Anomaly-Resistant Decentralized State Estimation Under Minimum Error Entropy With Fiducial Points for Wide-Area Power Systems

This paper investigates the anomaly-resistant decentralized state estimation(SE) problem for a class of wide-area power systems which are divided into several non-overlapping areas connected through transmission lines. Two classes of measurements(i.e., local measurements and edge measurements) are obtained, respectively, from the individual area and the transmission lines. A decentralized state estimator, whose performance is resistant against measurement with anomalies, is designed based on the minimum error entropy with fiducial points(MEEF) criterion. Specifically, 1) An augmented model, which incorporates the local prediction and local measurement, is developed by resorting to the unscented transformation approach and the statistical linearization approach;2) Using the augmented model, an MEEF-based cost function is designed that reflects the local prediction errors of the state and the measurement;and 3) The local estimate is first obtained by minimizing the MEEF-based cost function through a fixed-point iteration and then updated by using the edge measuring information. Finally, simulation experiments with three scenarios are carried out on the IEEE 14-bus system to illustrate the validity of the proposed anomaly-resistant decentralized SE scheme.

GLOBAL MAXIMUM-NORM ERROR ESTIMATES OF CURVED BOUNDARY ELEMENT METHODS FOR SOLVING SINGULAR BOUNDARY INTEGRAL EQUATIONS

In [1] J. C. Nedelec proposed a class of curved boundary element method (BEMs) for solving singular boundary integral equations and obtained the local error estimates of approximate solution inside the domain. Methods of this class have been applied in

The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model),we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model.The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation.The experimental results show that based on the weighted least squares criterion,the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation.The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.

Robust state of charge estimation of lithium-ion battery via mixture kernel mean p-power error loss LSTM with heap-based-optimizer

The state of charge(SOC)estimation of lithium-ion battery is an important function in the battery management system(BMS)of electric vehicles.The long short term memory(LSTM)model can be employed for SOC estimation,which is capable of estimating the future changing states of a nonlinear system.Since the BMS usually works under complicated operating conditions,i.e the real measurement data used for model training may be corrupted by non-Gaussian noise,and thus the performance of the original LSTM with the mean square error(MSE)loss may deteriorate.Therefore,a novel LSTM with mixture kernel mean p-power error(MKMPE)loss,called MKMPE-LSTM,is developed by using the MKMPE loss to replace the MSE as the learning criterion in LSTM framework,which can achieve robust SOC estimation under the measurement data contaminated with non-Gaussian noises(or outliers)because of the MKMPE containing the p-order moments of the error distribution.In addition,a meta-heuristic algorithm,called heap-based-optimizer(HBO),is employed to optimize the hyper-parameters(mainly including learning rate,number of hidden layer neuron and value of p in MKMPE)of the proposed MKMPE-LSTM model to further improve its flexibility and generalization performance,and a novel hybrid model(HBO-MKMPE-LSTM)is established for SOC estimation under non-Gaussian noise cases.Finally,several tests are performed under various cases through a benchmark to evaluate the performance of the proposed HBO-MKMPE-LSTM model,and the results demonstrate that the proposed hybrid method can provide a good robustness and accuracy under different non-Gaussian measurement noises,and the SOC estimation results in terms of mean square error(MSE),root MSE(RMSE),mean absolute relative error(MARE),and determination coefficient R2are less than 0.05%,3%,3%,and above 99.8%at 25℃,respectively.

Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation

An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.

Error Estimates for Mixed Finite Element Methods for Sobolev Equation

The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).

A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.

A POSTERIORI ERROR ESTIMATES OF FINITEELEMENT METHOD FOR PARABOLIC PROBLEMS

This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the parabolic context.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Adaptive Finite Element Method Based on Optimal Error Estimates for Linear Elliptic Problems on Nonconvex Polygonal Domains

The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration.

Feedback control and quantum error correction assisted quantum multi-parameter estimation

Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.

A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

The Error Estimates of Direct Discontinuous Galerkin Methods Based on Upwind-Baised Fluxes

In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that L2 norms error estimates can reach to order k + 1 by using time discretization methods.

Error Estimates of H^1-Galerkin Mixed Methods for the Viscoelasticity Wave Equation

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.

Bayesian Filtering for High-Dimensional State-Space Models With State Partition and Error Compensation

In the era of exponential growth of data availability,the architecture of systems has a trend toward high dimensionality,and directly exploiting holistic information for state inference is not always computationally affordable.This paper proposes a novel Bayesian filtering algorithm that considers algorithmic computational cost and estimation accuracy for high-dimensional linear systems.The high-dimensional state vector is divided into several blocks to save computation resources by avoiding the calculation of error covariance with immense dimensions.After that,two sequential states are estimated simultaneously by introducing an auxiliary variable in the new probability space,mitigating the performance degradation caused by state segmentation.Moreover,the computational cost and error covariance of the proposed algorithm are analyzed analytically to show its distinct features compared with several existing methods.Simulation results illustrate that the proposed Bayesian filtering can maintain a higher estimation accuracy with reasonable computational cost when applied to high-dimensional linear systems.

ERROR ESTIMATES OF GALERKIN METHOD FOR HIGH DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

Error estimates of Galerkin method for Kuramoto-Sivashingsky (K-S) equation in space dimension ≥3 are derived in the paper. These results furnish strong evidence for the computation of the solutions.

PARALLEL SCHWARZ ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES

In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of time-step and space-mesh. We prove that the, approximate solution has convergence independent of iteration times at each time-level. And the L^2 error estimates are given.

THE ERROR ESTIMATES OF HALLEY'S METHOD

In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.

LOCAL ERROR ESTIMATES FOR METHODS OF CHARACTERISTICS INCORPORATING STREAMLINE DIFFUSION

Allen and Liu (1995) introduced a new method for a time-dependent convection dominated diffusion problem, which combines the modified method of characteristics and method of streamline diffusion. But they ignored the fact that the accuracy of time discretization decays at half an order when the characteristic line goes out of the domain. In present paper, the author shows that, as a remedy, a simple lumped scheme yields a full accuracy approximation. Forthermore, some local error bounds independent of the small viscosity axe derived for this scheme outside the boundary layers.