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The structural reliability analysis in presence of mixed uncertain variables demands more computation as the entire configuration of fuzzy variables needs to be explored. Moreover, the existence of multiple design points plays an important role in the accuracy of results as the optimization algorithms may converge to a local design point by neglecting the main contribution from the global design point. Therefore, in this chapter, a novel uncertain analysis method for estimating the failure probability bounds of structural systems involving multiple design points in presence of mixed uncertain variables is presented. The proposed method involves weight function to identify multiple design points, multicut-high dimensional model representation technique for the limit state function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral, and fast Fourier transform for solving the convolution integral. The proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability analysis involving any number of fuzzy and random variables with any kind of distribution. The numerical examples presented demonstrate the accuracy and efficiency of the proposed method.

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  1. Breitung K (1984) Asymptotic approximations for multinormal integrals. ASCE J Eng Mech 110(3):357–366

    Article  Google Scholar 

  2. Rackwitz R (2001) Reliability analysis – a review and some perspectives. Struct Saf 23(4):365–395

    Article  Google Scholar 

  3. Sakamoto J, Mori Y, Sekioka T (1997) Probability analysis method using fast Fourier transform and its application. Struct Saf 19(1):21–36

    Article  Google Scholar 

  4. Rao BN, Chowdhury R (2008) Probabilistic analysis using high dimensional model representation and fast Fourier transform. Int J Comput Methods Eng Sci Mech 9(6):342–357

    Article  MATH  Google Scholar 

  5. Au SK, Papadimitriou C, Beck JL (1999) Reliability of uncertain dynamical systems with multiple design points. Struct Saf 21:113–133

    Article  Google Scholar 

  6. Kiureghian AD, Dakessian T (1998) Multiple design points in first and second order reliability. Struct Saf 20(1):37–49

    Article  Google Scholar 

  7. Briabant V, Oudshoorn A, Boyer C, Delcroix F (1999) Nondeterministic possibilisticapproaches for structural analysis and optimal design. AIAA J 37(10):1298–1303

    Google Scholar 

  8. Penmetsa RC, Grandhi RV (2003) Uncertainty propagation using possibility theory and function approximations. Mech Based Des Struct Mach 81(15):1567–1582

    Google Scholar 

  9. Rabitz H, Alis OF, Shorter J, Shim K (1999) Efficient input-output model representations. Comput Phys Commun 117(1–2):11–20

    Article  MATH  Google Scholar 

  10. Kaymaz I, McMahon CA (2005) A response surface method based on weighted regression for structural reliability analysis. Probab Eng Mech 20(1):11–17

    Article  Google Scholar 

  11. Adduri PR, Penmetsa RC (2008) Confidence bounds on component reliability in the presence of mixed uncertain variables. Int J Mech Sci 50(3):481–489

    Article  Google Scholar 

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Correspondence to A. S. Balu .

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Balu, A.S., Rao, B.N. (2013). Failure Probability Bounds Using Multicut-High-Dimensional Model Representation. In: Chakraborty, S., Bhattacharya, G. (eds) Proceedings of the International Symposium on Engineering under Uncertainty: Safety Assessment and Management (ISEUSAM - 2012). Springer, India.

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