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020 _a9781003478119
_q(electronic bk.)
020 _a1003478115
_q(electronic bk.)
020 _a9781040193228
_q(electronic bk. : EPUB)
020 _a1040193226
_q(electronic bk. : EPUB)
020 _a9781040193204
_q(electronic bk. : PDF)
020 _a104019320X
_q(electronic bk. : PDF)
020 _z9781032740560
020 _z9781032763538
024 3 _a9781003478119
024 7 _a10.1201/9781003478119
_2doi
035 _a(OCoLC)1468699711
035 _a(OCoLC-P)1468699711
050 4 _aQA279.2
_b.C33 2025eb
072 7 _aMAT
_x026000
_2bisacsh
072 7 _aMAT
_x027000
_2bisacsh
072 7 _aPBW
_2bicssc
082 0 4 _a519.2/87
_223/eng/20241114
100 1 _aCacuci, Dan Gabriel,
_eauthor.
245 1 0 _aAdvances in High-Order Predictive Modeling
_bMethodologies and Illustrative Problems
264 1 _aBoca Raton, FL :
_bCRC Press,
_c[2025]
300 _a1 online resource (xiv, 288 pages).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 0 _aAdvances in Applied Mathematics
505 0 _aCHAPTER 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 _aContinuing 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.
588 _aOCLC-licensed vendor bibliographic record.
650 7 _aMATHEMATICS / Reference
_2bisacsh
650 7 _aMATHEMATICS / Research
_2bisacsh
650 0 _aPrediction theory.
650 0 _aSensitivity theory (Mathematics)
650 0 _aMaximum entropy method.
650 0 _aNewton-Raphson method.
650 0 _aUncertainty (Information theory)
856 4 0 _3Taylor & Francis
_uhttps://www.taylorfrancis.com/books/9781003478119
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _cE-BOOK
999 _c49626
_d49626