Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-Scale Systems

by Cacuci; Dan Gabriel

• ISBN13: 9781584881162
• ISBN10: 158488116X
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-05-16
• Publisher: CRC Press

Summary

There are many methods for performing sensitivity and uncertainty analysis. Two of the modern--and most useful--deterministic methods, the Adjoint Sensitivity Analysis Procedure (ASAP) and the Global Adjoint Sensitivity Analysis (GASAP), received detailed theoretical treatment in Volume I of this book. This volume extends the underlying theory of these methods into practice with a focus on their application to large-scale systems.Sensitivity and Uncertainty Analysis Volume II: Applications to Large-Scale Systems begins with a review of the most prominent screening design, statistical, and deterministic methods. The authors then explore applications of the ASAP to transient one-dimensional two-phase flow problems, in particular its implementation into a large-scale code that simulates the thermal-hydraulic characteristics of light water nuclear reactors. They go on to build the theoretical foundation for the modular implementation of the ASAP for complex simulations systems and present the general sensitivity theory for the response functional of a physical system defined at critical points. The remaining chapters are devoted to applications of the ASAP to sensitivity analyses of large-scale models used for numerical weather prediction and climatic research and simulation.The examples presented clearly demonstrate the advantages of using the ASAP for large-scale systems characterized by many variables and parameters, particularly its exceptional computational efficiency. Rigorous but accessible, this book will build a thorough familiarity with ASAP and its advantages and make ASAP a valuable addition to your analytical toolbox.

Author Biography

Dan Gabriel Cacuci is Ordinarius Chair Professor and Director of the Institute for Nuclear Technology and Reactor Safety, University of Karlsruhe, Germany, and Adjunct Professor in the Department of Nuclear Engineering, University of California at Berkeley, USA Mihaela Ionescu-Bujor is a Task Force Leader in the Fusion Program of the Research Center Karlsruhe, Germany Ionel Michael Navon is a professor in the School of Computational Science and Department of Mathematics, Florida State University, Tallahassee, USA

Table of Contents

I. A COMPARATIVE REVIEW OF SENSITIVITY AND UNCERTAINTY ANALYSIS METHODS FOR LARGE-SCALE SYSTEMS	1	(36)
A. STATISTICAL METHODS	5	(21)
1. Introduction	5	(1)
2. Sampling-Based Methods	6	(10)
3. Reliability Algorithms: FORM and SORM	16	(1)
4. Variance-Based Methods	16	(5)
5. Design of Experiments and Screening Design Methods	21	(5)
B. DETERMINISTIC METHODS	26	(6)
1. Deterministic Methods for Local Sensitivity Analysis	26	(3)
2. Deterministic Methods for Local Uncertainty Analysis	29	(2)
3. Deterministic Methods for Extending the Use of Local Sensitivities; Global Deterministic Sensitivity Analysis	31	(1)
C. COMPUTATIONAL CONSIDERATIONS	32	(5)
II. APPLICATIONS OF THE ADJOINT SENSITIVITY ANALYSIS PROCEDURE (ASAP) TO TWO-PHASE FLOW SYSTEMS	37	(86)
A. ASAP FOR GENERIC TWO-PHASE FLOW PROBLEMS	38	(17)
1. Basic One-Dimensional Two-Phase Flow Equations	39	(1)
2. The Adjoint Sensitivity Analysis Procedure (ASAP)	40	(6)
3. Characteristic of the Adjoint Sensitivity System	46	(1)
4. Illustrative Example: The Homogeneous Equilibrium Model (HEM) for Two-Phase Flow	47	(8)
B. ASAP FOR THE RELAP5/MOD3.2 TWO-FLUID MODEL (REL/TF)	55	(68)
1. The RELAP5/MOD3.2 Two-Fluid Model	57	(8)
2. ASAP of the Two-Fluid Model in RELAP5/MOD3.2	65	(15)
3. Consistency between the Differential/Integral And the Discretized Equations/Models for Sensitivity Analysis	80	(2)
4. Validation of the Adjoint Sensitivity Model (ASM-REL/TF)	82	(9)
5. Sensitivities of Thermodynamic Properties of Water	91	(32)
III. FORWARD AND ADJOINT SENSITIVITY ANALYSIS PROCEDURES FOR AUGMENTED SYSTEMS	123	(48)
A. THEORETICAL BASIS FOR THE ASAP FOR AUGMENTED SYSTEMS	124	(24)
1. Sensitivity Analysis of the Primary (Nonaugmented) System	124	(7)
2. Sensitivity Analysis of the Augmented System	131	(12)
3. Discussion: Constructing the Augmented Adjoint Sensitivity Model from the Original Adjoint Sensitivity Model and Viceversa	143	(5)
B. ILLUSTRATIVE EXAMPLE: ASAP FOR THE COUPLED TWO-FLUID WITH HEAT STRUCTURES MODEL IN RELAP5/MOD3.2 (REL/TF+HS)	148	(23)
1. ASM-REL/TFH: The Augmented Two-Fluid/Heat Structure Adjoint Sensitivity Model	148	(10)
2. Summary Description of the QUENCH-04 Experiment	158	(13)
IV. FORWARD AND ADJOINT SENSITIVITY ANALYSIS PROCEDURES FOR RESPONSES DEFINED AT CRITICAL POINTS	171	(60)
A. FSAP AND ASAP FOR RESPONSES AT CRITICAL POINTS: GENERAL THEORY	172	(22)
1. The Forward Sensitivity Analysis Procedure (FSAP)	174	(3)
2. The Adjoint Sensitivity Analysis Procedure (ASAP)	177	(4)
3. Discussion	181	(2)
4. Illustrative Example: A Simple Particle Diffusion Problem	183	(11)
B. ILLUSTRATIVE EXAMPLE: ASAP FOR THE MAXIMUM CLAD TEMPERATURE PREDICTED BY A REACTOR SAFETY CODE	194	(37)
V. USING THE ASAP TO GAIN NEW INSIGHTS INTO PARADIGM ATMOSPHERIC SCIENCES PROBLEMS	231	(52)
A. A PARADIGM RADIATIVE-CONVECTIVE MODEL (RCM) OF THE ATMOSPHERE	232	(5)
B. APPLYING THE ASAP FOR EFFICIENT AND EXHAUSTIVE SENSITIVITY ANALYSIS OF THE RCM	237	(11)
C. PHYSICAL INTERPRETATION OF SOLUTIONS, EIGENVALUES, AND EIGENVECTORS OF THE ADJOINT SENSITIVITY SYSTEM FOR ATMOSPHERIC MODELS	248	(11)
1. Physical Interpretation of the Adjoint Functions	250	(3)
2. Interpretation of Eigenvalues and Eigenvectors Associated with the Adjoint Functions	253	(5)
3. Numerical Efficiency	258	(1)
D. EFFICIENT ESTIMATION OF FEEDBACK EFFECTS FOR CLIMATE MODELS	259	(3)
E. AN ISENTROPIC TWO-LAYER MODEL FOR NUMERICAL WEATHER PREDICTION	262	(8)
F. APPLYING THE ASAP FOR EFFICIENT SENSITIVITY ANALYSIS OF BLOCKING INDEXES IN THE TWO-LAYER ISENTROPIC MODEL	270	(13)
1. Blocking Index in Physical Space	275	(3)
2. Blocking Index in Spectral Space	278	(1)
3. Illustrative Sensitivity Analysis Results	278	(3)
4. Computational Costs	281	(2)
VI. ADJOINT SENSITIVITY ANALYSIS PROCEDURE FOR OPERATIONAL METEOROLOGICAL APPLICATIONS	283	(60)
A. ADJOINT SENSITIVITY ANALYSIS PROCEDURE (ASAP) FOR THE EARTH'S RADIATION BUDGET IN THE NCEP MEDIUM-RANGE FORECASTING MODEL	283	(23)
1. Derivation and Verification of the Adjoint Sensitivity Model Corresponding to the NCEP Nonlinear Radiation Model	284	(4)
2. Illustrative Sensitivity Analysis Results	288	(18)
B. FSU-GSM FORECAST ERROR SENSITIVITY TO INITIAL CONDITIONS: APPLICATION TO INDIAN SUMMER MONSOON	306	(13)
1. Modeling the Nominal Conditions on June 8, 1988 with the FSU GSM	307	(3)
2. Illustrative Sensitivity Analysis Results	310	(9)
C. SENSITIVITY TO LARGE-SCALE ENVIRONMENTAL FIELDS OF THE RELAXED ARAKAWA-SCHUBERT PARAMETRIZATION IN THE NASA GEOS-1 GCM	319	(24)
1. Sensitivity Analysis of the GEOS-1 GCM Using the ASAP	320	(3)
2. The RAS Parameterization Scheme in GEOS-1 GCM	323	(4)
3. Sensitivity Analysis Results	327	(16)
REFERENCES	343	(8)
INDEX	351