Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems
Cacuci, Dan Gabriel,
Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems - 1 online resource (xiv, 288 pages). - Advances in Applied Mathematics .
CHAPTER 1: 2nd-BERRU-PM: Second-Order Maximum Entropy Predictive Modeling Methodology for Reducing Uncertainties in Predicted Model Responses and Parameters 1.1. Introduction 1.2. Generic Mathematical Modeling of a Physical System 1.3. Construction of the Minimally Discrepant Maximum Entropy Distribution 1.4. Construction of the Second-Order Minimally Discrepant Maximum Entropy Distribution of Experimentally Measured Responses and Parameters 1.5. 2nd-BERRU-PMD: Second Order MaxEnt Predictive Modeling Methodology with Deterministically Included Computed Responses 1.6. 2nd-BERRU-PMP: Second-Order MaxEnt Predictive Modeling Methodology with Probabilistically Included Computed Responses 1.6.1. Second-Order MaxEnt Probabilistic Representation of the Computational Model 1.6.2. General Case 2nd-BERRU-PMP: Inclusion of Additional External Measurements for Both Responses and Parameters 1.6.3. Practical Case 2nd-BERRU-PMP: Inclusion of Response Measurements 1.7. Inter-Comparison: 2nd-BERRU-PMP vs. 2nd-BERRU-PMD 1.7.1. Inter-Comparison: Best-Estimate Predicted Mean Values for Responses 1.7.2. Inter-Comparison: Best-Estimate Predicted Mean Values for Parameters 1.7.3. Inter-Comparison: Best-Estimate Predicted Response Covariances 1.7.4. Inter-Comparison: Best-Estimate Predicted Parameter Covariances 1.7.5. Inter-Comparison: Best-Estimate Predicted Correlations Between Parameters and Responses 1.8. Review of Principles Underlying the Data Adjustment and Data Assimilation Procedures 1.8.1. Principles Underlying the Data Adjustment Procedure 1.8.2. Principles Underlying the Data Assimilation Procedure 1.9. Discussion and Conclusions CHAPTER 2: Application of the 2nd-BERRU-PM Methodology to the PERP Reactor Physics Benchmark 2.1. Introduction 2.2. Mathematical Modeling of the OECD/NEA Polyethylene-Reflected Plutonium Metal Sphere (PERP) Reactor Physics Benchmark 2.3: Mean and Variance of the PERP Benchmark⁰́₉s Computed Leakage Response 2.3.1. ⁰́₋High precision⁰́₊ parameters; uniform relative standard deviations 2.3.2. ⁰́₋Typical precision⁰́₊ parameters; uniform relative standard deviations 2.3.3. ⁰́₋Low precision⁰́₊ parameters; uniform relative standard deviations 2.4: Illustrative Application of the 2nd-BERRU-PM Methodology to the PERP Benchmark: Mathematical Expressions for the Best Estimate Predicted Mean and Variance for the PERP Leakage Response 2.4.1. Best-Estimate Predicted Mean Value, , for the PERP Leakage Response 2.4.2. Best-Estimate Predicted Standard Deviation for PERP Leakage Response 2.5: Typical-Precision Consistent Measured Response (neutrons/sec; ) 2.5.1. High-precision (3% relative standard deviations) parameters 2.5.2: Typical precision (5% relative standard deviations) parameters 2.5.3. Low precision (10% relative standard deviations) parameters 2.6: Low-Precision Consistent Measured Response (neutrons/sec; ); High Precision Parameters (relative SD=3%) 2.7: Typical-Precision Inconsistent Measured Response ( neutrons/sec;) 2.7.1. High-precision (2% relative standard deviations) parameters 2.7.2. Typical-precision (5% relative standard deviations) parameters 2.7.3. Low-precision (10% relative standard deviations) parameters 2.8: High-Precision Apparently Inconsistent Measured Response ( neutrons/sec; ) and High Precision Parameters (SD=3%) 2.8.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.3. Including Contributions from the 1st + 2nd + 3rd-Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.4. Including Contributions from the 1st + 2nd + 3rd + 4th -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.9: High-Precision Possibly Inconsistent Measured Response ( neutrons/sec; ) and Low Precision Parameters (SD=10%) 2.9.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.9.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.10: Low-Precision Apparently Inconsistent Measured Response ( neutrons/sec; ); Typical Precision Parameters (SD=5%) 2.10.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to All Important Parameters 2.10.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to All Important Parameters 2.10.3. Including Contributions from the 1st + 2nd + 3rd-Order Sensitivities of the Leakage Response to the Total Cross Sections 2.10.4. Including Contributions from the 1st + 2nd + 3rd + 4th -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.11: Measured Response Value Coincides with Nominally Computed Response Value 2.12. Concluding Remarks CHAPTER 3: A Novel Generic Fourth-Order Moment-Constrained Maximum Entropy Distribution 3.1. Introduction 3.2. Construction of the Fourth-Order Moment-Constrained Maximum Entropy (MaxEnt) Representation of Uncertain Multivariate Quantities 3.3. Concluding Remarks Appendix 3.A. Auxiliary Computations for Constructing the Moment-Constrained Fourth-Order MaxEnt Distribution Appendix 3.B. Approximations Inherent to the Fourth-Order Maximum Entropy Distribution
Continuing the author⁰́₉s previous work on modeling, this book presents the most recent advances in high-order predictive modeling. The author begins with the mathematical framework of the 2nd-BERRU-PM methodology, an acronym that designates the ⁰́₋second-order best-estimate with reduced uncertainties (2nd-BERRU) predictive modeling (PM).⁰́₊ The 2nd-BERRU-PM methodology is fundamentally anchored in physics-based principles stemming from thermodynamics (maximum entropy principle) and information theory, being formulated in the most inclusive possible phase-space, namely the combined phase-space of computed and measured parameters and responses. The 2nd-BERRU-PM methodology provides second-order output (means and variances) but can incorporate, as input, arbitrarily high-order sensitivities of responses with respect to model parameters, as well as arbitrarily high-order moments of the initial distribution of uncertain model parameters, in order to predict best-estimate mean values for the model responses (i.e., results of interest) and calibrated model parameters, along with reduced predicted variances and covariances for these predicted responses and parameters.
9781003478119 1003478115 9781040193228 1040193226 9781040193204 104019320X
9781003478119 10.1201/9781003478119 doi
MATHEMATICS / Reference
MATHEMATICS / Research
Prediction theory.
Sensitivity theory (Mathematics)
Maximum entropy method.
Newton-Raphson method.
Uncertainty (Information theory)
QA279.2 / .C33 2025eb
519.2/87
Advances in High-Order Predictive Modeling Methodologies and Illustrative Problems - 1 online resource (xiv, 288 pages). - Advances in Applied Mathematics .
CHAPTER 1: 2nd-BERRU-PM: Second-Order Maximum Entropy Predictive Modeling Methodology for Reducing Uncertainties in Predicted Model Responses and Parameters 1.1. Introduction 1.2. Generic Mathematical Modeling of a Physical System 1.3. Construction of the Minimally Discrepant Maximum Entropy Distribution 1.4. Construction of the Second-Order Minimally Discrepant Maximum Entropy Distribution of Experimentally Measured Responses and Parameters 1.5. 2nd-BERRU-PMD: Second Order MaxEnt Predictive Modeling Methodology with Deterministically Included Computed Responses 1.6. 2nd-BERRU-PMP: Second-Order MaxEnt Predictive Modeling Methodology with Probabilistically Included Computed Responses 1.6.1. Second-Order MaxEnt Probabilistic Representation of the Computational Model 1.6.2. General Case 2nd-BERRU-PMP: Inclusion of Additional External Measurements for Both Responses and Parameters 1.6.3. Practical Case 2nd-BERRU-PMP: Inclusion of Response Measurements 1.7. Inter-Comparison: 2nd-BERRU-PMP vs. 2nd-BERRU-PMD 1.7.1. Inter-Comparison: Best-Estimate Predicted Mean Values for Responses 1.7.2. Inter-Comparison: Best-Estimate Predicted Mean Values for Parameters 1.7.3. Inter-Comparison: Best-Estimate Predicted Response Covariances 1.7.4. Inter-Comparison: Best-Estimate Predicted Parameter Covariances 1.7.5. Inter-Comparison: Best-Estimate Predicted Correlations Between Parameters and Responses 1.8. Review of Principles Underlying the Data Adjustment and Data Assimilation Procedures 1.8.1. Principles Underlying the Data Adjustment Procedure 1.8.2. Principles Underlying the Data Assimilation Procedure 1.9. Discussion and Conclusions CHAPTER 2: Application of the 2nd-BERRU-PM Methodology to the PERP Reactor Physics Benchmark 2.1. Introduction 2.2. Mathematical Modeling of the OECD/NEA Polyethylene-Reflected Plutonium Metal Sphere (PERP) Reactor Physics Benchmark 2.3: Mean and Variance of the PERP Benchmark⁰́₉s Computed Leakage Response 2.3.1. ⁰́₋High precision⁰́₊ parameters; uniform relative standard deviations 2.3.2. ⁰́₋Typical precision⁰́₊ parameters; uniform relative standard deviations 2.3.3. ⁰́₋Low precision⁰́₊ parameters; uniform relative standard deviations 2.4: Illustrative Application of the 2nd-BERRU-PM Methodology to the PERP Benchmark: Mathematical Expressions for the Best Estimate Predicted Mean and Variance for the PERP Leakage Response 2.4.1. Best-Estimate Predicted Mean Value, , for the PERP Leakage Response 2.4.2. Best-Estimate Predicted Standard Deviation for PERP Leakage Response 2.5: Typical-Precision Consistent Measured Response (neutrons/sec; ) 2.5.1. High-precision (3% relative standard deviations) parameters 2.5.2: Typical precision (5% relative standard deviations) parameters 2.5.3. Low precision (10% relative standard deviations) parameters 2.6: Low-Precision Consistent Measured Response (neutrons/sec; ); High Precision Parameters (relative SD=3%) 2.7: Typical-Precision Inconsistent Measured Response ( neutrons/sec;) 2.7.1. High-precision (2% relative standard deviations) parameters 2.7.2. Typical-precision (5% relative standard deviations) parameters 2.7.3. Low-precision (10% relative standard deviations) parameters 2.8: High-Precision Apparently Inconsistent Measured Response ( neutrons/sec; ) and High Precision Parameters (SD=3%) 2.8.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.3. Including Contributions from the 1st + 2nd + 3rd-Order Sensitivities of the Leakage Response to the Total Cross Sections 2.8.4. Including Contributions from the 1st + 2nd + 3rd + 4th -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.9: High-Precision Possibly Inconsistent Measured Response ( neutrons/sec; ) and Low Precision Parameters (SD=10%) 2.9.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.9.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.10: Low-Precision Apparently Inconsistent Measured Response ( neutrons/sec; ); Typical Precision Parameters (SD=5%) 2.10.1. Including Only Contributions from the 1st -Order Sensitivities of the Leakage Response to All Important Parameters 2.10.2. Including Contributions from the 1st + 2nd -Order Sensitivities of the Leakage Response to All Important Parameters 2.10.3. Including Contributions from the 1st + 2nd + 3rd-Order Sensitivities of the Leakage Response to the Total Cross Sections 2.10.4. Including Contributions from the 1st + 2nd + 3rd + 4th -Order Sensitivities of the Leakage Response to the Total Cross Sections 2.11: Measured Response Value Coincides with Nominally Computed Response Value 2.12. Concluding Remarks CHAPTER 3: A Novel Generic Fourth-Order Moment-Constrained Maximum Entropy Distribution 3.1. Introduction 3.2. Construction of the Fourth-Order Moment-Constrained Maximum Entropy (MaxEnt) Representation of Uncertain Multivariate Quantities 3.3. Concluding Remarks Appendix 3.A. Auxiliary Computations for Constructing the Moment-Constrained Fourth-Order MaxEnt Distribution Appendix 3.B. Approximations Inherent to the Fourth-Order Maximum Entropy Distribution
Continuing the author⁰́₉s previous work on modeling, this book presents the most recent advances in high-order predictive modeling. The author begins with the mathematical framework of the 2nd-BERRU-PM methodology, an acronym that designates the ⁰́₋second-order best-estimate with reduced uncertainties (2nd-BERRU) predictive modeling (PM).⁰́₊ The 2nd-BERRU-PM methodology is fundamentally anchored in physics-based principles stemming from thermodynamics (maximum entropy principle) and information theory, being formulated in the most inclusive possible phase-space, namely the combined phase-space of computed and measured parameters and responses. The 2nd-BERRU-PM methodology provides second-order output (means and variances) but can incorporate, as input, arbitrarily high-order sensitivities of responses with respect to model parameters, as well as arbitrarily high-order moments of the initial distribution of uncertain model parameters, in order to predict best-estimate mean values for the model responses (i.e., results of interest) and calibrated model parameters, along with reduced predicted variances and covariances for these predicted responses and parameters.
9781003478119 1003478115 9781040193228 1040193226 9781040193204 104019320X
9781003478119 10.1201/9781003478119 doi
MATHEMATICS / Reference
MATHEMATICS / Research
Prediction theory.
Sensitivity theory (Mathematics)
Maximum entropy method.
Newton-Raphson method.
Uncertainty (Information theory)
QA279.2 / .C33 2025eb
519.2/87