This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel a...This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel approach that incorporates an L1-regularizer term in BF weight state estimation. We start by explaining the CMBB formation mechanism under conditions where there is a mismatch in the far-field signal model. Subsequently, we reformulate the BF weight state estimation challenge using a method known as variable-splitting, turning it into a noise minimization problem. This problem combines both linear and nonlinear quadratic terms with an L1-regularizer that promotes the sparsity. The optimization strategy is based on a variable-splitting method, implemented using the Alternating Direction Method of Multipliers(ADMM). Furthermore, a variable-splitting framework is developed to enhance BF weight state estimation, employing a Kalman Smoother(KS) optimization algorithm. The approach integrates the Rauch-TungStriebel smoother to perform posterior-smoothing state estimation by leveraging prior data. We provide proof of convergence for both linear and nonlinear CMBB state estimation technology using the variable-splitting KS and the iterated extended Kalman smoother. Simulations corroborate our theoretical analysis, showing that the proposed method achieves robust stability and effective convergence, even when faced with signal model mismatches.展开更多
The facies distribution of a reservoir is one of the biggest concerns for geologists,geophysicists,reservoir modelers,and reservoir engineers due to its high importance in the setting of any reliable decisionmaking/op...The facies distribution of a reservoir is one of the biggest concerns for geologists,geophysicists,reservoir modelers,and reservoir engineers due to its high importance in the setting of any reliable decisionmaking/optimization of field development planning.The approach for parameterizing the facies distribution as a random variable comes naturally through using the probability fields.Since the prior probability fields of facies come either from a seismic inversion or from other sources of geologic information,they are not conditioned to the data observed from the cores extracted from the wells.This paper presents a regularized element-free Galerkin(R-EFG)method for conditioning facies probability fields to facies observation.The conditioned probability fields respect all the conditions of the probability theory(i.e.all the values are between 0 and 1,and the sum of all fields is a uniform field of 1).This property achieves by an optimization procedure under equality and inequality constraints with the gradient projection method.The conditioned probability fields are further used as the input in the adaptive pluri-Gaussian simulation(APS)methodology and coupled with the ensemble smoother with multiple data assimilation(ES-MDA)for estimation and uncertainty quantification of the facies distribution.The history-matching of the facies models shows a good estimation and uncertainty quantification of facies distribution,a good data match and prediction capabilities.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
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
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
A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optima...A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother （UWNS）, was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother （EWNS） based on the first-order linearization.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
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
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
This paper addresses the computational problem of fixed-interval smoothing state estimation in linear time-varying Gaussian stochastic systems.A new fixed-interval Kalman smoothing algorithm is proposed,and the corres...This paper addresses the computational problem of fixed-interval smoothing state estimation in linear time-varying Gaussian stochastic systems.A new fixed-interval Kalman smoothing algorithm is proposed,and the corresponding form of the smoother is derived.The method is able to accommodate situations where process and measurement noises are correlated,a limitation often encountered in conventional approaches.The Kalman smoothing problem discussed in this paper can be reformulated as an equivalent constrained optimization problem,where the solution corresponds to a set of linear equations defined by a specific co-efficient matrix.Through multiple permutations,the co-efficient matrix of linear equations is transformed into a block tridiagonal form,and then both sides of the linear system are multiplied by the inverse of the co-efficient matrix.This approach is based on the transformation of linear systems described in the SPIKE algorithm and is particularly well-suited for large-scale sparse block tridiagonal matrix structures.It enables efficient,parallel,and flexible solutions while maintaining a certain degree of block diagonal dominance.Compared to directly solving block tridiagonal co-efficient matrices,this method demonstrates appreciable advantages in terms of numerical stability and computational efficiency.Consequently,the new smoothing algorithm yields a new smoother that features fewer constraints and broader applicability than traditional methods.The estimates,such as smoothed state,covariance,and cross-covariance,are essential for fields,such as system identification,navigation,guidance,and control.Finally,the effectiveness of the proposed smoothing algorithm and smoother is validated through numerical simulations.展开更多
土壤参数是模拟和计算土壤含水量等状态数据的重要因子,对农业管理及其研究具有重要意义。然而,由于土壤系统变饱和与非线性特征,现有主流数据同化方法估计土壤参数时仍面临挑战。采用基于深度学习的参数估计方法(Parameter Estimator w...土壤参数是模拟和计算土壤含水量等状态数据的重要因子,对农业管理及其研究具有重要意义。然而,由于土壤系统变饱和与非线性特征,现有主流数据同化方法估计土壤参数时仍面临挑战。采用基于深度学习的参数估计方法(Parameter Estimator with Deep Learning,PEDL)对土壤参数进行反演估计,通过两个理想算例验证PEDL估计土壤参数的效果,并与集合平滑多数据同化方法(Ensemble Smoother with Multiple Data Assimilation,ESMDA)进行了系统比较。研究结果表明:PEDL能成功识别观测数据与待估参数之间的非线性关系,无需迭代即可逼近土壤参数的真实值;PEDL获得的参数后验分布范围相较于ESMDA明显缩小;与迭代5次的ESMDA方法相比,PEDL估计结果不确定性更低,且总调用次数更少。该研究有助于提高土壤参数估计的精度,可有效提升土壤状态及相关农业模型预测可靠性。展开更多
In this paper, a new state-parameter estimation approach is presented based on the dual ensemble Kalman smoother(DEn KS) and simple biosphere model(Si B2) to sequentially estimate both the soil properties and soil moi...In this paper, a new state-parameter estimation approach is presented based on the dual ensemble Kalman smoother(DEn KS) and simple biosphere model(Si B2) to sequentially estimate both the soil properties and soil moisture profile by assimilating surface soil moisture observations. The Arou observation station, located in the upper reaches of the Heihe River in northwestern China, was selected to test the proposed method. Three numeric experiments were designed and performed to analyze the influence of uncertainties in model parameters, atmospheric forcing, and the model's physical mechanics on soil moisture estimates. Several assimilation schemes based on the ensemble Kalman filter(En KF), ensemble Kalman smoother(En KS), and dual En KF(DEn KF) were also compared in this study. The results demonstrate that soil moisture and soil properties can be simultaneously estimated by state-parameter estimation methods, which can provide more accurate estimation of soil moisture than traditional filter methods such as En KF and En KS. The estimation accuracy of the model parameters decreased with increasing error sources. DEn KS outperformed DEn KF in estimating soil moisture in most cases, especially where few observations were available. This study demonstrates that the DEn KS approach is a useful and practical way to improve soil moisture estimation.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
基金supported in Natural Science Foundation of Shandong Province,China(ZR2013FM018)。
文摘This paper aims to enhance the array Beamforming(BF) robustness by tackling issues related to BF weight state estimation encountered in Constant Modulus Blind Beamforming(CMBB). To achieve this, we introduce a novel approach that incorporates an L1-regularizer term in BF weight state estimation. We start by explaining the CMBB formation mechanism under conditions where there is a mismatch in the far-field signal model. Subsequently, we reformulate the BF weight state estimation challenge using a method known as variable-splitting, turning it into a noise minimization problem. This problem combines both linear and nonlinear quadratic terms with an L1-regularizer that promotes the sparsity. The optimization strategy is based on a variable-splitting method, implemented using the Alternating Direction Method of Multipliers(ADMM). Furthermore, a variable-splitting framework is developed to enhance BF weight state estimation, employing a Kalman Smoother(KS) optimization algorithm. The approach integrates the Rauch-TungStriebel smoother to perform posterior-smoothing state estimation by leveraging prior data. We provide proof of convergence for both linear and nonlinear CMBB state estimation technology using the variable-splitting KS and the iterated extended Kalman smoother. Simulations corroborate our theoretical analysis, showing that the proposed method achieves robust stability and effective convergence, even when faced with signal model mismatches.
文摘The facies distribution of a reservoir is one of the biggest concerns for geologists,geophysicists,reservoir modelers,and reservoir engineers due to its high importance in the setting of any reliable decisionmaking/optimization of field development planning.The approach for parameterizing the facies distribution as a random variable comes naturally through using the probability fields.Since the prior probability fields of facies come either from a seismic inversion or from other sources of geologic information,they are not conditioned to the data observed from the cores extracted from the wells.This paper presents a regularized element-free Galerkin(R-EFG)method for conditioning facies probability fields to facies observation.The conditioned probability fields respect all the conditions of the probability theory(i.e.all the values are between 0 and 1,and the sum of all fields is a uniform field of 1).This property achieves by an optimization procedure under equality and inequality constraints with the gradient projection method.The conditioned probability fields are further used as the input in the adaptive pluri-Gaussian simulation(APS)methodology and coupled with the ensemble smoother with multiple data assimilation(ES-MDA)for estimation and uncertainty quantification of the facies distribution.The history-matching of the facies models shows a good estimation and uncertainty quantification of facies distribution,a good data match and prediction capabilities.
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.
基金Projects(61203234,61135001,61075029,61074179) supported by the National Natural Science Foundation of ChinaProject(20110491692) supported by the Postdoctoral Science Foundation of China
文摘A new approach of smoothing the white noise for nonlinear stochastic system was proposed. Through presenting the Gaussian approximation about the white noise posterior smoothing probability density fimction, an optimal and unifying white noise smoothing framework was firstly derived on the basis of the existing state smoother. The proposed framework was only formal in the sense that it rarely could be directly used in practice since the model nonlinearity resulted in the intractability and infeasibility of analytically computing the smoothing gain. For this reason, a suboptimal and practical white noise smoother, which is called the unscented white noise smoother （UWNS）, was further developed by applying unscented transformation to numerically approximate the smoothing gain. Simulation results show the superior performance of the proposed UWNS approach as compared to the existing extended white noise smoother （EWNS） based on the first-order linearization.
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.
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.
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.
文摘This paper addresses the computational problem of fixed-interval smoothing state estimation in linear time-varying Gaussian stochastic systems.A new fixed-interval Kalman smoothing algorithm is proposed,and the corresponding form of the smoother is derived.The method is able to accommodate situations where process and measurement noises are correlated,a limitation often encountered in conventional approaches.The Kalman smoothing problem discussed in this paper can be reformulated as an equivalent constrained optimization problem,where the solution corresponds to a set of linear equations defined by a specific co-efficient matrix.Through multiple permutations,the co-efficient matrix of linear equations is transformed into a block tridiagonal form,and then both sides of the linear system are multiplied by the inverse of the co-efficient matrix.This approach is based on the transformation of linear systems described in the SPIKE algorithm and is particularly well-suited for large-scale sparse block tridiagonal matrix structures.It enables efficient,parallel,and flexible solutions while maintaining a certain degree of block diagonal dominance.Compared to directly solving block tridiagonal co-efficient matrices,this method demonstrates appreciable advantages in terms of numerical stability and computational efficiency.Consequently,the new smoothing algorithm yields a new smoother that features fewer constraints and broader applicability than traditional methods.The estimates,such as smoothed state,covariance,and cross-covariance,are essential for fields,such as system identification,navigation,guidance,and control.Finally,the effectiveness of the proposed smoothing algorithm and smoother is validated through numerical simulations.
文摘土壤参数是模拟和计算土壤含水量等状态数据的重要因子,对农业管理及其研究具有重要意义。然而,由于土壤系统变饱和与非线性特征,现有主流数据同化方法估计土壤参数时仍面临挑战。采用基于深度学习的参数估计方法(Parameter Estimator with Deep Learning,PEDL)对土壤参数进行反演估计,通过两个理想算例验证PEDL估计土壤参数的效果,并与集合平滑多数据同化方法(Ensemble Smoother with Multiple Data Assimilation,ESMDA)进行了系统比较。研究结果表明:PEDL能成功识别观测数据与待估参数之间的非线性关系,无需迭代即可逼近土壤参数的真实值;PEDL获得的参数后验分布范围相较于ESMDA明显缩小;与迭代5次的ESMDA方法相比,PEDL估计结果不确定性更低,且总调用次数更少。该研究有助于提高土壤参数估计的精度,可有效提升土壤状态及相关农业模型预测可靠性。
基金supported by the Natural National Science Foundation of China(Grant Nos.91325106&41271358)the Hundred Talent Program of the Chinese Academy of Sciences(Grant No.29Y127D01)+1 种基金the Cross-disciplinary Collaborative Teams Program for ScienceTechnology and Innovation of the Chinese Academy of Sciences
文摘In this paper, a new state-parameter estimation approach is presented based on the dual ensemble Kalman smoother(DEn KS) and simple biosphere model(Si B2) to sequentially estimate both the soil properties and soil moisture profile by assimilating surface soil moisture observations. The Arou observation station, located in the upper reaches of the Heihe River in northwestern China, was selected to test the proposed method. Three numeric experiments were designed and performed to analyze the influence of uncertainties in model parameters, atmospheric forcing, and the model's physical mechanics on soil moisture estimates. Several assimilation schemes based on the ensemble Kalman filter(En KF), ensemble Kalman smoother(En KS), and dual En KF(DEn KF) were also compared in this study. The results demonstrate that soil moisture and soil properties can be simultaneously estimated by state-parameter estimation methods, which can provide more accurate estimation of soil moisture than traditional filter methods such as En KF and En KS. The estimation accuracy of the model parameters decreased with increasing error sources. DEn KS outperformed DEn KF in estimating soil moisture in most cases, especially where few observations were available. This study demonstrates that the DEn KS approach is a useful and practical way to improve soil moisture estimation.
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.
