Abstract
Response surface method (RSM) is mostly adopted to overcome the computational challenge of Monte Carlo simulation (MCS)-based reliability assessment of system comprising implicit limit state function (LSF). In the present study, a hybrid response surface function (HRSF) based on exponential approximation and second-order polynomial estimation is investigated for improved response approximation for reliability analysis. The method calibrates each random variable according to the response function using an exponential function having a varying parameter that attempts to accommodate the nonlinearity of each variable in the LSF. The exponential function is further regressed using conventional quadratic polynomial model. The effectiveness of the proposed HRSF-based approach is elucidated numerically by considering several saturated designs and uniform design schemes. The performance of the proposed procedure is demonstrated by comparing the proposed response approximation and the usual polynomial RSM-based approximation with that of obtained by the most accurate direct MCS technique.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
N.R. Mann, R.E. Schafer, N.D. Singpurwalla, Methods for Statistical Analysis of Reliability and Life Data (Wiley, New York, 1974)
B. Richard, C. Cremona, L. Adelaide, A response surface method based on support vector machines trained with an adaptive experimental design. Struct. Saf. 39, 14–21 (2012)
L. Faravelli, Response surface approach for reliability analyses. J. Eng. Mech. 115(2), 2763–2781 (1989)
C.G. Bucher, U. Bourgund, A fast and efficient response surface approach for structural reliability problems. Struct. Saf. 7(1), 57–66 (1990)
M.R. Rajashekhar, B.R. Ellingwood, A new look at the response surface approach for reliability analysis. Struct. Saf. 12(3), 205–220 (1993)
S.H. Kim, S.W. Na, Response surface method using vector projected sampling points. Struct. Safety 19, 3–19 (1997)
I. Kaymaz, C.A. McMahon, A response surface method based on weighted regression for structural reliability analysis. Probab. Eng. Mech. 20, 11–17 (2005)
D.L. Allaix, V.I. Carbone, An improvement of the response surface method. Struct. Saf. 33, 165–172 (2011)
W. Zhao, Z. Qiu, An efficient response surface method and its application to structural reliability and reliability-based optimization. Finite Elem. Anal. Des. 67, 34–42 (2013)
S. Goswami, S. Ghosh, S. Chakraborty, Reliability analysis of structures by iterative improved response surface method. Struct. Saf. 60, 56–66 (2016)
G. Su, L. Peng, L. Hu, A Gaussian process-based dynamic surrogate model for complex engineering structural reliability analysis. Struct. Saf. 68, 97–109 (2017)
B. Keshtegar, O. Kisi, Modified response-surface method: new approach for modeling pan evaporation. J. Hydrol. Eng. 22(10) (2017). https://doi.org/10.1061/(ASCE)HE.1943-5584.0001541
B. Keshtegar, S. Heddam, Modelling daily dissolved oxygen concentration using modified response surface method and artificial neural network: a comparative study. Neural Comput. Appl. 1–12 (2017)
N.R. Draper, H. Smith, Applied Regression Analysis (Wiley-Interscience, 1998). ISBN 0-471-17082-8
C.J. Willmott, K. Matsuura, Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim. Res. 30, 79–82 (2005)
A.D. Kiureghian, M. De Stefano, Efficient algorithm for second order reliability analysis. J. Eng. Mech. 117 (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kabasi, S., Chakraborty, S. (2020). Hybrid Response Surface Function-Based Metamodeling of Response Approximation for Reliability Analysis. In: Varde, P., Prakash, R., Vinod, G. (eds) Reliability, Safety and Hazard Assessment for Risk-Based Technologies. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-9008-1_47
Download citation
DOI: https://doi.org/10.1007/978-981-13-9008-1_47
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9007-4
Online ISBN: 978-981-13-9008-1
eBook Packages: EngineeringEngineering (R0)