Adaptive simulation for system reliability analysis of large structures
Introduction
The reliability of a structural system may be estimated at two levels: component level and system level. At the level of components (i.e., individual performance criteria), limit state formulations and efficient analytical and simulation procedures have been developed for reliability estimation. System level reliability analysis addresses two types of issues: (1) multiple performance criteria, or multiple limit states and (2) multiple paths or sequences of individual component failures leading to overall system failure. Component failures may be modeled as ductile (full residual capacity after failure), brittle (no residual capacity after failure), or semi-brittle (partial residual capacity after failure).
The algorithms to compute system reliability can generally be grouped into two categories, namely, analytical methods and simulation methods. Analytical methods present elegant approaches to enumerate significant failure sequences, but involve restrictive simplifying assumptions on structural behavior and approximate bounds during the probability computation. The simulation methods are simpler to implement, robust in performance, and can incorporate realistic structural behavior, but they tend to be computationally expensive for practical high-reliability systems. Therefore, the objective of this article is to present a hybrid procedure that combines analytical and simulation methods in order to efficiently and accurately estimate structural system reliability.
Section snippets
Structural system reliability
For typical structural systems, failure is defined as the formation of an unstable collapse state under some applied loads. For large structures with a high degree of redundancy, there may be several possible ways to reach a collapse state. Each such path is called a failure sequence. For larger structures, there are a large number of failure sequences, and it is practically impossible to enumerate each sequence. However, in most of the cases, only a small fraction of the sequences contributes
Branch and bound method
The branch and bound method, as the name suggests, involves two main operations, namely, the branching operation and the bounding operation. In the branching operation, starting from an intact structure, failure is imposed at the most likely location as indicated by the reliability analysis of all the components. Starting from this failure, further analysis is carried out and the next failure is imposed at the location with the highest path probability. This process is continued progressively
Concept of importance-sampling
The basic formula to compute the system failure probability iswhere g1(x)⩽0,…,gn(x)⩽0 are the n failure domains corresponding to the n significant failure sequences of the system, fX(x) is the joint probability density function of all the input random variables (both load and resistance variables). In basic Monte Carlo simulation, the sample points are generated using fX(x). For importance-sampling, the preceding equation can be rewritten as
Computer implementation
The computer implementation of the proposed adaptive importance-sampling method for computing system failure probability can be divided into three distinct sections:
- 1.
branch and bound method,
- 2.
adaptive sampling,
- 3.
structural analysis.
Different tasks are used in each of these sections. Hence, these three sections can be kept separate from each other. The first two sections make use of the third section for all the structural analyses.
The first section consists of tasks related to the identification of
Application to ductile, brittle, and semi-ductile structures
The proposed method is general enough to include all three types of structural failure: brittle, ductile, and semi-ductile. In the case of ductile structures, the members carry their load capacity after failure, e.g., yielding of steel frame members due to bending. In the case of brittle failure (e.g., shear, buckling, fracture, etc.), the member does not have any residual capacity corresponding to that failure mode. And in the case of semi-ductile (or semi-brittle) failure, the members have a
Numerical examples
This section illustrates the application of the adaptive simulation technique to two practical structures. It describes in detail the procedure specific to each problem including the finite element modeling, adaptive simulation technique and finally the results. Both ductile and brittle failure modes are considered. The following two problems are considered: (1) a six-story two-bay building frame and (2) a transmission tower truss.
Conclusion
In this article, an adaptive simulation technique is proposed for the system reliability estimation of large structural systems. The method is implemented in combination with a commercial finite element code, and its application is illustrated for two realistic structures. The proposed technique is found to be efficient and reasonably accurate. The method in general, is applicable to ductile, brittle, and semi-ductile behavior, and overcomes the limitations of the analytical techniques. It also
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