传感器网络中带有一致性策略的分布式H∞滤波:考虑一致性跟踪误差

现有的带有一致性策略的分布式 滤波方法包含两个步骤:与相邻传感器节点交互通信的一致性步骤, 以及本地滤波步骤. 本文分析了一致性跟踪误差对于本地估计误差的影响, 并针对此影响, 提出了新的分布式H∞滤波方法. 当采样周期中一致性迭代次数有限时, 本文提出的方法能够抑制一致性跟踪误差对本地估计误差的影响;当采样周期中一致性迭代次数趋于无穷, 即一致性跟踪误差收敛到零时, 本文提出的分布式算法中的本地滤波就等价于集中式滤波. 仿真表明了本文方法的有效性.     

Focused local learning with wavelet neural networks

A novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set. This set can be either user-defined or determined using information derived from the wavelet transform modulus maxima representation. Next, during the network construction, a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error. Simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity.     

A posteriori error estimators for stabilized P1 nonconforming approximation of the Stokes problem

In this paper we derive and analyze some a posteriori error estimators for the stabilized P1 nonconforming approximation of the Stokes problem involving the strain tensor. This will be done by decomposing the numerical error in a proper way into conforming and nonconforming contributions. The error estimator for the nonconforming error is obtained in the standard way, and the implicit error estimator for the conforming error is derived by applying the equilibrated residual method. A crucial part of this work is construction of approximate normal stresses on interelement boundaries which will serve as equilibrated Neumann data for local Stokes problems. It turns out that such normal stresses can be simply computed by local weak residuals of the discrete system plus jumps of the velocity solution and that a stronger equilibration condition is satisfied to ensure solvability of local Stokes problems. We also derive a simple explicit error estimator based on the nonsymmetric tensor recovery of the normal stress error. Numerical results are provided to illustrate the performance of our error estimators.     

Local and global error estimations in linear structural dynamics

The study discusses the concept of error estimation in linear elastodynamics. Two different types of error estimators are presented. First ‘classical’ methods based on post-processing techniques are discussed starting from a semidiscrete formulation. The temporal error due to the finite difference discretization is measured independently of the spatial error of the finite element discretization. The temporal error estimators are applied within one time step and the spatial error estimators at a time point. The error is measured in the global energy norm. The temporal evolution of the error cannot be reflected. Furthermore the estimators can only evaluate the mean error of the whole spatial domain. As the second scheme local error estimators are presented. These estimators are designed to evaluate the error of local variables in a certain region by applying duality techniques. Local estimators are known from linear elastostatics and have later on been extended to nonlinear problems. The corresponding dual problem represents the influence of the local variable on the initial problem and may be related to the reciprocal theorem of Betti–Maxwell. In the present study this concept is transferred to linear structural dynamics. Because the dual problem is established over the total space–time domain, the spatial and temporal error of all time steps can be accumulated within one procedure. In this study the space–time finite element method is introduced as a single field formulation.     

Observer-critic structure-based adaptive dynamic programming for decentralised tracking control of unknown large-scale nonlinear systems

In this paper, a decentralised tracking control (DTC) scheme is developed for unknown large-scale nonlinear systems by using observer-critic structure-based adaptive dynamic programming. The control consists of local desired control, local tracking error control and a compensator. By introducing the local neural network observer, the subsystem dynamics can be identified. The identified subsystems can be used for the local desired control and the control input matrix, which is used in local tracking error control. Meanwhile, Hamiltonian-Jacobi-Bellman equation can be solved by constructing a critic neural network. Thus, the local tracking error control can be derived directly. To compensate the overall error caused by substitution, observation and approximation of the local tracking error control, an adaptive robustifying term is employed. Simulation examples are provided to demonstrate the effectiveness of the proposed DTC scheme.     

On a posteriori error estimates for the linear triangular finite element

Based on equilibration of side fluxes, an a posteriori error estimator is obtained for the linear triangular element for the Poisson equation, which can be computed locally. We present a procedure for constructing the estimator in which we use the Lagrange multiplier similar to the usual equilibrated residual method introduced by Ainsworth and Oden. The estimator is shown to provide guaranteed upper bound, and local lower bounds on the error up to a multiplicative constant depending only on the geometry. Based on this, we give another error estimator which can be directly constructed without solving local Neumann problems and also provide the two-sided bounds on the error. Finally, numerical tests show our error estimators are very efficient.     

Error Inhibiting Block One-step Schemes for Ordinary Differential Equations

The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in [1, 6, 8, 13, 15]). In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investigate the interplay between the local truncation error and the global error, and develop a methodology which defines the construction of explicit error inhibiting block one-step methods (alternatively written as explicit general linear methods [2]). These error inhibiting schemes are constructed so that the accumulation of the local truncation error over time is controlled, which results in a global error that is one order higher than the local truncation error. In this work, we delineate how to carefully choose the coefficient matrices so that the growth of the local truncation error is inhibited. We then use this theoretical understanding to construct several methods that have higher order global error than local truncation error, and demonstrate their enhanced order of accuracy on test cases. These methods demonstrate that the error inhibiting concept is realizable. Future work will further develop new error inhibiting methods and will analyze the computational efficiency and linear stability properties of these methods.     

Adaptive Local Postprocessing Finite Element Method for the Navier-Stokes Equations

An adaptive local postprocessing finite element method for the Navier-Stokes equations is presented in this paper. We firstly solve the problem on a relative coarse grid to get a rough approximation. Then, we correct the rough approximation by solving a series of approximate local residual equations defined on some local fine grids, which can be implemented in parallel. In addition, we also propose a reliable local a posteriori error estimator and construct an adaptive algorithm based on the corresponding a posterior error estimate. Finally, some numerical examples are presented to verify the algorithm.     

A local minimum for the 2-3-1 XOR network.

It was assumed proven that two-layer feedforward neural networks with t-1 hidden nodes, when presented with t input patterns, can not have any suboptimal local minima on the error surface. In this paper, however, we shall give a counterexample to this assumption. This counterexample consists of a region of local minima with nonzero error on the error surface of a neural network with three hidden nodes when presented with four patterns (the XOR problem). We will also show that the original proof is valid only when an unusual definition of local minimum is used.     

Error estimates and adaptive time stepping for various direct time integration methods

In this paper, the global and local error estimates and adaptive time stepping for the various direct time integration in dynamic analysis are presented. A successive quadratic function is used for the locally exact value of the acceleration and the corresponding parameters for the function are obtained from accelerations at three time stations at every time stage. The local error can be estimated simply by comparing the solutions obtained by direct time integration method (Newmark method and Wilson method) with the locally exact solutions. Based on this local error estimate an adaptive time stepping technique in a global sense is proposed. Numerical examples are carried out to verify the performance of the procedure.     

The local minima of the error surface of the 2-2-1 XOR network

All local minima of the error surface of the 2-2-1 XOR network are described. A local minimum is defined as a point such that all points in a neighbourhood have an error value greater than or equal to the error value in that point. It is proved that the error surface of the two-layer XOR network with two hidden units has a number of regions with local minima. These regions of local minima occur for combinations of the weights from the inputs to the hidden nodes such that one or both hidden nodes are saturated for at least two patterns. However, boundary points of these regions of local minima are saddle points. It will be concluded that from each finite point in weight space a strictly decreasing path exists to a point with error zero. This also explains why experiments using higher numerical precision find less “local minima”. This revised version was published online in June 2006 with corrections to the Cover Date.     

基于局部区域阈值的玻璃气泡的检测

玻璃气泡检测是安全玻璃强制检测的内容之一。为了实现安全玻璃中气泡的自动检测,必须正确提取玻璃中的气泡。首先求方差图像并二值化来确定气泡在图像中所在的局部区域,在该局部区域内,可认为光照是均匀的,然后运用局部区域阈值法保留较亮的目标,从而逐个提取出气泡。提出了一种根据直方图动态确定全局阈值将图像进行二值化的方法。     

Various approaches for constructing an ensemble of metamodels using local measures

Metamodels are approximate mathematical models used as surrogates for computationally expensive simulations. Since metamodels are widely used in design space exploration and optimization, there is growing interest in developing techniques to enhance their accuracy. It has been shown that the accuracy of metamodel predictions can be increased by combining individual metamodels in the form of an ensemble. Several efforts were focused on determining the contribution (or weight factor) of a metamodel in the ensemble using global error measures. In addition, prediction variance is also used as a local error measure to determine the weight factors. This paper investigates the efficiency of using local error measures, and also presents the use of the pointwise cross validation error as a local error measure as an alternative to using prediction variance. The effectiveness of ensemble models are tested on several problems with varying dimensionality: five mathematical benchmark problems, two structural mechanics problems and an automobile crash problem. It is found that the spatial ensemble models show better performances than the global ensemble for the low-dimensional problems, while the global ensemble is a more accurate model than the spatial ensembles for the high-dimensional problems. Ensembles based on pointwise cross validation error and prediction variance provide similar accuracy. The ensemble models based on local measures reduce cross validation errors drastically, but their performances are not that impressive in reducing the error evaluated at random test points, because the pointwise cross validation error is not a good surrogate for the error at a point.     

Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

We extend the error analysis of Adjerid and Baccouch [1], [2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.     

Local residual error estimator and adaptive finite element analysis of Poisson’s problems

A local residual error estimator based on the least-square residuals of the balance equation, constitutive relation and irrotationality condition is presented to enable adaptive finite element analyses of Poisson’s problems. The efficiency of the residual error indicator and the quality of the L² error indicator are investigated in problems with sharp and relatively sharp concentration of gradients. Both error estimators are highly dependent on the accuracy of the recovered or post-processed derivatives. Two types of post-processing are adopted: the L² projection and a local macroelement technique. In the proposed macroelement post-processing technique, the derivatives are recovered by solving local variational problems involving the residuals of the balance equation irrotationality condition and constitutive relation at special superconvergence points.     

Focussed adaptivity for laminated plates

Accurate computation of the critical response quantities for laminated composite structures has become essential, especially from the design and design certification point of view. Worst case scenario analysis (corresponding to the load envelope) of the structure require computation of local quantities of interest. In such a situation, control of both modelling error and discretisation error for the quantities of interest is required.In this study, for a fixed plate model, a novel adaptive procedure is presented, based on a posteriori estimation of the error in the quantity of interest. This focussed adaptive procedure involves prediction of the desired optimal mesh sizes in the neighborhood of the region of interest and away from the region of interest, based on an a priori estimate of the error in the quantity of interest. The final desired mesh is obtained in one shot. It is found that the error estimator, for the quantity of interest is reasonably robust. Further, the adaptive procedure is very effective in controlling the local error to within the specified tolerances.     

Optimized polygonal approximation by dominant point deletion

An algorithm for polygonal approximation based on dominant point (DP) deletion is presented in this paper. The algorithm selects an initial set of DPs and starts eliminating them one by one depending upon the error associated with each DP. The associated error value is based on global measure. A local optimization of few neighboring points is performed after each deletion. Although the algorithm does not guarantee an optimal solution, the combination of local and global optimization is expected to produce optimal results. The algorithm is extensively tested on various shapes with varying number of DPs and error threshold. In general, optimal results were observed for about 96% of the times. A good comparative study is also presented in this paper     

Boosting method for local learning in statistical pattern recognition

We propose a local boosting method in classification problems borrowing from an idea of the local likelihood method. Our proposal, local boosting, includes a simple device for localization for computational feasibility. We proved the Bayes risk consistency of the local boosting in the framework of Probably approximately correct learning. Inspection of the proof provides a useful viewpoint for comparing ordinary boosting and local boosting with respect to the estimation error and the approximation error. Both boosting methods have the Bayes risk consistency if their approximation errors decrease to zero. Compared to ordinary boosting, local boosting may perform better by controlling the trade-off between the estimation error and the approximation error. Ordinary boosting with complicated base classifiers or other strong classification methods, including kernel machines, may have classification performance comparable to local boosting with simple base classifiers, for example, decision stumps. Local boosting, however, has an advantage with respect to interpretability. Local boosting with simple base classifiers offers a simple way to specify which features are informative and how their values contribute to a classification rule even though locally. Several numerical studies on real data sets confirm these advantages of local boosting.     

Model-free Adaptive Dynamic Programming Based Near-optimal Decentralized Tracking Control of Reconfigurable Manipulators

In this paper, a model-free near-optimal decentralized tracking control (DTC) scheme is developed for reconfigurable manipulators via adaptive dynamic programming algorithm. The proposed controller can be divided into two parts, namely local desired controller and local tracking error controller. In order to remove the normboundedness assumption of interconnections, desired states of coupled subsystems are employed to substitute their actual states. Using the local input/output data, the unknown subsystem dynamics of reconfigurable manipulators can be identified by constructing local neural network (NN) identifiers. With the help of the identified dynamics, the local desired control can be derived directly with corresponding desired states. Then, for tracking error subsystems, the local tracking error control is investigated by the approximate improved local cost function via local critic NN and the identified input gain matrix. To overcome the overall error caused by the substitution, identification and critic NN approximation, a robust compensation is added to construct the improved local cost function that reflects the overall error, regulation and control simultaneously. Therefore, the closed-loop tracking system can be guaranteed to be asymptotically stable via Lyapunov stability theorem. Two 2-degree of freedom reconfigurable manipulators with different configurations are employed to demonstrate the effectiveness of the proposed modelfree near-optimal DTC scheme.     

融合DQ_CoALBP和LPQ算子的人脸活体检测

面向图片与视频攻击下的人脸活体检测任务,提出了一种差分量化相邻局部二值模式（DQ_CoALBP）算子,综合不同方向上的图像局部中心点与周围点之间的差值,同时为了更加充分地描述人脸的彩色纹理信息,在颜色空间通道上将该算子与局部相位量化（LPQ）直方图特征相融合,并利用支持向量机（SVM）分类器实现人脸反欺诈判别。在公开CASIA-FASD与Replay-Attack数据集上的实验结果表明,DQ_CoALBP算子的表现均优于LBP、LPQ、CoALBP与DQ_LBP四种算子。采用YCbCr颜色空间在融合DQ_CoALBP与LPQ算子时,CASIA-FASD数据集上的等错误率（EER）和半错误率（HTER）分别降至2.5%和3.7%,Replay-Attack数据集上实现了无差错检测,优于一些深度卷积神经网络模型。