Estimation of system reliability by using the PLS-regression based corrected response surface method

• Autorzy: Liu H. , Jiang W. , Hulio Z. H. , Wang Q.

Identyfikatory

DOI

10.17531/ein.2016.2.14

Warianty tytułu

PL

Ocena niezawodności systemu z wykorzystaniem poprawionej metody powierzchni odpowiedzi opartej na regresji cząstkowych najmniejszych kwadratów

• Języki publikacji: EN

Abstrakty

EN

A new computational method, referred as PLS-regression (PLSR) based corrected response surface method, has been developed for predicting the reliability of structural and mechanical systems subjecting to random loads, material properties, and geometry. The method involves a Corrected-Response Surface Model (C-RSM) based on the Partial Least Squares Regression Method (PLSRM) combined with some correction factors, and Monte Carlo Simulation (MCS), which is named as the Corrected-Partial Least Squares Regression-Response Surface Method (C-PLSRRSM). In order to develop an accurate surrogate model for the region determining the reliability of the system, a proper coefficient is presented to determine the sampling region of the input random variables. Due to a small number of original function evaluations, the proposed method is effective, particularly when a response evaluation entails costly finite-element, mesh-free, or other numerical analysis. Three numerical examples involving reliability problems of two structural systems and a mechanical system illustrate the method developed. Results indicate that the proposed method provides accurate and computationally efficient estimates of reliability. The proposed correction method, the PLSR based corrected response surface (C-PLSR-RS), can be the accurate surrogate model for calculating system reliabilities, especially for the implicit performance functions.

PL

Nowa metoda obliczeniowa o nazwie "poprawiona metoda powierzchni odpowiedzi oparta na regresji PLS" (C-PLSRRSM) została opracowana dla potrzeb przewidywania niezawodności systemów konstrukcyjnych i mechanicznych poddanych obciążeniom losowym oraz charakteryzujących się losową geometrią oraz losowymi właściwościami materiałowymi. W metodzie uwzględniono pewne czynniki korekcyjne oraz symulację Monte Carlo. W celu opracowania odpowiedniego modelu zastępczego dla regionu stanowiącego o niezawodności systemu, przedstawiono współczynnik, który pozwala określić obszar pobierania próbek wejściowych zmiennych losowych. Ze względu na niewielką liczbę ocen funkcji początkowych, proponowana metoda jest skuteczna zwłaszcza wtedy, gdy ocena odpowiedzi wymaga kosztownej analizy numerycznej metodą elementów skończonych czy metodą automatycznie generowanej siatki (free mesh). Opracowaną metodę zilustrowano za pomocą trzech przykładów numerycznych dotyczących niezawodności dwóch systemów konstrukcyjnych oraz jednego układu mechanicznego. Wyniki wskazują, że proponowana metoda zapewnia dokładne i wydajne obliczeniowo oszacowanie niezawodności. Proponowana metoda C-PLSR-RS może stanowić trafny model zastępczy do obliczania niezawodności systemu, zwłaszcza w przypadku uwikłanych funkcji stanu granicznego.

Słowa kluczowe

EN

reliability; mechanical system; partial least squares regression; response surface method; correction method

PL

niezawodność; układ mechaniczny; regresja cząstkowych najmniejszych kwadratów; metoda powierzchni odpowiedzi; metoda korekcji

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2016
• Tom: Vol. 18, no. 2
• Strony: 260--270
• Opis fizyczny: Bibliogr. 41 poz. rys., tab.

Twórcy

autor

Liu H.

• School of Mechanical Engineering Dalian University of Technology Linggong Road, No 2 Ganjingzi District, Dalian, Liaoning Province, China

autor

Jiang W.

• School of Mechanical Engineering Dalian University of Technology Linggong Road, No 2 Ganjingzi District, Dalian, Liaoning Province, China

autor

Hulio Z. H.

• School of Mechanical Engineering Dalian University of Technology Linggong Road, No 2 Ganjingzi District, Dalian, Liaoning Province, China

autor

Wang Q.

• School of Mechanical Engineering Dalian University of Technology Linggong Road, No 2 Ganjingzi District, Dalian, Liaoning Province, China

Bibliografia

• 1. Au S K, Beck J L. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics 2001; 16(4): 263-277, http://dx.doi.org/10.1016/S0266-8920(01)00019-4.
• 2. Bichon B J, Eldred M S, Swiler L P, Mahadevan S, McFarland J M. Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions. Aiaa Journal 2008; 46(10): 2459-2468, http://dx.doi.org/10.2514/1.34321.
• 3. Bichon B J, McFarland J M, Mahadevan S. Efficient surrogate models for reliability analysis of systems with multiple failure modes. Reliability Engineering & System Safety 2011; 96(10): 1386-1395, http://dx.doi.org/10.1016/j.ress.2011.05.008.
• 4. Cai G Q, Elishakoff I. Refined second-order reliability analysis. Structral safety 1994; 14(4): 267-276, http://dx.doi.org/10.1016/0167-4730(94)90015-9.
• 5. Campos-Requena V H, Rivas B L, Perez M A, Wilhelm M. Application of design of experiments, response surface methodology and partial least squares regression on nanocomposites synthesis. Polymer Bulletin 2014; 71(8): 1961-1982, http://dx.doi.org/10.1007/s00289-014-1166-6.
• 6. Ditlevsen O. Narrow Reliability Bounds for Structural Systems. Journal of Structural Mechanics 1979; 7(4): 453-472, http://dx.doi.org/10.1080/03601217908905329.
• 7. Du X P. System reliability analysis with saddle point approximation. Structural and Multidisciplinary Optimization 2010; 42(2): 193-208, http://dx.doi.org/10.1007/s00158-009-0478-x.
• 8. Du X P, Sudjianto A. First-order saddle point approximation for reliability analysis. Aiaa Journal 2004; 42(6): 1199-1207, http://dx.doi.org/10.2514/1.3877.
• 9. Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. Structural Safety 2011; 33(2): 145-154, http://dx.doi.org/10.1016/j.strusafe.2011.01.002.
• 10. Faravelli L. Response-Surface Approach for Reliability-Analysis. Journal of Engineering Mechanics-Asce 1989; 115(12): 2763-2781, http://dx.doi.org/10.1061/(ASCE)0733-9399(1989)115:12(2763).
• 11. Garthwaite P H. An Interpretation of Partial Least-Squares. Journal of the American Statistical Association 1994; 89(425): 122-127, http://dx.doi.org/10.1080/01621459.1994.10476452.
• 12. Gayton N, Bourinet J M, Lemaire M. CQ2RS: a new statistical approach to the response surface method for reliability analysis. Structural Safety 2003; 25(1): 99-121, http://dx.doi.org/10.1016/S0167-4730(02)00045-0.
• 13. Geladi P, Kowalski B R. Partial Least-Squares Regression - a Tutorial. Analytica Chimica Acta 1986; 185: 1-17, http://dx.doi.org/10.1016/0003-2670(86)80028-9.
• 14. Gupta S, Manohar C S. An improved response surface method for the determination of failure probability and importance measures. Structural Safety 2004; 26(2): 123-139, http://dx.doi.org/10.1016/S0167-4730(03)00021-3.
• 15. Hohenbichler M, Gollwitzer S, Kruse W, Rackwitz R. New light on first-and second-order reliability methods. Structural safety 1987; 4(4): 267-284, http://dx.doi.org/10.1016/0167-4730(87)90002-6.
• 16. Huang B Q, Du X P. Probabilistic uncertainty analysis by mean-value first order Saddle point Approximation. Reliability Engineering & System Safety 2008; 93(2): 325-336, http://dx.doi.org/10.1016/j.ress.2006.10.021.
• 17. Huang X Z, Zhang Y M, Wu M C. Research on the method for reliability analysis of structural systems based on the dimensional-reduction integration. Chinese journal of theoretical and applied mechanics 2013; 45(3): 456-460.
• 18. Huang Z, Turner B J, Dury S J, Wallis I R, Foley W J. Estimating foliage nitrogen concentration from HYMAP data using continuum removal analysis. Remote Sensing of Environment 2004; 93(1-2): 18-29, http://dx.doi.org/10.1016/j.rse.2004.06.008.
• 19. Mahadevan S, Raghothamachar P. Adaptive simulation for system reliability analysis of large structures. Computers & Structures 2000; 77(6): 725-734, http://dx.doi.org/10.1016/S0045-7949(00)00013-4.
• 20. Malthouse E C, Tamhane A C, Mah R S H. Nonlinear partial least squares. Computers & Chemical Engineering 1997; 21(8): 875-890, http://dx.doi.org/10.1016/S0098-1354(96)00311-0.
• 21. McDonald M, Mahadevan S. Design optimization with system-level reliability constraints. Journal of Mechanical Design 2008; 130(2): 1-10, http://dx.doi.org/10.1115/1.2813782.
• 22. Mckay M D, Beckman R J, Conover W J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics 1979; 21(2): 239-245.
• 23. Melchers R E. Importance Sampling in Structural Systems. Structural Safety 1989; 6(1): 3-10, http://dx.doi.org/10.1016/0167-4730(89)90003-9.
• 24. Mutingi M. System reliability optimization: a fuzzy multi-objective genetic algorithm approach. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2014; 16(3): 400-406.
• 25. Nie J, Ellingwood B R. Directional methods for structural reliability analysis. Structural Safety 2000; 22(3): 233-249, http://dx.doi.org/10.1016/S0167-4730(00)00014-X.
• 26. Niederreiter H, Spanier J. Monte Carlo and Quasi-Monte Carlo Methods. Berlin: Springer-Verlag, 2000.
• 27. Park J, Towashiraporn P. Rapid seismic damage assessment of railway bridges using the response-surface statistical model. Structural Safety 2014; 47: 1-12, http://dx.doi.org/10.1016/j.strusafe.2013.10.001.
• 28. Rackwitz R. Reliability analysis - a review and some perspectives. Structural Safety 2001; 23(4): 365-395, http://dx.doi.org/10.1016/S0167-4730(02)00009-7.
• 29. Rausand M, Hoyland A. System reliability theory: models, statistical methods, and application. 2nd edn. ed. New York: Wiley-interscience, 2000.
• 30. Schmidtlein S, Sassin J. Mapping of continuous floristic gradients in grasslands using hyperspectral imagery. Remote Sensing of Environment 2004; 92(1): 126-138, http://dx.doi.org/10.1016/j.rse.2004.05.004.
• 31. Shi L, Yang R J, Zhu P. An Adaptive Response Surface Method Using Bayesian Metric and Model Bias Correction Function. Journal of Mechanical Design 2014; 136(3), http://dx.doi.org/10.1115/1.4026095.
• 32. Shieh M D, Yeh Y E. Developing a design support system for the exterior form of running shoes using partial least squares and neural networks. Computers & Industrial Engineering 2013; 65(4): 704-718, http://dx.doi.org/10.1016/j.cie.2013.05.008.
• 33. Song J H, Kiureghian A D. Bounds on system reliability by linear programming. Journal of Engineering Mechanics-Asce 2003; 129(6): 627-636, http://dx.doi.org/10.1061/(ASCE)0733-9399(2003)129:6(627).
• 34. Szybka J, Broniec Z, Pilch R. Forecasting the failure of a thermal pipeline on the basis of risk assessment and exploitation analysis. Eksploatacja i Niezawodnosc -Maintenance and Reliability 2011; (4): 5-10.
• 35. Wang H. Partial least squares regression method and application. Beijing: National defense industry press, 1999.
• 36. Wold S, Sjostrom M, Eriksson L. PLS-regression: a basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems 2001; 58(2): 109-130, http://dx.doi.org/10.1016/S0169-7439(01)00155-1.
• 37. Won J, Choi C, Choi J. Improved dimension reduction method (DRM) in uncertainty analysis using kriging interpolation. Journal of Mechanical Science and Technology 2009; 23(5): 1249-1260, http://dx.doi.org/10.1007/s12206-008-0721-1.
• 38. Youn B D, Wang P F. Complementary Intersection Method for System Reliability Analysis. Journal of Mechanical Design 2009; 131(4): 1-15, http://dx.doi.org/10.1115/1.3086794.
• 39. Zhao W, Wang W. Application of non-linear partial least squares regression method to response surface method with uniform design. Acta aeronautica et astronautica sinica 2012; 33(5): 839-847.
• 40. Zhao W, Wang W. Application of partial least squares regression in response surface for analysis of structural reliability. Engineering mechanics 2013; 30(2): 272-277.
• 41. Zou T, Mahadevan S, Mourelatos Z, Meernik P. Reliability analysis of automotive body-door subsystem. Reliability Engineering & System Safety 2002; 78(3): 315-324, http://dx.doi.org/10.1016/S0951-8320(02)00178-3.