Data-driven sensitivity indices for models with dependent inputs using polynomial chaos expansions

Abstract Generalized Polynomial Chaos Expansion (gPCE) is widely used in uncertainty quantification and sensitivity analysis for applications in the aerospace industry. gPCE uses the spectrum projection to fit a polynomial model, the gPCE model, to a sparse grid Design of Experiments (DOEs). The gPCE model can be used to make predictions, analytically determine uncertainties, and calculate sensitivity indices. However, the model’s accuracy is very dependent on having complete DOEs. When a sampling point is missing from the sparse grid DOE, this severely impacts the accuracy of the gPCE analysis and often necessitates running a new DOE. Missing data points are a common occurrence in engineering testing and simulation. This problem complicates the use of the gPCE analysis. In this paper, we present a statistical imputation method for addressing this missing data problem. This methodology allows gPCE modeling to handle missing values in the sparse grid DOE. Using a series of numerical results, the study demonstrates the convergence characteristics of the methodology with respect to reaching steady state values for the missing points. The article concludes with a discussion of the convergence rate, advantages, and feasibility of using the proposed methodology.

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Data-driven polynomial chaos expansions: A weighted least-square approximation

Journal of Computational Physics ◽

10.1016/j.jcp.2018.12.020 ◽

2019 ◽

Vol 381 ◽

pp. 129-145 ◽

Cited By ~ 3

Author(s):

Ling Guo ◽

Yongle Liu ◽

Tao Zhou

Keyword(s):

Polynomial Chaos ◽

Least Square ◽

Data Driven ◽

Weighted Least Square ◽

Polynomial Chaos Expansions

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Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty-Based Design Optimization

Mathematical Problems in Engineering ◽

10.1155/2019/7498526 ◽

2019 ◽

Vol 2019 ◽

pp. 1-19 ◽

Cited By ~ 1

Author(s):

Xiao Wei ◽

Haichao Chang ◽

Baiwei Feng ◽

Zuyuan Liu

Keyword(s):

Sensitivity Analysis ◽

Design Optimization ◽

Polynomial Chaos ◽

Early Stage ◽

Computational Cost ◽

Sensitivity Index ◽

Uncertain Variables ◽

Polynomial Coefficients ◽

Sensitivity Indices ◽

Polynomial Chaos Expansions

In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.

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