitat Viana FA, Venter G, Balabanov V (2010) An algorithm for fast optimal Latin hypercube design of experiments. Int J Numer Methods Eng 82(2):135–156MathSciNetMATH Viana FA, Venter G, Balabanov V (2010) An algorithm for fast optimal Latin hypercube design of experiments. Int J Numer Methods Eng 82(2):135–156MathSciNetMATH
Zurück zum Zitat Wong FS (1985) Slope reliability and response surface method. J Geotech Eng 111(1):32–53CrossRef Wong FS (1985) Slope reliability and response surface method. J Geotech Eng 111(1):32–53CrossRef
Zurück zum Zitat Zhao L, Choi KK, Lee I (2011) Metamodeling method using dynamic kriging for design optimization. AIAA J 49(9):2034–2046CrossRef Zhao L, Choi KK, Lee I (2011) Metamodeling method using dynamic kriging for design optimization. AIAA J 49(9):2034–2046CrossRef
Zurück zum Zitat Zhao L, Choi KK, Lee I, Gorsich D (2013) Conservative surrogate model using weighted kriging variance for sampling-based RBDO. J Mech Des 091(9):003 Zhao L, Choi KK, Lee I, Gorsich D (2013) Conservative surrogate model using weighted kriging variance for sampling-based RBDO. J Mech Des 091(9):003
Metadaten
Titel
Local maximum-entropy based surrogate model and its application to structural reliability analysis
verfasst von
Jiang Fan
Huming Liao
Hao Wang
Junheng Hu
Zhiying Chen
Jian Lu
Bo Li
Publikationsdatum
28.07.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 1/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1760-y

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