An adaptive directional importance sampling method for structural reliability

• Published in: Probabilistic engineering mechanics Vol. 26; no. 2; pp. 134 - 141
• Main Author: Grooteman, Frank
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.2011; Elsevier
• Subjects: Adaptive; Aircraft; Aircraft components; Directional simulation; Exact sciences and technology; Experimental design; Failure probability; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Importance sampling; Limit states; Mathematics; Nodular iron; Physics; Probability and statistics; Response surfaces; Robustness; Sampling; Sciences and techniques of general use; Solid mechanics; Statistics; Stochasticity; Structural and continuum mechanics; Structural reliability; Structural reliability; Adaptive; Directional simulation; Failure probability; Importance sampling; Alternating direction method; Nuclear industry; Probabilistic approach; Potential theory; Potential function; Stochastic method; Modeling; Adaptive method; Sphere; Airplane; Sampling methods; Response surface; Robustness; Potential method; Aircraft
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2010.11.002

In this paper, an adaptive directional importance sampling (ADIS) method is presented. The algorithm is based on a directional simulation scheme in which the most important directions are sampled exact and the others by means of a response surface approach. These most important directions are determined by a β -sphere enclosing the most important part(s) of the limit state. The β -sphere and response surface are constantly updated during sampling with information that becomes available from the exact evaluations making the scheme adaptive. Various widely used test problems, representing a broad range of complex limit states that can occur in practice, of which several that pose potential problems to stochastic methods in general, demonstrate the high efficiency, accuracy and robustness of the method. As such, the ADIS method is of particular interest in applications with a low probability of failure and medium number (up to about 40) of stochastic variables, for instance in aircraft and nuclear industry.