Constrained ensemble Kalman filter based on Kullback–Leibler divergence

Li, Ruoxia; Jan, Nabil Magbool; Huang, Biao; Prasad, Vinay

doi:10.1016/j.jprocont.2019.05.011

Cited by 14 publications

(8 citation statements)

References 24 publications

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“…The evaluation indices used to measure the difference between two distributions such as Kullback–Leibler divergence (KL-divergence) and Jensen–Shannon divergence (JS-divergence), are given as follows with where P , M , and Q are discrete probability distributions and X is the probability space. Higher values of the evaluation indices indicate that a large difference exists between the two distributions.…”

Section: Proposed Data Enhancement Methodsmentioning

confidence: 99%

Data Enhancement for Data-Driven Modeling in Power Plants Based on a Conditional Variational-Adversarial Generative Network

Peng

Shao

et al. 2021

Ind. Eng. Chem. Res.

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The quality of data directly affects the performance of data-driven models that are developed to monitor the operation of power plants. Constrained by external instructions and other factors, the operational data of a power plant generally present an irregular distribution, which leads to data imbalance. In this paper, a novel data generation method called a conditional variational autoencoder and generative adversarial networks (CVAE-GAN) is proposed. The original samples are first mapped to the latent variables by the encoder network in the CVAE. On combining with the conditional variables, the latent variables are then mapped to a new sample space by the generation network of the proposed model. The CVAE-GAN model trained with the original imbalanced dataset can generate a uniformly distributed dataset under the guidance of incremental L 2 -discrepancy. A numerical simulation case is given to validate the superiority of the proposed model over other common generative models. Then, the proposed model is applied for NO x emission prediction in a coal-fired power plant. The results demonstrate that the accuracy of NO x emission predictions is improved by training the model with the dataset generated by the proposed method.

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Section: Proposed Data Enhancement Methodsmentioning

confidence: 99%

Data Enhancement for Data-Driven Modeling in Power Plants Based on a Conditional Variational-Adversarial Generative Network

Peng

Shao

et al. 2021

Ind. Eng. Chem. Res.

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“…(There are other methods for dealing with linear inequality constraints in the EnKF, e.g. by using truncated normals [52] or using constrained optimization [5,56]. The point here is not to deal with inequality constraints per se, but to introduce transforms as a means of generalizing the EnKF to non-Gaussian distributions.)…”

Section: Gaussian Anamorphosismentioning

confidence: 99%

A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters

Grooms

2021

Preprint

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This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA) methods and two-step updates, of which the rank histogram filter (RHF) is a prototypical example. GA-EnKF methods apply univariate transforms to the state and observation variables to make their distribution more Gaussian before applying an EnKF. The two-step methods use a scalar Bayesian update for the first step, followed by linear regression for the second step. The connection of the two-step framework to the full Bayesian problem is made, which opens the door to more advanced two-step methods in the full Bayesian setting. A new method for the first part of the two-step framework is proposed, with a similar form to the RHF but a different motivation, called the 'improved RHF' (iRHF). A suite of experiments with the Lorenz-'96 model demonstrate situations where the GA-EnKF methods are similar to EnKF, and where they outperform EnKF. The experiments also strongly support the accuracy of the RHF and iRHF filters for nonlinear and non-Gaussian observations; these methods uniformly beat the EnKF and GA-EnKF methods in the experiments reported here. The new iRHF method is only more accurate than RHF at small ensemble sizes in the experiments reported here.

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“…Substituting from (23) into (24) while using model properties (4), then after simple mathematical manipulations one gets the covariance matrices of the prediction error as given by (8) for i ∈ {1, 2, . .…”

Section: A: the Prediction Stepmentioning

confidence: 99%

“…Its main idea was to fuse the constraints and the auxiliary dynamics to achieve a constrained dynamical model on which the linear minimum mean square error estimator of the LEC system was applied [22]. For inequality-constrained nonlinear systems, algorithms based on the particle filter [23], the EnKF [24], and the interior point method [25] were developed. Other examples of constrained state estimators can be found in [26]- [29].…”

Section: Introduction a Literature Reviewmentioning

confidence: 99%

A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

Hassan

2020

IEEE Access

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In this paper, a decomposed state estimator is developed for stochastic constrained nonlinear discrete-time dynamical systems with uncertain parameters. The proposed estimator can deal with general nonlinear uncertain stochastic systems without any pre-defined specifications on the system structure and/or the measurement model. Moreover, it can handle estimation problems for nonlinear stochastic systems subject to a set of imposed linear and/or nonlinear equality and/or inequality constraints. The mathematical structure of the proposed estimator is developed using multiple projection approach and its performance is analyzed and compared with the global (un-decomposed) structure. The main features of the proposed estimator are: it reduces the processing time, it can handle estimation problems with bad initial conditions of the estimator, it can be implemented on modern parallel processing facilities to further reduce the processing time, and last but not least, it minimizes the rounding off errors and hence improves the numerical stability of the algorithm. Simulations results on different real applications are presented to show the effectiveness of the developed approach, and its improved performance when compared with other techniques reported in the literature. INDEX TERMS Constrained stochastic uncertain nonlinear systems, decomposed state estimation, extended Kalman filter, large scale systems, performance analysis.

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Constrained ensemble Kalman filter based on Kullback–Leibler divergence

Cited by 14 publications

References 24 publications

Data Enhancement for Data-Driven Modeling in Power Plants Based on a Conditional Variational-Adversarial Generative Network

Data Enhancement for Data-Driven Modeling in Power Plants Based on a Conditional Variational-Adversarial Generative Network

A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters

A Generalized Decomposed State Estimation Approach for Uncertain Constrained Stochastic Nonlinear Systems

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