Construction of ellipsoid convex model of bounded uncertainties with outlier detection for application in non-probabilistic topology optimization

Abstract

The ellipsoid convex model can be suitably used for structural analysis and design optimization under uncertain-but-bounded parameters and loads. Such a model can be constructed using measured samples of the uncertainties. However, the presence of outliers is often unavoidable due to system fluctuations in the measurements. Thus, it is necessary to detect any outliers among the samples before constructing the uncertainty model to prevent over-conservativeness. To this end, the present paper proposes a rational approach for constructing ellipsoid convex models with outlier detection. The concept of the local outlier factor (LOF) is utilized, in conjunction with the k-nearest natural neighbor to adaptively determine the neighborhood range. Then the outliers are detected using the scaled median absolute deviation method, based on the LOF values obtained. Finally, the minimum-volume ellipsoid convex model is constructed with a mathematically strict and efficient semi-definite programming formulation using the normal samples. The validity of the proposed approach is demonstrated with numerical examples. The application of the constructed uncertainty model in non-probabilistic robust topology optimization is demonstrated, and the results show the effectiveness of the proposed approach.