Abstract
In traditional reliability analysis, the uncertain parameters are generally treated by some ideal probability distributions with infinite tails, which, however, seems inconsistent with the practical situations as nearly all the uncertain parameters in engineering structures will get their values within a limited interval. To eliminate such an inconsistence and thereby improve the precision of the reliability analysis, the truncated probability distributions are then employed to quantify the uncertainty in this paper, and a corresponding reliability analysis method is developed. Two cases of positional relations are summarized for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty. The probability and non-probability convex model methods are employed to deal with these two cases, respectively, and based on it, a hybrid reliability model is then constructed for truncated distribution problems. An efficient approach is also provided to distinguish these two positional relations and thereby determine which one of the probability and non-probability methods should be used when computing a real hybrid reliability. Five numerical examples are investigated to demonstrate the effectiveness of the present method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hasofer A.M., Lind N.C.: Exact and invariant second-moment code format. ASME J. Eng. Mech. Div. 100, 111–121 (1974)
Rackwitz R., Fiessler B.: Structural reliability under combined random load sequences. Comput. Struct. 9, 489–494 (1978)
Hohenbichler M., Rackwitz R.: Non-normal dependent vectors in structural safety. ASME J. Eng. Mech. Div. 107, 1227–1238 (1981)
Breitung K.W.: Asymptotic approximation for multinormal integrals. ASCE J. Eng. Mech. 110, 357–366 (1984)
Breitung K.W.: Asymptotic Approximations for Probability Integrals. Springer, Berlin (1994)
Polidori D.C., Beck J.L., Papadimitriou C.: New approximations for reliability integrals. ASCE J. Eng. Mech. 125, 466–475 (1994)
Thoft-Christensen P., Murotsu Y.: Application of Structural Systems Reliability Theory. Springer, Berlin (1986)
Ang A.H.S., Tang W.H.: Probability Concepts in Engineering Planning and Design. vol II: Decision, Risk and Reliability. Wiley, New York (1984)
Rubinstein R.Y., Kroese D.P.: Simulation and The Monte-Carlo Method, 2nd edn. Wiley, New York (2007)
Augusti G., Baratta A., Gasciati F.: Probabilistic Methods in Structural Engineering. Chapman and Hall, London (1984)
Kirjner-Neto C., Polak E., Kiureghian D.: An outer approximations approach to reliability-based optimal design of structures. J. Optim. Theory Appl. 98, 1–16 (1998)
Royset J.O., Kiureghian A.D., Polak E.: Reliability-based optimal structural design by the decoupling approach. Reliab. Eng. Syst. Saf. 73, 213–221 (2001)
Cheng G.D., Xu L., Jiang L.: A sequential approximate programming strategy for reliability-based structural optimization. Comput. Struct. 84, 1353–1367 (2006)
Liang J.H., Mourelatos Z.P., Nikolaidis E.: A single-loop approach for system reliability-based desing optimization. ASME J. Mech. Des. 129, 1215–1224 (2007)
Luo Y.J., Kang Z., Luo Z., Alex L.: Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Struct. Multidiscip. Optim. 39, 297–310 (2008)
Kang Z., Luo Y.J.: Reliability-based structural optimization with probability and convex set hybrid models. Struct. Multidiscip. Optim. 42, 89–102 (2010)
Du X.P., Chen W.: Sequential optimization and reliability assessment method for efficient probabilistic design. ASME J. Mech. Des. 126, 225–233 (2004)
Sweet A.L., Tu J.F.: Evaluating tolerances and process capability when using truncated probability density functions. Int. J. Prod. Res. 44, 3493–3508 (2006)
Sun Z.L., He X.H.: Reliability calculation method based on cutting-off tail distribution at two ends. Mach. Des. Manuf. 4, 10–12 (1997)
He S.Q., Wang S.: Structural Reliability Analysis and Design. National Defence Industry Press, Beijing (1993)
Xu F.Y., Chen A.R.: Structural reliability analysis based on truncated probabilistic distribution. Eng. Mech. 23, 52–57 (2006)
Melchers R.E., Ahammed M., Middleton C.: FORM for discontinuous and truncated probability density functions. Struct. Saf. 25, 305–313 (2003)
Ben-Haim Y., Elishakoff I.: Convex Models of Uncertainties in Applied Mechanics. Elsevier, Amsterdam (1990)
Qiu Z.P., Wang XJ.: Parameter perturbation method for dynamic responses of structures with uncertain-but-bounded parameters based on interval analysis. Int. J. Solids Struct. 42, 4958–4970 (2005)
Au F.T.K., Cheng Y.S., Tham L.G., Zeng G.W.: Robust design of structures using convex models. Comput. Struct. 81, 2611–2619 (2003)
Jiang C., Han X., Liu G.R.: Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval. Comput. Methods Appl. Mech. Eng. 196, 4791–4890 (2007)
Guo X., Bai W., Zhang W.S.: Extremal structural response analysis of truss structures under load uncertainty via SDP relaxation. Comput. Struct. 87, 246–253 (2009)
Ganzerli S., Pantelides C.P.: Optimum structural design via convex model superposition. Comput. Struct. 74, 639–647 (2000)
Ganzerli S., Pantelides C.P.: Load and resistance convex model for optimum design. J. Struct. Multidiscip. Optim. 17, 259–268 (1999)
Sun Z.L., Chen L.Y.: Practical Theory and Method for Mechanical Reliability Design. Science Press, Beijing (2003)
Madsen H.O., Krenk S., Lind N.C.: Methods of Structural Safety. Prentice-Hall, Englewood Cliffs (1986)
Guo S.X., Lu Z.Z., Feng Y.S.: A non-probabilistic model of structural reliability based on interval analysis. J. Comput. Mech. 18, 56–60 (2001)
Chen X.Y., Tang C.Y., Tsui C.P., Fan J.P.: Modified scheme based on semi-analytic approach for computing non-probabilistic reliability index. Acta Mech. Solida. Sin. 23, 115–123 (2010)
Yuan Y.X., Sun W.Y.: Optimization Theories and Methods. Scientific Press, Beijing (2005)
Du X.P.: Saddlepoint approximation for sequential optimization and reliability analysis. ASME J. Mech. Des. 130, 011022–0110011 (2008)
Jiang C., Han X.: A new uncertain optimization method based on intervals and an approximation management model. CMES-Comp. Model. Eng. 22, 97–118 (2007)
Belytschko T., Liu W.K., Moran B.: Nonlinear Finite Elements for Continua and Structures, 3rd edn. Wiley, Chichester (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, C., Han, X. & Lu, G.Y. A hybrid reliability model for structures with truncated probability distributions. Acta Mech 223, 2021–2038 (2012). https://doi.org/10.1007/s00707-012-0691-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-012-0691-3