Volume II SENSITIVITY and UNCERTAINTY ANALYSIS. Applications to Large-Scale Systems

Transcription

1 Volume II SENSITIVITY and UNCERTAINTY ANALYSIS Applications to Large-Scale Systems

2 TABLE OF CONTENTS I. A COMPARATIVE REVIEW OF SENSITIVITY AND UNCERTAINTY ANALYSIS METHODS FOR LARGE-SCALE SYSTEMS 1 A. STATISTICAL METHODS 5 1. Introduction 5 2. Sampling-Based Methods 6 3. Reliability Algorithms: FORM and SORM Variance-Based Methods Design of Experiments and Screening Design Methods 21 B. DETERMINISTIC METHODS Deterministic Methods for Local Sensitivity Analysis Deterministic Methods for Local Uncertainty Analysis Deterministic Methods for Extending the Use of Local Sensitivities; Global Deterministic Sensitivity Analysis 31 C. COMPUTATIONAL CONSIDERATIONS 32 II. APPLICATIONS OF THE ADJOINT SENSITIVITY ANALYSIS PROCEDURE (ASAP) TO TWO-PHASE FLOW SYSTEMS 37 A. ASAP FOR GENERIC TWO-PHASE FLOW PROBLEMS Basic One-Dimensional Two-Phase Flow Equations The Adjoint Sensitivity Analysis Procedure (ASAP) Characteristic of the Adjoint Sensitivity System Illustrative Example: The Homogeneous Equilibrium Model (HEM) for Two-Phase Flow 47 B. ASAP FOR THE RELAP5/MOD3.2 TWO-FLUID MODEL (REL/TF) The RELAP5/MOD3.2 Two-Fluid Model ASAP of the Two-Fluid Model in RELAP5/MOD Consistency between the Differential/Integral And the Discretized Equations/Models for Sensitivity Analysis Validation of the Adjoint Sensitivity Model (ASM-REL/TF) Sensitivities of Thermodynamic Properties of Water 91

3 III. FORWARD AND ADJOINT SENSITIVITY ANALYSIS PROCEDURES FOR AUGMENTED SYSTEMS 123 A. THEORETICAL BASIS FOR THE ASAP FOR AUGMENTED SYSTEMS Sensitivity Analysis of the Primary (Nonaugmented) System Sensitivity Analysis of the Augmented System Discussion: Constructing the Augmented Adjoint Sensitivity Model from the Original Adjoint Sensitivity Model and Viceversa 143 B. ILLUSTRATIVE EXAMPLE: ASAP FOR THE COUPLED TWO-FLUID WITH HEAT STRUCTURES MODEL IN RELAP5/MOD3.2 (REL/TF+HS) ASM-REL/TFH: The Augmented Two-Fluid/Heat Structure Adjoint Sensitivity Model Summary Description of the QUENCH-04 Experiment 15 8 IV. FORWARD AND ADJOINT SENSITIVITY ANALYSIS PROCEDURES FOR RESPONSES DEFINED AT CRITICAL POINTS 171 A. FSAP AND ASAP FOR RESPONSES AT CRITICAL POINTS: GENERAL THEORY The Forward Sensitivity Analysis Procedure (FSAP) The Adjoint Sensitivity Analysis Procedure (ASAP) Discussion Illustrative Example: A Simple Particle \ Diffusion Problem 183 B. ILLUSTRATIVE EXAMPLE: ASAP FOR THE MAXIMUM CLAD TEMPERATURE PREDICTED BY A REACTOR SAFETY CODE 194 V. USING THE ASAP TO GAIN NEW INSIGHTS INTO PARADIGM ATMOSPHERIC SCIENCES PROBLEMS 231 A. A PARADIGM RADIATIVE-CONVECTIVE MODEL (RCM) OF THE ATMOSPHERE 232 B. APPLYING THE ASAP FOR EFFICIENT AND EXHAUSTIVE SENSITIVITY ANALYSIS OF THE RCM 237

4 C. PHYSICAL INTERPRETATION OF SOLUTIONS, EIGENVALUES, AND EIGENVECTORS OF THE ADJOINT SENSITIVITY SYSTEM FOR ATMOSPHERIC MODELS Physical Interpretation of the Adjoint Functions Interpretation of Eigenvalues and Eigenvectors Associated with the Adjoint Functions Numerical Efficiency 258 D. EFFICIENT ESTIMATION OF FEEDBACK EFFECTS FOR CLIMATE MODELS 259 E. AN ISENTROPIC TWO-LAYER MODEL FOR NUMERICAL WEATHER PREDICTION 262 F. APPLYING THE ASAP FOR EFFICIENT SENSITIVITY ANALYSIS OF BLOCKING INDEXES IN THE TWO-LAYER ISENTROPIC MODEL Blocking Index in Physical Space Blocking Index in Spectral Space Illustrative Sensitivity Analysis Results Computational Costs 281 VI. ADJOINT SENSITIVITY ANALYSIS PROCEDURE FOR OPERATIONAL METEOROLOGICAL APPLICATIONS 283 A. ADJOINT SENSITIVITY ANALYSIS PROCEDURE (ASAP) FOR THE EARTH'S RADIATION BUDGET IN THE NCEP MEDIUM-RANGE FORECASTING MODEL Derivation and Verification of the Adjoint Sensitivity Model Corresponding to the NCEP Nonlinear Radiation Model Illustrative Sensitivity Analysis Results 288 B. FSU-GSM FORECAST ERROR SENSITIVITY TO INITIAL CONDITIONS: APPLICATION TO INDIAN SUMMER MONSOON Modeling the Nominal Conditions on June 8, 1988 with the FSU GSM Illustrative Sensitivity Analysis Results 310

5 C. SENSITIVITY TO LARGE-SCALE ENVIRONMENTAL FIELDS OF THE RELAXED ARAKAWA-SCHUBERT PARAMETRIZATION IN THE NASA GEOS-1GCM Sensitivity Analysis of the GEOS-1 GCM Using the ASAP The RAS Parameterization Scheme in GEOS-1 GCM Sensitivity Analysis Results 327 REFERENCES 343 INDEX 351