We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation....We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation.Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening.We also present numerical tests supporting the theoretical results and the heuristic ideas.The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.展开更多
In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Comput...In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Computational Fluid Dynamics(CFD),particularly for incompressible flow problems.When treating(nearly)incompressible solids,similar equation systems arise so that it is reasonable to adopt the‘Vanka idea’for CSM.While there exist numerous studies about Vanka smoothers in the CFD literature,only few publications describe applications to solid mechanical problems.With this paper we want to contribute to close this gap.We depict and compare four different Vanka-like smoothers,two of them are oriented towards the stabilised equal-order Q_(1)/Q_(1)finite element pair.By means of different test configurations we assess how far the smoothers are able to handle the numerical difficulties that arise for nearly incompressible material and anisotropic meshes.On the one hand,we show that the efficiency of all Vanka-smoothers heavily depends on the proper parameter choice.On the other hand,we demonstrate that only some of them are able to robustly deal with more critical situations.Furthermore,we illustrate how the enclosure of the multigrid scheme by an outer Krylov space method influences the overall solver performance,and we extend all our examinations to the nonlinear finite deformation case.展开更多
This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integri...This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integrity attack strategy is first proposed by modifying a zero-dynamics attack model.The stealthiness of the generated attacks is rigorously investigated under the condition that the adversary does not know precisely the system state values.In order to help detect such attacks,a backward-in-time detection residual is proposed based on an equivalent quantity of the system state change,due to the attack,at a time prior to the attack occurrence time.A key characteristic of this residual is that its magnitude increases every time a new attack occurs.To estimate this unknown residual,an optimal fixed-point smoother is proposed by minimizing a piece-wise linear quadratic cost function with a set of specifically designed weighting matrices.The smoother design guarantees robustness with respect to process disturbances and measurement noise,and is also able to maintain sensitivity as time progresses to intermittent integrity attack by resetting the covariance matrix based on the weighting matrices.The adaptive threshold is designed based on the estimated backward-in-time residual,and the attack detectability analysis is rigorously investigated to characterize quantitatively the class of attacks that can be detected by the proposed methodology.Finally,a simulation example is used to demonstrate the effectiveness of the developed methodology.展开更多
In practical applications, the system observation error is widespread. If the observation equation of the system has not been verified or corrected under certain environmental conditions,the unknown system errors and ...In practical applications, the system observation error is widespread. If the observation equation of the system has not been verified or corrected under certain environmental conditions,the unknown system errors and filtering errors will come into being.The incremental observation equation is derived, which can eliminate the unknown observation errors effectively. Furthermore, an incremental Kalman smoother is presented. Moreover, a weighted measurement fusion incremental Kalman smoother applying the globally optimal weighted measurement fusion algorithm is given.The simulation results show their effectiveness and feasibility.展开更多
Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using white noise estimators, an optimal fusion distributed Kalman smoother is given for discre...Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using white noise estimators, an optimal fusion distributed Kalman smoother is given for discrete multi-channel ARMA (autoregressive moving average) signals. The smoothing error cross-covanance matrices between any two sensors are given for measurement noises. Furthermore, the fusion smoother gives higher precision than any local smoother does.展开更多
For improving the localization accuracy,a multi-interval extended finite impulse response(EFIR)-based Rauch-Tung-Striebel(R-T-S)smoother is proposed for the range-only ultra wide band(UWB)simultaneous localization and...For improving the localization accuracy,a multi-interval extended finite impulse response(EFIR)-based Rauch-Tung-Striebel(R-T-S)smoother is proposed for the range-only ultra wide band(UWB)simultaneous localization and mapping(SLAM)for robot localization.In this mode,the EFIR R-T-S(ERTS)smoother employs EFIR filter as the forward filter and the R-T-S smoothing method to smooth the EFIR filter’s output.When the east or the north position is considered as stance,the ERTS is used to smooth the position directly.Moreover,the estimation of the UWB Reference Nodes’(RNs’)position is smoothed by the R-T-S smooth method in parallel.The test illustrates that the proposedmulti-interval ERTS smoothing for range-only UWB SLAMis able to provide accurate estimation.Compared with the EFIR filter,the proposed method improves the localization accuracy by about 25.35%and 40.66%in east and north directions,respectively.展开更多
Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical gro...Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical groundwater inverse problem,and the solution is usually ill-posed.Especially considering the spatial variability of hydraulic conductivity field,the identification process is more challenging.In this paper,the solution framework of groundwater contaminant source identification is composed with groundwater pollutant transport model(MT3DMS)and a data assimilation method(Iterative local update ensemble smoother,ILUES).In addition,Karhunen-Loève expansion technique is adopted as a PCA method to realize dimension reduction.In practical problems,the geostatistical method is usually used to characterize the hydraulic conductivity field,and only the contaminant source information is inversely calculated in the identification process.In this study,the identification of contaminant source information under Kriging K-field is compared with simultaneous identification of source information and K-field.The results indicate that it is necessary to carry out simultaneous identification under heterogeneous site,and ILUES has good performance in solving high-dimensional parameter inversion problems.展开更多
Meta-learning provides a framework for the possibility of mimicking artificial intelligence.How-ever,data distribution of the training set fails to be consistent with the one of the testing set as the limited domain d...Meta-learning provides a framework for the possibility of mimicking artificial intelligence.How-ever,data distribution of the training set fails to be consistent with the one of the testing set as the limited domain differences among them.These factors often result in poor generalization in existing meta-learning models.In this work,a novel smoother manifold for graph meta-learning(SGML)is proposed,which derives the similarity parameters of node features from the relationship between nodes and edges in the graph structure,and then utilizes the similarity parameters to yield smoother manifold through embedded propagation module.Smoother manifold can naturally filter out noise from the most important components when generalizing the local mapping relationship to the global.Besides suiting for generalizing on unseen low data issues,the framework is capable to easily perform transductive inference.Experimental results on MiniImageNet and TieredImageNet consistently show that applying SGML to supervised and semi-supervised classification can improve the performance in reducing the noise of domain shift representation.展开更多
A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consiste...A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.展开更多
Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored no...Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k);2) the observation matrix H;3) the variance of the state vector x(k);4) the system matrix for the colored observation noise vc(k);5) the variance of the colored observation noise;6) the input noise variance in the state equation for the colored observation noise.展开更多
In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neu...In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neural Network is derived with the aid of a Super-Population Model. This current study is motivated by the fact that Local Polynomials and Kernel methods have in preceding related studies, been shown to provide good estimators for Finite Population Totals but in low dimensions. Even in these situations however, bias at boundary points presents a big challenge when using these estimators in estimating Finite Population parameters. The challenge worsens as the dimension of regressors increase. This is because as the dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values in the design space becomes unfeasible, resulting in a decrease in the fastest achievable rates of convergence of the Regression Function Estimators towards the target curve, rendering Kernel Methods and Local Polynomials ineffective to address these challenges. This study considers the technique of Artificial Neural Networks which yields robust estimators in high dimensions and reduces the estimation bias with marginal increase in variance. This is due to its Multi-Layer Structure, which can approximate a wide range of functions to any required level of precision. The estimator’s properties are developed, and a comparison with existing estimators was conducted to evaluate the estimator’s performance using real data sets acquired from the United Nations Development Programme 2020. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development Index against other factors. The theoretical and practical results imply that the Neural Network estimator is highly recommended for survey sampling estimation of the finite population total.展开更多
In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is establishe...In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.展开更多
It is widely accepted that natural resources should only be sustainably exploited and utilized to effectively preserve our planet for future generations.To better manage the natural resources,and to better understand ...It is widely accepted that natural resources should only be sustainably exploited and utilized to effectively preserve our planet for future generations.To better manage the natural resources,and to better understand the closely linked Earth systems,the concept of Digital Earth has been strongly promoted since US Vice President Al Gore’s speech in 1998.One core element of Digital Earth is the use and integration of remote sensing data.Only satellite imagery can cover the entire globe repeatedly at a sufficient high-spatial resolution to map changes in land cover and land use,but also to detect more subtle changes related for instance to climate change.To uncover global change effects on vegetation activity and phenology,it is important to establish high quality time series characterizing the past situation against which the current state can be compared.With the present study we describe a time series of vegetation activity at 10-daily time steps between 1998 and 2008 covering large parts of South America at 1 km spatial resolution.Particular emphasis was put on noise removal.Only carefully filtered time series of vegetation indices can be used as a benchmark and for studying vegetation dynamics at a continental scale.Without temporal smoothing,subtle spatio-temporal patterns in vegetation composition,density and phenology would be hidden by atmospheric noise and undetected clouds.Such noise is immanent in data that have undergone solely a maximum value compositing.Within the present study,the Whittaker smoother(WS)was applied to a SPOT VGT time series.The WS balances the fidelity to the observations with the roughness of the smoothed curve.The algorithm is extremely fast,gives continuous control over smoothness with only one parameter,and interpolates automatically.The filtering efficiently removed the negatively biased noise present in the original data,while preserving the overall shape of the curves showing vegetation growth and development.Geostatistical variogram analysis revealed a significantly increased signal-to-noise ratio compared to the raw data.Analysis of the data also revealed spatially consistent key phenological markers.Extracted seasonality parameters followed a clear meridional trend.Compared to the unfiltered data,the filtered time series increased the separability of various land cover classes.It is thus expected that the data set holds great potential for environmental and vegetation related studies within the frame of Digital Earth.展开更多
In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform conver...In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations.It turns out to be robust for relatively large physical parameters.By extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.展开更多
It is understood that the forward-backward probability hypothesis density (PHD) smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show ...It is understood that the forward-backward probability hypothesis density (PHD) smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality (i.e., the number of targets) estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.展开更多
I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonpa...I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.展开更多
文摘We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation.Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening.We also present numerical tests supporting the theoretical results and the heuristic ideas.The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.
基金has been supported by DFG,under grant TU 102/11-3。
文摘In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Computational Fluid Dynamics(CFD),particularly for incompressible flow problems.When treating(nearly)incompressible solids,similar equation systems arise so that it is reasonable to adopt the‘Vanka idea’for CSM.While there exist numerous studies about Vanka smoothers in the CFD literature,only few publications describe applications to solid mechanical problems.With this paper we want to contribute to close this gap.We depict and compare four different Vanka-like smoothers,two of them are oriented towards the stabilised equal-order Q_(1)/Q_(1)finite element pair.By means of different test configurations we assess how far the smoothers are able to handle the numerical difficulties that arise for nearly incompressible material and anisotropic meshes.On the one hand,we show that the efficiency of all Vanka-smoothers heavily depends on the proper parameter choice.On the other hand,we demonstrate that only some of them are able to robustly deal with more critical situations.Furthermore,we illustrate how the enclosure of the multigrid scheme by an outer Krylov space method influences the overall solver performance,and we extend all our examinations to the nonlinear finite deformation case.
基金This work was supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skodowska-Curie(101027980(CSPCPS-A-ICA),739551(KIOS CoE-TEAMING))the Italian Ministry for Research in the Framework of the 2017 Program for Research Projects of National Interest(PRIN)(2017YKXYXJ)+3 种基金the National Natural Science Foundation of China(61903188,62073165,62020106003)the Natural Science Foundation of Jiangsu Province(BK20190403)the 111 Project(B20007)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper proposes a passive methodology for detecting a class of stealthy intermittent integrity attacks in cyberphysical systems subject to process disturbances and measurement noise.A stealthy intermittent integrity attack strategy is first proposed by modifying a zero-dynamics attack model.The stealthiness of the generated attacks is rigorously investigated under the condition that the adversary does not know precisely the system state values.In order to help detect such attacks,a backward-in-time detection residual is proposed based on an equivalent quantity of the system state change,due to the attack,at a time prior to the attack occurrence time.A key characteristic of this residual is that its magnitude increases every time a new attack occurs.To estimate this unknown residual,an optimal fixed-point smoother is proposed by minimizing a piece-wise linear quadratic cost function with a set of specifically designed weighting matrices.The smoother design guarantees robustness with respect to process disturbances and measurement noise,and is also able to maintain sensitivity as time progresses to intermittent integrity attack by resetting the covariance matrix based on the weighting matrices.The adaptive threshold is designed based on the estimated backward-in-time residual,and the attack detectability analysis is rigorously investigated to characterize quantitatively the class of attacks that can be detected by the proposed methodology.Finally,a simulation example is used to demonstrate the effectiveness of the developed methodology.
基金supported by the National Natural Science Foundation of China(6110420961503126)
文摘In practical applications, the system observation error is widespread. If the observation equation of the system has not been verified or corrected under certain environmental conditions,the unknown system errors and filtering errors will come into being.The incremental observation equation is derived, which can eliminate the unknown observation errors effectively. Furthermore, an incremental Kalman smoother is presented. Moreover, a weighted measurement fusion incremental Kalman smoother applying the globally optimal weighted measurement fusion algorithm is given.The simulation results show their effectiveness and feasibility.
文摘Based on the multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using white noise estimators, an optimal fusion distributed Kalman smoother is given for discrete multi-channel ARMA (autoregressive moving average) signals. The smoothing error cross-covanance matrices between any two sensors are given for measurement noises. Furthermore, the fusion smoother gives higher precision than any local smoother does.
文摘For improving the localization accuracy,a multi-interval extended finite impulse response(EFIR)-based Rauch-Tung-Striebel(R-T-S)smoother is proposed for the range-only ultra wide band(UWB)simultaneous localization and mapping(SLAM)for robot localization.In this mode,the EFIR R-T-S(ERTS)smoother employs EFIR filter as the forward filter and the R-T-S smoothing method to smooth the EFIR filter’s output.When the east or the north position is considered as stance,the ERTS is used to smooth the position directly.Moreover,the estimation of the UWB Reference Nodes’(RNs’)position is smoothed by the R-T-S smooth method in parallel.The test illustrates that the proposedmulti-interval ERTS smoothing for range-only UWB SLAMis able to provide accurate estimation.Compared with the EFIR filter,the proposed method improves the localization accuracy by about 25.35%and 40.66%in east and north directions,respectively.
基金supported by the Fundamental Research Funds for the Central Universities(No.22120190013)National Natural Science Foundation of China(No.41807187)
文摘Identification of the location and intensity of groundwater pollution source contributes to the effect of pollution remediation,and is called groundwater contaminant source identification.This is a kind of typical groundwater inverse problem,and the solution is usually ill-posed.Especially considering the spatial variability of hydraulic conductivity field,the identification process is more challenging.In this paper,the solution framework of groundwater contaminant source identification is composed with groundwater pollutant transport model(MT3DMS)and a data assimilation method(Iterative local update ensemble smoother,ILUES).In addition,Karhunen-Loève expansion technique is adopted as a PCA method to realize dimension reduction.In practical problems,the geostatistical method is usually used to characterize the hydraulic conductivity field,and only the contaminant source information is inversely calculated in the identification process.In this study,the identification of contaminant source information under Kriging K-field is compared with simultaneous identification of source information and K-field.The results indicate that it is necessary to carry out simultaneous identification under heterogeneous site,and ILUES has good performance in solving high-dimensional parameter inversion problems.
基金Supported by the National Natural Science Foundation of China(No.61171131)the Key R&D Program of Shandong Province(No.YD01033)the China Scholarship Council Project(No.021608370049).
文摘Meta-learning provides a framework for the possibility of mimicking artificial intelligence.How-ever,data distribution of the training set fails to be consistent with the one of the testing set as the limited domain differences among them.These factors often result in poor generalization in existing meta-learning models.In this work,a novel smoother manifold for graph meta-learning(SGML)is proposed,which derives the similarity parameters of node features from the relationship between nodes and edges in the graph structure,and then utilizes the similarity parameters to yield smoother manifold through embedded propagation module.Smoother manifold can naturally filter out noise from the most important components when generalizing the local mapping relationship to the global.Besides suiting for generalizing on unseen low data issues,the framework is capable to easily perform transductive inference.Experimental results on MiniImageNet and TieredImageNet consistently show that applying SGML to supervised and semi-supervised classification can improve the performance in reducing the noise of domain shift representation.
基金the Fundamental Research Fund of Northwestern Polytechnical University( Grant No. JC20120210,JC20110238)
文摘A square-root version of the divided difference Rauch-Tung-Striebel (RTS) smoother is proposed in this paper. The square-root variant essentially propagates the square roots of the covariance matrices and can consistently improve the numerical stability because all the resulting covariance matrices are guaranteed to stay positive semi-definite. Furthermore, the square-root form ensures reliable implementation in an embedded system with fixed or limited precision although it is algebraically equivalent to the standard form. The new smoothing algorithm is tested in a challenging two-dimensional maneuvering target tracking problem with unknown and time-varying turn rate, and its performance is compared with that of other de-facto standard filters and smoothers. The simulation results indicate that the proposed RTS smoother markedly outperforms the associated filters and gives slightly smaller error than an unscented-based RTS smoother.
文摘Almost estimators are designed for the white observation noise. In the estimation problems, rather than the white observation noise, there might be actual cases where the observation noise is modeled by the colored noise process. This paper examines to design a new estimation technique of recursive least-squares (RLS) Wiener fixed-point smoother and filter for colored observation noise in linear discrete-time wide-sense stationary stochastic systems. The observation y(k) is given as the sum of the signal z(k)=Hx(k) and the colored observation noise vc(k). The RLS Wiener estimators explicitly require the following information: 1) the system matrix for the state vector x(k);2) the observation matrix H;3) the variance of the state vector x(k);4) the system matrix for the colored observation noise vc(k);5) the variance of the colored observation noise;6) the input noise variance in the state equation for the colored observation noise.
文摘In this paper, the problem of Nonparametric Estimation of Finite Population Totals in high dimensional datasets is considered. A robust estimator of the Finite Population Total based on Feedforward Backpropagation Neural Network is derived with the aid of a Super-Population Model. This current study is motivated by the fact that Local Polynomials and Kernel methods have in preceding related studies, been shown to provide good estimators for Finite Population Totals but in low dimensions. Even in these situations however, bias at boundary points presents a big challenge when using these estimators in estimating Finite Population parameters. The challenge worsens as the dimension of regressors increase. This is because as the dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values in the design space becomes unfeasible, resulting in a decrease in the fastest achievable rates of convergence of the Regression Function Estimators towards the target curve, rendering Kernel Methods and Local Polynomials ineffective to address these challenges. This study considers the technique of Artificial Neural Networks which yields robust estimators in high dimensions and reduces the estimation bias with marginal increase in variance. This is due to its Multi-Layer Structure, which can approximate a wide range of functions to any required level of precision. The estimator’s properties are developed, and a comparison with existing estimators was conducted to evaluate the estimator’s performance using real data sets acquired from the United Nations Development Programme 2020. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development Index against other factors. The theoretical and practical results imply that the Neural Network estimator is highly recommended for survey sampling estimation of the finite population total.
基金the National Science Foundation(Grant Nos.DMS0409297,DMR0205232,CCF-0430349)US National Institute of Health-National Cancer Institute(Grant No.1R01CA125707-01A1)+2 种基金the National Natural Science Foundation of China(Grant No.10571172)the National Basic Research Program(Grant No.2005CB321704)the Youth's Innovative Program of Chinese Academy of Sciences(Grant Nos.K7290312G9,K7502712F9)
文摘In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
文摘It is widely accepted that natural resources should only be sustainably exploited and utilized to effectively preserve our planet for future generations.To better manage the natural resources,and to better understand the closely linked Earth systems,the concept of Digital Earth has been strongly promoted since US Vice President Al Gore’s speech in 1998.One core element of Digital Earth is the use and integration of remote sensing data.Only satellite imagery can cover the entire globe repeatedly at a sufficient high-spatial resolution to map changes in land cover and land use,but also to detect more subtle changes related for instance to climate change.To uncover global change effects on vegetation activity and phenology,it is important to establish high quality time series characterizing the past situation against which the current state can be compared.With the present study we describe a time series of vegetation activity at 10-daily time steps between 1998 and 2008 covering large parts of South America at 1 km spatial resolution.Particular emphasis was put on noise removal.Only carefully filtered time series of vegetation indices can be used as a benchmark and for studying vegetation dynamics at a continental scale.Without temporal smoothing,subtle spatio-temporal patterns in vegetation composition,density and phenology would be hidden by atmospheric noise and undetected clouds.Such noise is immanent in data that have undergone solely a maximum value compositing.Within the present study,the Whittaker smoother(WS)was applied to a SPOT VGT time series.The WS balances the fidelity to the observations with the roughness of the smoothed curve.The algorithm is extremely fast,gives continuous control over smoothness with only one parameter,and interpolates automatically.The filtering efficiently removed the negatively biased noise present in the original data,while preserving the overall shape of the curves showing vegetation growth and development.Geostatistical variogram analysis revealed a significantly increased signal-to-noise ratio compared to the raw data.Analysis of the data also revealed spatially consistent key phenological markers.Extracted seasonality parameters followed a clear meridional trend.Compared to the unfiltered data,the filtered time series increased the separability of various land cover classes.It is thus expected that the data set holds great potential for environmental and vegetation related studies within the frame of Digital Earth.
基金supported in part by the National Science Fund for Dist inguished Young Scholars 11725106,China NSF grant 11831016.
文摘In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations.We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations.It turns out to be robust for relatively large physical parameters.By extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.
基金co-supported by the National Natural Science Foundation of China(No.61171127)NSF of China(No.60972024)NSTMP of China(No.2011ZX03003-001-02 and No.2012ZX03001007-003)
文摘It is understood that the forward-backward probability hypothesis density (PHD) smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality (i.e., the number of targets) estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.
基金Supported by Biological & Biotechnology Research Council and the Engineering & Physical Science Research Council of the United Kingdom,and by the Research Grant Council of Hong Kong.
文摘I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.