scholarly journals Predictive Modeling of a Paradigm Mechanical Cooling Tower: I. Adjoint Sensitivity Model

Energies ◽  
2016 ◽  
Vol 9 (9) ◽  
pp. 718 ◽  
Author(s):  
Dan Cacuci ◽  
Ruixian Fang
Keyword(s):  
Predictive Modeling ◽  
Cooling Tower ◽  
Adjoint Sensitivity

scholarly journals The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): II. Illustrative Application

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8315
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Closed Form ◽  
Linear Systems ◽  
Predictive Modeling ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Third Order ◽  
Analysis Methodology ◽  
Illustrative Application

This work illustrates the application of the nth-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “nth-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the nth-CASAM-L. The results presented in this work underscore the fundamentally important role of the nth-CASAM-L in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

scholarly journals TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

2021 ◽  
Vol 247 ◽  
pp. 20005
Author(s):  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Predictive Modeling ◽  
Curse Of Dimensionality ◽  
Current Data ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Response Distribution ◽  
Parameter Uncertainties ◽  
Adjoint Sensitivity

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.

scholarly journals TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

2021 ◽  
Vol 247 ◽  
pp. 00002
Author(s):  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Predictive Modeling ◽  
Curse Of Dimensionality ◽  
Current Data ◽  
Model Parameters ◽  
Mathematical Framework ◽  
Response Distribution ◽  
Parameter Uncertainties ◽  
Adjoint Sensitivity

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.

Application of Ozone to Spraying Water in Cooling Tower of Transformer

2018 ◽  
Vol 138 (12) ◽  
pp. 939-947
Author(s):  
Hideo Hashimoto ◽  
Koh Hashiguchi ◽  
Hideki Fukui ◽  
Yusaku Ono ◽  
Mika Nakatoge ◽  
...  
Keyword(s):  
Cooling Tower
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