Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—I: Adjoint Sensitivity Analysis

Cacuci, Dan Gabriel; Fang, Ruixian

doi:10.1080/00295450.2017.1294429

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…Variance reduction techniques such as Multi level Monte Carlo (MLMC) [6] methods have also gained popularity in recent times. Non sampling approach includes perturbation method, where a truncated multi-dimensional Taylor expansion for the output quantities of interest is used [2]. A class of methods called spectral method uses the uncertain parameter to be represented as an expansion called spectral expansion [5].…”

Section: Introductionmentioning

confidence: 99%

A Finite Element Method - Informed Neural Network For Uncertainty Quantification

Kodakkal¹,

Meethal²,

Obst³

et al. 2021

14th WCCM-ECCOMAS Congress

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Sampling approaches for uncertainty quantification for real-world engineering problems are associated with large computational time and cost. This cost comes from the expensive deterministic simulation. Usage of surrogate models is a common way to overcome this issue in engineering applications. A conventional Neural Network (NN) can be used for building such surrogates. However, these neural networks are built based on input-output pairs. It is not possible to verify that the predicted output satisfies underlying physics. In this contribution, a physics-informed neural network based on a hybrid model of machine learning and classical Finite Element Method (FEM) is presented for forward propagation of uncertainty. The method uses FEM during both training and prediction stages. A surrogate model based on neural network for high dimensional problem is constructed by constraining the predictions of the neural network with the discretized partial differential equation of the system. During the training stage, the predicted solution from the FEM informed Neural Network(FEM-NN) is used to compute the residual using stiffness matrices and force vectors. This residual is used as a custom loss function from NN. This makes the whole training unsupervised as it does not require any output values. Hence, the need for expensive FEM solves is circumvented. The FEM-NN hybrid also gives an estimate of the accuracy of prediction by means of the calculated residual along with the prediction. The framework does not require mandatory expensive linear solves of the discretized equation instead substitutes the prediction from the neural network for computing the residual. This reduces the expensive training phase of the problem and can be applicable to real-world FEM simulations. The trained neural network is then sampled in a Monte Carlo (MC) manner to evaluate the statistics of the Quantities of Interest (QoI). The resulting FEM-NN hybrid is physics confirming and data-efficient. The efficacy of the framework is presented by a series of test case examples. The results are compared with classical MC results. The suitability of the method for the uncertainty quantification is studied and presented.

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Section: Introductionmentioning

confidence: 99%

A Finite Element Method - Informed Neural Network For Uncertainty Quantification

Kodakkal¹,

Meethal²,

Obst³

et al. 2021

14th WCCM-ECCOMAS Congress

View full text Add to dashboard Cite

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Q-tables formation method for automated monitoring of electromechanical converters parameters with application of linear integral criterion

Malev

Pogoditsky

Malacion³

2020

«Izvestiya vysshikh uchebnykh zavedenii. PROBLEMY ENERGETIKI»

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In the process of functioning working sets with electromechanical converters included in their composition, it is necessary to take into account the influence of endogenous and exogenous disturbances that cause deviations of the parameters of electric machines from the nominal values given by the manufacturer in the appropriate documentation. These deviations of the parameters, even those within the permissible range of changes, have a noticeable effect on the quality of functioning of electromechanical converters and working sets as a whole. During the life cycle of the work of electromechanical converters, their parameters change as a result of natural wear and senescence, which necessitates continuous or periodic analysis and monitoring of the state objects under study. The paper considers a method based on the calculation of the linear integral criterion Q and the formation of Q – tables, which allows monitoring the functioning of electromechanical converters with unstable parameters during operation as part of working sets. Simulink – models of linear integral criterion calculation system and system of automated monitoring of electromechanical DC converter parameters are presented, which allow estimating unstable parameters. In these models static characteristics are implemented in tabular form reflecting the dependencies between the parameters of the electromechanical converters and the linear integral criterion. The results of the study allow us to obtain estimates of changes in the unstable parameters of electromechanical DC converters with the required accuracy.

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Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—I: Adjoint Sensitivity Analysis

Cited by 2 publications

References 6 publications

A Finite Element Method - Informed Neural Network For Uncertainty Quantification

A Finite Element Method - Informed Neural Network For Uncertainty Quantification

Q-tables formation method for automated monitoring of electromechanical converters parameters with application of linear integral criterion

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