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The second-order adjoint sensitivity analysis methodology /
"The author has achieved the breakthrough of generalizing the First-Order Theory presented in his previous books, to the efficient computations of arbitrarily high-order sensitivities for nonlinear systems (HONASAP). This breakthrough has many applications, especially when there is a need to qu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boca Raton :
CRC Press,
2018.
|
| Colección: | Advances in applied mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Cacuci, Dan Gabriel, |e author. | |
| 245 | 1 | 4 | |a The second-order adjoint sensitivity analysis methodology / |c Dan Gabriel Cacuci. |
| 264 | 1 | |a Boca Raton : |b CRC Press, |c 2018. | |
| 264 | 4 | |c ©2018 | |
| 300 | |a 1 online resource (xx, 305 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Advances in applied mathematics | |
| 520 | 2 | |a "The author has achieved the breakthrough of generalizing the First-Order Theory presented in his previous books, to the efficient computations of arbitrarily high-order sensitivities for nonlinear systems (HONASAP). This breakthrough has many applications, especially when there is a need to quantify nonlinear behavior or to quantify uncertainties in design parameter/system responses in large-scale systems. This book presents the theory of the HONASAP with applications, from simple, analytically solvable, paradigm problems to large-scale applications in thermal hydraulics, particle transport, etc."--Provided by publisher | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Motivation for computing first- and second-order sensitivities of system responses to the system -- Illustrative application of the 2nd-ASAM to a linear evolution problem -- The 2nd-ASAM for linear systems -- Application of the 2nd-ASAM to a linear heat conduction and convection benchmark problem -- Application of the 2nd-ASAM to a linear particle diffusion problem -- Application of the 2nd-ASAM for computing sensitivities of detector responses to uncollided radiation transport -- The 2nd-ASAM for nonlinear systems -- Application of the 2nd-ASAM to a nonlinear heat conduction problem. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Sensitivity theory (Mathematics) | |
| 650 | 0 | |a Large scale systems. | |
| 650 | 0 | |a Nonlinear systems. | |
| 650 | 0 | 4 | |a Applied Mathematics. |
| 650 | 0 | 4 | |a Mathematics & Statistics for Engineers. |
| 650 | 0 | 4 | |a Mathematical Physics. |
| 650 | 6 | |a Théorie de la sensibilité (Mathématiques) | |
| 650 | 6 | |a Systèmes de grandes dimensions. | |
| 650 | 6 | |a Systèmes non linéaires. | |
| 650 | 7 | |a SCIENCE |x System Theory. |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Operations Research. |2 bisacsh | |
| 650 | 7 | |a Large scale systems. |2 fast |0 (OCoLC)fst00992666 | |
| 650 | 7 | |a Nonlinear systems. |2 fast |0 (OCoLC)fst01038810 | |
| 650 | 7 | |a Sensitivity theory (Mathematics) |2 fast |0 (OCoLC)fst01112599 | |
| 776 | 0 | 8 | |i Print version: |a Cacuci, Dan Gabriel. |t Second-order adjoint sensitivity analysis methodology. |d Boca Raton : CRC Press, 2018 |z 9781498726481 |w (DLC) 2017040197 |w (OCoLC)1010700690 |
| 830 | 0 | |a Advances in applied mathematics. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1714558 |z Texto completo |
| 880 | 0 | 0 | |6 505-00/(S |t -- |g 8.3.2. |t Computation of the Second-Order Sensitivities R(2)2i(α0) Δ [∂]2T(zr)/([∂]q [∂]αi) -- |g 8.3.3. |t Computation of the Second-Order Sensitivities R(2)3i(alpha;0) Δ [∂]2T(zr)/([∂]Ta [∂]αi) -- |g 8.3.4. |t Computation of the Second-Order Sensitivities R(2)4i(alpha;0) Δ [∂]2T(zr)/([∂]k0 [∂]αi) -- |g 8.3.5. |t Computation of the Second-Order Sensitivities R(2)5i(α0) Δ [∂]2T(zr)/([∂]c [∂]αi) -- |g 8.3.6. |t Computation of Standard Deviation and Skewness of the Temperature Distribution -- |g 8.4. |t Concluding Remarks. |
| 880 | 0 | 0 | |6 505-00/(S |g Machine generated contents note: |g 1. |t Motivation for Computing First- and Second-Order Sensitivities of System Responses to the System's Parameters -- |g 1.1. |t Fundamental Role of Response Sensitivities for Uncertainty Quantification -- |g 1.2. |t Fundamental Role of Response Sensitivities for Predictive Modeling -- |g 1.3. |t Advantages and Disadvantages of Statistical and Deterministic Methods for Computing Response Sensitivities -- |g 2. |t Illustrative Application of the 2nd-ASAM to a Linear Evolution Problem -- |g 2.1. |t Exact Computation of the First-Order Response Sensitivities -- |g 2.2. |t Exact Computation of the Second-Order Response Sensitivities -- |g 2.2.1. |t Computing the Second-Order Response Sensitivities Corresponding to the First-Order Sensitivities [∂]ρ(t1)/[∂]βi -- |g 2.2.2. |t Computing the Second-Order Response Sensitivities Corresponding to the First-Order Sensitivities [∂]ρ(t1)/[∂]wi -- |g 2.2.3. |t Computing the Second-Order Response Sensitivities Corresponding to the First-Order Sensitivities [∂]ρ(t1)/[∂]q -- |g 2.2.4. |t Computing the Second-Order Response Sensitivities Corresponding to the First-Order Sensitivities [∂]ρ(t1)/[∂]ρin -- |g 2.2.5. |t Discussion of the Essential Features of the 2nd-ASAM -- |g 2.2.6. |t Illustrative Use of Response Sensitivities for Predictive Modeling -- |g 3. |t 2nd-ASAM for Linear Systems -- |g 3.1. |t Mathematical Modeling of a General Linear System -- |g 3.2. |t 1st-LASS for Computing Exactly and Efficiently First-Order Sensitivities of Scalar-Valued Responses for Linear Systems -- |g 3.3. |t 2nd-LASS for Computing Exactly and Efficiently First-Order Sensitivities of Scalar-Valued Responses for Linear Systems -- |g 3.4. |t Concluding Remarks -- |g 4. |t Application of the 2nd-ASAM to a Linear Heat Conduction and Convection Benchmark Problem -- |g 4.1. |t Heat Transport Benchmark Problem: Mathematical Modeling -- |g 4.2. |t Computation of First-Order Sensitivities -- |g 4.2.1. |t Computation of First-Order Sensitivities of the Heated Rod Temperature, T(r, z), at an Arbitrary Location (r0, z0) -- |g 4.2.2. |t Computation of First-Order Sensitivities of the Heated Rod Temperature, Tmax(zmax), at the Location zmax -- |g 4.2.3. |t Computation of First-Order Sensitivities of the Heated Rod Temperature, Ts(z1), at an Arbitrary Location z1 -- |g 4.2.4. |t Computation of First-Order Sensitivities of the Coolant Temperature -- |g 4.2.5. |t Verification of the ANSYS/FLUENT Adjoint Solver -- |g 4.3. |t Applying the 2nd-ASAM to Compute the Second-Order Sensitivities and Uncertainties for the Heat Transport Benchmark Problem -- |g 4.3.1. |t Computation of the Second-Order Sensitivities and Uncertainties of the Heated Rod Temperature, T(r, z), at an Arbitrary Location (r0, z0) -- |g 4.3.1.1. |t Computation of the Second-Order Response Sensitivities [∂]2T(r0, z0)/([∂]α1 [∂]αj), α1 [≡] q, and j = 1 ..., Nα = 6 -- |g 4.3.1.2. |t Computation of the Second-Order Response Sensitivities 9[∂]2T(r0, z0)/([∂]α2 [∂]αj), α2 [≡] k, and j = 1 ..., Nα = 6 -- |g 4.3.1.3. |t Computation of the Second-Order Response Sensitivities [∂]2T(r0, z0)/([∂]α3 [∂]αj), α3 [≡] h, and j = 1 ..., Nα = 6 -- |g 4.3.1.4. |t Computation of the Second-Order Response Sensitivities [∂]2T(r0, z0)/([∂]α4 [∂]αj), α4 [≡] W, and j = 1 ..., Nα = 6 -- |g 4.3.1.5. |t Computation of Second-Order Response Sensitivities [∂]2T(r0, z0)/([∂]α5 [∂]αj), α5 [≡] cp, and j = 1 ..., Nα = 6 -- |g 4.3.1.6. |t Computation of Second-Order Response Sensitivities [∂]2T(r0, z0)/([∂]α6 [∂]αj), α6 [≡] Tinlet, and j = 1 ..., Nα = 6 -- |g 4.3.1.7. |t Quantitative Comparison of Second-Order Sensitivities of the Rod Temperature Distribution to G4M Reactor Model Parameters -- |g 4.3.1.8. |t Quantitative Contributions of Second-Order Sensitivities to the Uncertainty in the Rod Temperature Distribution for G4M Reactor Model Parameters -- |g 4.3.2. |t Computation of Second-Order Sensitivities of the Coolant Temperature, Tfi(z) -- |g 4.4. |t Concluding Remarks -- |g 5. |t Application of the 2nd-ASAM to a Linear Particle Diffusion Problem -- |g 5.1. |t Problem Description -- |g 5.2. |t Applying the 2nd-ASAM to Compute the First-Order Response Sensitivities to Model Parameters -- |g 5.3. |t Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities to Model Parameters -- |g 5.3.1. |t Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities S4i Δ [∂]2R/([∂]Σd[∂]αi) -- |g 5.3.2. |t Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities S3i Δ [∂]2R/([∂]Q[∂]αi) -- |g 5.3.3. |t Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities S1i Δ [∂]2R/([∂]Σa[∂]αi) -- |g 5.3.4. |t Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities S2i Δ [∂]2R/([∂]D[∂]αi) -- |g 5.4. |t Role of Second-Order Response Sensitivities for Quantifying Non-Gaussian Features of the Response Uncertainty Distribution -- |g 5.5. |t Illustrative Application of First-Order Response Sensitivities for Predictive Modeling -- |g 5.5.1. |t Assimilating an Imprecise but Consistent Measurement -- |g 5.5.2. |t Assimilating a Precise and Consistent Measurement -- |g 5.5.3. |t Assimilating Two Consistent Measurements -- |g 5.5.4. |t Assimilating Four Consistent Measurements -- |g 6. |t Application of the 2nd-ASAM for Computing Sensitivities of Detector Responses to Uncollided Radiation Transport -- |g 6.1. |t Ray-Tracing Form of the Forward and Adjoint Boltzmann Transport Equations -- |g 6.2. |t Application of the 2nd-ASAM to Compute the First-Order Response Sensitivities to Variations in Model Parameters -- |g 6.3. |t Application of the 2nd-ASAM to Compute the Second-Order Response Sensitivities to Variations in Model Parameters -- |g 6.3.1. |t Computation of the Second-Order Sensitivities S(2)i, j Δ [∂]S(1)i[∂]Ni [∂]αj, i = 1 ..., Nm, j = 1 ..., Nα -- |g 6.3.2. |t Computation of the Second-Order Sensitivities S(2)i+3Nm, j Δ [∂]S(1)i[∂]μi [∂]αj, i = 1 ..., Nm, j = 1 ..., Nα -- |g 6.3.3. |t Computation of the Second-Order Sensitivities S(2)i+2Nm, j Δ [∂]S(1)[∂]σi [∂]αj, i = 1 ..., Nm, j = 1 ..., Nα -- |g 6.3.4. |t Computation of the Second-Order Sensitivities S(2)i+2Nm, j Δ [∂]S(1)[∂]qi [∂]αj, i = 1 ..., Nd, j = 1 ..., Nα -- |g 6.4. |t Concluding Remarks -- |g 7. |t 2nd-ASAM for Nonlinear Systems -- |g 7.1. |t Mathematical Modeling of a General Nonlinear System -- |g 7.2. |t 1st-LASS for Computing Exactly and Efficiently the First-Order Sensitivities -- |g 7.3. |t 2nd-LASS for Computing Exactly and Efficiently the Second-Order Sensitivities of Scalar-Valued Responses for Nonlinear Systems -- |g 7.4. |t Concluding Remarks -- |g 8. |t Application of the 2nd-ASAM to a Nonlinear Heat Conduction Problem -- |g 8.1. |t Mathematical Modeling of Heated Cylindrical Test Section -- |g 8.2. |t Application of the 2nd-ASAM for Computing the First-Order Sensitivities -- |g 8.3. |t Application of the 2nd-ASAM to Compute the Second-Order Sensitivities -- |g 8.3.1. |t Computation of the Second-Order Sensitivities R(2)1i Δ [∂]2T(zr)/([∂]Q[∂]αi). |
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