Nonlinear Error Research Articles

An integrated method for compensating and correcting nonlinear error in five-axis machining utilizing cutter contacting point data

In current five-axis computer numerical control (CNC) machining, the use of minute linear path segments as an approximation for the ideal cutter contacting (CC) point trajectory is still prevalent. However, introducing rotation axes leads to a deviation of the actual CC point trajectory from the ideal, resulting in nonlinear errors. An integrated method is proposed in this paper for compensating and correcting both the contour error, associated with the approximation of the part surface by the ideal CC point trajectory and the nonlinear error of the CC point trajectory based on the information in the CC point data. By analyzing the spatial relationship between the tool posture and the CC point path during the five-axis linear interpolation process, two adjacent machining tool positions containing CC point data information are selected as the starting and ending points of the five-axis linear interpolation machining. The ideal tool center point and the actual CC point are calculated during the interpolation process, as well as the distance and the unit vector in the perpendicular direction between the actual CC point and the ideal CC point trajectory segment. In the comprehensive error compensation and correction phase, the obtained unit vectors are used as direction vectors for error compensation, and the tool center point during interpolation is first compensated and corrected. This ensures the actual CC point and the contour curve are on the same plane. The compensation direction for contour error is calculated using the start/end tool axis vectors and the ideal CC point trajectory vectors. The size of the contour error approximating the contour curve is calculated through the chord error. A second compensation and correction are applied to the tool center point for interpolation, ultimately achieving comprehensive compensation and correction of nonlinear errors. The data calculations were conducted in the MATLAB environment using actual machining data. After compensation and correction, the contour error was reduced by 76%, the nonlinear error of the CC point trajectory decreased to below 0.88 μm, and the comprehensive nonlinear error of the CC point trajectory was reduced from 19 to 1.5 μm, a reduction of 93%. This demonstrates significant practical value in enhancing the accuracy of five-axis CNC machining. Through actual machining verification, after using the method described in this paper, the average surface roughness decreased from 1.133 to 0.220 μm, and the maximum surface roughness decreased from 6.667 to 1.240 μm. This significantly demonstrates that the compensation and correction method proposed in this paper can significantly improve the surface quality of machined parts.

High-speed and high-precision measurement of biaxial in-plane displacements: tens of nanometers principle error suppression in microprobe sensors

When the microprobe sensor is faced with the demand of high-speed biaxial displacement measurement, due to the characteristics of phase generated carrier (PGC) technology, accompanying optical intensity modulation (AOIM) and unfavorable phase modulation depth (PMD) will bring about the tens of nanometer cyclic nonlinear errors, further hindering high-speed and high-precision measurement. Herein, a light source intensity stabilization system based on semiconductor optical amplifier (SOA) feedback control is achieved to eliminate the error caused by AOIM in the presence of high-frequency and large-amplitude laser modulation. Based on this, the reasons for large nonlinear errors in biaxial measurements and the inability to ensure the stability of the accuracy of multiple measurement axes are methodically examined, and an effective nonlinear error elimination methodology based on the normalized amplitude correction of active temperature scanning is proposed. The continuity and linearity of the temperature scanning are also discussed. The performed experiments show that the above approach is capable of reducing the displacement demodulation error from the nanometer scale to the sub-nanometer scale. Further, the nonlinear error is reduced to within 0.1 nm for both measurement axes and the performance becomes consistent. The dual-axis measurement resolution of the microprobe sensor reaches 0.4 nm and the measurement speed is better than 1.2 m/s with the standard deviation of lower than 0.5 nm.

Fault-tolerant control of automatic carrier landing using direct lift control based on nonsingular terminal sliding mode and active disturbance rejection control

This paper presents a fault-tolerant control scheme, combining nonsingular terminal sliding mode and active disturbance rejection control (NTSM-ADRC) to address actuator failure and external disturbances during the automatic carrier landing process of a carrier-based aircraft using direct lift control (DLC). First, the carrier-based aircraft model, the carrier air-wake model, and the actuator fault model were established. Second, the NTSM-ADRC controller is designed, The unmodeled dynamics of the system, the air-wake disturbance, and the fault term are treated as total disturbances and estimated accurately by extended state observer (ESO). To improve the response characteristics of the controller, the nonlinear error feedback control law is designed by combining the NTSMC. The Lyapunov function is constructed to prove the stability of the closed-loop system. The controller is applied to the aircraft DLC channel, attitude auxiliary channel, and approach power compensation system. The DLC improves the performance of fixed-wing aircraft by directly generating high lift through the flaps to change the aircraft trajectory. Finally, the method is tested by introducing various types of actuator failures. Simulation results demonstrate that the designed longitudinal fault-tolerant carrier landing system exhibits strong robustness and fault tolerance, thereby improving the accuracy of aircraft landing trajectory tracking.

Overlap Time Compensation and Characteristic Analysis for Current Source Photovoltaic Grid-Connected Inverter

In the current source photovoltaic grid-connected system, to prevent the DC-link inductor from incurring an opening circuit fault, it is necessary to include the overlap time in the switching signals. However, current error and serious harmonic distortion in the inverter-side and grid-side currents are generated, which will cause additional losses and reduce the power quality of the grid, so it is important to compensate for the current error caused by the overlap time. In this paper, the relationship between the nonlinear current errors caused by the overlap time and the AC-side voltage is analyzed. Then, the mathematical expression of the low-order harmonics with losses caused by the overlap time is derived. On this basis, a current error compensation method with a discrete filter of AC-side voltage is proposed. Finally, a simulation and experiment are carried out to verify the correctness and effectiveness of the theoretical analysis and compensation scheme presented in this paper. With an overlap time of 3 μs, the THD of the grid-side current decreases from 5.93% to 1.59% after compensation.

Nonlinear error elimination using the fusion of PGC-DCM, geometric fitting, and Atan algorithms.

A phase generated carrier (PGC) demodulation scheme is always accompanied by nonlinear errors. We propose a fusion of PGC differential and cross multiplying (PGC-DCM), geometric fitting, and arctangent (Atan) algorithms for fiber optic interferometric sensors to eliminate nonlinear errors. The output amplitude of the PGC-DCM algorithm is used to judge whether the Lissajous figure of quadrature signals is larger than 1/2 ellipse arc. When the Lissajous figure exceeds 1/2 ellipse arc, the contaminated quadrature signals are corrected by the ellipse correction parameters calculated from the geometric fitting; otherwise, the previous fitting parameters are employed for correction. Geometric fitting is realized by minimizing the Sampson error, and its failure problem under small signals is solved by using the temporary stability of fitting results. Finally, desired signals are extracted from the corrected quadrature signals by the Atan algorithm. Experimental results show that the fusion combines the merits of the three algorithms and expands the application of the geometric fitting in PGC demodulation schemes.

A Picometre-Level Resolution Test Method without Nonlinearity for Heterodyne Interferometer Measurement Electronics

The wide application of displacement measurement in high-precision equipment production and high-precision metrology is placing increasing pressure on the resolution of heterodyne interferometers. However, as the core component of an interferometer, since measurement electronics includes the cross-physical process of photoelectric conversion, its resolution is rarely evaluated, either on an individual level or as a whole. Therefore, in this paper, we propose a picometer resolution test method for measurement electronics, that uses intensity modulation signals based on an AOM to replace the beat frequency interference signals, and an ordinary commercial guide rail to equivalently generate the pm-level displacement of the heterodyne interferometer under laboratory conditions. Based on the detailed analysis of the type of noise in the test device, the correlation between the light intensity and the nonlinear error was established, and nonlinearity was suppressed to 10% of the original level. Furthermore, this test method allows one to perform a 0.1 mrad phase step test at 1 MHz signal frequency, equivalent to a 2.5 pm resolution test in a double-pass heterodyne interferometer. Simultaneously, it can be directly applied to the resolution test for measurement electronics with a center frequency in the range of 1 MHz to 20 MHz.

Circuit design of a novel front readout circuit for SiC neutron detector with leakage current compensation

Radiation detectors have broad application prospects in environmental radiation monitoring, radiation source identification, biomedical imaging, space exploration, astrophysics, other radiation detection and imaging fields. Among the third generation semiconductors, the properties of 4H-SiC are more suitable for making high-temperature and strong radiation neutron detectors. SiC materials have become a current research hotspot. In this paper a special readout integrated circuit is designed for the extremely weak current pulse signal output by SiC trench neutron detector. A leakage current compensation circuit is designed for the influence of leakage current on charge sensitive amplifier(CSA) output baseline. The noise of CSA output is analyzed and the noise minimization is carried out. The circuit can quickly respond to the input signal and extract the energy and time information. The circuit is designed based on the DB Hitek 0.18μm CMOS process model. The layout design is achieved and the post-simulation is completed. Simulated results show that the equivalent input charge range of the system is about 2fC ∼ 20fC. The charge conversion gain is 88mV/fC. The nonlinear error is within 1.6 %. Moreover, the equivalent noise charge is 22e-. The circuit has the advantages of high gain, high linearity and low noise. Therefore, the circuit can effectively adapt to the characteristics of the charge signal output from SiC trench neutron detectors and amplify the output charge signal.

Gap Self-Sensing Method for Maglev System Using Partial Electromagnet Coil

The use of dedicated sensor to measure levitation gap in maglev system leads to the problems of large volume, inconvenient installation and high cost. In this article, a gap self-sensing method using partial electromagnet coil is proposed to solve these problems. The entire electromagnet coil provides levitation force, while a small part of the electromagnet coil (the subcoil) on the side facing the levitated object is injected with high frequency excitation for gap self-sensing. The theoretical derivation shows the effects of levitation gap on the impedance of the subcoil. The frequency of the injected excitation and the structure of the subcoil are determined with finite element analysis for high sensitivity. The crosstalk between the gap self-sensing system and the levitation system is suppressed by the designed signal processing based on series resonance. The prototype in this article can cover a gap measurement range of 0–20 mm for maglev ball, with a nonlinearity error of 0.2% and a measurement accuracy of 0.2 mm. The closed-loop feedback control experiment shows that the performances of the proposed gap self-sensing system meet the control requirements.

Effect of Turbulent Wind Conditions on the Dynamic Characteristics of a Herringbone Planetary Gear System of a Wind Turbine

Due to complex environmental factors, the gear transmission systems of wind turbines are continuously affected by large torque load excitation with periodic and random properties. This paper shares the load-sharing and dynamic characteristics of a herringbone planetary gear system applied in a wind turbine. The gear dynamic model is established using a typical lumped parameter method, in which the nonlinear transmission errors of the gear pairs and left and right-side coupling stiffness of the herringbone gears are included. With the help of the blade element momentum theory, the precise calculation of the hub load of the wind turbine, which is the external excitation of the gear system, is implemented, in which the wind shear, tower shadow, turbulent effect, and tip loss correction are taken into consideration. The nonlinear dynamic characteristics of the system are obtained using the Runge-Kutta method and then discussed. The results show that the turbulent effect plays a major role in the impact on the load-sharing characteristics, and a reasonable set of the support stiffness of rotational components can improve the load-sharing characteristics of the system. The purpose of this research is to provide some useful references in numerical modelling and methods for designers and researchers of wind turbine transmission systems.

A dual-stage correction approach for high-precision phase-shifter in Fizeau interferometers

This paper proposes a dual-stage correction approach for a high-accuracy phase-shifter in Fizeau laser interferometers, effectively reducing the phase shift errors in PSI (Phase-Shifting interferometry) and improving the precision of surface profile measurements. The precision of PSI depends on the displacement accuracy of the reference mirror, and the function of the phase shifter is to drive the reference mirror to generate wavelength-level displacements with nanometer-level accuracy. The first-stage correction aims to reduce the nonlinearity error of the reference mirror by ULPS (Ultra-High Linearity Phase Shifter). The second-stage correction aims to reduce the average velocity error and plane velocity uniformity error of the reference mirror by AVIC (Auto Velocity Iterative Correction). The experimental results indicate that, after the first-stage correction, ULPS exhibits a 0.05 % nonlinearity, a 2.5 nm repeatability, and a 0.2 nm resolution under a load of 20 kg, and its nonlinearity surpassing all phase-shifters documented in the literature. After the second-stage correction, the average velocity error and plane velocity uniformity error of the reference mirror are reduced to 0.07 %.

The optimal algorithm for eliminating nonlinear error in phase measurement profilometry based on global statistical phase feature function

In a digital fringe projection structured light system, the nonlinear phase error is generated by the gamma effect of both the projector, camera, and other electronic devices. One of the existing nonlinear correction methods is active correction by projecting ideal fringes as far as possible, and the other is passive compensation after capturing aberrant fringes. The former has higher accuracy but needs to capture a large number of fringe patterns, while the latter does not need many fringe patterns, but is not only greatly affected by random noise and out-of-focus effects, but also has poor accuracy. In this paper, an optimal algorithm for eliminating nonlinear error based on global statistical phase feature function (GSPF) is proposed. The phase distribution can be estimated from the difference between the global cumulative distribution function (CDF) and the normalized (CDF). For an ideal fringe pattern without nonlinear error and a fringe pattern with nonlinear error, the region wrapped by the x-axis normalized CDF is much smaller than the region wrapped by the x-axis global CDF, and the larger the nonlinear error is, the larger the difference between the two is. Therefore, the GSPF can be used for nonlinear error correction. Then the optimal nonlinear error correction is performed based on the minimum difference between the compensated phase entropy and the ideal phase entropy. The method does not require too many steps of phase-shifting, and only three fringe patterns are needed to realize accurate and robust correction. Experimental results show that the method is fast, highly accurate and robust. Using this technique, high accuracy measurements can be achieved with the traditional three-step phase-shifting algorithm.

High precision temperature measurement for cryogenic temperature sensors based on deep learning technology

Nonlinear error compensation is a significant factor that affects the measurement accuracy of temperature sensors. Cryogenic temperature sensors require a precise calibration technique to achieve accurate temperature measurements. BP (Back Propagation) neural networks are not suitable for sensor temperature prediction due to slow convergence and poor learning ability. In this study, a Chebyshev polynomial-based BiLSTM (Bi-directional Long Short-Term Memory) algorithm (C-BiLSTM) is proposed to improve the accuracy of measurement. Firstly, we demonstrate vacuum packaged temperature sensors based on zirconium oxynitride (ZrOxNy) thin films with ultra-high sensitivity at cryogenic temperatures. Secondly, a dataset consisting of sensor resistance and temperature values was obtained from five above-mentioned sensors, which contains 29 calibration points in the temperature range of 16 K-300 K measured by the Calibration System. Then, the dataset was divided into two temperature ranges (16 K-54.358 K and 40 K-300 K). In the range 16–54.358 K, 14 set-points are selected as training set and 3 set-points as testing set. In the range 40–300 K, 12 set-points are selected as training set and 2 set-points as testing set. Thirdly, a neural network model was built and trained using the TensorFlow framework. By comparing C-BiLSTM we proposed with the BP neural network and BiLSTM, the results show that the C-BiLSTM model converges faster and greatly improves the prediction accuracy after adding Chebyshev polynomial features. The fitting error and prediction error are less than 1 mK in the temperature range of 16 K-40 K. They can also keep less than 10 mK even at the wide temperature range of 40 K-300 K, which is a significant improvement respect to improving the accuracy of temperature measurement.

Feedback control of the COVID-19 outbreak based on active disturbance rejection control

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimal financial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional-–integral–-derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model.

Distributed State Estimation for Flapping-Wing Micro Air Vehicles with Information Fusion Correction.

In this paper, we explore a nonlinear interactive network system comprising nodalized flapping-wing micro air vehicles (FMAVs) to address the distributed H∞ state estimation problem associated with FMAVs. We enhance the model by introducing an information fusion function, leading to an information-fusionized estimator model. This model ensures both estimation accuracy and the completeness of FMAV topological information within a unified framework. To facilitate the analysis, each FMAV's received signal is individually sampled using independent and time-varying samplers. Transforming the received signals into equivalent bounded time-varying delays through the input delay method yields a more manageable and analyzable time-varying nonlinear network error system. Subsequently, we construct a Lyapunov-Krasovskii functional (LKF) and integrate it with the refined Wirtinger and relaxed integral inequalities to derive design conditions for the FMAVs' distributed H∞ state estimator, minimizing conservatism. Finally, we validate the effectiveness and superiority of the designed estimator through simulations.

Post-stack seismic inversion through probabilistic neural networks and deep forward neural networks

Seismic inversion, a nonlinear, non-unique-solution, and human-prone error problem, seeks the optimal solution in multivariate space, a task that AI algorithms perform better. So, inversion with AI becomes appropriate to extract information from post-stack data. A probabilistic neural network (PNN) and deep feedforward neural network (DFNN) inverted seismic data using multiattributes, and their results were compared with those provided by a model-based inversion (MBI). Applied to a post-stack volume of the Frontier Formation at the Teapot-Dome field, Wyoming-USA, the three methods provided porosity volumes (ϕ), gamma rays (GR), and Lamé impedances (µρ, λρ). The comparison between well-logs and the provided volumes revealed a reliable PNN prediction, while DFNN achieved the best geologically correlated parameter sections and a less reliable MBI prediction. The geomorphological time-slice analysis discriminated high ϕ-µρ areas and low GR–λρ areas, geologically interpreted as a deltaic environment, with distributary channels and beachfront lobes subject to the action of the tides, which agrees with the well-log interpretation and the basin geological evolution. The results enhanced the stacked section’s importance by the geological information contained, which would contribute to reducing the prospecting risk. Finally, PNN and DFNN encouraging results reaffirm their best searching-in-multivariate space ability.

Improved nonlinear active disturbance rejection control for a continuous-wave pulse generator with cascaded extended state observer

The generator rotor is crucial for the high-rate and reliable continuous-wave mud pulse transmission system. However, its dynamic responses are constrained by resistant load shocks and harsh operating environments. This study proposes an enhanced nonlinear active disturbance rejection control (EADRC) that integrates cascaded extended state observer (CESO) and enhanced nonlinear state error feedback (NLSEF) to address the abovementioned issues. The rotor motion model considering hydraulic torque is analyzed to characterize external load shocks, and an optimized nonlinear function, fal(·), is designed to improve slow convergence speed in high-error states. CESO is constructed to achieve timely and accurate disturbance estimations, while enhanced NLSEF is established to combine current and future system information for efficient feedback. Moreover, estimation capability and stability are theoretically proven based on the Lyapunov function. Simulations and experiments show that the proposed EADRC exhibits rapid response, high accuracy, and strong robustness in rotor speed control.

A high-pass shaped LMS algorithm based predistortion technique for fractional-[formula omitted] BB-DPLLs

In this paper, we prove that rather than the second-order ΔΣ modulator (DSM) as typically believed using the first-order one yields a faster convergence for the linear-piecewise predistortion technique employed in digital/time converter (DTC) based fractional-N Bang-Bang digital phase-locked-loops (BB-DPLLs). We also propose a novel technique that addresses the limit-cycle issue happening in near-integer channels of the conventional BB-DPLLs. With the first-order DSM-based novel technique, simulation results show that the worst fractional spurs are below −83 dBc at 12 kHz offset frequency assuming the DTC’s integral nonlinearity error is as large as 5 least-significant-bits.

Interferometric polarization compensation based on one single polarization-maintaining fiber.

In an interferometry system based on one single polarization-maintaining fiber (PMF), defects like the laser's ellipticity, the alignment error between the PMF and the laser source, and the PMF's internal stress will cause the emitted light from the PMF to be incompletely linearly polarized, resulting in nonlinear errors that cannot be ignored. This paper proposes a novel method that can realize polarization compensation for heterodyne interferometry, reduce the ellipticity of the emitted light, and thereby reduce the nonlinear error of the system. When using a PMF with an Extinction Ratio (ER) of 22 dB, the experimental results show that this method can reduce the polarization and increase the ER to 33.95 dB. After polarization compensation, the nonlinear error is reduced from 7.22 nm to 2.02 nm. The proportion of the nonlinear error reduction reaches to 71.99%, which greatly improves the accuracy of the system.

Adaptive multipole models of optically pumped magnetometer data.

Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set. The Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors (shielding factor is the reciprocal of the maximum fractional nonlinearity error). Furthermore, this projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub-optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128-channel OPM system and demonstrate up to 40 dB software shielding in real data.

Quality, Accuracy, and Bias in ChatGPT-Based Summarization of Medical Abstracts.

Worldwide clinical knowledge is expanding rapidly, but physicians have sparse time to review scientific literature. Large language models (eg, Chat Generative Pretrained Transformer [ChatGPT]), might help summarize and prioritize research articles to review. However, large language models sometimes "hallucinate" incorrect information. We evaluated ChatGPT's ability to summarize 140 peer-reviewed abstracts from 14 journals. Physicians rated the quality, accuracy, and bias of the ChatGPT summaries. We also compared human ratings of relevance to various areas of medicine to ChatGPT relevance ratings. ChatGPT produced summaries that were 70% shorter (mean abstract length of 2,438 characters decreased to 739 characters). Summaries were nevertheless rated as high quality (median score 90, interquartile range [IQR] 87.0-92.5; scale 0-100), high accuracy (median 92.5, IQR 89.0-95.0), and low bias (median 0, IQR 0-7.5). Serious inaccuracies and hallucinations were uncommon. Classification of the relevance of entire journals to various fields of medicine closely mirrored physician classifications (nonlinear standard error of the regression [SER] 8.6 on a scale of 0-100). However, relevance classification for individual articles was much more modest (SER 22.3). Summaries generated by ChatGPT were 70% shorter than mean abstract length and were characterized by high quality, high accuracy, and low bias. Conversely, ChatGPT had modest ability to classify the relevance of articles to medical specialties. We suggest that ChatGPT can help family physicians accelerate review of the scientific literature and have developed software (pyJournalWatch) to support this application. Life-critical medical decisions should remain based on full, critical, and thoughtful evaluation of the full text of research articles in context with clinical guidelines.