Linear Error Research Articles

Evaluating the accuracy of one-piece and three-piece 3D-printed indirect bonding transfer trays: An in vitro study.

Recent developments in computer-aided design/computer-aided manufacturing (CAD/CAM) and 3D printing have enabled the fabrication of digital indirect bonding (IDB) transfer trays. These modern products require thorough investigation. The aim of the study was to determine the accuracy of one-piece and three-piece IDB transfer trays in vitro. An initial dental scan (IDS) of a randomly selected patient with digitally positioned brackets served as the master scan (MS) for designing 16 IDB transfer trays of each type. They were 3D printed and used for bonding 448 brackets to the models. Subsequently, the models were scanned with a TRIOS® 3 Intraoral Scanner (3Shape A/S, Copenhagen, Denmark), producing actual scans (ASs). The accuracy of bracket positioning was measured digitally on both MSs and ASs. The measurements were compared to the Objective Grading System for dental casts provided by the American Board of Orthodontics (ABO). The 2 types of IDB transfer trays showed comparable accuracy. All linear errors were within the clinically acceptable range, whereas the angular measurements demonstrated significant variability, resulting in clinically unacceptable transfer errors that ranged from 3.3% to 90.3%. The study results cannot be unconditionally extrapolated to other types of IDB transfer trays due to the diversity of their properties and features. The study evaluated the in vitro accuracy of IDB transfer trays. The revealed number of errors may be even higher in vivo due to limitations in visibility, salivary flow, interference from the tongue, and difficulties in achieving a proper fit of the IDB transfer tray to the teeth.

Biofidelity and Limitations of Instrumented Mouthguard Systems for Assessment of Rigid Body Head Kinematics.

Instrumented mouthguard systems (iMGs) are commonly used to study rigid body head kinematics across a variety of athletic environments. Previous work has found good fidelity for iMGs rigidly fixed to anthropomorphic test device (ATD) headforms when compared to reference systems, but few validation studies have focused on iMG performance in human cadaver heads. Here, we examine the performance of two boil-and-bite style iMGs in helmeted cadaver heads. Three unembalmed human cadaver heads were fitted with two instrumented boil-and-bite mouthguards [Prevent Biometrics and Diversified Technical Systems (DTS)] per manufacturer instructions. Reference sensors were rigidly fixed to each specimen. Specimens were fitted with a Riddell SpeedFlex American football helmet and impacted with a rigid impactor at three velocities and locations. All impact kinematics were compared at the head center of gravity. The Prevent iMG performed comparably to the reference system up to ~ 60g in linear acceleration, but overall had poor correlation (CCC = 0.39). Prevent iMG angular velocity and BrIC generally well correlated with the reference, while underestimating HIC and overestimating HIC duration. The DTS iMG consistently overestimated the reference across all measures, with linear acceleration error ranging from 10 to 66%, and angular acceleration errors greater than 300%. Neither iMG demonstrated consistent agreement with the reference system. While iMG validation efforts have utilized ATD testing, this study highlights the need for cadaver testing and validation of devices intended for use in-vivo, particularly when considering realistic (non-idealized) sensor-skull coupling, when accounting for interactions with the mandible and when subject-specific anatomy may affect device performance.

A short-term power load forecasting system based on data decomposition, deep learning and weighted linear error correction with feedback mechanism

Accurate power load forecasting enables Independent System Operators (ISOs) to precisely quantify the demand patterns of users and achieve efficient management of the smart grid. However, with the increasing variety of power consumption patterns, the power load data displays increasingly irregular characteristics, which posing great challenges for accurate load forecasting. In order to solve above problem, a novel power load forecasting system is proposed based on data denoising, customized deep learning and weighted linear error correction. Specifically, we first proposed an improved optimization algorithm IGWO-JAYA which enhanced the Grey Wolf Optimizer (GWO) algorithm by using Halton low-discrepancy sequence and the mechanism of JAYA algorithm. In data denoising, the proposed optimizer was employed to optimize the Variational Mode Decomposition (VMD), enabling data-driven intelligent denoising. The customized deep learning framework contained multi-layer Convolution Neural Network (CNN), Bi-directional Long Short-Term Memory (Bi-LSTM) and Multi-Head Attention mechanism. The effective integration of these layers can significantly improve the capacity for nonlinear fitting of deep learning. In weighted linear error correction, the IGWO-JAYA algorithm was employed to determine the appropriate weight for point forecasting values and residual forecasting values. By weighting them, the forecasting precision has been further enhanced. To verify the forecasting ability of the system, we conducted experiments on power load datasets from four states in Australia and found that it has the best performance compared with all rivals. In the discussion, we demonstrated the convergence efficiency of the IGWO-JAYA algorithm by CEC test function.

Design of Fluxgate Current Sensor Based on Magnetization Residence Times and Neural Networks.

This study introduces a novel fluxgate current sensor with a compact, ring-shaped configuration that exhibits improved performance through the integration of magnetization residence times and neural networks. The sensor distinguishes itself with a unique magnetization profile, denoted as M waves, which emerge from the interaction between the target signal and ambient magnetic interference, effectively enhancing interference suppression. These M waves highlight the non-linear coupling between the magnetic field and magnetization residence times. Detection of these residence times is accomplished using full-wave rectification circuits and a Schmitt trigger, with a digital output provided by timing sequence detection. A dual-layer feedforward neural network deciphers the target signal, exploiting this non-linear relationship. The sensor achieves a linearity error of 0.054% within a measurement range of 15 A. When juxtaposed with conventional sensors utilizing the residence-time difference strategy, our sensor reduces linearity error by more than 40-fold and extends the effective measurement range by 150%. Furthermore, it demonstrates a significant decrease in ambient magnetic interference.

Real-time haptic characterisation of Hunt-Crossley model based on radial basis function neural network for contact environment

Dynamic soft tissue characterisation is an important element in robotic minimally invasive surgery. This paper presents a novel method by combining neural network with recursive least square (RLS) estimation for dynamic soft tissue characterisation based on the nonlinear Hunt-Crossley (HC) model. It develops a radial basis function neural network (RBFNN) to compensate for the error caused by natural logarithmic factorisation (NLF) of the HC model for dynamic RLS estimation of soft tissue properties. The RBFNN weights are estimated according to the maximum likelihood principle to evaluate the probability distribution of the neural network modelling residual. Further, by using the linearisation error modelled by RBFNN to compensate for the linearised HC model, an RBFNN-based RLS algorithm is developed for dynamic soft tissue characterisation. Simulation and experimental results demonstrate that the proposed method can effectively model the natural logarithmic linearisation error, leading to improved accuracy for RLS estimation of the HC model parameters.

Small-sample linear profile error uncertainty assessment based on grey system

The uncertainty assessment of the profile error of the cam profile, as defined in the national standard method, is difficult to carry out under conditions of small sample size and absence of probability distribution assumptions. This paper proposes a small-sample assessment model for the uncertainty of the profile error based on grey system. Firstly, the coordinate transformation is conducted using Vector Alignment Method to reduce systematic errors, and the non-uniform rational B-splines curve interpolation is utilized to fit the cam profile curve and perform error assessment. Subsequently, based on the error assessment results, Grey Information Measurement Model (GIMM) for the uncertainty of the profile error in small samples is established. This model employs Grey Relational Analysis to eliminate outliers and evaluates the uncertainty of the profile error by solving grey correlation coefficients. Maximum-Minimum Information Measure Method is used to assess the optimal sample size. Finally, numerical experiments and experimental tests were conducted on the uncertainty of camshaft profile error in automobiles. A total of 15 sets of profile data were compared with Guide to the Representation of Uncertainty in Measurement (GUM) and Monte Carlo Method (MCM) under different sample sizes. The results showed that GIMM achieved evaluation with only 8 sets of data samples under small sample and poor information conditions, with an uncertainty of 0.6338 μm, compared to 0.6346 μm for GUM and 0.6391 μm for MCM. The acceptance rate of GIMM reached 95.2%. This model outperforms other methods, providing a simplified and reliable assessment of cam profile error uncertainty.

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement. We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control (CNC) machine tools. This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method. We consider a three-axis gantry-type CNC machine tool, and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain. The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle. A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg–Marquardt nonlinear least squares method, and the geometric error is solved using Taylor’s first-order linearization iteration. The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer. For a volume of 800 mm × 1000 mm × 350 mm, the maximum differences of the linear, angular, and spatial position errors were 2.0 μm, 2.7 μrad, and 12.0 μm, respectively, which verifies the accuracy of the proposed algorithm. This research proposes a modeling method for the precise measurement of errors in machine tools, and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

Impacts of inter-satellite links on the ECOM model performance for BDS-3 MEO satellites

Inter-satellite link (ISL) plays an essential role in current and future Global Navigation Satellite System (GNSS). In this study, we investigate the impact of ISL observations on precise orbit determination for BeiDou-3 Navigation Satellite System (BDS-3) Medium Earth Orbit (MEO) satellites based on different Extended CODE Orbit Models (ECOM). Thanks to the better observation geometry of the Ka-band ISL data compared to the L-band data for BDS-3 MEO satellites, the ISL solution substantially reduces Orbit Boundary Discontinuity (OBD) errors, except for C30, which suffers from unstable Ka-band hardware delay. From the external quality analysis, ISL significantly enhances the reliability of the orbit of MEO satellites manufactured by the China Academy of Space Technology (CAST). The standard deviation (STD) of the satellite laser ranging (SLR) residuals is approximately 2.5 cm, and the root mean square (RMS) is reduced by 10–23% compared to L-band solutions. Besides, the Sun-elongation angle dependent systematic error in SLR residuals nearly vanishes based on the reduced 5-parameter ECOM (ECOM1) or extended 7-parameter ECOM (ECOM2) with ISL data. This is because the ISL reduces the correlation between state parameters and solar radiation pressure (SRP) parameters as well as those among SRP parameters, leading to a more accurate estimation of both orbit and SRP perturbations, particularly those along B direction. This confirms that the deficiency of the SRP models for BDS-3 CAST satellites can be compensated by using better observation geometry from ISL data. On the other hand, for the satellite manufactured by Shanghai Engineering Center for Microsatellites (SECM), the ISL allows for a more accurate estimation of the Bc1 parameter in the ECOM1 model. This only reduces linear systematic error, possibly because the impact generated by the satellite bus cannot be entirely absorbed by the B-direction parameters.

Cylindrical hot cathode ionisation gauge – Construction and testing

Hot cathode ionisation gauges are indispensable in measuring high and ultra-high vacuum. In the present work the construction details and the metrological evaluation of a novel gauge design — the cylindrical ionisation gauge is presented. With the aim of enhancing accuracy and stability both in the short and long term, details of the mechanical assembling of electrodes and precautions to minimize leakage currents influencing ion current measurement are described. Performance evaluations demonstrate high short-term stability, with linearity error, reproducibility, and repeatability values consistently below 1 %, placing the gauge at the same level as the most stable ionisation gauges. Operating across a pressure range of at least 6 orders of magnitude, the gauge exhibits low linearity error from high to ultra-high vacuum ranges. Its capability to measure pressures below 10−9 mbar remains open and requires further investigation.

Accurate kinematic calibration of a six-DoF serial robot by using hybrid models with reduced dimension and minimized linearization errors

PurposeIn typical model-based calibration, linearization errors are derived inevitably, and non-negligible negative impact will be induced on the identification results if the rotational kinematic errors are not small enough or the lengths of links are too long, which is common in the industrial cases. Thus, an accurate two-step kinematic calibration method minimizing the linearization errors is presented for a six-DoF serial robot to improve the calibration accuracy.Design/methodology/approachThe negative impact of linearization on identification accuracy is minimized by removing the responsible linearized kinematic errors from the complete kinematic error model. Accordingly, the identification results of the dimension-reduced new model are accurate but not complete, so the complete kinematic error model, which achieves high identification accuracy of the rest of the error parameters, is combined with this new model to create a two-step calibration procedure capable of highly accurate identification of all the kinematic errors.FindingsThe proportions of linearization errors in measured pose errors are quantified and found to be non-negligible with the increase of rotational kinematic errors. Thus, negative impacts of linearization errors are analyzed quantitatively in different cases, providing the basis for allowed kinematic errors in the new model. Much more accurate results were obtained by using the new two-step calibration method, according to a comparison with the typical methods.Originality/valueThis new method achieves high accuracy with no compromise on completeness, is easy to operate and is consistent with the typical method because the second step with the new model is conveniently combined without changing the sensors or measurement instrument setup.

Three-dimensional micro-force measurement method based on broadband optical coherence

In response to the high-precision and multi-dimensional force measurement requirements in the fields of biology and medicine, this paper proposes a novel three-dimensional microforce measurement method based on the broadband optical coherence. A novel, compact, and low-coupling elastic element was designed, with a maximum outer diameter of 26 mm and a capacity of 50 g in the X-, Y-, and Z-directions, respectively. The functional relationship between the displacements of the three detecting points on the elastic element and the applied external force was derived based on the elastic mechanics theory. And it was also verified by the finite element method. A self-built optics system was set up to sense the displacements of the three points on the elastic element. The experiments results showed that the resolution in the X-, Y-, and Z-directions was 0.10 mN, 0.11 mN and 0.13 mN, respectively. In the measuring range of (10–50) g, the maximum coupling rate was 4.55 %, and the maximum linear error was 4.70 %. The maximum repeatability error was only 0.615 %. The method and sensor were verified with good characteristics of high resolution, low coupling rate, high linearity and high accuracy, comparing to other reported researches. The multi-dimensional force measuring method could be used in the fields of biology and medicine.

A new kernel two-parameter prediction under multicollinearity in partially linear mixed measurement error model

A Partially linear mixed effects model relating a response Y to predictors ( X , Z , T ) with the mean function X T β + Zb + g ( T ) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.

A dislocation-based finite element method for plastic collapse assessment in solid mechanics

A displacement-based dislocation map has been used to build the eigenstress stress, which is the base of the structure’s limit analysis. The limit load has been calculated as the upper bound of any equilibrated stress that respects the compatibility inequalities by means of a linear optimization program. The eigenstress stress nodal parameters were assumed as the design variables, and the compatibility inequalities have been obtained from the Mises–Schleicher criterion, assuming that the stress belongs to the corresponding plastic domain. The numerical application has considered a linear secant representation of the domain, with a penalty factor on stresses, to correct the linearization error. Examples concerning a simply supported cantilever beam, a pipe section, and a plate with a circular hole highlighted the accuracy of the procedure with respect to the established literature. Moreover, the procedure has been applied to investigate plane structure examples. A square plate with variable elliptic holes has been analyzed, and the influence of ellipticity on the collapse load has been shown. The effects of porosity and heterogeneity of the structure with respect to the collapse load are shown considering the porous cantilever and representative volume element. The evaluation of the limit load along different element directions envisaged a point-wise calculation of the compatibility domain of the porous material to be used in the macro-scale analysis of the structures made of porous micro-cells.

A fully actuated system approach: Desired compensation adaptive robust control for uncertain nonlinear systems

A desired compensation adaptive robust control (DCARC) framework is presented for two types of fully actuated systems (FASs) subject to both parametric and nonlinear uncertainties based on the Lyapunov theory. The designed controller consists of three parts: (i) a fundamental linear state error feedback term; (ii) an adaptive feedforward compensation term; (iii) a robust compensation term. Different from the existing FAS approaches, the adaptive compensation in the proposed controller relies on the noise-free desired trajectory and online parameter estimate only. A better overall tracking performance with an accelerated transient response is expected, arising from significantly reducing interaction between the robustness part and the adaptation part. Through theoretical analysis, the proposed controller ensures that the estimation error of the unknown parameter vector and the tracking error finally converge to a bounded ellipsoid. The comparative simulation of a permanent magnet (PM) stepper motor demonstrates the effectiveness of the presented approach.

Hybrid Optimized LMMSE-Based Channel Estimation with Low Power Trellis Coded Modulation

Data transfer in a wireless channel environment is plagued by numerous security issues and power transmission loss. Channel state information is crucial to attaining the performance benefit of reconfigurable intelligent surfaces (RISs) in wireless systems. Because of the Doppler effect, mobility makes accurate channel estimate (CE) more difficult. The parameter estimation approach is employed as an alternative to direct estimation in the channel matrix to address the aforementioned problems. Also, to lower the Mean Square Error (MSE) between the estimated and original channel, training-based CE, such as Linear Minimum Mean Square Error (LMMSE), and Least Square Error (LSE), are widely used in some wireless standards. To optimize the channel, certain intelligent optimized strategies are presented. For the Optimal CE, a Trellis Coded Modulation (TCM) with hybrid optimization in LMMSE has been provided. Moth amalgamated Elephant Herding Optimization (MAEHO) algorithm is the proposed hybrid optimization. Finally, the performance of the accepted model is determined in comparison to other existing techniques using a variety of metrics.

Minimizing electric fields and increasing peripheral nerve stimulation thresholds using a body gradient array coil.

To demonstrate the performance of gradient array coils in minimizing switched-gradient-induced electric fields (E-fields) and improving peripheral nerve stimulation (PNS) thresholds while generating gradient fields with adjustable linearity across customizable regions of linearity (ROLs). A body gradient array coil is used to reduce the induced E-fields on the surface of a body model by modulating applied currents. This is achieved by performing an optimization problem with the peak E-field as the objective function and current amplitudes as unknown variables. Coil dimensions and winding patterns are fixed throughout the optimization, whereas other engineering metrics remain adjustable. Various scenarios are explored by manipulating adjustable parameters. The array design consistently yields lower E-fields and higher PNS thresholds across all scenarios compared with a conventional coil. When the gradient array coil generates target gradient fields within a 44-cm-diameter spherical ROL, the maximum E-field is reduced by 10%, 18%, and 61% for the X, Y, and Z gradients, respectively. Transitioning to a smaller ROL (24 cm) and relaxing the gradient linearity error results in further E-field reductions. In oblique gradients, the array coil demonstrates the most substantial reduction of 40% in the Z-Y direction. Among the investigated scenarios, the most significant increase of 4.3-fold is observed in the PNS thresholds. Our study demonstrated that gradient array coils offer a promising pathway toward achieving high-performance gradient coils regarding gradient strength, slew rate, and PNS thresholds, especially in scenarios in which linear magnetic fields are required within specific target regions.

Phase Noise Effects on OFDM Chirp Communication Systems: Characteristics and Compensation

Orthogonal frequency-division multiplexing (OFDM) chirp waveforms are an attractive candidate to be a dual-function signal scheme for the joint radar and communication systems. OFDM chirp signals can not only be employed to transmit communication data through classic phase modulation, but also can perform radar detection by applying linear frequency modulation for subcarriers. However, the performance of the OFDM chirp communication system under the phase noise environment still remains uninvestigated. This paper tries to discuss the influence of phase noise on OFDM chirp communication systems and proposes effective phase noise estimation and compensation methods. We find that the phase noise effect on OFDM chirp communication systems consists of a common phase error (CPE) and an inter-carrier interference (ICI). If not compensated, the performance of the dual-function systems can be seriously degraded. In particular, an exact expression for the signal-plus-interference to noise ratio (SINR) for the OFDM chirp communication system is derived and some critical parameters are analyzed to exhibit the phase noise effects on system performance. Moreover, two low-complexity estimation approaches, maximum likelihood (ML) and linear minimum mean square error (LMMSE), as well as two compensation approaches, the de-correlation and cancellation algorithms, are respectively utilized to eliminate the phase noise impairment. Finally, the phase noise effects and the effectiveness of the compensation approach are verified by extensive numerical results.

Singularity-free adaptive control of discrete-time linear systems without prior knowledge of the high-frequency gain

This paper proposes a new output feedback model reference adaptive control (MRAC) method for discrete-time linear time-invariant systems with arbitrary relative degrees. The proposed method does not require any prior knowledge of the high-frequency gain represented by kp, thereby completely eliminating the common design condition in the traditional discrete-time MRAC framework: the sign of kp is known, as well as an upper bound on |kp|. Specifically, an output feedback adaptive control law is developed, which incorporates a time-varying gain function to effectively address the singularity issue. The developed adaptive control law leads to the derivation of a linear estimation error equation for the closed-loop system. Consequently, a gradient algorithm based parameter update law is directly formulated by utilizing the estimation error and some other available signals without requiring any prior knowledge of kp. In comparison to the traditional MRAC and Nussbaum function-based methods, it does not necessitate any additional design conditions or involve any transient performance issues, while still ensuring closed-loop stability and asymptotic output tracking for any given bounded reference signal. The simulation study showcases the design procedure and evaluates the efficacy of the proposed control method.

Monetary policy, threshold of profitability and dynamics of private investment in the West African Economic and Monetary Union

This study investigates the interactions between optimal monetary policy, investment profitability thresholds, and private sector investment dynamics within the West African Economic and Monetary Union. Analyzing data from 2000 to 2021, it employs advanced econometric models (linear, asymmetric, and threshold effect dynamic panel error correction models) to provide a nuanced understanding of the investment environment in the union. The findings reveal the confluence of low returns and high borrowing costs for private investment. Notably, this study suggests that simply pursuing an expansionary monetary policy does not offer a sufficient solution. Instead, it proposes a more accommodative stance by the Central Bank, featuring lower policy rates, to alleviate the negative impact of high credit costs on private investment and ultimately stimulate economic activity.

Adversarial Danger Identification on Temporally Dynamic Graphs.

Multivariate time series forecasting plays an increasingly critical role in various applications, such as power management, smart cities, finance, and healthcare. Recent advances in temporal graph neural networks (GNNs) have shown promising results in multivariate time series forecasting due to their ability to characterize high-dimensional nonlinear correlations and temporal patterns. However, the vulnerability of deep neural networks (DNNs) constitutes serious concerns about using these models to make decisions in real-world applications. Currently, how to defend multivariate forecasting models, especially temporal GNNs, is overlooked. The existing adversarial defense studies are mostly in static and single-instance classification domains, which cannot apply to forecasting due to the generalization challenge and the contradiction issue. To bridge this gap, we propose an adversarial danger identification method for temporally dynamic graphs to effectively protect GNN-based forecasting models. Our method consists of three steps: 1) a hybrid GNN-based classifier to identify dangerous times; 2) approximate linear error propagation to identify the dangerous variates based on the high-dimensional linearity of DNNs; and 3) a scatter filter controlled by the two identification processes to reform time series with reduced feature erasure. Our experiments, including four adversarial attack methods and four state-of-the-art forecasting models, demonstrate the effectiveness of the proposed method in defending forecasting models against adversarial attacks.