The Second-Order Adjoint Sensitivity Analysis Methodology for Nonlinear Systems—I: Theory

Cacuci, Dan Gabriel

doi:10.13182/nse16-16

Cited by 43 publications

(36 citation statements)

References 20 publications

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“…The adjoint sensitivity analysis methodology used in PART I [1] for computing exactly and efficiently the 1 st -order response sensitivities to model parameters has been recently extended to computing efficiently and exactly the 2nd-order response sensitivities to parameters for linear [13] and nonlinear [14] large-scale systems. As has been shown in [15][16][17][18], the 2nd-order response sensitivities have the following major impacts on the computed moments of the response distribution: (a) they cause the "expected value of the response" to differ from the "computed nominal value of the response"; and (b) they contribute decisively to causing asymmetries in the response distribution.…”

Section: Discussionmentioning

confidence: 99%

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Predictive Modeling of a Paradigm Mechanical Cooling Tower Model: II. Optimal Best-Estimate Results with Reduced Predicted Uncertainties

2016

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This work uses the adjoint sensitivity model of the counter-flow cooling tower derived in the accompanying PART I to obtain the expressions and relative numerical rankings of the sensitivities, to all model parameters, of the following model responses: (i) outlet air temperature; (ii) outlet water temperature; (iii) outlet water mass flow rate; and (iv) air outlet relative humidity. These sensitivities are subsequently used within the "predictive modeling for coupled multi-physics systems" (PM_CMPS) methodology to obtain explicit formulas for the predicted optimal nominal values for the model responses and parameters, along with reduced predicted standard deviations for the predicted model parameters and responses. These explicit formulas embody the assimilation of experimental data and the "calibration" of the model's parameters. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.

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Section: Discussionmentioning

confidence: 99%

“…The derivatives of the air/water vapor energy balance equations [cf. Equations (A10)-(A12)] with respect to the parameter α (14) ≡ a 1 are as follows:…”

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confidence: 99%

Predictive Modeling of a Paradigm Mechanical Cooling Tower Model: II. Optimal Best-Estimate Results with Reduced Predicted Uncertainties

2016

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“…All in all, the application of the PM_CMPS methodology has produced and improved, calibrated and validated model for simulating the functioning of a buoyancy-operated cooling tower under unsaturated conditions. Ongoing work aims at using second-order sensitivities, to be computed by applying the 2nd-ASAM presented in [13,14]. The availability of second-order response sensitivities will enable the computation of non-Gaussian features, such as skewness and kurtosis, of the response distributions of interest.…”

Section: Discussionmentioning

confidence: 99%

Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties

Rocco

Cacuci

2016

Energies

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Nuclear and other large-scale energy-producing plants must include systems that guarantee the safe discharge of residual heat from the industrial process into the atmosphere. This function is usually performed by one or several cooling towers. The amount of heat released by a cooling tower into the external environment can be quantified by using a numerical simulation model of the physical processes occurring in the respective tower, augmented by experimentally measured data that accounts for external conditions such as outlet air temperature, outlet water temperature, and outlet air relative humidity. The model's responses of interest depend on many model parameters including correlations, boundary conditions, and material properties. Changes in these model parameters induce changes in the computed quantities of interest (called "model responses"), which are quantified by the sensitivities (i.e., functional derivatives) of the model responses with respect to the model parameters. These sensitivities are computed in this work by applying the general adjoint sensitivity analysis methodology (ASAM) for nonlinear systems. These sensitivities are subsequently used for: (i) Ranking the parameters in their importance to contributing to response uncertainties; (ii) Propagating the uncertainties (covariances) in these model parameters to quantify the uncertainties (covariances) in the model responses; (iii) Performing model validation and predictive modeling. The comprehensive predictive modeling methodology used in this work, which includes assimilation of experimental measurements and calibration of model parameters, is applied to the cooling tower model under unsaturated conditions. The predicted response uncertainties (standard deviations) thus obtained are smaller than both the computed and the measured standards deviations for the respective responses, even for responses where no experimental data were available.

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“…The first one discusses the necessary and sufficient conditions for the existence and uniqueness of adjoint operators, whereas the second extends the scope of the adjoint formalism to a larger variety of responses, which includes general operators. It is worth adding that, along with his collaborators, the author went on to publish a number of relevant references on a wide range of applications of the method …”

Section: Introductionmentioning

confidence: 99%

“…It is worth adding that, along with his collaborators, the author went on to publish a number of relevant references on a wide range of applications of the method. 5,[17][18][19][20][21][22][23][24][25] Two of the above works by Cacuci are especially relevant to our purposes. Cacuci et al 14 devise a sequence of formal steps to construct the adjoint problem.…”

Section: Introductionmentioning

confidence: 99%

On the use of the continuous adjoint method to compute nongeometric sensitivities

Hayashi

Volpe

Ceze

2017

Numerical Methods in Fluids

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Summary This work explores an alternative approach to computing sensitivity derivatives of functionals, with respect to a broader range of control parameters. It builds upon the complementary character of Riemann problems that describe the Euler flow and adjoint solutions. In a previous work, we have discussed a treatment of the adjoint boundary problem, which made use of such complementarity as a means to ensure well‐posedness. Here, we show that the very same adjoint solution that satisfies those boundary conditions also conveys information on other types of sensitivities. In essence, then, that formulation of the boundary problem can extend the range of applications of the adjoint method to a host of new possibilities.

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The Second-Order Adjoint Sensitivity Analysis Methodology for Nonlinear Systems—I: Theory

Cited by 43 publications

References 20 publications

Predictive Modeling of a Paradigm Mechanical Cooling Tower Model: II. Optimal Best-Estimate Results with Reduced Predicted Uncertainties

Predictive Modeling of a Paradigm Mechanical Cooling Tower Model: II. Optimal Best-Estimate Results with Reduced Predicted Uncertainties

Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties

On the use of the continuous adjoint method to compute nongeometric sensitivities

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