Error Compensation Research Articles

An accurate measurement method of irregular coal gangue volume based on adaptive image restoration and error compensation

To improve the accuracy of volume measurement for irregularly shaped coal gangue, defects in the depth image and various errors in volume measurement are analyzed. The gray difference similarity (Gds) is proposed for pre-classifying defects, and the depth and RGB information are used interactively for adaptive repair. To minimize the impact of abnormal gray distribution and irrelevant information on the repair process, the areas to be repaired are divided into abnormal regions or layers based on gray and distance weights. Taking into account parameters like geometric morphology (GeMo), volume (Ve), and GeMo × Ve, the influence of wrong imaging and gaps is fully considered. The reverse compensation of errors is achieved by applying the principles of mathematical statistics and the nonlinear surface fitting algorithm. The results show that compared with other algorithms, the proposed algorithm has the smallest measurement error of 6.614 % and is not easily affected by external factors.

Two-stage forecasting of TCN-GRU short-term load considering error compensation and real-time decomposition

Two-stage forecasting of TCN-GRU short-term load considering error compensation and real-time decomposition

Identification and compensation method for unbalance error in signal detection chain of Rate-Integrating hemispherical resonator gyro

In this work, a notable effective method is proposed to actualize the identification and compensation for unbalance error in signal detection chain of Rate-Integrating Hemispherical Resonator Gyro (RI-HRG). RI-HRG has excellent dynamic performance and measuring range, which has been verified in multiple field applications. Firstly, the unbalance error model is established with equivalent electrode-misalignment-angle and equivalent relative-chain-gain-deviation, considering about the effect of the inevitable signal coupling, assembly error and electronic components parameter inconsistency error. Then, a high-efficient and high-accuracy identification method is proposed based on the parameter estimation of the free vibration signal envelope, by which the adverse effect of gyro circumferential asymmetry is effectively suppressed. Finally, the compensation method based on feedforward gain controller is designed and implemented with digital control circuit. The experimental results show that the zero bias stability of RI-HRG is improved from 1.0461°/h to 0.0494°/h, which strongly prove the effectiveness of the proposed methods.

Fast fixed-time extended state observer based command filtering backstepping control of free-flying flexible-joint space robots

System parameter perturbations, external disturbances, and input saturation issues seriously affect the on-orbit operation precision and rapid response capabilities of the free-flying flexible-joint space robots (FFSR). To this end, a fixed-time extended state observer (ESO) based non-singular command filtering backstepping controller is proposed. The fast fixed-time ESO is designed to estimate the parameter perturbations and external disturbances. To avoid the “computational explosion” caused by multiple derivatives of the virtual control law in backstepping control, a second-order command filter is employed to obtain the derivative of virtual control laws. Meanwhile, to reduce the filtering errors induced by the command filter, a non-singular fixed-time filtering error compensation algorithm is developed. Furthermore, considering the constraints of control moment gyroscope (CMG) and joint motors, an anti-saturation compensation algorithm is introduced to drive the system out of the saturated region rapidly, thus reducing actuator saturation effects on the control system performance. Theoretical analysis shows the proposed controller can ensure the system tracking error converges to any arbitrarily small neighborhood of the origin within fixed time. Simulation results demonstrate that the designed non-singular fixed-time command filtering backstepping controller exhibits fast convergence speed and high tracking accuracy.

On-machine inspection and compensation for thin-walled parts with sculptured surface considering cutting vibration and probe posture

Abstract On-machine inspection has a significant impact on improving high-precision and efficient machining of sculptured surfaces. Due to the lack of machining information and the inability to adapt the parameters to the dynamic cutting conditions, theoretical modeling of profile inspection usually leads to insufficient adaptation, which causes inaccuracy problems. To address the above issues, a novel coupled model for profile inspection is proposed by combining the theoretical model and the data-driven model. The key process is to first realize local feature extraction based on the acquired vibration signals. The hybrid sampling model, which fuses geometric feature terms and vibration feature terms, is modeled by the lever principle. Then, the weight of each feature term is adaptively assigned by a multi-objective multi-verse optimizer. Finally, an inspection error compensation model based on the attention mechanism considering different probe postures is proposed to reduce the impact of pre-travel and radius errors on inspection accuracy. The anisotropy of the probe system error and its influence mechanism on the inspection accuracy are analyzed quantitatively and qualitatively. Compared with the previous models, the proposed hybrid profile inspection model can significantly improve the accuracy and efficiency of on-machine sampling. The proposed compensation model is able to correct the inspection errors with better accuracy. Simulations and experiments demonstrate the feasibility and validity of the proposed methods. The proposed model and corresponding new findings contribute to high-precision and efficient on-machine inspection, and help to understand the coupling mechanism of inspection errors.

Event-triggered predefined-time control for full-state constrained nonlinear systems: A novel command filtering error compensation method

Event-triggered predefined-time control for full-state constrained nonlinear systems: A novel command filtering error compensation method

Fixed-time disturbance observers-based fault-tolerant control for a class of nonlinear systems with prescribed performance

This paper explores the issue of fault-tolerant control for a class of nonlinear systems that encounter the actuator fault and external disturbances. The uncertainties arising from the actuator fault and external disturbances are treated as lumped uncertainties, and fixed-time observers are designed to observe them. The fault-tolerant controller with full-state constraints is then developed using the fixed-time backstepping method, integrating the Improved Prescribed Performance Function (IPPF) method and the Barrier Lyapunov Function (BLF) method. Additionally, command filters with error compensations are devised to resolve the ‘explosion of complexity’ problem during the controller derivation process. The parameters of the designed controller are optimised using the Northern Goshawk Optimization (NGO) algorithm to enhance nonlinear systems’ dynamic performance. Lastly, the validity and practicality of the proposed approach are verified through the comparative study of simulations and experiments, with the permanent magnet synchronous motor (PMSM) position system employed as a case study.

Closed-Form Method for Unified Far-Field and Near-Field Localization Based on TDOA and FDOA Measurements

When the near-field and far-field information of a target is uncertain, it is necessary to choose a suitable localization method. The modified polar representation (MPR) method integrates the two scenarios and achieves a unified localization with direction of arrival (DOA) estimation in the far field and position estimation in the near field. Previous studies have only proposed solutions for stationary environments and have not considered the motion factor. Therefore, this paper proposes a new unified positioning algorithm using multi-sensor time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements without prior target source information. The method represents the position of the target source using MPR and describes the localization problem as a weighted least squares (WLS) problem with two constraints. We first obtain the initial estimates by WLS without considering the constraints and then investigate a two-step error correction method based on the constraints. The first step corrects the initial estimate using the Taylor series expansion technique, and the second step corrects the DOA estimate in the previous step using the direct error compensation technique based on the properties of the second constraint. Simulation experiments show that the method is effective for the unified positioning of moving targets and can achieve the Cramer–Rao lower bound (CRLB).

Neural-network-based trajectory error compensation for industrial robots with milling force disturbance

ABSTRACT Industrial robots are increasingly used in advanced manufacturing fields such as aerospace due to their high efficiency and low cost. In robotic machining applications, deviation of the tool centre point trajectory from the desired path due to load disturbances acting on the end-effector of an industrial robot can result in poor dimensional accuracy and surface quality of products. Therefore, improving robot trajectory accuracy under external load disturbances is extremely important. This study proposes an error compensation methodology using neural networks optimized by a hybrid marine predators-grid search algorithm to compensate for robot trajectory error. Two neural networks are developed: one for predicting load disturbances and the other for predicting trajectory errors in robotic machining. The milling experiment results show that the compensated robot trajectory errors in x, y, and z directions are reduced by 65%, 76%, and 77% respectively, which proves the effectiveness of this method in improving the robotic milling accuracy.

A novel phase measuring deflectometry based on polar coordinate

Phase measuring deflectometry (PMD) is a method measure the surface of a mirror. However, when measuring convex mirrors, Cartesian coordinate fringes experience extreme compression. To address this issue, this paper proposes a novel PMD based on polar coordinate. This new method defines two linearly independent phase modulation directions, using the orthogonal basis of polar coordinate. It establishes polar coordinate fringes with rotational symmetry and radial pre-modulation, effectively reducing the impact of extreme compression at the edges. To correct the phase errors in polar coordinate fringes, a phase error compensation algorithm based on greyscale gradient is introduced. The algorithm calculates the influence factor of the eight connected domains around the error points to be compensated, utilising the phase grey gradient. The wavefront gradient data obtained through polar coordinate fringes are radial and tangential. Hence, a surface reconstruction method is proposed based on the Zernike partial derivative polynomial based on polar coordinate. In this method, the tangential partial derivatives and radial partial derivatives of the first 36 terms of Zernike in polar coordinate to construct Gram matrix equations. As a result, linearly independent Zernike recovery coefficients are obtained from coupled aliasing gradient data. Compared to the Cartesian coordinate system, the proposed method significantly reduces the fitting coefficient errors. Experimental measurements of convex mirrors with radii of curvature of 200 mm and 100 mm were conducted. The results demonstrate that compared to traditional PMD, this technique not only effectively suppresses extreme compression and increases the measurement area but also improves measurement accuracy by six times.

Long-range LBL underwater acoustic navigation considering Earth curvature and Doppler effect

The accuracy of underwater acoustic navigation is significantly influenced by geometry configuration and systematic errors coming from geophysical environment. Long baseline (LBL) systems exhibit superior positioning precision than other acoustic navigation systems, primarily attributable to the better Geometric Dilution of Precision (GDOP). However, the geometry configuration tends to degrade when the underwater vehicle is far away from the seafloor beacons. Factors such as acoustic ray bending error, Doppler effect and Earth curvature may seriously affect the navigation accuracy. To address these issues, we present a robust Kalman filter with systematic error compensation for long-range LBL systems. Firstly, a reversed acoustic ray tracking method is proposed for a unique phenomenon in acoustic wave propagation. Following that, we construct an acoustic positioning model with a time bias parameter, to weaken the impact of Doppler effect on acoustic ranging. This additional parameter was estimated with the state of the user vehicle in real time. At last, an observation equation of pressure gauge considering Earth curvature is presented for depth constraint. Long-range LBL experiments conducted in the South China Sea is employed to validate the performance of the proposed methods, taking the positioning results of inverted ultra-short baseline (iUSBL) system as reference. The results show that the proposed method outperform traditional method with a decrease of about 60 % in the three-dimensional root mean square (3DRMS) of navigation errors. With mentioned three improvements, the 3DRMS of the long-range LBL system with the longest distance of 20 km from the beacon center is less than 14 m. These findings can provide theoretical basis for other long-range LBL systems.

Machine learning for aspherical lens form accuracy improvement in precision molding of infrared chalcogenide glass

Precision glass molding (PGM) is an effective approach to manufacturing infrared chalcogenide glass (ChG) aspherical lens with complex shapes. However, infrared ChG aspherical lens often experiences form error in the designed profile and the final profile obtained by PGM. To reduce the form error of infrared ChG aspherical lens in the PGM process, a form error compensation model based on the random forest (RF) algorithm is proposed. The infrared ChG aspherical lens profile was first machined on an electroless nickel-phosphorus (Ni–P) plating to serve as the mold for PGM. After molding, the profile data of the lens was extracted, and a compensation model based on RF was constructed to optimize the model parameters using the evaluation parameters such as root mean square error (RMSE), coefficient of determination (R2), and out-of-bag (OOB). Finally, the generated compensated profile based on the compensation model was used for the compensation machining of the mold. Through this compensation approach, we have demonstrated a substantial 63.5 % reduction in the form error of the fabricated infrared ChG aspherical lens, decreasing the Peak-to-Valley (PV) value from 1.04 μm to 0.38 μm.

Thermal error prediction and optimal design of cooling structure for oscillating head housing

The thermal error of machine tool has always been an important reason affecting the accuracy of machine tool. In modern methods to reduce thermal error, thermal error compensation method and thermal error isolation method are two methods with high operability. Thermal error compensation method emphasizes predicting deformation in advance and then compensating in advance. Thermal error isolation method emphasizes the reduction of numerical value in thermal error propagation path. In this paper, the machine tool swing head is taken as the research object, and the above two methods are innovatively combined; Build an experimental platform and a simulation model to ensure the accuracy of the experiment through mutual verification; The POA-LSTM prediction model is established to predict the expansion of the swing head shell structure caused by thermal load accumulation, and compared with the LSTM prediction model. The results show that the prediction accuracy of the POA-LSTM prediction model in Z direction and X direction is 98.89 % and 98.38 %, respectively, which is higher than that of LSTM's 89.33 % and 89.47 %. The experiment for shell structure optimization is designed to reduce the thermal expansion of the pendulum and improve the machining accuracy. As a result, the thermal expansion inhibition effect on the whole pendulum is 26.14 %, and the thermal expansion inhibition effects on the X-direction, Y-direction and Z-direction are 34.93 %, 33.35 % and 30.24 % respectively.

A design approach of fractional model error compensator for fractional dynamical systems with polytopic uncertainty and disturbance

A design approach of fractional model error compensator for fractional dynamical systems with polytopic uncertainty and disturbance

Active prediction compensation strategy: A new positioning compensation technique for improving the accuracy of the dual ball screw feed mechanism under load

The dual ball screw feed mechanism (DBSFM) is commonly employed in high-end machining applications. However, its accuracy is challenging to enhance due to variations in the axial stiffness of the dual actuators under load, making geometric error compensation (GEC) difficult. To address this, our research establishes a comprehensive error model that integrates geometric error and load-induced error (LIE) to improve feeding accuracy. The axial stiffness matrix of the DBSFM is identified using motor current information, and an active prediction error matrix is defined based on the geometric error model, milling force model, and axial stiffness matrix. We propose and analyze the active prediction compensation (APC) strategy as a new method to enhance accuracy under load. Experimental validation using a gantry-type machine tool demonstrates that the APC strategy can reduce the positioning error of the DBSFM to ±2 μm under load, representing significant improvements over the established GEC method. Specifically, the APC strategy achieves a 53.07% and 57.04% enhancement in accuracy along the two axes. This work illustrates the effectiveness of the APC strategy in reducing positioning errors and improving feeding accuracy in DBSFM machining processes.

Design, Analysis and Experiment of a Modular Deployable Continuum Robot

Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot.

Command filtering‐based adaptive backstepping control for a class of discrete‐time uncertain nonlinear systems with mismatched disturbances

SummaryThis paper investigates the adaptive fuzzy backstepping control problem for uncertain discrete‐time nonlinear systems with mismatched disturbances. A novel adaptive fuzzy command filtered backstepping approach is proposed, which can overcome the noncausal problem by using the command filter. The filter errors generated by filter are removed by constructing error compensation mechanism. The fuzzy logic systems are used to approximate the uncertain nonlinear dynamics, and the unknown mismatched disturbances are actively attenuated by using adaptive control technique. Based on the proposed new weighed Lyapunov functions, all the signals in the close‐loop system are proved to be uniformly ultimately bounded. The viability of proposed method is demonstrated by simulation results.

Geometry accuracy control in abrasive water jet taper hole machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates

AbstractThe primary factors affecting the geometric accuracy of abrasive water jet (AWJ) machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates are the cutting front drag and kerf width deviation caused by energy dissipation. Firstly, this study comprehensively analyzes the influence of the coupling relationship between cutting front drag and kerf width deviation on the geometric accuracy of hole machining. Secondly, a gradient distribution theory for jet traverse speed with cutting depth is proposed for taper hole machining characteristics. Finally, a general geometric error model applicable to both straight and taper hole machining of ultra‐thick CFRP laminates using AWJ is established, along with a geometric error compensation method. A series of experiments validate the accuracy of the proposed geometric error model and compensation method. The novelty of this research lies in unifying the geometric error models for straight and taper hole machining of ultra‐thick CFRP laminates by considering the gradient distribution of jet traverse speed. The proposed error compensation method reduces the high degree of freedom required for machine tools. This study provides a general geometric error model and compensation strategy for AWJ hole machining of ultra‐thick CFRP laminates, which has significant engineering value for achieving 3D controllable AWJ machining of complex ultra‐thick CFRP components.Highlights The high geometric precision taper holes machining technique is a necessary prerequisite for achieving precise machining of complex trajectories in ultra‐thick CFRP with abrasive water jet. The influence of the coupling relationship between cutting front drag and kerf taper on the geometric accuracy of hole processing is comprehensively analyzed. A model considering the gradient distribution of traverse speed during taper holes machining was established, and a geometric error model considering this gradient distribution of traverse speed was developed. A taper holes machining geometric error compensation method with high engineering applicability was proposed. Geometric error prediction experiments and error compensation experiments were conducted, and the results proved the accuracy of the geometric error model and error compensation method.

Laser-Tracing Multi-Station Measurements in a Non-Uniform-Temperature Field

Due to the increasing requirements for the improvement of the accuracy of large coordinate-measuring machines (CMMs), the laser-tracing multi-station measurement technology, as one of the advanced precision measurement technologies, is worth studying in depth in terms of its practical application for the compensation of errors in large CMMs. Since it is difficult to maintain a constant temperature of about 20 °C in the actual workshop under the influence of solar radiation and convective heat transfer, there is a gradient in the spatial temperature distribution, and the overall temperature changes with the influence of external factors with synchronous hysteresis, it is difficult for the actual calibration environment to meet the standard environmental requirements. Therefore, the influence of temperature and other environmental factors on the accuracy of laser ranging and large-scale CMM calibration should not be ignored. In this paper, on the basis of analyzing the temperature distribution and change rule of large CMM measurement space under different working conditions, the radial basis function (RBF) neural network algorithm was used to build a non-uniform-temperature field model, and based on this model and the measurement principle of the laser-tracking instrument, the method of laser tracking and interferometric ranging accuracy enhancement was put forward under a non-uniform-temperature field. Finally, based on the multi-station technique of laser tracing, an accurate solution for the volumetric error of large CMMs under the condition of non −20 °C ambient temperature was realized. Simulation results proved that compared with the traditional temperature-compensation method, the proposed method improved the measurement accuracy of the volumetric error of a large-scale CMM using laser-tracing multi-station technology in a non-uniform-temperature field by 33.5%. This study provides a new approach for improving the accuracy of laser-tracer multi-station measurement systems.

Adaptive QSMO-Based Sensorless Drive for IPM Motor with NN-Based Transient Position Error Compensation

In commercial electrical equipment, the popular sensorless drive scheme for the interior permanent magnet synchronous motor, based on the quasi-sliding mode observer (QSMO) and phase-locked loop (PLL), still faces challenges such as position errors and limited applicability across a wide speed range. To address these problems, this paper analyzes the frequency domain model of the QSMO. A QSMO-based parameter adaptation method is proposed to adjust the boundary layer and widen the speed operating range, considering the QSMO bandwidth. A QSMO-based phase lag compensation method is proposed to mitigate steady-state position errors, considering the QSMO phase lag. Then, the PLL model is analyzed to select the estimated speed difference for transient position error compensation. Specifically, a transient position error compensator based on a feedback time delay neural network (FB-TDNN) is proposed. Based on the back propagation learning algorithm, the specific structure and optimal parameters of the FB-TDNN are determined during the offline training process. The proposed parameter adaptation method and two position error compensation methods were validated through simulations in simulated wide-speed operation scenarios, including sudden speed changes. Overall, the proposed scheme fully mitigates steady-state position errors, substantially mitigates transient position errors, and exhibits good stability across a wide speed range.