Nonlinear Correction Research Articles

Real-time correction of gain nonlinearity in electrostatic actuation for whole-angle micro-shell resonator gyroscope

MEMS gyroscopes are well known for their outstanding advantages in Cost Size Weight and Power (CSWaP), which have inspired great research attention in recent years. A higher signal-to-noise ratio (SNR) for MEMS gyroscopes operating at larger vibrating amplitudes provides improved measuring resolution and ARW performance. However, the increment of amplitude causes strong nonlinear effects of MEMS gyroscopes due to their micron size, which has negative influences on the performance. This paper carries out detailed research on a general nonlinear mechanism on the sensors using parallel-plate capacitive transducers, which is called the gain nonlinearity in electrostatic actuation. The theoretical model established in this paper demonstrates the actuation gain nonlinearity causes the control-force coupling and brings extra angle-dependent bias with the 4th component for the whole-angle gyroscopes, which are verified by the experiments carried out on a micro-shell resonator gyroscope (MSRG). Furthermore, a real-time correction method is proposed to restore a linear response of the electrostatic actuation, which is realized by the gain modification with an online parameter estimation based on the harmonic-component relationship of capacitive detection. This real-time correction method could reduce the 4th component of the angle-dependent bias by over 95% from 0.003°/s to less than 0.0001°/s even under different temperatures. After the correction of actuation gain nonlinearity, the bias instability (BI) of whole-angle MSRG is improved by about 3.5 times from 0.101°/h to 0.029°/h and the scale factor nonlinearity (SFN) is reduced by almost one order of magnitude from 2.02 ppm to 0.21 ppm.

Nonlinear correction method of digital fringe projection 3D measurement system based on precise precoding

Nonlinear correction method of digital fringe projection 3D measurement system based on precise precoding

Extending MGCAMB tests of gravity to nonlinear scales

Modified Growth with CAMB (MGCAMB) is a patch for the Einstein-Boltzmann solver CAMB for cosmological tests of gravity. Until now, MGCAMB was limited to scales well-described by linear perturbation theory. In this work, we extend the framework with a phenomenological model that can capture nonlinear corrections in a broad range of modified gravity theories. The extension employs the publicly available halo model reaction code ReACT, developed for modeling the nonlinear corrections to cosmological observables in extensions of the ΛCDM model. The nonlinear extension makes it possible to use a wider range of data from large scale structure surveys, without applying a linear scale cut. We demonstrate that, with the 3×2pt Dark Energy Survey data, we achieve a stronger constraint on the linear phenomenological functions μ and Σ, after marginalzing over the additional nonlinear parameter p 1, compared to the case without the nonlinear extension and using a linear cut. The new version of MGCAMB is now forked with CAMB on GitHub allowing for compatibility with future upgrades.

Generalized, Three-Dimensional Wind Tunnel Wall Correction Using Nonlinear Least-Squares Optimization

A novel three-dimensional technique for correcting wind tunnel measurements for wall interference has been developed. The flow around the test body and its wake is approximated as a series of inviscid singularities, while the wind tunnel walls and model support are approximated using a panel method. A nonlinear least-squares approach with trust-region reflective optimization is then used to obtain the strength and locations of singularities together with the domain boundary panel strengths by fitting to measured wall pressures. The technique is demonstrated using computational fluid dynamics for the test case of a well-documented slender delta wing body with high blockage and validated against both experiments and legacy data. The nonlinear least-squares wall correction method is shown to demonstrate a significant improvement in wall corrections compared to the classical two-variable technique.

Ultraviolet extinction correlation with 3D dust maps using white dwarfs

ABSTRACT Accurate astrometric and photometric measurements from Gaia have led to the construction of 3D dust extinction maps which can now be used for estimating the integrated extinctions of Galactic sources located within 5 kpc. These maps based on optical observations may not be reliable for use in the ultraviolet (UV) which is more sensitive to reddening. Past studies have focussed on studying UV extinction using main-sequence stars but lack comparison with 3D dust maps. White dwarfs with well-modelled hydrogen-dominated (DA) atmospheres provide an advantage over main-sequence stars affected by magnetic activity. In this work, we study the variation of UV extinction with 3D dust maps utilizing Hubble Space Telescope (HST) and Galaxy Evolution Explorer (GALEX) observations of DA white dwarfs located within 300 pc. We used HST COS spectroscopic data of 76 sightlines to calculate the optical extinction from Si ii column densities and validate our results with the kinematic model predictions of the local interstellar medium. Also, we combined GALEX and Gaia photometric observations of 1158 DA white dwarfs to study UV reddening by comparing observed and modelled colour–colour relations. We calculated GALEX non-linearity corrections and derived reddening coefficients [$R(NUV-G)=6.52\pm 1.53$ and $R(FUV-G)=6.04\pm 2.41$] considering their variations with optical extinction ($\rm{A_{V}}\lt 0.1$ mag), and found them to be in good agreement with known extinction laws. HST analysis suggests a positive bias of 0.01–0.02 mag in the optical extinction from 3D maps depending on the Galactic latitude. These results independently confirm the validity of 3D dust maps to de-redden the optical and UV observations of white dwarfs.

Robust and efficient calibration method of liquid-crystal spatial light modulator based on the linear combination strategy

Abstract Phase-only spatial light modulators (SLMs) play a vital role in virous fields. However, its modulation accuracy is compromised by the static aberration and the phase response nonlinearity. To enhance the modulation accuracy, this paper presents an innovative full calibration method for SLMs, effectively addressing both static aberration and nonlinear phase responses using only two shots of camera. The main highlight of this paper is the binding of a novel linear combination strategy and a unique kinoform. This binding can eliminate phase distortion between two shots of camera, making our method dramatically robust in correcting phase response nonlinearity. Additionally, benefit from the accurate correction of phase response nonlinearity, the static aberration is accurately compensated by the single-shot spatial carrier phase-shifting technology. In conclusion, the proposed method's strong robustness, precision, and efficiency position it as an ideal solution for SLM calibration.

Sound absorption of slit resonator with embedded aperture in linear and nonlinear regimes

This paper presents a slit resonator with embedded aperture (SREA) by embedding the slit-type neck into the cavity, and investigates its sound absorption characteristics in linear and nonlinear regimes. The theoretical acoustic impedance model of the SREA is established through transfer matrix method. The theoretical, simulation and experimental results demonstrate that the SREA enhances oscillating mass without altering acoustic capacity through the embedded slit-type neck, enabling it to achieve quasi-perfect absorption at lower frequencies with the same external geometry as traditional slit resonator. The formation and shielding of acoustic vortex caused by the high sound intensity increase the normalized acoustic resistance and decreases the acoustic reactance, causing the peak sound absorption coefficient to decline. This paper introduces a nonlinear correction expression for the normalized acoustic resistance of SREA by analogy with cylindrical neck.

Illumination Correction and Enhancement Algorithm for Defective Powder Spreading Images in Selective Laser Sintering

Abstract Based on the uneven illumination distribution and low defect contrast in the powder spreading images acquired during the selective laser sintering manufacturing process, which affects subsequent defect detection, an adaptive nonlinear illumination correction and enhancement algorithm is proposed. Local illumination correction is performed using gray valueitting curves and is combined with global gamma correction to improve correction capability in overly dark areas. A nonlinear enhancement function is constructed to boost the contrast of the image’s illumination component. Finally, a gradient-based L0 norm minimization algorithm is used to smooth non-defect areas. Experimental results show that the proposed algorithm signi icantly improves correction and enhancement, outperforming comparison algorithms overall. Compared to the original images, the coef icient of variation decreases by an average of 0.179, and the standard deviation increases by an average of 26.7%, demonstrating the effectiveness of the proposed algorithm.

VLTI/GRAVITY interferometric measurements of the innermost dust structure sizes around active galactic nuclei

We present new Very Large Telescope Interferometer (VLTI)/GRAVITY near-infrared interferometric measurements of the angular size of the innermost hot dust continuum for 14 type 1 active galactic nuclei (AGNs). The angular sizes are resolved on scales of ∼0.7 mas and the inferred ring radii range from 0.028 to 1.33 pc, comparable to those reported previously and a factor of 10−20 smaller than the mid-infrared sizes in the literature. Combining our new data with previously published values, we compiled a sample of 25 AGNs with bolometric luminosity ranging from 1042 to 1047 erg s−1, with which we studied the radius-luminosity (R − L) relation for the hot dust structure. Our interferometric measurements of radius are offset by a factor of 2 from the equivalent relation derived through reverberation mapping. Using a simple model to explore the dust structure’s geometry, we conclude that this offset can be explained if the 2 μm emitting surface has a concave shape. Our data show that the slope of the relation is in line with the canonical R ∝ L0.5 when using an appropriately non-linear correction for bolometric luminosity. In contrast, using optical luminosity or applying a constant bolometric correction to it results in a significant deviation in the slope, suggesting a potential luminosity dependence on the spectral energy distribution. Over four orders of magnitude in luminosity, the intrinsic scatter around the R − L relation is 0.2 dex, suggesting a tight correlation between the innermost hot dust structure size and the AGN luminosity.

A novel dynamic structural adaptive multivariable grey model and its application in China's solar energy generation forecasting

Accurately predicting China's solar energy generation is crucial for energy planning and environmental protection. However, the nonlinearity and complexity of the data pose challenges to prediction. This article proposes a dynamic structural adaptive multivariate grey model to overcome these challenges. The model constructs a dynamic nonlinear correction function with an uncertain structure that can adaptively adjust to the data characteristics. Additionally, the Gaussian function is utilized to derive the time response function, overcoming the mechanism defects present in traditional multivariate grey models. The whale optimization algorithm is applied to optimize the background value of the model, improving accuracy. The model is compatible with 14 classical models via parameter changes and has strong compatibility. The results show that the fitting error and test error of the model are 0.23 % and 1.95 % respectively, which is significantly better than the other 11 methods, indicative of strong robustness and accuracy. The forecast indicates that China's solar energy generation will experience a consistent upward trajectory from 2023 to 2030, with an average annual growth rate of 12.11 %. This study significantly contributes to the advancement of the theory of multivariate grey dynamic prediction and provides essential data support for strategic planning within China's solar power industry.

Modified homotopy approach for diffractive production in the saturation region

In this paper we continue to develop the homotopy method for solving of the nonlinear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the nonlinear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure. Published by the American Physical Society 2024

Causal fermion systems as an effective collapse theory

Abstract It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr"odinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski-Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale~$\ell_{\min}$.

The 3D Lyman-α forest power spectrum from eBOSS DR16

Abstract We measure the three-dimensional power spectrum (P3D) of the transmitted flux in the Lyman-α (Ly-α) forest using the complete extended Baryon Oscillation Spectroscopic Survey data release 16 (eBOSS DR16). This sample consists of ∼ 205,000 quasar spectra in the redshift range 2 ≤ z ≤ 4 at an effective redshift z = 2.334. We propose a pair-count spectral estimator in configuration space, weighting each pair by exp (ik · r), for wave vector k and pixel pair separation r, effectively measuring the anisotropic power spectrum without the need for fast Fourier transforms. This accounts for the window matrix in a tractable way, avoiding artifacts found in Fourier-transform based power spectrum estimators due to the sparse sampling transverse to the line-of-sight of Ly-α skewers. We extensively test our pipeline on two sets of mocks: (i) idealized Gaussian random fields with a sparse sampling of Ly-α skewers, and (ii) log-normal LyaCoLoRe mocks including realistic noise levels, the eBOSS survey geometry and contaminants. On eBOSS DR16 data, the Kaiser formula with a non-linear correction term obtained from hydrodynamic simulations yields a good fit to the power spectrum data in the range (0.02 ≤ k ≤ 0.35) h Mpc−1 at the 1 − 2σ level with a covariance matrix derived from LyaCoLoRe mocks. We demonstrate a promising new approach for full-shape cosmological analyses of Ly-α forest data from cosmological surveys such as eBOSS, the currently observing Dark Energy Spectroscopic Instrument and future surveys such as the Prime Focus Spectrograph, WEAVE-QSO and 4MOST.

Numerical Modeling of the Interaction of a Monodisperse Gas Suspension with a Shock Wave Moving at an Angle to the Separation Boundary of a Homogeneous Gas and a Gas Suspension

The work is devoted to the study of the influence of the dispersed phase on the dynamics of gas suspensions during numerical modeling of the dynamics of gas suspensions. In this study, based on the continuum technique of dynamics of inhomogeneous media, the interaction of a shock wave propagating from a homogeneous gas with a gas suspension was numerically simulated. For each of the components of the mixture, a complete hydrodynamic system of equations of motion was solved, which included the equations of conservation of density, the equations of conservation of the spatial components of the momentum of the mixture components, and the equations of conservation of energy of the components. The carrier medium was described as a viscous, compressible heat-conducting gas. The mathematical model took into account interfacial heat transfer. The mathematical model also took into account the interphase exchange of momentum, which included the force of aerodynamic drag, the dynamic force of Archimedes and the force of added masses. The system of equations of the mathematical model was integrated using the finite difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Large volumetric contents of the dispersed phase were considered. The influence of interfacial interaction on the process of shock wave propagation has been studied.

Discrete strong extremum principles for finite element solutions of advection‐diffusion problems with nonlinear corrections

AbstractA nonlinear correction technique for finite element methods of advection‐diffusion problems on general triangular meshes is introduced. The classic linear finite element method is modified, and the resulting scheme satisfies discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well‐known restrictions on diffusion coefficients and geometry of mesh‐cell (e.g., “acute angle” condition), and we need not to perform upwind treatment on the advection term separately. Moreover, numerical example shows that when a discrete scheme does not satisfy the strong extremum principle, even if it maintains the global physical bound, non‐physical numerical oscillations may still occur within local regions where no numerical result is beyond the physical bound. Thus, it is worth to point out that our new nonlinear finite element scheme can avoid non‐physical oscillations around sharp layers in advection‐dominate regions, due to maintaining discrete strong extremum principle. Convergence rates are verified by numerical tests for both diffusion‐dominate and advection‐dominate problems.

Scattering Elimination in 2D IR Immune from Detector Artifacts.

Highly scattering samples, such as polymer droplets or solid-state powders, are difficult to study via coherent two-dimensional infrared (2D IR) spectroscopy. Previously, researchers have employed (quasi-) phase cycling, local-oscillator chopping, and polarization control to reduce scattering, but the latter method poses a limit on polarization-dependent measurements. Here, we present a method for Scattering Elimination Immune from Detector Artifacts (SEIFDA) in pump-probe 2D IR experiments. Our method extends the negative probe delay method of removing scattering from pump-probe spectroscopy to 2D experiments. SEIFDA works well for all polarizations when combined with the optimized noise reduction scheme to remove additive and multiplicative noise. We demonstrate that our method can be employed with any polarization scheme and reliably lowers the scattering at parallel polarization to comparable levels to the conventional 8-frame phase cycling with probe chopping (8FPCPC) at perpendicular polarization. Our system can acquire artifact free spectra in parallel polarization when the signal intensity is as little as 5% of the intensity of the interference between the pump pulses scattered into the detector. It reduces the time required to characterize the scattering term by at least 50% over 8FPCPC. Through detailed analysis of detector nonlinearity, we show that the performance of 8FPCPC can be improved by incorporating nonlinear correction factors, but it is still worse than that of SEIFDA. Application of SEIFDA to study the encapsulation of Nile red in polymer droplets demonstrates that this method will be very useful for probing highly scattering systems.

Nonlinearity-suppressed micro-probe fiber optic interferometer for accurate long-range displacement measurements

Fiber-optic interferometry technology has advanced rapidly in recent years. However, accurate measurement of the displacement over long ranges remains a challenge. This study reveals that fiber interferometers with Fabry–Perot cavities experience non-elliptic multi-order nonlinear errors due to parasitic interference, leading to nonlinearity correction failures in the case of reflectivity mismatch. We proposes a nonlinearity-suppressed microprobe fiber interferometer to measure long-range displacement with high accuracy. The proposed microprobe interferometer structurally avoids non-elliptic nonlinearities from higher-order harmonics and ensures the effectiveness of the nonlinearity correction method. Moreover, we optimized the micro-sensing probe parameters based on an established multimedia transmission interference model to further improve the measurement accuracy of long-range displacement. Nonlinear errors are reduced from 2.3 nm to 0.92 nm in the application range 0–700 mm. The findings of this study demonstrate that the proposed nonlinearity-suppressed microprobe fiber interferometer is suitable for sub-nanometer accuracy measurements over displacements of several hundred millimeters, especially in limited-space scenarios. It has great potential for industries seeking breakthroughs in long-range displacement measurement, such as robotics, medical devices and manufacturing.

Nonlinear Maxwell’s theory mimics dark energy

In a recent study (Sadeghi and Noori Gashti, 2024) the so-called Reissner–Nordström (RN) black hole surrounded by perfect fluid dark matter (PFDM) has been investigated. Here in this Letter, we prove that technically such a black hole does not exist in the context of Maxwell’s linear theory coupled minimally to a PFDM. Furthermore, it is shown that this black hole is the result of nonlinear corrections to the linear Maxwell’s Lagrangian in the Einstein–Maxwell theory. The energy–momentum tensor is split into Maxwell’s linear theory and a correction term. The latter i.e., the correction part of the energy–momentum tensor represents an anisotropic dark energy. This result brings the question if nonlinear electrodynamics can be the source of dark matter/energy.

Model experimental studies on active heave compensation control strategy for electric-driven offshore cranes

Ship-mounted heave compensation offshore cranes are indispensable for isolating connected payloads from the support vessel during lifting operations under harsh sea conditions. In this paper, an innovative adaptive robust control strategy is presented for the electric-driven active heave compensation (EDAHC) system, combining an equivalent model predictive control (EMPC) method with a bias proportional integral derivative (BPID) framework to effectively mitigate the adverse effects of wave-induced heave motions from the support vessel on the suspended payload. Building upon the inherent field-oriented control in the permanent magnet synchronous motor (PMSM), the BPID-based control structure is introduced, motivated by its prompt responsiveness and robust resistance against model discrepancies and irregular disturbances. Facilitated by a torque compensation mechanism, the EMPC-based control scheme, synthesized with an autoregressive integrated moving average (ARIMA)-based heave motion prediction algorithm, is subsequently developed to achieve nonlinear friction deadzone correction and adaptive regulation of BPID parameters, thereby ensuring optimal performance of the EDAHC system within specified state and input constraints. Comparative experimental tests conducted on a scaled EDAHC testbed validate the superior capabilities of the proposal in station-keeping, position tracking, constraint satisfaction, and robustness against parametric uncertainties.

Nonlinear corrections to the momentum sum rule

Nonlinear corrections to the momentum sum rule