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E-grāmata: Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification

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  • Formāts: 144 pages
  • Izdošanas datums: 26-Jun-2012
  • Izdevniecība: National Academies Press
  • Valoda: eng
  • ISBN-13: 9780309256353
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Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty QuantificationPalielināt
  • Formāts: 144 pages
  • Izdošanas datums: 26-Jun-2012
  • Izdevniecība: National Academies Press
  • Valoda: eng
  • ISBN-13: 9780309256353
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Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification.



As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes.



Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.

Table of Contents



Front Matter Summary 1 Introduction 2 Sources of Uncertainty and Error 3 Verification 4 Emulation, Reduced-Order Modeling, and Forward Propagation 5 Model Validation and Prediction 6 Making Decisions 7 Next Steps in Practice, Research, and Education for Verification, Validation, and Uncertainty Quantification Appendixes Appendix A: Glossary Appendix B: Agendas of Committee Meetings Appendix C: Committee Biographies Appendix D: Acronyms
Summary
1 Introduction
1.1 Overview and Study Charter
7(1)
1.2 VVUQ Definitions
8(1)
1.3 Scope of This Study
9(1)
1.3.1 Focus on Prediction with Physics/Engineering Models
9(1)
1.3.2 Focus on Mathematical and Quantitative Issues
9(1)
1.4 VVUQ Processes and Principles
10(3)
1.4.1 Verification
10(1)
1.4.2 Validation
11(1)
1.4.3 Prediction
11(1)
1.4.4 Uncertainty Quantification
12(1)
1.4.5 Key VVUQ Principles
13(1)
1.5 Uncertainty and Probability
13(1)
1.6 Ball-Drop Case Study
14(4)
1.6.1 The Physical System
16(1)
1.6.2 The Model
16(1)
1.6.3 Verification
16(1)
1.6.4 Sources of Uncertainty
16(1)
1.6.5 Propagation of Input Uncertainties
17(1)
1.6.6 Validation and Prediction
17(1)
1.6.7 Making Decisions
17(1)
1.7 Organization of This Report
18(1)
1.8 References
18(1)
2 Sources of Uncertainty and Error
2.1 Introduction
19(1)
2.2 Projectile-Impact Example Problem
20(3)
2.3 Initial Conditions
23(1)
2.4 Level of Fidelity
24(1)
2.5 Numerical Accuracy
24(1)
2.6 Multiscale Phenomena
25(1)
2.7 Parametric Settings
26(1)
2.8 Choosing a Model Form
26(1)
2.9 Summary
26(1)
2.10 Climate-Modeling Case Study
27(3)
2.10.1 Is Formal UQ Possible for Truly Complex Models?
28(1)
2.10.2 Future Directions for Research and Teaching Involving UQ for Climate Models
29(1)
2.11 References
30(1)
3 Verification
31(6)
3.1 Introduction
31(1)
3.2 Code Verification
32(1)
3.3 Solution Verification
33(2)
3.4 Summary of Verification Principles
35(1)
3.5 References
36(1)
4 Emulation, Reduced-Order Modeling, and Forward Propagation
37(15)
4.1 Approximating the Computational Model
38(3)
4.1.1 Computer Model Emulation
38(1)
4.1.2 Reduced-Order Models
39(2)
4.2 Forward Propagation of Input Uncertainty
41(1)
4.3 Sensitivity Analysis
42(4)
4.3.1 Global Sensitivity Analysis
43(1)
4.3.2 Local Sensitivity Analysis
44(2)
4.4 Choosing Input Settings for Ensembles of Computer Runs
46(1)
4.5 Electromagnetic Interference in a Tire Pressure Sensor: Case Study
46(3)
4.5.1 Background
46(1)
4.5.2 The Computer Model
46(2)
4.5.3 Robust Emulators
48(1)
4.5.4 Representative Result
49(1)
4.6 References
49(3)
5 Model Validation and Prediction
52(34)
5.1 Introduction
52(7)
5.1.1 Note Regarding Methodology
54(3)
5.1.2 The Ball-Drop Example Revisited
57(1)
5.1.3 Model Validation Statement
58(1)
5.2 Uncertainties in Physical Measurements
59(1)
5.3 Model Calibration and Inverse Problems
60(3)
5.4 Model Discrepancy
63(4)
5.5 Assessing the Quality of Predictions
67(3)
5.6 Automobile Suspension Systems Case Study
70(4)
5.6.1 Background
70(1)
5.6.2 The Computer Model
70(1)
5.6.3 The Process Being Modeled and Data
70(1)
5.6.4 Modeling the Uncertainties
71(1)
5.6.5 Analysis and Results
72(2)
5.7 Inference from Multiple Computer Models
74(1)
5.8 Exploiting Multiple Sources of Physical Observations
75(1)
5.9 PECOS Case Study
75(4)
5.9.1 Overview
75(1)
5.9.2 Verification
76(1)
5.9.3 Code Verification
76(1)
5.9.4 Solution Verification
77(1)
5.9.5 Validation
78(1)
5.10 Rare, High-Consequence Events
79(1)
5.11 Conclusion
80(3)
5.12 References
83(3)
6 Making Decisions
86(9)
6.1 Overview
86(1)
6.2 Decisions Within VVUQ Activities
86(1)
6.3 Decisions Based on VVUQ Information
87(1)
6.4 Decision Making Informed by VVUQ in the Stockpile Stewardship Program
88(2)
6.5 Decision Making Informed by VVUQ at the Nevada National Security Site
90(3)
6.5.1 Background
90(1)
6.5.2 The Physical System
91(1)
6.5.3 Computational Modeling of the Physical System
92(1)
6.5.4 Parameter Estimation
92(1)
6.5.5 Making (Extrapolative) Predictions and Describing Uncertainty
93(1)
6.5.6 Reporting Results to Decision Makers and Stakeholders
93(1)
6.6 Summary
93(1)
6.7 References
94(1)
7 Next Steps in Practice, Research, and Education for Verification, Validation, and Uncertainty Quantification
95(14)
7.1 VVUQ Principles and Best Practices
95(3)
7.1.1 Verification Principles and Best Practices
96(1)
7.1.2 Validation and Prediction Principles and Best Practices
97(1)
7.2 Principles and Best Practices in Related Areas
98(2)
7.2.1 Transparency and Reporting
98(1)
7.2.2 Decision Making
99(1)
7.2.3 Software, Tools, and Repositories
99(1)
7.3 Research for Improved Mathematical Foundations
100(3)
7.3.1 Verification Research
100(1)
7.3.2 UQ Research
101(1)
7.3.3 Validation and Prediction Research
102(1)
7.4 Education Changes for the Effective Integration of VVUQ
103(3)
7.4.1 VVUQ at the University
103(3)
7.4.2 Spreading the Word
106(1)
7.5 Closing Remarks
106(1)
7.6 References
106(3)
APPENDIXES
A Glossary
109(11)
B Agendas of Committee Meetings
120(4)
C Committee Biographies
124(6)
D Acronyms
130
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