General Error Model Research Articles

Modeling and simulation of optical system error transmission in the laser tracker

The optical system of the laser tracker utilizes plane mirrors to construct a reflective path, reducing its size and weight. However, maintaining the alignment of the laser with the ideal optical axis during its propagation in the optical system poses significant challenges in the design, fabrication, and assembly of the optical system. This paper explores the principle of error propagation during the assembly process of the optical system and improves the accuracy of the output laser through a numerical simulation and optimization methods. A general error model for the optical system is established to understand the principle of error propagation. A Monte Carlo numerical simulation and sensitivity analysis are used to study the influence of various errors on the accuracy of the output laser. The machining errors are optimized using a simulated annealing method to balance the manufacturing difficulty and system accuracy. The assembly process is also optimized to reduce the degrees of freedom and the number of optical parts required, and verified by experiments. The experimental results indicate that the average position error of the output laser is 15.743 µm, and the average angle error is 1.427′′. This study provides what we believe is a novel approach and methodology for the design and alignment of optical systems.

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.

Simultaneous compensation of geometric and compliance errors for robotics with consideration of variable payload effects

In order to satisfy the high accuracy requirements of robotic applications, it is necessary to consider not only the geometric errors but also the compliance errors which are caused by the self-gravity of the link and the external payloads. A general error model is developed based on the modified Denavit-Hartenberg (DH) model. For the parameters in the error model, there is a coupling between the compliance coefficients and the link parameters, making it difficult to use only the compliance coefficients to compute the compliance errors due to external payloads. As the external payload for the robot manipulator varies, the parameter identification of the model should be conducted again. In this paper, a novel algorithm using a variable payload method is proposed to first identify the compliance coefficients using different payloads and end effector position information. Second, the kinematic parameter errors and link parameters are identified with the given compliance coefficients. Then, the algorithm generates a modified trajectory using the calibrated DH tables for the precision compensation. Simulation and experimental results demonstrate that the positioning accuracy can be improved by 80 % to 90 % even under different payloads. The root mean square, mean, maximum, and standard deviation of the residual errors by using the proposed algorithm could outperform the conventional kinematic algorithm.

Geometric error self-calibration method of five-axis dispensing machine based on the product of exponentials formula

Geometric error identification and kinematic calibration are common and effective methods for improving the machining accuracy of five-axis machines. Compared with the traditional measurement methods characterized by complicated inspection processes and high cost, this paper proposes a self-calibration method for a five-axis dispensing machine based on monocular vision and the product of the exponentials formula. The proposed method can automatically identify geometric errors and complete kinematic calibration, even for simultaneous five-axis motion. First, a ChArUco marker-based pose detection system is designed to achieve a wide range of calibration space for a five-axis dispensing machine. Based on this, the proposed sub-pixel checkpoint detection framework has higher pose detection performance accuracy at different depths of the field. Then, a general kinematic error model of five-axis machines is established using screw theory to avoid singularities. Moreover, the identification method of its geometric error is proposed for an RRTTT-type five-axis dispensing machine. Finally, an arc-shaped dispensing trajectory for the 3D glasses' inner wall is used for experimental validation. The experimental results show that the average orientation quantization error decreases from 0.0112 rad to 0.0039 rad. In contrast, the average position error decreases from 0.1627 mm to 0.0473 mm before and after the self-calibration, respectively. Thus, the convenience, effectiveness, and accuracy of the self-calibration method are validated on this five-axis dispensing machine.

A comprehensive error evaluation method for non-rigid body gantry machine tools considering quasi-static crosstalk based on optimized multilateration measurement

For large-scale machine tools, the impact of non-rigid body behavior on volumetric error accuracy cannot be ignored, which hasn't been considered in general volumetric error model. This paper presents a comprehensive error evaluation method for large-scale gantry machine tools considering non-rigid body effect, aiming to provide guidance for volumetric error calibration process. An extended kinematic model is established based on the analysis of crosstalk influence on geometric error motions. An optimized multilateration measurement with improved accuracy and robustness is carried out for volumetric error identification, verified by Monte Carlo simulations. The main novelty of the optimization is to introduce a space uniformity index to generate specialized calibration point sets for any measurement points. A new volumetric error prediction method based on classified descriptions of geometric error motions is proposed, according to their relationship with crosstalk. Experimental results show that the proposed method achieves higher prediction accuracy in crosstalk-sensitive directions.

An Adaptive Decoupling Register Control Method for Roll-to-Roll Printing Systems

Abstract Model-based decoupling control methods have been widely used in the register control of Roll-to-Roll (R2R) printing systems due to their advantage in dealing with couplings. While they achieve a certain decoupling effect, their registrations are influenced by the accuracy of the model and decoupling compensation. In this paper, a hybrid model is presented to calculate an appropriate compensation to eliminate the complex velocity-error relations in the R2R system, which consists of a general register error model and a data-based supplement model. Then, an adaptive decoupling control (ADC) method is proposed, in which the feedback gains are determined by solving a Riccati equation. The effectiveness of the hybrid model is validated by experiments, while the superior performance of the ADC is demonstrated by simulations. The results indicate that the hybrid model is more accurate than the general model and ADC method can rapidly reduce the register errors into a range of ±10 μm. In addition, simulated comparisons of ADC, direct decoupling proportional differential (DDPD), and improved DDPD control methods also show that the ADC owns the highest register precision and smoothest control signal.

A Unified Bayesian Framework for Joint Estimation and Anomaly Detection in Environmental Sensor Networks

Advanced large-scale environmental monitoring systems relying on the emerging aerial/terrestrial technologies of wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs), and mobile crowdsensing, impose strong requirements on the reliability of the collected data. Unfortunately, sensing units can suddenly suffer unexpected anomalies due to accidental faults or malicious causes. Outlier detection methods have been widely employed to identify and discard unreliable measurements from large data sets, but further improvements in the sensing processes can be obtained by adopting advanced signal processing algorithms that take full advantage of all the collected information without rejecting the measurements. In this paper, we propose a novel unified Bayesian framework that enable simultaneous estimation of a common parameter of interest and identification of multiple and possibly different types of anomalies that can affect sensors in environmental sensor networks. Specifically, we consider two rather general error models based on Gaussian mixtures able to capture different variations affecting the quality of the collected measurements. For each model, we illustrate the optimal joint maximum-likelihood and maximum a-posteriori (ML-MAP) estimation method, which represents the benchmark for the problem at hand, and propose novel reduced-complexity two-step algorithms able to achieve almost the same performance of the joint ML-MAP, but at a fraction of its computational cost. The derivations of all the algorithms are also extended to handle the more general case in which the probability of occurrence of anomalies is unknown and should be inferred from the data using an Empirical Bayes approach. Extensive performance analyses using both synthetic and real experimental data acquired in a network of environmental monitoring stations deployed in the Apulia region, south of Italy, demonstrate the effectiveness of the proposed framework.

Robust Adaptive General Formation Control of a Class of Networked Quadrotor Aircraft

This article is concerned with the consensus formation control problem of a class of networked quadrotor aircraft partially bounded and state-dependent perturbations. A general distributed consensus error model is first developed to formulate the formation behavior of the networked quadrotor aircraft. Then, by using adaptive techniques, virtual position control strategies are proposed to eliminate the impacts of perturbations, so that the following quadrotor aircraft can boundedly track the desired position trajectory with a satisfying pattern. Furthermore, based on the designed virtual position control strategies, the attitude reference angles are constructed and adaptive attitude control strategies are further designed to guarantee that the attitude angles track the reference angles asymptotically. In terms of the asymptotic tracking results of attitude control systems, the bounded consensus formation results are obtained based on the Lyapunov stability theorem. Numerical simulations are carried out to verify the efficiency of the designed position formation as well as attitude tracking control strategies of the networked quadrotor aircraft.

Determining quantum topological semion code decoder performance and error correction effectiveness with reinforcement learning

Quantum error correction technology is a vital method to eliminate noise during the operation of quantum computers. To solve the problem caused by noise, in this paper, reinforcement learning is used to encode defects of Semion codes, and the experience replay technique is used to realize the design of decoder. Semion codes are quantum topological error correction codes with the same symmetry group Z2 as Kitaev toric codes, we used the topological characteristics of error correction codes to map qubits to multi-dimensional space, and error correction accuracy of the decoder is calculated to be 77.5%. Calculate the threshold of topological quantum Semion code, depending on the code distance, resulting in different thresholds, pthreshold = 0.081574 when the code distance is d = 3, 5, 7 and threshold pthreshold = 0.09542 when the code distance is d = 5, 7, 9. And we design the Q-network to optimize the cost of quantum circuit gates and compare the size of the cost reduction under different thresholds. Reinforcement learning is an important method for designing Semion code decoders and optimizing numerical values, providing more general error models and error correction codes for future machine engineering decoders.

Redundant Parallel Beam Multiaxis Force Sensor—Accuracy Space

The principle of the redundant parallel beam multi-axis force sensor is a transformation from displacement domain to force domain. This paper proposed a general force error model of a distributed force measurement system with redundant multi-axis force sensors based on the measurement <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$/$ </tex-math></inline-formula> surveying adjustment method to transform displacement sensor errors to force errors. The optimum accuracy space is defined according to the error model. According to the accuracy space, the torque error increase sharply when the measuring point is far away from the optimum accuracy space, but the force error remains constant. A long-distance arrangement of displacement sensors can increase the size of the optimum accuracy space and a high-precision displacement sensor can increase the measurement accuracy in the whole space. A deformation filter can minimize the affection of the loading platform deformation on the measurement accuracy. A dual-measurement system is recommended to increase both the force accuracy and the torque accuracy when the measuring point is far from the optimum accuracy space of the main multi-axis force sensing system. The error point cloud is used to verify the proposed error model.

Improved unscented Kalman filter algorithm-based rapid identification of thermal errors of machine tool spindle for shortening thermal equilibrium time

Thermal equilibrium of machine tools is needed before machining to ensure the accuracy. To shorten the warm-up time and improve the machining efficiency, a rapid identification of thermal errors is proposed. It can predict the thermal errors in the shortest identification time so that the thermal error compensation can be started in advance to shorten the thermal equilibrium time. A Singular Value Decomposition-Adaptive Unscented Kalman Filter algorithm (SVD-AUKF) is proposed with singular value decomposition and adaptive rule for the fast identification. A general exponential thermal error model is established and applied into the SVD-AUKF. RMSE of the thermal error data within each time is calculated for the evaluation to obtain the shortest identification time. K hysteresis rule, Δt judgment rule and maximum time rule are proposed for the prediction accuracy. Different experiments are proposed with two machine tools to testify the effectiveness of the shortest identification time.

Qubit readout error mitigation with bit-flip averaging.

Quantum computers are becoming increasingly accessible and may soon outperform classical computers for useful tasks. However, qubit readout errors remain a substantial hurdle to running quantum algorithms on current devices. We present a scheme to more efficiently mitigate these errors on quantum hardware and numerically show that our method consistently gives advantage over previous mitigation schemes. Our scheme removes biases in the readout errors, allowing a general error model to be built with far fewer calibration measurements. Specifically, for reading out n-qubits, we show a factor of 2n reduction in the number of calibration measurements without sacrificing the ability to compensate for correlated errors. Our approach can be combined with, and simplify, other mitigation methods, allowing tractable mitigation even for large numbers of qubits.

A Novel Linear Calibration Model for Three-Axis Fluxgate Magnetometer

With low cost, simple structure and high accuracy, the three-axis fluxgate magnetometer (TFM) has been frequently used in many fields. However, the systematic errors are a major obstacle to the performance of TFM. Based on Taylor expansion and Cholesky decomposition, a new linear error calibration model is proposed from the general error model of TFM. In our new model, the parameter matrix can be decomposed to two parts: one is completely equivalent to the parameter matrix of the traditional linear model, and the other is a matrix containing second-order terms composed of error parameters, which was neglected in the traditional linear model. Thus, compared with the traditional model, our new linear model can acquire better calibration performances. In simulations, the functional link artificial neural network algorithm is provided to solve the model parameters. Simulation results show that the new model improves the calibration effect by 32.9 to 33.8% compared with the existing linear calibration model. After that, a single three-axis fluxgate magnetometer experimental platform is set up and related physical experiment is carried out. The results further prove the advantages and the practical value of the proposed model. Compared with the reference method, the effect is improved by 79.3%. The conclusions of this paper can expand the linear calibration method of three-axis magnetometer and improve the accuracy of such methods.

A General Design Method for Phasor Estimation in Different Applications

Driven by the increasing development and complexity of bulk power systems, the requirements of phasor estimation methods differ for different scenarios and applications. In this study, a general design method for phasor estimation algorithms in different applications is proposed based on a complex finite impulse response (FIR) bandpass filter. A design framework based on mathematical error models is proposed to facilitate the design of a complex bandpass filter for different requirements and to reduce the trial and error process. The general error models between the filter gain and the error limitations of all variables measured by the phasor measurement units (PMUs) are established separately, according to the absolute value inequality. The filter design criteria obtained from the error models can determine the passband and stopband gain range of the complex bandpass filters. Three phasor algorithms for different classes of PMUs are designed, and their performances are validated and compared using experimental tests. The results demonstrate that the proposed method can design phasor algorithms to provide accurate measurements under different scenarios.

General first-order target registration error model considering a coordinate reference frame in an image-guided surgical system.

Point-based rigid registration (PBRR) techniques are widely used in many aspects of image-guided surgery (IGS). Accurately estimating target registration error (TRE) statistics is of essential value for medical applications such as optically surgical tool-tip tracking and image registration. For example, knowing the TRE distribution statistics of surgical tool tip can help the surgeon make right decisions during surgery. In the meantime, the pose of a surgical tool is usually reported relative to a second rigid body whose local frame is called coordinate reference frame (CRF). In an n-ocular tracking system, fiducial localization error (FLE) should be considered inhomogeneous, that means FLE is different between fiducials, and anisotropic that indicates FLE is different in all directions. In this paper, we extend the TRE estimation algorithm relative to a CRF from homogeneous and anisotropic to heterogeneous FLE cases. Arbitrary weightings can be assumed in solving the registration problems in the proposed TRE estimation algorithm. Monte Carlo simulation results demonstrate the proposed algorithm's effectiveness for both homogeneous and inhomogeneous FLE distributions. The results are further compared with those using the other two algorithms. When FLE distribution is anisotropic and homogeneous, the proposed TRE estimation algorithm's performance is comparable with that of the first one. When FLE distribution is heterogeneous, proposed TRE estimation algorithm outperforms the other two classical algorithms in all test cases when ideal weighting scheme is adopted in solving two registrations. Possible clinical applications include the online estimation of surgical tool-tip tracking error with respect to a CRF in IGS. Graphical Abstract This paper provides the target registration error model considering a coordinate reference frame in surgical navigation.

A Simple and Precise Correction Method for DVL Measurements Under the Dynamic Environment

To mitigate the Doppler velocity logs (DVL) measurement errors in inertial navigation system (INS)/DVL integrated navigation system under dynamic environment, a simple and precise correction method is proposed. First, the general DVL velocity measurement error model under various dynamics is explored. Then, the corresponding correction scheme is presented, which suits both frequency shift outputs and direct velocity outputs of DVL. Different from the existing approaches, no assumptions are pre-required to describe the regular patterns of the DVL velocity measurement. The attitude and velocity data of INS are well investigated to build the relationship between the DVL velocities at transmitting epoch and receiving epoch. Simulations are conducted to evaluate the effectiveness of the proposed algorithm under various trajectories, where the DVL outputs without correction and the correction methods based on constant velocity assumptions are employed for comparison. The results indicate that the existing correction methods may achieve good navigation accuracy in specific trajectories, where the motion coincides with the assumptions. However, only the proposed correction method well fits all the possible situations, which shows greater adaptability and robustness than any other existing solutions.

Quantum error correction for the toric code using deep reinforcement learning

We implement a quantum error correction algorithm for bit-flip errors on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Q-function is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which significantly simplifies the state space representation independently of the number of defect pairs. The training is done using experience replay, where data from the algorithm being played out is stored and used for mini-batch upgrade of the Q-network. We find performance which is close to, and for small error rates asymptotically equivalent to, that achieved by the Minimum Weight Perfect Matching algorithm for code distances up tod=7. Our results show that it is possible for a self-trained agent without supervision or support algorithms to find a decoding scheme that performs on par with hand-made algorithms, opening up for future machine engineered decoders for more general error models and error correcting codes.

Observing Requirements for Long-Term Climate Records at the Ocean Surface

Observations of conditions at the ocean surface have been made for centuries, contributing to some of the longest instrumental records of climate change. Most prominent is the climate data record of sea surface temperature (SST), which is itself essential to the majority of activities in climate science and climate service provision. A much wider range of surface marine observations is available however, providing a rich source of data on past climate. We present a general error model describing the characteristics of observations used for the construction of climate records, illustrating the importance of multi-variate records with rich metadata for reducing uncertainty in climate data records. We describe the data and metadata requirements for the construction of stable, multi-century marine climate data records for variables important for describing the changing climate: SST, mean sea level pressure, air temperature, humidity, winds, clouds and waves. Available sources of surface marine data are reviewed in the context of the error model. We outline the need for a range of complementary observations, including very high quality observations at a limited number of locations and also observations that sample more broadly but with greater uncertainty. We describe how high-resolution modern records, particularly those of high-quality, can help to improve the quality of observations throughout the historical record. We recommend the extension of internationally-coordinated data management and curation to observation types that do not have a primary focus of the construction of climate records. The benefits of reprocessing the existing surface marine climate archive to improve and quantify data and metadata quality and homogeneity. We also recommend the expansion of observations from research vessels and high quality moorings, routine observations from ships and from data and metadata rescue. Other priorities include: field evaluation of sensors; resources for the process of establishing user requirements and determining whether requirements are being met; and research to estimate uncertainty, quantify biases and to improve methods of construction of climate data records. The requirements developed in this paper encompass specific actions involving a variety of stakeholders, including funding agencies, scientists, data managers, observing network operators, satellite agencies and international co-ordination bodies.

Analysing correlated noise on the surface code using adaptive decoding algorithms

Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit Pauli errors are commonly used to study the behaviour of error-correcting codes, but in general we might expect the environment to introduce correlated errors to a system. Given some knowledge of structures that errors commonly take, it may be possible to adapt the error-correction procedure to compensate for this noise, but performing full state tomography on a physical system to analyse this structure quickly becomes impossible as the size increases beyond a few qubits. Here we develop and test new methods to analyse blue a particular class of spatially correlated errors by making use of parametrised families of decoding algorithms. We demonstrate our method numerically using a diffusive noise model. We show that information can be learnt about the parameters of the noise model, and additionally that the logical error rates can be improved. We conclude by discussing how our method could be utilised in a practical setting blue and propose extensions of our work to study more general error models.

Multi-User Analog Beamforming in Millimeter Wave MIMO Systems Based on Path Angle Information

We aim to design an analog-only beamforming scheme for downlink multi-user mm-wave systems to optimize the beamforming gain and the inter-user interference at the same time. Traditional analog beamforming schemes, such as the beam selection method, use the array response vector corresponding to the strongest path of the channel to generate a beam pointing to the user. In multi-user systems, such schemes will lead to large inter-user interference, especially when the users are closely located. In this paper, we formulate a multi-objective problem to strike a balance between the beamforming gain and the inter-user interference. To solve the problem, we first use the weighted-sum method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the analog beamforming with constant-magnitude constraints tractable. Furthermore, to alleviate the effects of the channel estimation and feedback quantization errors, we design a robust beamforming scheme to provide robustness against imperfect channel information. We first develop a channel error model for the scattering clustered channel model, which can serve as a general channel error model for the mm-wave channels. Then, we formulate a multi-objective problem using the stochastic approach to suppress the interference and enhance the beamforming gain at the same time. The simulation results show that our proposed non-robust multi-user analog beamformer outperforms the traditional analog beamforming method when the SNR is high and our proposed robust beamformer can provide up to 109% improvement in the sum-rate compared with the beam selection method.