Linear Error Model Research Articles

Kinematic Calibration of Industrial Robots Based on Distance Information Using a Hybrid Identification Method

To improve the positioning accuracy of industrial robots and avoid using the coordinates of the end effector, a novel kinematic calibration method based on the distance information is proposed. The kinematic model of an industrial robot is established. The relationship between the moving distance of the end effector and the kinematic parameters is analyzed. Based on the results of the analysis and the kinematic model of the robot, the error model with displacements as the reference is built, which is linearized for the convenience of the following identification. The singular value decomposition (SVD) is used to eliminate the redundant parameters of the error model. To solve the problem that traditional optimization algorithms are easily affected by data noise in high dimension identification, a novel extended Kalman filter (EKF) and regularized particle filter (RPF) hybrid identification method is presented. EKF is used in the preidentification of the linearized error model. With the preidentification results as the initial parameters, RPF is used to identify the kinematic parameters of the linearized error model. Simulations are carried out to validate the effectiveness of the proposed method, which shows that the method can identify the error of the parameters and after compensation the accuracy of the robot is improved.

GMM Estimation of a Partially Linear Additive Spatial Error Model

This article presents a partially linear additive spatial error model (PLASEM) specification and its corresponding generalized method of moments (GMM). It also derives consistency and asymptotic normality of estimators for the case with a single nonparametric term and an arbitrary number of nonparametric additive terms under some regular conditions. In addition, the finite sample performance for our estimates is assessed by Monte Carlo simulations. Lastly, the proposed method is illustrated by analyzing Boston housing data.

A side-sensitive group runs median control chart with measurement errors

The Shewhart median (denoted as ) chart can be used in place of the Shewhart chart for detecting mean shifts when outliers are present because the sample mean is easily affected by outliers. However, the Shewhart median chart is slow in detecting small and moderate mean shifts. In this study, the side-sensitive group runs median (called SSGR ) chart is proposed to enhance the speed of the Shewhart median chart in detecting small and moderate mean shifts. Additionally, by adopting a linear covariate error model, the effect of measurement errors on the performance of the SSGR chart is studied. The average run length (ARL) and standard deviation of the run length (SDRL) criteria are used as performance measures, for cases with and without measurement error. The Markov chain method is used to compute the ARL and SDRL values of the SSGR and competing charts. Performance analyses show that the SSGR chart surpasses the synthetic chart for detecting all shift sizes but for detecting small shifts, the exponentially weighted moving average (EWMA) chart performs better than the SSGR chart. Finally, the application of the SSGR chart is described with an example.

The Mixed Liu Estimator in Stochastic Restricted Linear Measurement Error Model

Ghapani and Babdi [1] proposed a mixed Liu estimator in linear measurement error model with stochastic linear restrictions. In this article, we propose an alternative mixed Liu estimator in the linear measurement error model with stochastic linear restrictions. The performance of the new mixed Liu estimator over the mixed estimator, Liu estimator, and mixed Liu estimator proposed by Ghapani and Babdi [1] are discussed in the sense of mean squared error matrix. Finally, a simulation study is given to show the performance of these estimators.

Estimation of stride-by-stride spatial gait parameters using inertial measurement unit attached to the shank with inverted pendulum model

Inertial measurement unit (IMU)-based gait analysis systems have become popular in clinical environments because of their low cost and quantitative measurement capability. When a shank is selected as the IMU mounting position, an inverted pendulum model (IPM) can accurately estimate its spatial gait parameters. However, the stride-by-stride estimation of gait parameters using one IMU on each shank and the IPMs has not been validated. This study validated a spatial gait parameter estimation method using a shank-based IMU system. Spatial parameters were estimated via the double integration of the linear acceleration transformed by the IMU orientation information. To reduce the integral drift error, an IPM, applied with a linear error model, was introduced at the mid-stance to estimate the update velocity. the gait data of 16 healthy participants that walked normally and slowly were used. The results were validated by comparison with those extracted from an optical motion-capture system; the results showed strong correlation (r>0.9) and good agreement with the gait metrics (stride length, stride velocity, and shank vertical displacement). In addition, the biases of the stride length and stride velocity extracted using the motion capture system were smaller in the IPM than those in the previous method using the zero-velocity-update. The error variabilities of the gait metrics were smaller in the IPM than those in the previous method. These results indicated that the reconstructed shank trajectory achieved a greater accuracy and precision than that of previous methods. This was attributed to the IPM, which demonstrates that shank-based IMU systems with IPMs can accurately reflect many spatial gait parameters including stride velocity.

Hierarchical Control of Trajectory Planning and Trajectory Tracking for Autonomous Parallel Parking

For the parallel parking problem in narrow space, this paper proposes a trajectory tracking control method with a novel trajectory planning layer for autonomous parallel parking based on a numerical optimization algorithm and model predictive control. In the trajectory planning layer, the vehicle kinematics model suitable for the low-velocity parking scene is established. Considering the vehicle physical constraints, boundary condition constraints, and obstacle avoidance constraints during the parking process, the parking trajectory planning task is described as an optimal control problem, further transformed into a nonlinear programming problem by Gauss pseudo-spectral method. Taking the shortest parking completion time as the optimization objective function, the parking trajectories of the large, medium and small parking spaces are obtained, respectively. A parking trajectory tracking controller based on the model predictive control algorithm is designed in the trajectory tracking control layer. The linear error model is used as the prediction model, and the quadratic programming is adopted as the rolling optimization algorithm in the tracking controller. The velocity and front-wheel swing angle are obtained as control signals for parking trajectory tracking. Through CarSim and Simulink's co-simulation, the feasibility and effectiveness of the proposed parallel parking trajectory planning and tracking control method are verified. The co-simulation results show that the maximum tracking errors of horizontal and longitudinal positions are less than 0.15m. The maximum tracking errors of heading angle are less than 2° under three different parking spaces. Real vehicle tests are carried out to verify the effectiveness of the proposed hierarchical control method. The test results show that the vehicle can park in the parking space safely, quickly and accurately when the actual parking space is detected. The proposed method can plan the parking trajectory with the constraints and the shortest time and control the vehicle to complete the parking operation accurately along the planned trajectory.

An Improved Inertial Matching Algorithm for Hull Deformation With Large Misalignment Angle

Inertial matching measurement method has been widely used to measure hull deformation in real time to establish a unified attitude reference for ships in previous decades, but most current methods were based on linear error model which adopted small angle approximation. Therefore, the large misalignment angle in the hull deformation will bring great challenges to the accuracy of inertial matching measurement methods. In order to solve this problem, we divided the hull deformation with large misalignment angle into two parts: large angle based on coarse registration and small angle of the residual part. Three improvements were made as the following: (1) The quaternion optimization method (Q) was utilized to get the coarse registration result; (2) Based on the result, we derived a brand-new residual small-angle measurement algorithm. (3) We introduced neural network Karman filter (NNKF) to calculate the hull deformation in real time to further reduce the nonlinear error of the system. The experiment results illustrated that the proposed method, namely, Q-NNKF, can accurately measure the hull deformation in real time and effectively suppressed the nonlinear error caused by large misalignment angle.

Time- and Frequency-Interleaving: Distinctions and Connections

This paper connects the linear steady-state systematic error models of the time- and frequency-interleaved analog-to-digital converters (ADCs). Exposing their relations is of importance because estimation and compensation methods developed for one architecture may therefore apply to the other. Most critical impairments in both ADC structures include static mismatches and random jitter. The former has been well studied and can be generalized to the model connection, whereas not much is known regarding the latter. To support designers becoming more capable of making optimal design and architectural decisions on parallel ADCs, comprehensive phase noise analysis and comparison are carried out to reveal the distinctions between these two sampling architectures. Design examples with considerations are also provided for demonstration purposes.

Support Vector Machine-based Soft Sensors in the Isomerisation Process

This paper presents the development of soft sensor empirical models using support<br /> vector machine (SVM) for the continual assessment of 2,3-dimethylbutane and 2-methylpentane mole percentage as important product quality indicators in the refinery isomerisation process. During the model development, critical steps were taken, including selection and pre-processing of the industrial process data, which are broadly discussed in this paper. The SVM model results were compared with dynamic linear output error model and nonlinear Hammerstein-Wiener model. Evaluation of the developed models on independent data sets showed their reliability in the assessment of the component contents. The soft sensors are to be embedded into the process control system, and serve primarily as a replacement during the process analysersb failure and service periods.

The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA [Formula: see text] scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA [Formula: see text] scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) [Formula: see text] schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the Ratio of Two Normally Distributed Variables

Investigating the effect of measurement errors on the control chart monitoring the ratio of two normal random variables is an important task to facilitate the use of this kind of control chart in practice. Moreover, a deep insight into the problem can help practitioners to find a way to reduce unexpected impacts of measurement errors on the chart performance. This paper provides a study on the performance of the exponentially weighted moving average control chart monitoring the ratio in the presence of measurement errors. We extend the linear covariate error model applied in previous studies to a more general situation, which makes the study more realistic. The numerical results show that although the precision error and the accuracy error have negative influences on the proposed chart performance when these errors are not large these influences are not significant.

Modeling and Calibration of the Gyro– Accelerometer Asynchronous Time in Dual-Axis RINS

Rotational inertial navigation system (RINS) could improve the navigation performance by rotating the IMU around gimbals, and the structure and function of the dual-axis RINS also help realize the process of self-calibration. However, the gyro–accelerometer asynchronous time is not considered in current studies. Coupled into the navigation error, the gyro–accelerometer asynchronous time can lead to velocity accuracy decline during the process of rotation. Therefore, the modeling and calibration of the gyro–accelerometer asynchronous time would enhance the systemic reliability. In this article, in order to solve the abovementioned problem: 1) we model the gyro–accelerometer asynchronous time and perform an error analysis of gyro–accelerometer asynchronous time; 2) we propose a compensation method of the outer lever arm to improve the accuracy of the observed velocity and position; and 3) we derive a continuous linear 40-D RINS error model considering the abovementioned two error parameters compared with the traditional method, the PWCS method, and the SVD method is utilized to provide the observability degrees of the proposed state during the self-calibration process. Experimental results illustrated that the proposed method can improve the accuracy in the long-endurance navigation.

Monitoring multivariate coefficient of variation with upward Shewhart and EWMA charts in the presence of measurement errors using the linear covariate error model

AbstractIn practice, measurement errors exist and ignoring their presence may lead to erroneous conclusions in the actual performance of control charts. The implementation of the existing multivariate coefficient of variation (MCV) charts ignores the presence of measurement errors. To address this concern, the performances of the upward Shewhart‐MCV and exponentially weighted moving average MCV charts for detecting increasing MCV shifts, using a linear covariate error model, are investigated. Explicit mathematical expressions are derived to compute the limits and average run lengths of the charts in the presence of measurement errors. Finally, an illustrative example using a real‐life dataset is presented to demonstrate the charts’ implementation.

Design of a variable sampling interval exponentially weighted moving average median control chart in presence of measurement errors

AbstractIn the literature, many control charts monitoring the median is designed under a perfect condition that there is no measurement error. This may make the practitioners confusing to apply these control charts because the measurement error is the true problem in practice. In this paper, we consider the effect of measurement error on the performance of the exponentially weighted moving average (EWMA) control chart combining with the variable sampling interval (VSI) strategy. A linear covariate error model is supposed to model the measurement error. The performance of the VSI EWMA median control chart is evaluated through the average time to signal. The numerical simulation shows that the measurement errors have a negative influence on the proposed chart.

Assessment of local influence in spatial elliptical linear measurement error models

In this paper, we consider estimation and inference procedures in spatial linear models when some of the covariates are measured with errors. It is assumed that the additive error distributed according to the law belonging to the class of elliptically contoured distributions. The development of the corrected score function with the family of elliptical distributions is the basis for derivation of the estimators. For sensitivity analysis, the local influence approach is used for assessing influence of small perturbations on the parameter estimates. A simulation study is presented illustrating the good performance of the proposed approach, including the robustness property for the heavier tail models. We further illustrate the proposed procedures by an application in a real dataset.

The Performance of the EWMA Median Chart in the Presence of Measurement Error

Measurement error always exists in quality control applications and may considerably affect the ability of control charts to detect an out-of-control situation. In this paper, we study the performance of the EWMA median chart using a Markov Chain approach with a linear covariate error model and a corrected formula for the distribution of the sample median. The performance is evaluated through the Average Run Length. Several figures and tables are presented and enumerated to show the statistical performance of the EWMA median control chart for different sources of measurement errors. The positive effect of taking multiple measurements for each item in a subgroup on the performance of the EWMA median chart is also investigated. An example illustrates the use of this study is introduced. The numerical simulation shows that the measurement errors have a negative influence on the proposed chart.

Comparison of Single-Valued Forecasts in a User-Oriented Framework

Abstract We compare single-valued forecasts from a consensus of numerical weather prediction models to forecasts from a single model across a range of user decision thresholds and sensitivities, using the relative economic value framework, and present this comparison in a new graphical format. With the help of a simple linear error model, we obtain theoretical results and perform synthetic calculations to gain insights into how the results relate to the characteristics of the different forecast systems. We find that multimodel consensus forecasts are more beneficial for users interested in decisions near the climatological mean, due to their reduced spread of errors compared to the constituent models. Single model forecasts may present greater benefit for users sensitive to extreme events if the forecasts have smaller conditional biases than the consensus forecasts and hence better resolution of such events. The results support use of consensus averaging approaches for single-valued forecast services in typical conditions. However, it is hard to cater for all user sensitivities in more extreme conditions. This underscores the importance of providing probability-based services for unusual conditions.

Effect of the measurement errors on two one‐sided Shewhart control charts for monitoring the ratio of two normal variables

AbstractMonitoring the ratio between two random normal variables plays an important role in many industrial manufacturing processes. In this paper, we suggest designing two one‐sided Shewhart control charts monitoring this ratio. The numerical results show that the one‐sided charts have more advantages compared with the two‐sided Shewhart chart proposed previously in the literature. Moreover, we investigate the effect of measurement error on the performance of these control charts where the measurement error is supposed to follow a linear covariate error model. The change of model parameters from an in‐control condition to an out‐of‐control is presented without using a strict assumption about the independence of the shift size from measurement errors. A valuable finding from this study is that taking multiple measurements per item is not an effective way to reduce the negative effect of measurement error on the Shewhart charts' performance.

Linearizing Power Flow Model: A Hybrid Physical Model-Driven and Data-Driven Approach

Linear power flow model is advantageous for the fast operational analysis and the efficient optimization of the power systems. In this letter, we propose a hybrid physical model-driven and data-driven approach for linearizing power flow model. In this proposed approach, the linear power flow model contains two parts, i.e., the existing physical-equation-based linear power flow model and the linearized error model. The linearized errors are obtained by the partial least squares regression based data-driven approach. The proposed linear power flow model can retain the useful inherent information from the physical model and utilize the ability of data analysis to extract the inexplicit linear relationship. Simulations on the four test systems have validated that the proposed hybrid linear model exhibits a much better performance on the branch power flow calculation than other linear power flow models.

Online updating method to correct for measurement error in big data streams

When huge amounts of data arrive in streams, online updating is an important method to alleviate both computational and data storage issues. The scope of previous research for online updating is extended in the context of the classical linear measurement error model. In the case where some covariates are unknowingly measured with error at the beginning of the stream, but then are measured without error after a particular point along the data stream, the updated estimators ignoring the measurement error are biased for the true parameters. Once the covariates measured without error are first observed, a method to correct the bias of the estimators, as well as to correct the biases in their variance estimator, is proposed; after correction, the traditional online updating method can then proceed as usual. Further, asymptotic distributions for the corrected and updated estimators are established. Simulation studies and a real data analysis with an airline on-time dataset are provided to illustrate the performance of the proposed method.