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Amidst the accelerating pace of automation in sheet metal bending, the need for small-batch, multi-varietal, efficient, and adaptable production modalities has become increasingly pronounced. To address this need and to enhance the efficacy of the bending process, this study presents the design and development of an embedded soft PLC (Programmable Logic Controller) rooted in the Codesys development platform and leveraging the ARM Cortex-A55 architecture. This controller employs the EtherCAT communication protocol to facilitate seamless and efficient interactions with fully electric servo-driven CNC (Computerized Numerical Control) bending machinery. To mitigate the challenge of bending springback errors, a finite element simulation model is constructed and refined through the application of ALE (Arbitrary Lagrangian-Eulerian) adaptive grid technology, thereby bolstering simulation precision. Subsequently, an enhanced WOA-BP (Whale Optimization Algorithm—Backpropagation) model, integrating Latin hypercube sampling and neural network techniques, is deployed to anticipate and counteract these springback errors. Experimental outcomes demonstrate that the proposed methodology effectively constrains the final forming angle deviation to within 0.3°, significantly enhancing the reliability and precision of the bending system. This achievement not only underscores the technical feasibility but also contributes to advancing the frontier of sheet metal bending automation.

This paper is aimed to address the issue of decreased accuracy in the ship block docking caused by the structural errors of posture adjustment mechanism. First, inverse kinematic analysis is performed to investigate the sources of static errors in the mechanism. Subsequently, based on the closed-loop vector method, a pose error model for the moving platform is established, which includes eight categories of error terms. The impact of various structural errors on the pose accuracy of the moving platform is then compared and analyzed under both single-limb and multi-limb configurations. Therefore, a compensation method based on the whale optimization algorithm optimized radial basis function neural network is proposed. By transforming pose errors into actuator length errors, it establishes a predictive model between the theoretical pose of the dynamic platform and actuator length errors. After optimizing the network parameters, it yields the actuator length compensation to correct the actual pose of the dynamic platform. Simulation and experimental results validate the effectiveness of this method in enhancing the motion accuracy of the parallel mechanism. The mean pose accuracy of the moving platform is improved by 85.07%, demonstrating a significant compensation effect.

Metal mirrors will be widely used in the coming decades. Therefore, as one of the enabling technologies for metal optical freeform surface manufacturing, ultra-precision (UP) diamond turning error compensation has become a research hotspot. However, for the tool offset error and tool radius error, which are the main errors in UP diamond turning, no precise and efficient calculation method has been found in the literature. In this study, a more precise and efficient algorithm was developed and validated in three ways using on-machine measurement data and profilometer measurement data. After one compensation, the tool offset error can be reduced to below 0.1 μm, and the tool radius error can be reduced to below 1 micrometer, which will significantly improve the UP turning accuracy and efficiency of optical parts.

A self-calibration method utilizing spherical constraints is proposed for calibration of robot end-effectors. The method establishes a mathematical model to account for both the geometric errors of the robot and the deformation errors of the end-effector. A nonlinear least-squares parameter identification technique based on spherical constraints is employed to achieve autonomous calibration of the end-effector. Contrasted with methodologies relying on point plane or distance constraints, this novel technique delivers superior positioning accuracy, streamlined operational procedures and enhanced efficiency. Both simulation and experimental validation confirm that the self-calibration method using spherical constraints improves the positioning accuracy of the robot end-effector from 3 mm to 0.3 mm, showing the effectiveness of the method.

Aspherical surfaces, with their varying curvature, minimize aberrations and enhance clarity, making them essential in optics, aerospace, medical devices, and telecommunications. However, manufacturing these surfaces is challenging because of systematic errors in CNC equipment, tool wear, measurement inaccuracies, and environmental disturbances. These issues necessitate precise error compensation to achieve the desired surface shape. Traditional methods for spherical optics are inadequate for aspherical components, making accurate surface shape error detection and compensation crucial. This study integrates advanced metrology with optimized material removal functions in the grinding and polishing processes. By combining numerical control technology, computer technology, and data analysis, we developed CAM software (version 1) tailored for aspherical surfaces. This software uses a compensation correction algorithm to process error data and generate NC programs for machining. Our approach automates and digitizes the grinding and polishing process, improving efficiency and surface accuracy. This advancement enables high-precision mass production of rotationally symmetrical aspherical optical components, addressing existing manufacturing challenges and enhancing optical system performance.

To improve the machining accuracy of free-form surface parts, a coarse-to-fine free-form surface machining error decomposition and compensation method is proposed in this paper. First, the machining error was coarsely decomposed using variational mode decomposition (VMD), and the correlation coefficients between the intrinsic mode function (IMF) and the machining error were obtained to filter out the IMF components that were larger than the thresholding value of the correlation coefficients, which was the coarse systematic error. Second, the coarse systematic errors were finely decomposed using empirical mode decomposition (EMD), which still filters out the IMF components that are larger than the thresholding value of the set correlation coefficient based on the correlation coefficient. Then, the wavelet thresholding method was utilized to finely decompose all the IMF components whose correlation coefficients in the first two decomposition processes were smaller than the threshold value of the correlation coefficient set. The decomposed residual systematic errors were reconstructed with the IMF components screened in the EMD fine decomposition, which gave the fine systematic error. Finally, the machining surface was reconstructed according to the fine systematic error, and its corresponding toolpath was generated to compensate for the machining error without moving the part. The simulation and analysis results of the design show that the method has a more ideal processing error decomposition ability and can decompose the systematic error contained in the processing error in a more complete way. The results of actual machining experiments show that, after using the method proposed in this paper to compensate for the machining error, the maximum absolute machining error decreased from 0.0580 mm to 0.0159 mm, which was a 72.5% reduction, and the average absolute machining error decreased from 0.0472 mm to 0.0059 mm, which was an 87.5% reduction. It was shown that the method was effective and feasible for free-form surface part machining error compensation.

In vector-controlled Permanent Magnet Synchronous Motors (PMSMs), measuring the motor flux angle, particularly the rotor position, is essential. If a pulse error occurs during motor control using an encoder, it becomes impossible to accurately estimate the rotor position, leading to incorrect position angle information being used in the coordinate transformation. This mismatch causes discrepancies between the commanded three-phase stator current and the actual current applied to the motor. As a result, the motor and inverter output and efficiency decrease, and the control performance deteriorates. Therefore, research is necessary to compensate for such errors. This paper proposes an algorithm that detects pulse errors occurring in incremental encoders and automatically switches to the Hall sensor control mode to compensate for the encoder pulse errors. The proposed algorithm, based on Hall sensors, has the advantage of not significantly affecting control delays, which could be problematic in high-speed operating ranges; thus, effective control is maintained even in such situations.

In order to solve the problem of the low end positioning accuracy of large hydraulic rock drilling robotic arms due to machining error and the working environment, this paper proposes an end positioning error compensation method based on an Improved Secretary Bird Optimization Algorithm (ISBOA) optimized Back Propagation (BP) neural network. Firstly, the good point set strategy is used to initialize the secretary bird population position to make the initial population distribution more uniform and accelerate the convergence speed of the algorithm. Then, the ISBOA is used to optimize the initial weights and biases of the BP neural network, which effectively overcomes the defect of the BP neural network falling into a local optimum. Finally, by establishing the mapping relationship between the joint value of the robot arm and the end positioning error, the error compensation is realized to improve the positioning accuracy of the rock drilling robot arm. The experimental results show that the average positioning error of the rock drilling robotic arm is reduced from 187.972 mm to 28.317 mm, and the positioning accuracy is improved by 84.94%, which meets the engineering requirements.

In order to solve the problem of insufficient end positioning accuracy due to factors such as gravity and material strength during the inverse solution process of a large hydraulic robotic arm, this paper proposes an inverse solution algorithm based on an adaptive spider wasp optimization (ASWO) optimized back propagation (BP) neural network. Firstly, the adaptability of the SWO algorithm is enhanced by analyzing the phase change in population fitness and dynamically adjusting the trade-off rate, crossover rate, and population size in real time. Then, the ASWO algorithm is used to optimize the initial weights and biases of the BP neural network, effectively addressing the problem of the BP neural network falling into local optima. Finally, a neural network mapping relationship between the actual position of the robotic arm’s end-effector and the corresponding joint values is established to reduce the influence of forward kinematic errors on the accuracy of the inverse solution. Experimental results show that the average positioning error of the robotic arm in the XYZ direction is reduced from (91.3, 87.38, 117.31) mm to (18.16, 24.67, 27.21) mm, significantly improving positioning accuracy by 80.11%, 71.78%, and 76.81%, meeting project requirements.

Kinematic calibration plays a pivotal role in enhancing the absolute positioning accuracy of industrial robots, with parameter identification and error compensation constituting its core components. While the conventional parameter identification method, based on linearization, has shown promise, it suffers from the loss of high-order system information. To address this issue, we propose an unscented Kalman filter (UKF) with adaptive process noise covariance for robot kinematic parameter identification. The kinematic model of a typical 6-degree-of-freedom industrial robot is established. The UKF is introduced to identify the unknown constant parameters within this model. To mitigate the reliance of the UKF on the process noise covariance, an adaptive process noise covariance strategy is proposed to adjust and correct this covariance. The effectiveness of the proposed algorithm is then demonstrated through identification and error compensation experiments for the industrial robot. Results indicate its superior stability and accuracy across various initial conditions. Compared to the conventional UKF algorithm, the proposed approach enhances the robot’s accuracy stability by 25% under differing initial conditions. Moreover, compared to alternative methods such as the extended Kalman algorithm, particle swarm optimization algorithm, and grey wolf algorithm, the proposed approach yields average improvements of 4.13%, 26.47%, and 41.59%, respectively.

Though lithium-ion batteries are extensively applied in electric vehicles as a power source due to their excellent advantages in recent years, the security risk has inarguably always existed. The state of health (SOH) of lithium-ion batteries is one of the most important indicators related to security, the prediction of SOH is paid close attention spontaneously. To improve the prediction accuracy of SOH, this paper constructs an SOH prediction model based on a multi-kernel relevance vector machine and error compensation (EC-MKRVM). The provided model comprises a pre-estimation model and an error compensation model, both of which use the multi-kernel relevance vector machine (MKRVM) algorithm. The pre-estimation model takes the feature factors extracted in the charging segment as the input variable and the SOH pre-estimation value as the output. The error compensation model takes the pre-estimation error sequence as the input variable and the SOH prediction error as the output. Finally, the SOH prediction error is used to compensate for the SOH pre-estimation value of the pre-estimation model, and the final SOH prediction value is obtained. To verify the effectiveness and advancement of the model, the CACLE dataset is used for comparative experimental analysis. The results show that the proposed prediction model in this paper has higher prediction accuracy.

Based on a multi-source error model, this paper discusses the principle of error element identification and uses the mirror bias method to compensate the geometric errors of a process system. Firstly, a nine-line measurement method to determine the geometric error of the linear feed axes of machine tools is introduced, and the geometric error identification model based on the “nine-line method” is established. Then, using a ballbar mounted in the axial, tangential, and radial directions of the machine, the geometric error elements of the rotation axis are identified by three simple measurements in each direction. Subsequently, for the more common flat vise clamping workpiece in actual production, the workpiece position error is identified by using the traditional process of dimensional chain, and the workpiece attitude error is identified by fitting the angle between the positioning plane and the horizontal plane by the least squares method. Finally, based on the tool position points and tool axis vectors obtained from the multi-source error model, the error compensation value is solved using inverse machine tool kinematics to offset the machining error by mirroring the error value of the same size, and based on the “S-shaped specimen” to compensate the processing experiments, after compensation, the processing error is reduced by 30~45%, verifying the effectiveness of the compensation method.

Deep hole measurement is a crucial step in both deep hole machining and deep hole maintenance. Single-camera vision presents promising prospects in deep hole measurement due to its simple structure and low-cost advantages. However, the measurement error caused by the heating of the imaging sensor makes it difficult to achieve the ideal measurement accuracy. To compensate for measurement errors induced by imaging sensor heating, this study proposes an error compensation method for laser and vision-based deep hole measurement instruments. This method predicts the pixel displacement of the entire field of view using the pixel displacement of fixed targets within the camera’s field of view and compensates for measurement errors through a perspective transformation. Theoretical analysis indicates that the perspective projection matrix changes due to the heating of the imaging sensor, which causes the thermally induced measurement error of the camera. By analyzing the displacement of the fixed target point, it is possible to monitor changes in the perspective projection matrix and thus compensate for camera measurement errors. In compensation experiments, using target displacement effectively predicts pixel drift in the pixel coordinate system. After compensation, the pixel error was suppressed from 1.99 pixels to 0.393 pixels. Repetitive measurement tests of the deep hole measurement instrument validate the practicality and reliability of compensating for thermal-induced errors using perspective transformation.

Large compressors have complex structures and constantly changing operating conditions. It is challenging to build physical models of compressors to analyse their performance parameters. An improved error-based stacked ensemble learning prediction model is proposed in this work. This model simplifies the modelling steps in a data-driven manner and obtains accurate prediction results. An enhanced integrated model employs K-fold cross-validation to assign dataset weights based on validation set errors, achieving a 12.4% reduction in average output error. Additionally, the output error of the meta-model undergoes a Box–Cox transformation for error compensation, decreasing the average output error by 14.0%. The Stacking model, combining the above improvements, notably reduces the root-mean-square errors for power, surge, and blocking boundaries by 24.2%, 20.6%, and 23.3%, respectively. This integration significantly boosts prediction accuracy.

Aiming at the influence of the magnetic flux density uniformity error (MFDUE) of the Lorentz force magnetic bearing (LFMB) on the sensitivity accuracy of magnetically suspended control and sensing gyroscopes (MSCSGs) on the angular rate of a spacecraft, a high precision measurement method of the angular rate of a spacecraft based on the MFDUE compensation of LFMB is proposed. Firstly, the structure of MSCSG and the sensitivity principle of MSCSG to the spacecraft angular rate are introduced. The mechanism influencing the accuracy of MSCSG to spacecraft angular rate sensitivity is deduced based on the definition of magnetic flux density uniformity. Secondly, the 3D magnetic flux distribution of LFMB is analyzed using ANSYS. The relationship between the rotor tilt angle, tilt angular rate, and magnetic flux density is established. The induced current calculation model due to MFDUE is proposed, and the LFMB magnetic flux density error compensation is realized. Finally, the simulation results show that the estimation accuracy of the induced current by the proposed method can reach 96%, and the simulation and the experiment show that the error compensation method can improve the accuracy of MSCSG in measuring the spacecraft angular rate by 12.5%.

In the field of robotic automation, achieving high position accuracy in robotic vision systems (RVSs) is a pivotal challenge that directly impacts the efficiency and effectiveness of industrial applications. This study introduces a comprehensive modeling approach that integrates kinematic and joint compliance factors to significantly enhance the position accuracy of a system. In the first place, we develop a unified kinematic model that effectively reduces the complexity and error accumulation associated with the calibration of robotic systems. At the heart of our approach is the formulation of a joint compliance model that meticulously accounts for the intricacies of the joint connector, the external load, and the self-weight of robotic links. By employing a novel 3D rotary laser sensor for precise error measurement and model calibration, our method offers a streamlined and efficient solution for the accurate integration of vision systems into robotic operations. The efficacy of our proposed models is validated through experiments conducted on a FANUC LR Mate 200iD robot, showcasing notable improvements in the position accuracy of robotic vision system. Our findings contribute a framework for the calibration and error compensation of RVS, holding significant potential for advancements in automated tasks requiring high precision.

In the pedestrian navigation system, researchers have reduced measurement errors and improved system navigation performance by fusing measurements from multiple low-cost inertial measurement unit (IMU) arrays. Unfortunately, the current data fusion methods for inertial sensor arrays ignore the system error compensation of individual IMUs and the correction of position information in the zero-velocity interval. Therefore, these methods cannot effectively reduce errors and improve accuracy. An error compensation method for pedestrian navigation systems based on a low-cost array of IMUs is proposed in this paper. The calibration method for multiple location-free IMUs is improved by using a sliding variance detector to segment the angular velocity magnitude into stationary and motion intervals, and each IMU is calibrated independently. Compensation is then applied to the velocity residuals in the zero-velocity interval after zero-velocity update (ZUPT). The experimental results show a significant improvement in the average noise performance of the calibrated IMU array, with a 3.01-fold increase in static noise performance. In the closed-loop walking experiment, the average horizontal position error of a single calibrated IMU is reduced by 27.52% compared to the uncalibrated IMU, while the calibrated IMU array shows a 2.98-fold reduction in average horizontal position error compared to a single calibrated IMU. After compensating for residual velocity, the average horizontal position error of a single IMU is reduced by 0.73 m, while that of the IMU array is reduced by 64.52%.

Deadbeat predictive current control (DPCC) has excellent dynamics and can achieve current control with less computational effort. However, its control performance relies on the precision of the parameters of the motor. Current static error will be generated and control performance will be decreased when the predictive model parameters do not correspond to the practical parameters of the motor. In this article, a weakened integral sliding mode compensation method is proposed which converts the current error into a voltage compensation term and adds it to the prediction control output to effectively compensate for the steady-state error. In addition, a boundary layer is introduced to weaken the integral so as to solve the problems of integral saturation and overshoot caused by the introduction of the integral term when the error is large. Moreover, weight factors are introduced to optimize the feedback current, which enhances the robustness of the system. In the end, the effectiveness of this method is verified via simulation and experimental results.

The CFETR multi-purpose overload robot (CMOR) is a key subsystem of the remote handling system of the China fusion engineering test reactor (CFETR). This paper first establishes the kinematic and dynamic models of CMOR and analyzes the working process in the vacuum chamber. Based on the uncertainty of rigid-flexible coupling, a CMOR adaptive robust sliding mode controller (ARSMC) is designed based on the Hamilton-Jacobi equation to enhance the robustness of the control system. In addition, to compensate the influence of non-geometric factors on position accuracy, an error compensation method is designed. Based on the matrix differentiation method, the CMOR coupling parameter errors are decoupled, and then the gridded workspace principle is used to identify the parameter errors and improve the motion control accuracy. Finally, the CMOR rigid-flexible coupling simulation system is established by ADAMS-MATLAB/Simulink to analyze the dynamic control effect of ARSMC. The simulation results show that the CMOR end position error exceeds 0.1 m for single joint motion. The average value of CMOR end position error is less than 0.025 m after compensation, and the absolute error value is reduced by 4 times, improves the dynamic control accuracy of CMOR.

Phase measurement profilometry (PMP) is primarily employed to analyze the morphology of a functional surface with precision. Historically, one of the most complex and persistent challenges in PMP has been reducing errors stemming from inconsistent indicators at the edges of a surface. In response to this challenge, we propose an optimized error compensation methodology specifically designed to handle edge artefacts. This methodology introduces the Hilbert transform and object surface albedo as tools to detect the edges of the artefact region that need to be compensated. Moreover, we analyze the characteristics of the sinusoidal fringe waveform propagation direction and investigate the reconstruction results of the fringe vertical to the current directions to compensate for edge artefacts. The experimental results for various objects show that the optimized approach can compensate for edge artefacts by projecting in two directions and reducing the projection by half. The compensated root mean square error (RMSE) for planar objects can be reduced by over 45%.

The straightness error of guideways is one of the key indicators of an ultra-precision machine, which plays an important role in the machining accuracy of a workpiece. In order to measure the straightness error of a long-distance ultra-precision guideway accurately, a splicing measurement for the straightness error of a guideway using a high-precision flat mirror and displacement sensor was proposed in this paper, and the data splicing processing algorithm based on coordinate transformation was studied. Then, comparative experiments on a splicing measurement and direct measurement of the straightness error were carried out on a hydrostatic guideway grinder. The maximum difference between the two measurements was 0.3 μm, which was far less than the straightness error of 5.8 μm. The experiment demonstrated the correctness of the proposed splicing measurement method and data processing algorithm. To suppress the influence of the straightness error on machining accuracy, a straightness error compensation algorithm based on error rotation transformation and vertical axis position correction was proposed, and the grinding experiment of a plane optics with a size of 1400 mm × 500 mm was carried out. Without error compensation grinding, the flatness error of the element was 7.54 μm. After error compensation grinding, the flatness error was significantly reduced to 2.98 μm, which was less than the straightness errors of the guideways. These results demonstrated that the straightness error of the grinding machine had been well suppressed.

The sight of the high-orbit thermal infrared staring camera is concentrated and sensitive to temperature changes, and therefore its image point positioning is key to ensuring the geometric quality of the thermal infrared staring image and eliminating the errors of the imaging system in orbit. According to the geometric imaging characteristics of the high-orbit thermal infrared staring camera, internal and external positioning compensation models are proposed in this paper based on the two-dimensional pointing angle of temperature change, and four kinds of experimental schemes of image point positioning compensation are designed. The experimental results show that the method proposed in this paper has a good compensation effect on the image point positioning error.

Phase-shift profilometry (PSP) holds great promise for high-precision 3D shape measurements. However, in the case of measuring moving objects, as PSP requires multiple images to calculate the phase, the movement of the object causes artifacts in the measurement, which in turn has a significant impact on the accuracy of the 3D surface measurement. Therefore, we propose a method to reduce motion artifacts using feature information in the image and simulate it using the six-step term shift method as a case study. The simulation results show that the phase of the object is greatly affected when the object is in motion and that the phase shift due to motion can be effectively reduced using this method. Finally, artifact optimization was carried out by way of specific copper tube vibration experiments at a measurement frequency of 320 Hz. The experimental results prove that the method is well implemented.

Wide-range application scenarios, such as industrial, medical, rescue, etc., are in various demand for human spatial positioning technology. However, the existing MEMS-based sensor positioning methods have many problems, such as large accuracy errors, poor real-time performance and a single scene. We focused on improving the accuracy of IMU-based both feet localization and path tracing, and analyzed three traditional methods. In this paper, a planar spatial human positioning method based on high-resolution pressure insoles and IMU sensors was improved, and a real-time position compensation method for walking modes was proposed. To validate the improved method, we added two high-resolution pressure insoles to our self-developed motion capture system with a wireless sensor network (WSN) system consisting of 12 IMUs. By multi-sensor data fusion, we implemented dynamic recognition and automatic matching of compensation values for five walking modes, with real-time spatial-position calculation of the touchdown foot, enhancing the 3D accuracy of its practical positioning. Finally, we compared the proposed algorithm with three old methods by statistical analysis of multiple sets of experimental data. The experimental results show that this method has higher positioning accuracy in real-time indoor positioning and path-tracking tasks. The methodology can have more extensive and effective applications in the future.

This study addresses the challenges associated with incomplete or missing information in obstacle detection methods that employ a single sensor. Additionally, it tackles the issue of motion distortion in LiDAR point cloud data during synchronization and mapping in complex environments. The research introduces two significant contributions. Firstly, a novel obstacle detection method, named the point-map fusion (PMF) algorithm, was proposed. This method integrates point cloud data from the LiDAR, camera, and odometer, along with local grid maps. The PMF algorithm consists of two components: the point-fusion (PF) algorithm, which combines LiDAR point cloud data and camera laser-like point cloud data through a point cloud library (PCL) format conversion and concatenation, and selects the most proximate point cloud to the quadruped robot dog as the valid data; and the map-fusion (MF) algorithm, which incorporates local grid maps acquired using the Gmapping and OctoMap algorithms, leveraging Bayesian estimation theory. The local grid maps obtained by the Gmapping and OctoMap algorithms are denoted as map A and map B, respectively. This sophisticated methodology enables seamless map fusion, which significantly enhances the precision and reliability of the approach. Secondly, a motion distortion removal (MDR) method for LiDAR point cloud data based on odometer readings was proposed. The MDR method utilizes legged odometer data for linear data interpolation of the original distorted LiDAR point cloud data, facilitating the determination of the corresponding pose of the quadruped robot dog. Subsequently, the LiDAR point cloud data are then transformed to the quadruped robot dog coordinate system, efficiently mitigating motion distortion. Experimental results demonstrated that the proposed PMF algorithm achieved a 50% improvement in success rate compared to using only LiDAR or the PF algorithm in isolation, while the MDR algorithm enhanced mapping accuracy by 45.9% when motion distortion was taken into account. The effectiveness of the proposed methods was confirmed through rigorous experimentation.

There are many influencing factors present in different situations of power load. There is also a strong imbalance in the number of load samples. In addition to examining the problem of low training efficiency of existing algorithms, this paper proposes a short-term power load prediction method based on feature selection and error compensation under imbalanced samples. After clustering the load data, we expand some sample data to balance the sample categories and input the load data and filtered feature sequences into the improved GRU for prediction. At the same time, the errors generated during the training process are used as training data. An error correction model is constructed and trained, and the results are used for error compensation to further improve prediction accuracy. The experimental results show that the overall prediction accuracy of the model has increased by 80.24%. After expanding a few samples, the prediction accuracy of the region where the samples are located increased by 59.41%. Meanwhile, due to the improvement of the algorithms, the running time was reduced by approximately 14.92%.

As one of the fastest-growing new energy sources, wind power technology has attracted widespread attention from all over the world. In order to improve the quality of wind power generation, wind speed prediction is an indispensable task. In this paper, an error correction-based Variational Mode Decomposition and Broad Learning System (VMD-BLS) hybrid model is proposed for wind speed prediction. First, the wind speed is decomposed into multiple components by the VMD algorithm, and then an ARMA model is established for each component to find the optimal number of sequence divisions. Second, the BLS model is used to predict each component, and the prediction results are summed to obtain the wind speed forecast value. However, in some traditional methods, there is always time lag, which will reduce the forecast accuracy. To deal with this, a novel error correction technique is developed by utilizing BLS. Through verification experiment with actual data, it proves that the proposed method can reduce the phenomenon of prediction lag, and can achieve higher prediction accuracy than traditional approaches, which shows our method’s effectiveness in practice.

This paper proposes a methodology for creating simplified structural schemes and forward geometric models for industrial robots with serial architecture, with the goal of reducing thermal deformation errors that negatively impact positioning accuracy during operation. Unlike classical approaches, the proposed methodology introduces modifications to the order of matrix multiplication and incorporates new parameters to create a forward geometric model that better corresponds to the deformation characteristics of these robots. Details are presented on how to build and employ this extended model and integrate it into a thermal error compensation algorithm. The implementation of the algorithm in a software application is presented along with experimental results that demonstrate its effectiveness. This work addresses a real phenomenon that occurs in industrial robot operation and has implications for improving the performance of robots in manufacturing applications.

Wind speed prediction is very important in the field of wind power generation technology. It is helpful for increasing the quantity and quality of generated wind power from wind farms. By using univariate wind speed time series, this paper proposes a hybrid wind speed prediction model based on Autoregressive Moving Average-Support Vector Regression (ARMA-SVR) and error compensation. First, to explore the balance between the computation cost and the sufficiency of the input features, the characteristics of ARMA are employed to determine the number of historical wind speeds for the prediction model. According to the selected number of input features, the original data are divided into multiple groups that can be used to train the SVR-based wind speed prediction model. Furthermore, in order to compensate for the time lag introduced by the frequent and sharp fluctuations in natural wind speed, a novel Extreme Learning Machine (ELM)-based error correction technique is developed to decrease the deviations between the predicted wind speed and its real values. By this means, more accurate wind speed prediction results can be obtained. Finally, verification studies are conducted by using real data collected from actual wind farms. Comparison results demonstrate that the proposed method can achieve better prediction results than traditional approaches.

The operating attitude of a shearer based on a three-dimensional (3D) space scale is the necessary basic information for realizing intelligent mining. Aiming to address the problem of the insufficient perception accuracy of shearers, in this paper, the rotation model of the actual turning mechanism of the strapdown inertial navigation system (SINS) of shearers is established, and the error propagation characteristics of different single-axis rotation modulation schemes are revealed. Through theory and simulation, the optimal rotation modulation scheme is determined to be the improved four-position turn–stop modulation with a rotation of

When performing a digital image correlation (DIC) measurement, multi-camera stereo-DIC is generally preferred over single-camera 2D-DIC. Unlike 2D-DIC, stereo-DIC is able to minimise the in-plane strain error that results from out-of-plane motion. This makes 2D-DIC a less viable alternative for strain measurements than stereo-DIC, despite being less financially and computationally expensive. This work, therefore, proposes a strain-gauge-based method for the compensation of errors from out-of-plane motion in 2D-DIC strain measurements on planar specimens. The method was first developed using equations for the theoretical strain error from out-of-plane motions in 2D-DIC and was then applied experimentally in tensile tests to two different dog-bone specimen geometries. The compensation method resulted in a clear reduction in the strain error in 2D-DIC. The strain-gauge-based method thus improves the accuracy of a 2D-DIC measurement, making it a more viable option for performing full-field strain measurements and providing a possible alternative in cases where stereo-DIC is not practical or is unavailable.

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Intelligent mining is the demand and inevitable development direction of China’s coal industry, and the shearer attitude based on the 3D spatial scale is the essential basic information for realizing intelligent mining at the fully mechanized mining face. The traditional shearer attitude monitoring technology cannot meet the accuracy requirements of attitude sensing of mining equipment at an intelligent working face. In this paper, based on the basic principle of strapdown inertial navigation system (SINS), a real-time solution algorithm for shearer attitude is constructed, and the specific process of SINS coarse alignment and fine alignment is studied. The main error terms affecting the accuracy of SINS are analyzed, and the initial alignment error, installation deviation angle error, and vibration effect error are compensated and analyzed through simulation one by one. According to the working characteristics of the shearer, the coning error and sculling error of the shearer’s SINS are compensated and analyzed through simulation. This paper provides a complete set of theories and methods for improvement of the accuracy of the shearer attitude sensing in underground operation; simulation results also verify that the theories and methods can significantly improve the perception accuracy which can provide theoretical and technical reference for the production state prediction of fully mechanized mining face and intelligent control of underground mining equipment.

The measurement of Earth’s gravitational field is important in geophysics, geodynamics, geodesy, oceanography, and space science. The ocean covers 71% of the earth’s surface; therefore, measuring the ocean’s gravitational field is crucial. Compared with shipborne gravimetry, underwater gravimetry near the seafloor is closer to gravity sources and can obtain short-wavelength gravity information that is useful for small-scale deposit detection and seawater intrusion monitoring. This article focuses on gravimetric errors caused by the poor dynamics of the carrier; an error compensation method for underwater gravimetry based on correlation analysis is proposed. By analyzing the error sources that affect the dynamics of the carrier, the relationship between the gravimetry error and impact factors related to the dynamics was established, and the model’s parameters were estimated by the least-squares fitting method. The experimental data show that this method can effectively compensate for gravimetric errors caused by carrier dynamics and provide the theoretical basis and algorithm model for underwater gravimetry in the bottom-tracking mode.

Heterodyne interferometry is playing an increasingly important role in the field of high-end equipment manufacturing. In photolithography, the precision requirement of displacement metrology is increasing to a deep sub-nanometer scale with the decrease in the critical dimension of chips. The error caused by light intensity changes was investigated, and its principle was found to be related to the time difference in photoelectric conversion. On the basis of the analysis of dynamic characteristics of interference light intensity changes in a heterodyne Michaelson interferometer, the influencing factors, and the features of the measurement error, equivalent measurement and real-time compensation methods were investigated and proposed. Experiments revealed that the error was 220 pm using the method of best-gain detection, while it was 4.8 nm using the method of auto-gain detection over a wide dynamic range when the light intensity was reduced by 30%. However, the proposed compensation method successfully reduced the error to less than 40 pm. Therefore, the real-time compensation method based on equivalent measurement can maintain the signal-to-noise ratio while improving the precision of photoelectric conversion, removing the error caused by intensity changes, and helping heterodyne interferometry achieve deep sub-nanometer precision.

The geometric accuracy of a hemispherical shell resonator (HSR) affects the assembly accuracy and final performance of a hemispherical resonant gyroscope in many ways. During the precision grinding of a resonator, the tool-setting error and wear error affect the form and positional accuracy of the inner and outer spherical surfaces. In this study, a compensation method for generating grinding of the HSR is proposed to address this problem. The geometric errors of the inner and outer spherical surfaces are systemically analyzed and a geometric model of the tool setting and wheel wear is established for generating grinding of the HSR. According to this model, a mapping relationship between the wheel pose and size, form, and positional error of the HSR was proposed. Experiments regarding machining, on-machine measurements, and error compensation were performed using the mapping relationship. The results demonstrate that the proposed method can reduce the radius error of the inner and outer spherical surfaces from 10 μm to 1 μm, sphericity from 5 μm to 1.5 μm, and concentricity from 15 μm to 3 μm following grinding. The form and positional errors are simultaneously improved, verifying the effectiveness of the proposed method.

Flexible-joint manipulators (FJMs) have been widely used in the fields of industry, agriculture, medical service, aerospace, etc. However, the FJMs in practical applications inevitably encounter various uncertainties including matched and mismatched disturbances. In this paper, we consider the high precision tracking control problem of FJMs in the presence of unknown lumped matched and mismatched disturbances. An efficient model-assisted composite control approach is proposed by integrating two reduced-order extended state observers (RESOs), a second-order command filtered backstepping (SCFB) technique and an error compensation dynamic system. Unlike some existing methods, the RESOs constructed with partial known model information are capable of estimating and compensating the matched and mismatched disturbances simultaneously. In addition, by employing the SCFB with an error compensation system, the proposed approach can not only overcome the problem of “explosion of complexity” inherent in backstepping, but also reduce the filtering errors arising from the command filters. The stability of the resulting control system and the convergence of error signals are guaranteed by Lyapunov stability theory. Comparative simulations are conducted for a single-link FJM with both matched and mismatched disturbances, and the results show that the proposed approach achieves a better tracking performance, i.e., compared with conventional backstepping method and adaptive fuzzy command filtered control method, the tracking accuracy is improved by 99.5% and 99.2%, respectively.

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.

Background: In the process of fracture reduction, there are some errors between the actual trajectory and the ideal trajectory due to mechanism errors, which would affect the smooth operation of fracture reduction. To this end, based on self-developed parallel mechanism fracture reduction robot (FRR), a novel method to reduce the pose errors of FRR is proposed. Methods: Firstly, this paper analyzed the pose errors, and built the model of the robot pose errors. Secondly, mechanism errors of FRR were converted into drive bar parameter’s errors, and the influence of each drive bar parameter on the robot pose error were analyzed. Thirdly, combining with Cauchy opposition-based learning and differential evolution algorithm (DE), an improved whale optimization algorithm (CRLWOA-DE) is proposed to compensate the end-effector’s pose errors, which could improve the speed and accuracy of fracture reduction, respectively. Results: The iterative accuracy of CRLWOA-DE is improved by 50.74%, and the optimization speed is improved by 22.62% compared with the whale optimization algorithm (WOA). Meanwhile, compared with particle swarm optimization (PSO) and ant colony optimization (ACO), CRLWOA-DE is proved to be more accurate. Furthermore, SimMechanics in the software of MATLAB was used to reconstruct the fracture reduction robot, and it was verified that the actual motion trajectory of the CRLWOA-DE optimized kinematic stage showed a significant reduction in error in both the x-axis and z-axis directions compared to the desired motion trajectory. Conclusions: This study revealed that the error compensation in FRR reset process had been realized, and the CRLWOA-DE method could be used for reducing the pose error of the fracture reduction robot, which has some significance for the bone fracture and deformity correction.

Random drift error is one of the important factors of MEMS (micro-electro-mechanical-system) sensor output error. Identifying and compensating sensor output error is an important means to improve sensor accuracy. In order to reduce the impact of white noise on neural network modeling, the ensemble empirical mode decomposition (EEMD) method was used to separate white noise from the original signal. The drift signal after noise removal is modeled by GRNN (general regression neural network). In order to achieve a better modeling effect, cross-validation and parameter optimization algorithms were designed to obtain the optimal GRNN model. The algorithm is used to model and compensate errors for the generated random drift signal. The results show that the mean value of original signal decreases from 0.1130 m/s2 to −1.2646 × 10−7 m/s2, while the variance decreases from 0.0133 m/s2 to 1.0975 × 10−5 m/s2. In addition, the displacement test was carried out by MEMS acceleration sensor. Experimental results show that the displacement measurement accuracy is improved from 95.64% to 98.00% by compensating the output error of MEMS sensor. By comparing the GA-BP (genetic algorithm-back propagation) neural network and the polynomial fitting method, the EEMD-GRNN method proposed in this paper can effectively identify and compensate for complex nonlinear drift signals.

A phase error correction method is proposed to compensate for the phase error in super-resolution correlated imaging based on metamaterial antennas. The varying carrier frequencies of a metamaterial antenna can generate the random radiation field for super-resolution correlation imaging, but the variation of the signal carrier frequency leads to large phase errors in the imaging results. In this proposed method, the sampling matrix in the super-resolution correlated imaging algorithm is used to compensate for the phase errors. Each element of the matrix is multiplied by a compensation phase corresponding to the phase error, and the error is subtly removed from the algorithm. In the experiment, the antenna pattern at each frequency of the metamaterial antenna is measured and recorded. In addition, an external field experiment is also carried out, and the collected data are imaged with the improved algorithm. Experimental results show that this technology can effectively solve the effect of phase errors on imaging results caused by signal carrier frequency changes.

This paper proposes a general design method for cams based on the kinematics and dynamics of a mechanical system. According to the actuator’s trajectory, the cam profile is generated in reverse based on the kinematic model of the system. Firstly, the cam design’s optimising problem is converted into the execution trajectory’s optimisation to obtain the optimum operation trajectory according to the actuator’s requirements. Secondly, the relationship between the cam profile and the actuation trajectory is modelled based on the kinematics and dynamics of the mechanical system. Then, applying the cubic spline interpolation method, the cam profile is generated, and the error compensation methods are illustrated through numerical analysis. Finally, the validity of the presented design method is verified through experiments, which demonstrate the reliability of this method.

This paper presents a novel method for inner profile measurement and geometric parameter evaluation, such as the radius of the bottom, steepness and straightness of the steep sidewall of a high aspect ratio aspheric workpiece, by utilizing a two-probe measuring system, which includes a lateral displacement gauge for the inner steep sidewall profile measurement and an axial displacement gauge for the inner deep underside profile measurement. To qualify the measurement accuracy, the systematic errors associated with the measurement procedure, including the miscalibration, misalignment and the roundness error of the gauge probes, as well as the slide motion error of the four-axis motion platform, are all evaluated and separated from the measurement results. A point cloud registration algorithm is employed to stitch the evaluated inner sidewall profile and the inner underside profile to form an entire inner profile of the workpiece. To verify the performance of the newly proposed method, the inner profile of a high aspect ratio aspheric workpiece, which has a tapered cone shape with a maximum inner radius of 40 mm, a maximum inner depth of 140 mm and a steep sidewall angle approaching 85°, is measured in experiments. The measurement result is compared with that of a coordinate measuring machine (CMM), and the comparison verifies the feasibility of the proposed measurement system.

Demand forecasting plays a crucial role in a company’s operating costs. Excessive inventory can increase costs and unnecessary waste can be reduced if managers plan for uncertain future demand and determine the most favorable decisions. Managers are demanding increasing accuracy in forecasting as technology advances. Most of the literature discusses forecasting results’ inaccuracy by suspending the model and reloading the data for model retraining and correction, which is extensively employed but causes a bottleneck in practice since users do not have the sufficient ability to correct the model. This study proposes an error compensation mechanism and uses the individuals and moving-range (I-MR) control chart to evaluate the requirement for compensation to solve the current bottleneck using forecasting models. The approach is validated using the case companies’ historical data, and the model is developed using a rolling long short-term memory (LSTM) to output the predicted values; then, five indicators are proposed for screening to determine the prediction statistics to be subsequently employed. Root mean squared error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) compare the LSTM, rolling LSTM combined index, and LSTM-autoregressive moving average (ARMA) models. The results demonstrate that the RMSE, MAPE, and MAE of LSTM-ARMA are smaller than those of the other two models, indicating that the error compensation mechanism that is proposed in this study can enhance the prediction’s accuracy.

Three-axis milling machine tools are widely used in manufacturing enterprises, and they have enormous potential demands for remanufacturing to improve their performance. During remanufacturing a three-axis milling machine tool, the structure needs to be reconstructed, so it is necessary to identify sensitive geometric errors of the remanufactured machine tool. In the traditional sensitive geometric error identification method, complex error modeling and analysis must be conducted. Therefore, professional knowledge is required, and the process of the identification is cumbersome. This paper focused on the quick identification of sensitive geometric errors for remanufacturing of three-axis milling machine tools. Firstly, sensitive geometric errors of a three-axis milling machine tool were identified based on the multi-body system theory and partial differential method. Then, mapping laws between the sensitive geometric errors and the machine tool structure were firstly presented. According to the proposed mapping laws, the sensitive geometric errors can be identified quickly and easily without complex error modeling and analysis. Finally, the simulation and experiment show that the straightness error of milling is improved up to 0.007 mm by compensating the sensitive geometric errors identified by the proposed mapping laws. The table lookup method based on the mapping laws can quickly identify the sensitive geometric errors of three-axis milling machine tools, which is beneficial for the efficiency and precision of remanufacturing of machine tools.

This paper presents an air bearing stage that uses flexure for yaw motion compensation. The proposed stage realizes motion in three degrees of freedom (DOF), which are the X, Y, and Θz directions. To work with Θz as the rotational motion of the stage, we applied a flexure consisting of four bar linkages. The stage from a previous study in which flexure is applied to compensate for yaw motion error has the limitation of increasing the structural stiffness of the stage due to the rotational stiffness. In this study, we propose a combination of a new stage structure and flexure to ensure the high structural stiffness of the stage and the very low rotational stiffness of the flexure at the same time. Modeling and design optimization were performed to apply adequate flexure to the proposed stage. Experiments were carried out to verify yaw motion error compensation and the performance of the stage. The proposed stage has a maximum yaw motion error of 0.86 arcsec during the scanning motion and 48 ms settling time, while the stepping motion is improved by 34.2% compared to the previous study.

Ultrasonic ranging has been widely used in automobiles, unmanned aerial vehicles (UAVs), robots and other fields. With the appearance of micromachined ultrasonic transducers (MUTs), the application of ultrasonic ranging technology presents a more extensive trend. This review focuses on ultrasonic ranging technology and its development history and future trend. Going through the state-of-the-art ultrasonic ranging methods, this paper covers the principles of each method, the signal processing methodologies, the overall system performance as well as key ultrasonic transducer parameters. Moreover, the error sources and compensation methods of ultrasonic ranging systems are discussed. This review aims to give an overview of the ultrasonic ranging technology including its current development and challenges.

Thermal compensation control can correct errors caused by the thermal deformation of phased array antenna (PAA) panels. Thermal deformation of the panel is needed to calculate the compensation value. While the PAA is working, thermal deformation is unconditional to measure, but predicting it by temperature is feasible. However, thermal deformation is also affected by other factors, such as the structural shape, assembly method, and material parameters, and it is difficult to measure these parameters of PAA because of the complex structure. In contrast, the measurement method of the temperature and thermal deformation of the PAA in the laboratory is much easier. Therefore, a comprehensive influence parameters (CIPs)-finite element method (FEM) method was proposed in this study, it can extract the influence of above parameters on thermal deformation from temperature and thermal deformation measurement data and build a thermal deformation prediction model. Experiments have verified that the CIPs-FEM can greatly reduce the difficulty of thermal deformation modeling and have a high prediction accuracy.

Continuous chaos may collapse in the digital world. This study proposes a method of error compensation for a two-dimensional digital system based on the generalized mean value theorem of differentiation that can restore the fundamental performance of chaotic systems. Different from other methods, the compensation sequence of our method comes from the chaotic system itself and can be applied to higher-dimensional digital chaotic systems. The experimental results show that the improved system is highly consistent with the real chaotic system, and it has excellent chaotic characteristics such as high complexity, randomness, and ergodicity.

This study proposed an error-matching measurement and compensation method for curve mating and complex mating. With use of polynomial curve fitting and least squares methods for error analysis, an algorithm for error identification and error compensation were proposed. Furthermore, based on the proposed method, an online error-matching compensation system with an autorevising function module for autogenerating an error-compensated NC program for machining was built. Experimental verification results showed that the proposed method can effectively improve the accuracy of assembly matching. In a curve-type mating experiment, the matching error without compensation was 0.116 mm, and it decreased to 0.048 mm after compensation. The assembly accuracy was improved by 28%. In a complex-type mating experiment, the verification results showed that the error reductions after compensation for three mating shapes (straight line, triangle, and curve shape) were 81%, 87%, and 79%, respectively. It showed that the proposed method can improve the assembly accuracy for complex mating shapes, which would also be improved without losing production efficiency.