Error field penetration in J-TEXT tokamak based on two-fluid drift-MHD model

An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces.We have studied the plasma responses using Fitzpatrick's improved two-fluid model and program LAYER.We calculated the error field penetration threshold for J-TEXT.In addition,we find that the island width increases slightly as the error field amplitude increases when the error field amplitude is below the critical penetration value.However,the island width suddenly jumps to a large value because the shielding effect of the plasma against the error field disappears after the penetration.By scanning the natural mode frequency,we find that the shielding effect of the plasma decreases as the natural mode frequency decreases.Finally,we obtain the m/n=2/1 penetration threshold scaling on density and temperature.

Relationships between Terrain Features and Forecasting Errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

Neural network based method for compensating model error

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.

Error modeling of 3-RSR parallel robot based on D-H transformation matrix

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.

Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio events? Results from a Theoretical Model

Within a theoretical ENSO model, the authors investigated whether or not the errors superimposed on model parameters could cause a significant ＂spring predictability barrier＂ （SPB） for El Nio events. First, sensitivity experiments were respectively performed to the air-sea coupling parameter, α and the thermocline effect coefficient μ. The results showed that the uncertainties superimposed on each of the two parameters did not exhibit an obvious season-dependent evolution; furthermore, the uncertainties caused a very small prediction error and consequently failed to yield a significant SPB. Subsequently, the conditional nonlinear optimal perturbation （CNOP） approach was used to study the effect of the optimal mode （CNOP-P） of the uncertainties of the two parameters on the SPB and to demonstrate that the CNOP-P errors neither presented a unified season-dependent evolution for different El Nio events nor caused a large prediction error, and therefore did not cause a significant SPB. The parameter errors played only a trivial role in yielding a significant SPB. To further validate this conclusion, the authors investigated the effect of the optimal combined mode （i.e. CNOP error） of initial and model errors on SPB. The results illustrated that the CNOP errors tended to have a significant season-dependent evolution, with the largest error growth rate in the spring, and yielded a large prediction error, inducing a significant SPB. The inference, therefore, is that initial errors, rather than model parameter errors, may be the dominant source of uncertainties that cause a significant SPB for El Nio events. These results indicate that the ability to forecast ENSO could be greatly increased by improving the initialization of the forecast model.

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Error model identification of inertial navigation platform based on errors-in-variables model

Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.

Relationships between the Limit of Predictability and Initial Error in the Uncoupled and Coupled Lorenz Models

In this study, the relationship between the limit of predictability and initial error was investigated using two simple chaotic systems： the Lorenz model, which possesses a single characteristic time scale, and the coupled Lorenz model, which possesses two different characteristic time scales. The limit of predictability is defined here as the time at which the error reaches 95% of its saturation level; nonlinear behaviors of the error growth are therefore involved in the definition of the limit of predictability. Our results show that the logarithmic function performs well in describing the relationship between the limit of predictability and initial error in both models, although the coefficients in the logarithmic function were not constant across the examined range of initial errors. Compared with the Lorenz model, in the coupled Lorenz model in which the slow dynamics and the fast dynamics interact with each other--there is a more complex relationship between the limit of predictability and initial error. The limit of predictability of the Lorenz model is unbounded as the initial error becomes infinitesimally small; therefore, the limit of predictability of the Lorenz model may be extended by reducing the amplitude of the initial error. In contrast, if there exists a fixed initial error in the fast dynamics of the coupled Lorenz model, the slow dynamics has an intrinsic finite limit of predictability that cannot be extended by reducing the amplitude of the initial error in the slow dynamics, and vice versa. The findings reported here reveal the possible existence of an intrinsic finite limit of predictability in a coupled system that possesses many scales of time or motion.

An Online Model Correction Method Based on an Inverse Problem:Part I—Model Error Estimation by Iteration

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.

An Error Equivalent Model of Revolute Joints with Clearances for Antenna Pointing Mechanisms

Joint clearances in antenna pointing mechanisms lead to uncertainty in function deviation. Current studies mainly focus on radial clearance of revolute joints, while axial clearance has rarely been taken into consideration. In fact, own?ing to errors from machining and assembly, thermal deformation and so forth, practically, axial clearance is inevitable in the joint. In this study, an error equivalent model(EEM) of revolute joints is proposed with considering both radial and axial clearances. Compared to the planar model of revolute joints only considering radial clearance, the journal motion inside the bearing is more abundant and matches the reality better in the EEM. The model is also extended for analyzing the error distribution of a spatial dual?axis("X–Y" type) antenna pointing mechanism of Spot?beam antennas which especially demand a high pointing accuracy. Three case studies are performed which illustrates the internal relation between radial clearance and axial clearance. It is found that when the axial clearance is big enough, the physical journal can freely realize both translational motion and rotational motion. While if the axial clearance is limited, the motion of the physical journal will be restricted. Analysis results indicate that the consideration of both radial and axial clearances in the revolute joint describes the journal motion inside the bearing more precise. To further validate the proposed model, a model of the EEM is designed and fabricated. Some suggestions on the design of revolute joints are also provided.

Initial Error-induced Optimal Perturbations in ENSO Predictions, as Derived from an Intermediate Coupled Model

The initial errors constitute one of the main limiting factors in the ability to predict the E1 Nino-Southem Oscillation （ENSO） in ocean-atmosphere coupled models. The conditional nonlinear optimal perturbation （CNOP） approach was em- ployed to study the largest initial error growth in the E1 Nino predictions of an intermediate coupled model （ICM）. The optimal initial errors （as represented by CNOPs） in sea surface temperature anomalies （SSTAs） and sea level anomalies （SLAs） were obtained with seasonal variation. The CNOP-induced perturbations, which tend to evolve into the La Nifia mode, were found to have the same dynamics as ENSO itself. This indicates that, if CNOP-type errors are present in the initial conditions used to make a prediction of E1 Nino, the E1 Nino event tends to be under-predicted. In particular, compared with other seasonal CNOPs, the CNOPs in winter can induce the largest error growth, which gives rise to an ENSO amplitude that is hardly ever predicted accurately. Additionally, it was found that the CNOP-induced perturbations exhibit a strong spring predictability barrier （SPB） phenomenon for ENSO prediction. These results offer a way to enhance ICM prediction skill and, particularly, weaken the SPB phenomenon by filtering the CNOP-type errors in the initial state. The characteristic distributions of the CNOPs derived from the ICM also provide useful information for targeted observations through data assimilation. Given the fact that the derived CNOPs are season-dependent, it is suggested that seasonally varying targeted observations should be implemented to accurately predict ENSO events.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

Possible Sources of Forecast Errors Generated by the Global/Regional Assimilation and Prediction System for Landfalling Tropical Cyclones. Part Ⅱ: Model Uncertainty

This paper investigates the possible sources of errors associated with tropical cyclone(TC) tracks forecasted using the Global/Regional Assimilation and Prediction System(GRAPES). In Part I, it is shown that the model error of GRAPES may be the main cause of poor forecasts of landfalling TCs. Thus, a further examination of the model error is the focus of Part II.Considering model error as a type of forcing, the model error can be represented by the combination of good forecasts and bad forecasts. Results show that there are systematic model errors. The model error of the geopotential height component has periodic features, with a period of 24 h and a global pattern of wavenumber 2 from west to east located between 60?S and 60?N. This periodic model error presents similar features as the atmospheric semidiurnal tide, which reflect signals from tropical diabatic heating, indicating that the parameter errors related to the tropical diabatic heating may be the source of the periodic model error. The above model errors are subtracted from the forecast equation and a series of new forecasts are made. The average forecasting capability using the rectified model is improved compared to simply improving the initial conditions of the original GRAPES model. This confirms the strong impact of the periodic model error on landfalling TC track forecasts. Besides, if the model error used to rectify the model is obtained from an examination of additional TCs, the forecasting capabilities of the corresponding rectified model will be improved.

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

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.

A New Method for Identifying the Model Error of Adjust ment System

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.

Approach for wideband direction-of-arrival estimation in the presence of array model errors

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.

Locating Error Considering Dimensional Errors Modeling for Multistation Manufacturing System

Multistation machining process is widely applied in contemporary manufacturing environment. Modeling of variation propagation in multistation machining process is one of the most important research scenarios. Due to the existence of multiple variation streams, it is challenging to model and analyze variation propagation in a multi-station system. Current approaches to error modeling for multistation machining process are not explicit enough for error control and ensuring final product quality. In this paper, a mathematic model to depict the part dimensional variation of the complex multistation manufacturing process is formulated. A linear state space dimensional error propagation equation is established through kinematics analysis of the influence of locating parameter variations and locating datum variations on dimensional errors, so the dimensional error accumulation and transformation within the multistation process are quantitatively described. A systematic procedure to build the model is presented, which enhances the way to determine the variation sources in complex machining systems. A simple two-dimensional example is used to illustrate the proposed procedures. Finally, an industrial case of multistation machining part in a manufacturing shop is given to testify the validation and practicability of the method. The proposed analytical model is essential to quality control and improvement for multistation systems in machining quality forecasting and design optimization.

EMPIRICAL LIKELIHOOD FOR LINEAR MODELS UNDER m-DEPENDENT ERRORS

In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.

A distributed dynamic mesh model of a helical gear pair with tooth profile errors

A dynamic model of a helical gear rotor system is proposed.Firstly,a generally distributed dynamic model of a helical gear pair with tooth profile errors is developed.The gear mesh is represented by a pair of cylinders connected by a series of springs and the stiffness of each spring is equal to the effective mesh stiffness.Combining the gear dynamic model with the rotor-bearing system model,the gear-rotor-bearing dynamic model is developed.Then three cases are presented to analyze the dynamic responses of gear systems.The results reveal that the gear dynamic model is effective and advanced for general gear systems,narrow-faced gear,wide-faced gear and gear with tooth profile errors.Finally,the responses of an example helical gear system are also studied to demonstrate the influence of the lead crown reliefs and misalignments.The results show that both of the lead crown relief and misalignment soften the gear mesh stiffness and the responses of the gear system increase with the increasing lead crown reliefs and misalignments.

Modeling Approach of Regression Orthogonal Experiment Design for Thermal Error Compensation of CNC Turning Center

The thermal induced errors can account for as much as 70% of the dimensional errors on a workpiece. Accurate modeling of errors is an essential part of error compensation. Base on analyzing the existing approaches of the thermal error modeling for machine tools, a new approach of regression orthogonal design is proposed, which combines the statistic theory with machine structures, surrounding condition, engineering judgements, and experience in modeling. A whole computation and analysis procedure is given. Therefore, the model got from this method are more robust and practical than those got from the present method that depends on the modeling data completely. At last more than 100 applications of CNC turning center with only one thermal error model are given. The cutting diameter variation reduces from more than 35 μm to about 12 μm with the orthogonal regression modeling and compensation of thermal error.