An Analysis of Sampling Methods and Uncertainty Propagation for Shallow Water Modeling Público

Fan, Muqi (Spring 2023)

Permanent URL: https://etd.library.emory.edu/concern/etds/6682x529c?locale=es
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Abstract

Numerical models depend on inputs and parameters that are often uncertain. This causes uncertainty in the output. In this work, we explore both sampling and uncertainty propagation methods. We aim to assess which sampling methods best represent uncertainties in inputs and also explore which uncertainty propagation methods best depict the uncertainty that results in the output. We assess these methods using a two-dimensional shallow water model.

Table of Contents

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . .1

2 Sampling Methodologies . . . . . . . . . . . . . . . . . . . . . . .3

2.1 Random Sampling . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Stratified Sampling Method . . . . . . . . . . . . . . . . . . . 4

2.3 Latin Hypercube Sampling . . . . . . . . . . . . . . . . . . . . 6

2.4 Comparing Sampling Methods . . . . . . . . . . . . . . . . . . 8

3 Procedures Measure Propagation of Uncertainty 9

3.1 Monte Carlo Analysis . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Monte Carlo Analysis . . . . . . . . . . . . . . . . . . . 10

3.1.2 Rejection Sampling . . . . . . . . . . . . . . . . . . . . 12

3.1.3 Importance Sampling . . . . . . . . . . . . . . . . . . . 13

3.2 Differential Analysis . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Response Surface Methodology(RSM) . . . . . . . . . . . . . . 15

3.4 Fourier Amplitude Sensitivity Test(FAST) . . . . . . . . . . . 20

4 Applications 23

4.1 Shallow Water Equation in 2D . . . . . . . . . . . . . . . . . . 23

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.1 Response Surface Method and Differential Analysis . . 28

4.2.2 The Differential Analysis . . . . . . . . . . . . . . . . . 29

4.2.3 The Fourier Amplitude Sensitivity test . . . . . . . . . 30

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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