Structural Reliability Analysis by Using Non-Probabilistic Multi-Cluster Ellipsoidal Model

Uncertainties are normally unavoidable in engineering practice, which should be taken into account in the structural design and optimization so as to reduce the relevant risks. Yet, the probabilistic models of the uncertainties are often unavailable in the problems due to the lack of samples, and the precision of the conventional non-probabilistic models are not satisfactory when the samples are of multi-cluster distribution. In view of this, an improved method by using a non-probabilistic multi-cluster ellipsoidal model (multi-CEM) for the critical structural reliability analysis is proposed in this paper, which describes the samples in a more accurate and compact way and helps to acquire more satisfactory reliability analysis results. Firstly, a Gaussian mixture model (GMM) is built for the multi-cluster samples with performing expectation maximization (EM) algorithm, based on which the multi-CEM can be constructed. In the structural reliability analysis, two cases, respectively, considering whether the components of the multi-CEM are intersected or not are researched in detail. The non-probabilistic reliability (NPR) indexes for each component of the multi-CEM are computed using the Hasofer–Lind–Rackwitz–Fiessler (HL-RF) algorithm, and then the multidimensional volume ratios of the safe domain to the whole uncertainty domain are computed based on these indexes, indicating the structural NPR. In the end, two numerical examples and a practical application are conducted and analyzed to testify the effectiveness of the method.