Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment...Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given.展开更多
Two traditional methods for compensating function model errors, the method of adding systematic parameters and the least-squares collection method, are introduced. A proposed method based on a BP neural network （call...Two traditional methods for compensating function model errors, the method of adding systematic parameters and the least-squares collection method, are introduced. A proposed method based on a BP neural network （called the H-BP algorithm） for compensating function model errors is put forward. The function model is assumed as y =f（x1, x2,… ,xn）, and the special structure of the H-BP algorithm is determined as （ n ＋ 1） ×p × 1, where （n ＋ 1） is the element number of the input layer, and the elements are xl, x2,…, xn and y＇ （ y＇ is the value calculated by the function model）; p is the element number of the hidden layer, and it is usually determined after many tests; 1 is the dement number of the output layer, and the element is △y = y0-y＇（y0 is the known value of the sample）. The calculation steps of the H-BP algorithm are introduced in detail. And then, the results of three methods for compensating function model errors from one engineering project are compared with each other. After being compensated, the accuracy of the traditional methods is about ± 19 mm, and the accuracy of the H-BP algorithm is ± 4. 3 mm. It shows that the proposed method based on a neural network is more effective than traditional methods for compensating function model errors.展开更多
Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can ...Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.展开更多
Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the pred...Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.展开更多
The presence of array imperfection and mutual coupling in sensor arrays poses several challenges for development of effective algorithms for the direction-of-arrival （DOA） estimation problem in array processing. A c...The presence of array imperfection and mutual coupling in sensor arrays poses several challenges for development of effective algorithms for the direction-of-arrival （DOA） estimation problem in array processing. A correlation domain wideband DOA estimation algorithm without array calibration is proposed, to deal with these array model errors, using the arbitrary antenna array of omnidirectional elements. By using the matrix operators that have the memory and oblivion characteristics, this algorithm can separate the incident signals effectively. Compared with other typical wideband DOA estimation algorithms based on the subspace theory, this algorithm can get robust DOA estimation with regard to position error, gain-phase error, and mutual coupling, by utilizing a relaxation technique based on signal separation. The signal separation category and the robustness of this algorithm to the array model errors are analyzed and proved. The validity and robustness of this algorithm, in the presence of array model errors, are confirmed by theoretical analysis and simulation results.展开更多
Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matri...Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.展开更多
An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given t...An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.展开更多
Initial condition and model errors both contribute to the loss of atmospheric predictability.However,it remains debatable which type of error has the larger impact on the prediction lead time of specific states.In thi...Initial condition and model errors both contribute to the loss of atmospheric predictability.However,it remains debatable which type of error has the larger impact on the prediction lead time of specific states.In this study,we perform a theoretical study to investigate the relative effects of initial condition and model errors on local prediction lead time of given states in the Lorenz model.Using the backward nonlinear local Lyapunov exponent method,the prediction lead time,also called local backward predictability limit(LBPL),of given states induced by the two types of errors can be quantitatively estimated.Results show that the structure of the Lorenz attractor leads to a layered distribution of LBPLs of states.On an individual circular orbit,the LBPLs are roughly the same,whereas they are different on different orbits.The spatial distributions of LBPLs show that the relative effects of initial condition and model errors on local backward predictability depend on the locations of given states on the dynamical trajectory and the error magnitudes.When the error magnitude is fixed,the differences between the LBPLs vary with the locations of given states.The larger differences are mainly located on the inner trajectories of regimes.When the error magnitudes are different,the dissimilarities in LBPLs are diverse for the same given state.展开更多
Initial errors and model errors are the source of prediction errors. In this study, the authors compute the conditional nonlinear optimal perturbation （CNOP）-type initial errors and nonlinear forcing singular vector...Initial errors and model errors are the source of prediction errors. In this study, the authors compute the conditional nonlinear optimal perturbation （CNOP）-type initial errors and nonlinear forcing singular vector （NFSV）- type tendency errors of the Zebiak-Cane model with respect to El Nifio events and analyze their combined effect on the prediction errors for E1 Nino events. The CNOP- type initial error （NFSV-type tendency error） represents the initial errors （model errors） that have the largest effect on prediction uncertainties for E1 Nifio events under the perfect model （perfect initial conditions） scenario. How- ever, when the CNOP-type initial errors and the NFSV- type tendency errors are simultaneously considered in the model, the prediction errors caused by them are not am- plified as the authors expected. Specifically, the predic- tion errors caused by the combined mode of CNOP-type initial errors and NFSV-type tendency errors are a little larger than those caused by the NFSV-type tendency er- rors. This fact emphasizes a need to investigate the opti- mal combined mode of initial errors and tendency errors that cause the largest prediction error for E1 Nifio events.展开更多
Dynamic equations of elastic linkage are formed by means of Kane equation and finitemethod. Eight main influential factors on the dynamic response of elastic linkage are considered inthese equations. Model error cause...Dynamic equations of elastic linkage are formed by means of Kane equation and finitemethod. Eight main influential factors on the dynamic response of elastic linkage are considered inthese equations. Model error caused by the eight factors are investigated. Some useful conclusionsabout model error are derived from theoretical analysis and the numerical calculation of twenty-sixexamples.展开更多
In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance c...In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.展开更多
Forecast errors of numerical weather prediction consist of model errors and the growth of initial condition errors,while the initial condition is often optimized based on short-term forecasts.Thus it is difficult to u...Forecast errors of numerical weather prediction consist of model errors and the growth of initial condition errors,while the initial condition is often optimized based on short-term forecasts.Thus it is difficult to untangle the initial condition error and model error,but it is essential to infer model errors not just for prediction but also for data assimilation(DA).A hybrid deep learning(DL)and DA method is proposed here,aiming to correct model errors.It uses a convolutional neural network(CNN)to extract characteristics of initial conditions and forecast errors,and then provides estimations for model errors.The CNN-based model error estimation method can consider the model error resulted from inaccurate model parameters,or simultaneously consider the model error and initial condition error.Based on the Lorenz05 model,offline and online experiments demonstrate that the CNN-based model error estimation method can effectively correct model errors resulted from inaccurate model parameters,including the forcing F,coupling coefficient c,and relative scale b.For both online and offline model error estimations,simultaneously considering model errors and initial condition errors are beneficial to infer the model errors,compared to considering model errors only.Moreover,using the observations to verify the forecasts has advantages over using the analyses,to estimate the model errors.Using observations can also achieve a faster convergence of model error estimation with online DA than using analyses.展开更多
Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was...Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was developed using the6 h average bias to correct the systematic bias during model integration.The primary purpose of this study is to investigate the impact of the SBCS in the high-resolution China Meteorological Administration Meso-scale(CMA-MESO)numerical weather prediction(NWP)model to reduce the systematic bias and to improve the data assimilation and forecast results through this method.The SBCS is improved upon and applied to the CMA-MESO 3-km model in this study.Four-week sequential data assimilation and forecast experiments,driven by rapid update and cycling(RUC),were conducted for the period from 2–29 May 2022.In terms of the characteristics of systematic bias,both the background and analysis show diurnal bias,and these large biases are affected by complex underlying surfaces(e.g.,oceans,coasts,and mountains).After the application of the SBCS,the results of the data assimilation show that the SBCS can reduce the systematic bias of the background and yield a neutral to slightly positive result for the analysis fields.In addition,the SBCS can reduce forecast errors and improve forecast results,especially for surface variables.The above results indicate that this scheme has good prospects for high-resolution regional NWP models.展开更多
Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining qualit...Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.展开更多
This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generali...This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.展开更多
This article investigates virtual reality (VR)-based teleoperation with robustness against modeling errors. VR technology is an effective way to overcome the large time delay during space robot teleoperation. However,...This article investigates virtual reality (VR)-based teleoperation with robustness against modeling errors. VR technology is an effective way to overcome the large time delay during space robot teleoperation. However, it depends highly on the accuracy of model. Model errors between the virtual and real environment exist inevitably. The existing way to deal with the problem is by means of either model matching or robot compliance control. As distinct from the existing methods, this article tries to combine m...展开更多
The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination ...The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination tracker dashboard. GIS-based exploratory analysis was conducted to select four variables (poverty, black race, population density, and vaccination) to explain COVID-19 occurrence during the study period. Consequently, spatial statistical techniques such as Moran’s I, Hot Spot Analysis, Spatial Lag Model (SLM), and Spatial Error Model (SEM) were used to explain the COVID-19 occurrence and vaccination rate across the 88 counties in Ohio. The result of the Local Moran’s I analysis reveals that the epicenters of COVID-19 and vaccination followed the same patterns. Indeed, counties like Summit, Franklin, Fairfield, Hamilton, and Medina were categorized as epicenters for both COVID-19 occurrence and vaccination rate. The SEM seems to be the best model for both COVID-19 and vaccination rates, with R2 values of 0.68 and 0.70, respectively. The GWR analysis proves to be better than Ordinary Least Squares (OLS), and the distribution of R2 in the GWR is uneven throughout the study area for both COVID-19 cases and vaccinations. Some counties have a high R2 of up to 0.70 for both COVID-19 cases and vaccinations. The outcomes of the regression analyses show that the SEM models can explain 68% - 70% of COVID-19 cases and vaccination across the entire counties within the study period. COVID-19 cases and vaccination rates exhibited significant positive associations with black race and poverty throughout the study area.展开更多
Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address th...Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address this issue,we propose a geometric error cost sensitivity-based accuracy allocation method for five-axis machine tools.A geometric error model consisting of 4l error components is constructed based on homogeneous transformation matrices.Volumetric points with positional and tool direction deviations are randomly sampled to evaluate the accuracy of the machine tool.The sensitivity of each error component at these sampling points is analyzed using the Sobol method.To balance the needs of geometric precision and manufacturing cost,a geometric error cost sensitivity function is developed to estimate the required cost.By allocating error components affecting tool direction deviation first and the remaining components second,this allocation scheme ensures that both deviations meet the requirements.We also perform numerical simulation of a BC-type(B-axis and C-axis type)five-axis machine tool to validate the method.The results show that the new allocation scheme reduces the total geometric error cost by 27.8%compared to a uniform allocation scheme,and yields the same positional and tool direction machining accuracies.展开更多
基金Project supported by the Open Research Fund Programof the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, WuhanUniversity (No.905276031-04-10) .
文摘Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given.
基金The National Basic Research Program of China(973 Program)(No.2006CB705501)the National High Technology Research and Development Program of China (863 Program)(No.2007AA12Z228)
文摘Two traditional methods for compensating function model errors, the method of adding systematic parameters and the least-squares collection method, are introduced. A proposed method based on a BP neural network （called the H-BP algorithm） for compensating function model errors is put forward. The function model is assumed as y =f（x1, x2,… ,xn）, and the special structure of the H-BP algorithm is determined as （ n ＋ 1） ×p × 1, where （n ＋ 1） is the element number of the input layer, and the elements are xl, x2,…, xn and y＇ （ y＇ is the value calculated by the function model）; p is the element number of the hidden layer, and it is usually determined after many tests; 1 is the dement number of the output layer, and the element is △y = y0-y＇（y0 is the known value of the sample）. The calculation steps of the H-BP algorithm are introduced in detail. And then, the results of three methods for compensating function model errors from one engineering project are compared with each other. After being compensated, the accuracy of the traditional methods is about ± 19 mm, and the accuracy of the H-BP algorithm is ± 4. 3 mm. It shows that the proposed method based on a neural network is more effective than traditional methods for compensating function model errors.
基金Project supported by the Special Scientific Research Project for Public Interest(Grant No.GYHY201206009)the Fundamental Research Funds for the Central Universities,China(Grant Nos.lzujbky-2012-13 and lzujbky-2013-11)the National Basic Research Program of China(Grant Nos.2012CB955902 and 2013CB430204)
文摘Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
基金supported by the National "863" High Technology Research and Development Program of China(2007AA703428)
文摘The presence of array imperfection and mutual coupling in sensor arrays poses several challenges for development of effective algorithms for the direction-of-arrival （DOA） estimation problem in array processing. A correlation domain wideband DOA estimation algorithm without array calibration is proposed, to deal with these array model errors, using the arbitrary antenna array of omnidirectional elements. By using the matrix operators that have the memory and oblivion characteristics, this algorithm can separate the incident signals effectively. Compared with other typical wideband DOA estimation algorithms based on the subspace theory, this algorithm can get robust DOA estimation with regard to position error, gain-phase error, and mutual coupling, by utilizing a relaxation technique based on signal separation. The signal separation category and the robustness of this algorithm to the array model errors are analyzed and proved. The validity and robustness of this algorithm, in the presence of array model errors, are confirmed by theoretical analysis and simulation results.
基金This work is supported by Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX18_0467)Jiangsu Province,China.During the revision of this paper,the author is supported by China Scholarship Council(No.201906840021)China to continue some research related to data processing.
文摘Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.
基金supported by the National Natural Science Foundation of China (Grant Nos.42005054,41975070)China Postdoctoral Science Foundation (Grant No.2020M681154)。
文摘Initial condition and model errors both contribute to the loss of atmospheric predictability.However,it remains debatable which type of error has the larger impact on the prediction lead time of specific states.In this study,we perform a theoretical study to investigate the relative effects of initial condition and model errors on local prediction lead time of given states in the Lorenz model.Using the backward nonlinear local Lyapunov exponent method,the prediction lead time,also called local backward predictability limit(LBPL),of given states induced by the two types of errors can be quantitatively estimated.Results show that the structure of the Lorenz attractor leads to a layered distribution of LBPLs of states.On an individual circular orbit,the LBPLs are roughly the same,whereas they are different on different orbits.The spatial distributions of LBPLs show that the relative effects of initial condition and model errors on local backward predictability depend on the locations of given states on the dynamical trajectory and the error magnitudes.When the error magnitude is fixed,the differences between the LBPLs vary with the locations of given states.The larger differences are mainly located on the inner trajectories of regimes.When the error magnitudes are different,the dissimilarities in LBPLs are diverse for the same given state.
基金sponsored by the National Basic Research Program of China (Grant No. 2012CB955202)the National Public Benefit (Meteorology) Research Foundation of China (Grant No. GYHY201306018)the National Natural Science Foundation of China (Grant Nos. 41176013 and 41230420)
文摘Initial errors and model errors are the source of prediction errors. In this study, the authors compute the conditional nonlinear optimal perturbation （CNOP）-type initial errors and nonlinear forcing singular vector （NFSV）- type tendency errors of the Zebiak-Cane model with respect to El Nifio events and analyze their combined effect on the prediction errors for E1 Nino events. The CNOP- type initial error （NFSV-type tendency error） represents the initial errors （model errors） that have the largest effect on prediction uncertainties for E1 Nifio events under the perfect model （perfect initial conditions） scenario. How- ever, when the CNOP-type initial errors and the NFSV- type tendency errors are simultaneously considered in the model, the prediction errors caused by them are not am- plified as the authors expected. Specifically, the predic- tion errors caused by the combined mode of CNOP-type initial errors and NFSV-type tendency errors are a little larger than those caused by the NFSV-type tendency er- rors. This fact emphasizes a need to investigate the opti- mal combined mode of initial errors and tendency errors that cause the largest prediction error for E1 Nifio events.
文摘Dynamic equations of elastic linkage are formed by means of Kane equation and finitemethod. Eight main influential factors on the dynamic response of elastic linkage are considered inthese equations. Model error caused by the eight factors are investigated. Some useful conclusionsabout model error are derived from theoretical analysis and the numerical calculation of twenty-sixexamples.
基金supported by the National Natural Science Foundation of China(No.42174011)。
文摘In the variance component estimation(VCE)of geodetic data,the problem of negative VCE is likely to occur.In the ordinary additive error model,there have been related studies to solve the problem of negative variance components.However,there is still no related research in the mixed additive and multiplicative random error model(MAMREM).Based on the MAMREM,this paper applies the nonnegative least squares variance component estimation(NNLS-VCE)algorithm to this model.The correlation formula and iterative algorithm of NNLS-VCE for MAMREM are derived.The problem of negative variance in VCE for MAMREM is solved.This paper uses the digital simulation example and the Digital Terrain Mode(DTM)to prove the proposed algorithm's validity.The experimental results demonstrated that the proposed algorithm can effectively correct the VCE in MAMREM when there is a negative VCE.
基金supported by the National Key R&D Program of China(Grant No.2023YFF0804803)the Fundamental Research Funds for the Central Universities-Cemac“GeoX”Interdisciplinary Program(Grant No.020714380207)。
文摘Forecast errors of numerical weather prediction consist of model errors and the growth of initial condition errors,while the initial condition is often optimized based on short-term forecasts.Thus it is difficult to untangle the initial condition error and model error,but it is essential to infer model errors not just for prediction but also for data assimilation(DA).A hybrid deep learning(DL)and DA method is proposed here,aiming to correct model errors.It uses a convolutional neural network(CNN)to extract characteristics of initial conditions and forecast errors,and then provides estimations for model errors.The CNN-based model error estimation method can consider the model error resulted from inaccurate model parameters,or simultaneously consider the model error and initial condition error.Based on the Lorenz05 model,offline and online experiments demonstrate that the CNN-based model error estimation method can effectively correct model errors resulted from inaccurate model parameters,including the forcing F,coupling coefficient c,and relative scale b.For both online and offline model error estimations,simultaneously considering model errors and initial condition errors are beneficial to infer the model errors,compared to considering model errors only.Moreover,using the observations to verify the forecasts has advantages over using the analyses,to estimate the model errors.Using observations can also achieve a faster convergence of model error estimation with online DA than using analyses.
基金supported by the National Natural Science Foundation of China(Grant Nos.U2242213,U2142213,42305167,42175105)。
文摘Systematic bias is a type of model error that can affect the accuracy of data assimilation and forecasting that must be addressed.An online bias correction scheme called the sequential bias correction scheme(SBCS),was developed using the6 h average bias to correct the systematic bias during model integration.The primary purpose of this study is to investigate the impact of the SBCS in the high-resolution China Meteorological Administration Meso-scale(CMA-MESO)numerical weather prediction(NWP)model to reduce the systematic bias and to improve the data assimilation and forecast results through this method.The SBCS is improved upon and applied to the CMA-MESO 3-km model in this study.Four-week sequential data assimilation and forecast experiments,driven by rapid update and cycling(RUC),were conducted for the period from 2–29 May 2022.In terms of the characteristics of systematic bias,both the background and analysis show diurnal bias,and these large biases are affected by complex underlying surfaces(e.g.,oceans,coasts,and mountains).After the application of the SBCS,the results of the data assimilation show that the SBCS can reduce the systematic bias of the background and yield a neutral to slightly positive result for the analysis fields.In addition,the SBCS can reduce forecast errors and improve forecast results,especially for surface variables.The above results indicate that this scheme has good prospects for high-resolution regional NWP models.
基金supported by the National Natural Science Foundation of China(Nos.52005413,52022082)Natural Science Basic Research Plan in Shaanxi Province of China(No.2021JM-054)the Fundamental Research Funds for the Central Universities(No.D5000220135)。
文摘Geometric error,mainly due to imperfect geometry and dimensions of machine components,is one of the major error sources of machine tools.Considering that geometric error has significant effects on the machining quality of manufactured parts,it has been a popular topic for academic and industrial research for many years.A great deal of research work has been carried out since the 1970s for solving the problem and improving the machining accuracy.Researchers have studied how to measure,detect,model,identify,reduce,and compensate the geometric errors.This paper presents a thorough review of the latest research activities and gives an overview of the state of the art in understanding changes in machine tool performance due to geometric errors.Recent advances in measuring the geometrical errors of machine tools are summarized,and different kinds of error identification methods of translational axes and rotation axes are illustrated respectively.Besides,volumetric geometric error modeling,tracing,and compensation techniques for five-axis machine tools are emphatically introduced.Finally,research challenges in order to improve the volumetric accuracy of machine tools are also highlighted.
基金supported by the National Science Foundation of China(Nos.42274037,41874034)the Beijing Natural Science Foundation(No.4202041)the National Key Research and Development Program of China(No.2020YFB0505804).
文摘This paper proposes an automatic algorithm to determine the properties of stochastic processes and their parameters for inertial error. The proposed approach is based on a recently developed method called the generalized method of wavelet moments (GMWM), whose estimator was proven to be consistent and asymptotically normally distributed. This algorithm is suitable mainly (but not only) for the combination of several stochastic processes, where the model identification and parameter estimation are quite difficult for the traditional methods, such as the Allan variance and the power spectral density analysis. This algorithm further explores the complete stochastic error models and the candidate model ranking criterion to realize automatic model identification and determination. The best model is selected by making the trade-off between the model accuracy and the model complexity. The validation of this approach is verified by practical examples of model selection for MEMS-IMUs (micro-electro-mechanical system inertial measurement units) in varying dynamic conditions.
基金National Natural Science Foundation of China (60675054)National High-Tech Research and Development Program (2006AA04Z228)"111" Project (B07018)
文摘This article investigates virtual reality (VR)-based teleoperation with robustness against modeling errors. VR technology is an effective way to overcome the large time delay during space robot teleoperation. However, it depends highly on the accuracy of model. Model errors between the virtual and real environment exist inevitably. The existing way to deal with the problem is by means of either model matching or robot compliance control. As distinct from the existing methods, this article tries to combine m...
文摘The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination tracker dashboard. GIS-based exploratory analysis was conducted to select four variables (poverty, black race, population density, and vaccination) to explain COVID-19 occurrence during the study period. Consequently, spatial statistical techniques such as Moran’s I, Hot Spot Analysis, Spatial Lag Model (SLM), and Spatial Error Model (SEM) were used to explain the COVID-19 occurrence and vaccination rate across the 88 counties in Ohio. The result of the Local Moran’s I analysis reveals that the epicenters of COVID-19 and vaccination followed the same patterns. Indeed, counties like Summit, Franklin, Fairfield, Hamilton, and Medina were categorized as epicenters for both COVID-19 occurrence and vaccination rate. The SEM seems to be the best model for both COVID-19 and vaccination rates, with R2 values of 0.68 and 0.70, respectively. The GWR analysis proves to be better than Ordinary Least Squares (OLS), and the distribution of R2 in the GWR is uneven throughout the study area for both COVID-19 cases and vaccinations. Some counties have a high R2 of up to 0.70 for both COVID-19 cases and vaccinations. The outcomes of the regression analyses show that the SEM models can explain 68% - 70% of COVID-19 cases and vaccination across the entire counties within the study period. COVID-19 cases and vaccination rates exhibited significant positive associations with black race and poverty throughout the study area.
基金supported by the Key R&D Program of Zhejiang Province(Nos.2023C01166 and 2024SJCZX0046)the Zhejiang Provincial Natural Science Foundation of China(Nos.LDT23E05013E05 and LD24E050009)the Natural Science Foundation of Ningbo(No.2021J150),China.
文摘Accuracy allocation is crucial in the accuracy design of machining tools.Current accuracy allocation methods primarily focus on positional deviation,with little consideration for tool direction deviation.To address this issue,we propose a geometric error cost sensitivity-based accuracy allocation method for five-axis machine tools.A geometric error model consisting of 4l error components is constructed based on homogeneous transformation matrices.Volumetric points with positional and tool direction deviations are randomly sampled to evaluate the accuracy of the machine tool.The sensitivity of each error component at these sampling points is analyzed using the Sobol method.To balance the needs of geometric precision and manufacturing cost,a geometric error cost sensitivity function is developed to estimate the required cost.By allocating error components affecting tool direction deviation first and the remaining components second,this allocation scheme ensures that both deviations meet the requirements.We also perform numerical simulation of a BC-type(B-axis and C-axis type)five-axis machine tool to validate the method.The results show that the new allocation scheme reduces the total geometric error cost by 27.8%compared to a uniform allocation scheme,and yields the same positional and tool direction machining accuracies.
