Efficient uncertainty propagation for parameterized p-box using sparse-decomposition-based polynomial chaos expansion

• Published in: Mechanical systems and signal processing 2020-04, Vol.138, p.106589, Article 106589
• Main Authors: Liu, H.B., Jiang, C., Xiao, Z.
• Format: Article
• Language: English
• Subjects: Boxes; Decomposition; Distribution functions; Epistemology; Parameter uncertainty; Parameterization; Parameterized p-box; Polynomial chaos expansion; Polynomials; Probability bounds; Propagation; Response functions; Sparse decomposition; Uncertainty analysis; Uncertainty propagation analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.106589

•The proposed method adopts the sparse-decomposition-based polynomial chaos expansion.•The proposed method can improve efficiency for the propagation of parameterized p-box.•The proposed method can provide sufficient accuracy for general engineering problems. Uncertainty propagation (UP) is the process of determining the effect of input uncertainties on a response of interest. These input uncertainties may be characterized as either aleatory uncertainties, which are irreducible variabilities inherent in nature, or epistemic uncertainties, which are reducible uncertainties resulting from a lack of knowledge. In this paper we propose an efficient uncertainty propagation analysis method for problems with parameterized probability-boxes (P-boxes) accounting for aleatory and epistemic uncertainties. Firstly, the sparse-decomposition-based polynomial chaos expansion (PCE) method is presented to tackle the aleatory uncertainty, in which a basis selection strategy based on the sparse decomposition is devised to automatically detect the significant basis set of PCE. Then, to deal with the epistemic uncertainty on the distribution parameters, the coefficients of the sparse-decomposition-based PCE are treated as quadratic polynomial functions of the interval-valued distribution parameters of parameterized p-boxes. Finally, the bounds of the first four moments and the cumulative distribution function (CDF) of the response function can be successfully obtained. Four numerical examples are analyzed to verify the effectiveness of the proposed method.