Sensitivity analysis for reliability-based optimization using an AFOSM method

Abstract A method of design sensitivity analysis for a failure probability is presented and formulas are derived, such that a gradient-based optimization technique can be applied for a general reliability-based optimal design formulation. It is based on using an advanced first order second moment (AFOSM) method in evaluating the probability. The resulting sensitivity coefficient contains only first order derivatives. Hence, it is very suitable for numerical implementation. The method is illustrated by several examples which include cases with state equations from a finite element method. A frame optimal design is also presented to demonstrate the method of solution for the reliability-based optimal design.

[1]  J. G. Jalón,et al.  A new direct method for the simple and efficient reanalysis of structures , 1985 .

[2]  Felix S. Wong,et al.  First-order, second-moment methods , 1985 .

[3]  Palle Thoft-Christensen,et al.  Structural Reliability Theory and Its Applications , 1982 .

[4]  Singiresu S Rao,et al.  Reliability-based optimization under random vibration environment , 1981 .

[5]  Tae Won Lee,et al.  A Reliability-Based Optimal Design Using Advanced First Order Second Moment Method , 1987 .

[6]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[7]  Dan M. Frangopol.  A reliability-based optimization technique for automatic plastic design , 1984 .

[8]  Ashok D. Belegundu,et al.  Lagrangian Approach to Design Sensitivity Analysis , 1985 .

[9]  G. Vanderplaats,et al.  Efficient calculation of optimum design sensitivity , 1984 .

[10]  O. Ditlevsen.  Generalized Second Moment Reliability Index , 1979 .

[11]  Fred Moses,et al.  Structural system reliability and optimization , 1977 .

[12]  M. Shinozuka.  Basic Analysis of Structural Safety , 1983 .

[13]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .

[14]  Singiresu S Rao,et al.  Structural optimization by chance constrained programming techniques , 1980 .

[15]  Dan M. Frangopols.  Computer-automated sensitivity analysis in reliability-based plastic design , 1986 .

[16]  B. Kwak,et al.  Optimum design in the presence of parametric uncertainty , 1976 .

[17]  Ove Ditlevsen,et al.  Taylor Expansion of Series System Reliability , 1984 .

[18]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[19]  Erik H. Vanmarcke,et al.  Matrix formulation of reliability analysis and reliability-based design , 1973 .

[20]  O. Ditlevsen.  Narrow Reliability Bounds for Structural Systems , 1979 .

[21]  B. Ayyub,et al.  Practical Structural Reliability Techniques , 1984 .

[22]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[23]  Lewis P. Felton,et al.  Optimum design of structures with random parameters , 1977 .

[24]  K. M. Mjelde.  Reliability Bounds for Serial Systems , 1984 .

[25]  C. Cornell.  Bounds on the Reliability of Structural Systems , 1967 .

[26]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[27]  E. Haug,et al.  Parametric optimal design , 1976 .