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20260416144419.0 |
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241114s2025 flu eo 000 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781003478119 |
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(electronic bk.) |
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1003478115 |
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(electronic bk.) |
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9781040193228 |
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(electronic bk. : EPUB) |
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1040193226 |
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(electronic bk. : EPUB) |
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| International Standard Book Number |
9781040193204 |
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(electronic bk. : PDF) |
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| International Standard Book Number |
104019320X |
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(electronic bk. : PDF) |
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| Cancelled/invalid ISBN |
9781032740560 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Cancelled/invalid ISBN |
9781032763538 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
026000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT |
| Subject category code subdivision |
027000 |
| Source |
bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBW |
| Source |
bicssc |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.2/87 |
| Edition number |
23/eng/20241114 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Cacuci, Dan Gabriel, |
| 245 10 - TITLE STATEMENT |
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| Title |
Advances in High-Order Predictive Modeling |
| Remainder of title |
Methodologies and Illustrative Problems |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource (xiv, 288 pages). |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Contents |
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 |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS / Reference |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
MATHEMATICS / Research |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Prediction theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Sensitivity theory (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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Maximum entropy method. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Newton-Raphson method. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Uncertainty (Information theory) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://www.taylorfrancis.com/books/9781003478119">https://www.taylorfrancis.com/books/9781003478119</a> |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf">http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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Electronic Books |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Relator term |
author. |
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Boca Raton, FL : |
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CRC Press, |
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[2025] |
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rdacontent |
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computer |
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rdamedia |
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online resource |
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rdacarrier |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Advances in Applied Mathematics |
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OCLC-licensed vendor bibliographic record. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Source of heading or term |
bisacsh |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Taylor & Francis |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
OCLC metadata license agreement |
