Nonlinear Correction Research Articles

Nonlinearity Correction Technology for Light Source of Frequency-Modulated Continuous-Wave Light Detection and Ranging (Invited)

Nonlinearity Correction Technology for Light Source of Frequency-Modulated Continuous-Wave Light Detection and Ranging (Invited)

Nonlinear Gradient Field Mapping Using a Spherical Grid Phantom for 3 and 7 Tesla MR Imaging Systems Equipped with High-performance Gradient Coils.

Recent high-performance gradient coils are fabricated mainly at the expense of spatial linearity. In this study, we measured the spatial nonlinearity of the magnetic field generated by the gradient coils of two MRI systems with high-performance gradient coils. The nonlinearity of the gradient fields was measured using 3D gradient echo sequences and a spherical phantom with a built-in lattice structure. The spatial variation of the gradient field was approximated to the 3rd order polynomials. The coefficients of the polynomials were calculated using the steepest descent method. The geometric distortion of the acquired 3D MR images was corrected using the polynomials and compared with the 3D images corrected using the harmonic functions provided by the MRI venders. As a result, it was found that the nonlinearity correction formulae provided by the vendors were insufficient and needed to be verified or corrected using a geometric phantom such as used in this study.

Correction procedure for a tomographic optical setup employing imaging fiber bundles andintensified cameras.

For reliable tomographic measurements the underlying 2D images from different viewing angles must be matched in terms of signal detection characteristics. Non-linearity effects introduced by intensified cameras and spatial intensity variations induced from inhomogeneous transmission of the optical setup can lead, if not corrected, to a biased tomographic reconstruction result. This paper presents a complete correction procedure consisting of a combination of a non-linearity and flatfield correction for a tomographic optical setup employing imaging fiber bundles and four intensified cameras. Influencing parameters on the camera non-linearity are investigated and discussed. The correction procedure is applied to 3D temperature measurements by two-color pyrometry and compared to results without correction. The present paper may serve as a guideline for an appropriate correction procedure for any type of measurement involving optical tomography and intensified cameras.

Nonlinear mechanical behavior and stress amplification effect correction of thin plate welded structure considering initial deformation

With the continuous development of light weight of ships, thin plate welded structures are widely used in superstructure of large hull structures and high-speed boats. However, the thin-plate welded structure has a special nonlinear mechanical behavior because of its small stiffness, more complicated welding deformation. The nonlinear mechanical behavior of thin plate welded structure is mainly caused by large slenderness ratio and complex initial buckling deformation, which can be characterized and quantified by defining global deformation angle αG and local deformation angle αL. Because of the welding angle deformation and welding dislocation, there is obvious stress amplification effect at the welding corner, but the traditional stress amplification correction formula is only suitable for thick plate welding structure. Aiming at the nonlinear mechanical behavior and secondary bending moment effect of thin plate welded structure, an analytical model of thin plate welded structure with initial deformation is established by combining theoretical derivation and numerical method. The results show that the additional bending moment effect caused by local welding deformation angle cannot be ignored. Finally, combined with a series of fatigue tests, the additional bending moment caused by bending deformation and angular deformation of typical welded joints is analyzed, and the notch stress field and fatigue strength correction of thin plate welded structures with initial defects are realized.

Advanced Frequency Study of Thick FGM Cylindrical Shells by Using TSDT and Nonlinear Shear

For the advanced frequency study of thick functionally graded material (FGM) circular cylindrical shells, it is interesting to consider the extra effects of nonlinear coefficient term in third-order shear deformation theory (TSDT) of displacements on the calculation of varied shear correction coefficient. The formulation for the advanced nonlinear shear correction coefficient are based on the energy equivalence principle. The values of nonlinear shear correction coefficient are usually functions of nonlinear coefficient term of TSDT, power-law exponent parameter and environment temperature. The free vibration frequencies of thick FGM circular cylindrical shells are investigated with the simply homogeneous equation by considering that simultaneous effects of the TSDT, the nonlinear shear correction coefficient of transverse shear force and the two direction of mode shapes. The novelty is more important and reasonable for the thick FGM circular cylindrical shells, especially for the ratio of length to thickness is five by considering the effects of advanced nonlinear shear correction coefficient and nonlinear coefficient term of TSDT on the advanced calculation of fundamental first natural frequencies.

Research on temperature compensation method for photoelectric sensors

In order to make the temperature error of fiber-optic current sensor (FGB) based on polarization modulation principle meet the requirements of engineering applications, the temperature error characteristics of FGB are analyzed theoretically, and the optimized BP neural network is used for the temperature compensation of FGB, which realizes the nonlinear temperature error correction of the sensor, and compares and analyzes the experimental results with those of other types of temperature compensation algorithms. The results show that the temperature compensation results based on the neural network algorithm are better than other compensation effects. Finally, the repeatability of the FGB was experimentally verified using its full temperature experiment, and the temperature errors of the FGB in the range of 20 ℃~ 100 ℃ were less than 0.5% after the correction of the neural network algorithm.

Dyonic Black Holes in Kaluza–Klein Theory with a Gauss–Bonnet Action

Kaluza–Klein theory attempts a unification of gravity and electromagnetism through the hypothesis that spacetime has five dimensions, of which only four are observed. The original model gives rise to the standard Einstein–Maxwell theory after dimensional reduction. However, in five dimensions, the Einstein–Hilbert action is not unique, and one can add to it a Gauss–Bonnet term, giving rise to nonlinear corrections in the dimensionally reduced action. We consider such a model, which reduces to Einstein gravity nonminimally coupled to nonlinear electrodynamics. The black hole solutions of the four-dimensional model modify the Reissner–Nordström solutions of general relativity. We show that in the modified solutions, the gravitational field presents the standard singularity at r=0, while the electric field can be regular everywhere if the magnetic charge vanishes.

Data driven models of the Madden-Julian Oscillation: understanding its evolution and ENSO modulation

Understanding the physical mechanisms of the Madden-Julian Oscillation (MJO) and its evolution is a major concern within the climate community. Its main importance relies on its ability to act as a source of predictability within the intra-seasonal time-scale in tropical and extratropical regions, therefore filling the gap between weather and climate forecasts. However, most atmospheric general circulation models fail to correctly represent MJO’s evolution, and their prediction skills are still far from MJO’s theoretical predictability. In this work we infer low dimensional models of the MJO from data by applying a recently developed machine learning technique, the Sparse Identification of Non-linear Dynamics (SINDy). We use the daily-mean outgoing longwave radiation MJO index (OMI) as input data to infer bi-dimensional climatological models of the MJO, and analyse the inferred models during El Niño and La Niña years. This approach allows us to diagnose the MJO’s behaviour in OMI’s phase space. Our results show that MJO can be most frequently represented by a harmonic oscillator, which represents the MJO’s eastward propagation and characteristic period. Upon this basic oscillatory behaviour, we find that small non-linear corrections play a fundamental role in representing MJO’s non-uniform speed of propagation, explaining its acceleration over the Pacific Ocean region. Particularly, we find that MJO’s evolution is most frequently non-linear [linear] during El Niño [La Niña] years. Overall, our work shows that SINDy can robustly model MJO’s evolution as a linear oscillator with small non-linear corrections, contributing to understand the MJO’s dynamics and dependency on El Niño-Southern Oscillation.

A nonlinear data-driven approach to bias correction of XCO2 for NASA's OCO-2 ACOS version 10

Abstract. Measurements of column-averaged dry air mole fraction of CO2 (termed XCO2) from the Orbiting Carbon Observatory-2 (OCO-2) contain systematic errors and regional-scale biases, often induced by forward model error or nonlinearity in the retrieval. Operationally, these biases are corrected for by a multiple linear regression model fit to co-retrieved variables that are highly correlated with XCO2 error. The operational bias correction is fit in tandem with a hand-tuned quality filter which limits error variance and reduces the regime of interaction between state variables and error to one that is largely linear. While the operational correction and filter are successful in reducing biases in retrievals, they do not allow for throughput or correction of data in which biases become nonlinear in predictors or features. In this paper, we demonstrate a clear improvement in the reduction in error variance over the operational correction by using a set of nonlinear machine learning models, one for land and one for ocean soundings. We further illustrate how the operational quality filter can be relaxed when used in conjunction with a nonlinear bias correction, which allows for an increase in sounding throughput by 14 % while maintaining the residual error in the operational correction. The method can readily be applied to future Atmospheric CO2 Observations from Space (ACOS) algorithm updates, to OCO-2's companion instrument OCO-3, and to other retrieved atmospheric state variables of interest.

SOH estimation method for lithium-ion batteries under low temperature conditions with nonlinear correction

The burgeoning growth of green energy in the transportation sector has resulted in increased expectations for battery longevity and safety. However, the capacity of lithium-ion batteries (LIBs) decreases with each successive charge and discharge cycle. And under harsh operating conditions, the capacity decay can exhibit strong nonlinearity. To enable effective battery management under such complex conditions, it is crucial to possess precise understanding of the state of health (SOH) of LIB. In this study, low-temperature aging experiments were designed to obtain capacity attenuation data of LIBs. Then the nonlinear component in capacity decay is identified and transformed into model nonlinear correction. Subsequently, we developed a long short-term memory (LSTM) neural network and extracted incremental capacity (IC) features based on experimentally collected data to train the model. The findings indicate that by training with only one cell aging dataset, the model can estimate the SOH for other samples. Furthermore, we introduced nonlinear correction features with an attention mechanism (AM) and analyzed the improvement of prediction accuracy through feature optimization and network adjustment to achieve SOH estimation with a maximum root mean square error (RMSE) of 0.92 %. This approach provides a potential solution for predicting SOH of LIBs at low temperature.

RAO-based translation process for estimating extreme value distribution of nonlinear ship response in irregular waves

The authors propose a new method named the RAO-based Translation Process (RTP) method for simply estimating the extreme value distribution of the nonlinear ship response in irregular waves based on the nonlinear response in regular waves. The proposed method combines the existing idea of the Nonlinear Correction (NLC) method, which is based on wave height-dependent RAO, with the theory of the translation process, and thus has both simplicity and a clear theoretical background. Furthermore, it is positioned as an extension of the Equivalent Design Wave (EDW) method used in conventional ship structural design. The validity of the proposed method is confirmed through a numerical study on the extreme value distribution of hull-girder sectional forces considering body nonlinear effects. The proposed method can be used for various purposes, and in particular, it can reduce the computational demand for strength evaluation by Direct Load and Structure Analysis (DLSA), which is a computationally extensive analysis method. Therefore, the proposed method is expected to make a significant contribution to structural design.

Nonlinear deterministic reconstruction and prediction of remotely measured ocean surface waves

Algorithms for reconstructing and predicting nonlinear ocean wave fields from remote measurements are presented. Three types of synthetic observations are used to quantify the influence of remote measurement modulation mechanisms on the algorithms’ performance. First, the observations correspond to randomly distributed surface elevations. Then, they are related to a marine radar model – the second type takes the wave shadowing modulation into account whereas the third one also includes the tilt modulation. The observations are numerically generated based on unidirectional waves of various steepness values. Linear and weakly nonlinear prediction algorithms based on analytical models are considered, as well as a highly nonlinear algorithm relying on the high-order spectral (HOS) method. Reconstructing surfaces from shadowed observations is found to have an impact limited to the non-visible regions, while tilt modulation affects the reconstruction more generally due to the indirect, more complex extraction of wave information. It is shown that the accuracy of the surface reconstruction mainly depends on the correct modelling of the wave shape nonlinearities. Modelling the nonlinear correction of the dispersion relation, in particular the frequency-dependent wave phase effects in the case of irregular waves, substantially improves the prediction. The suitability of the algorithms for severe wave conditions in finite depth and using non-perfect observations is assessed through wave tank experiments. It shows that only the third-order HOS solution predicts the right amplitude and phase of an emerging extreme wave, emphasizing the relevance of the corresponding physical modelling.

A Preclinical Positron Emission Tomography (PET) and Electron-Paramagnetic-Resonance-Imaging (EPRI) Hybrid System: PET Detector Module.

We report the design and experimental validation of a compact positron emission tomography (PET) detector module (DM) intended for building a preclinical PET and electron-paramagnetic-resonance-imaging hybrid system that supports sub-millimeter image resolution and high-sensitivity, whole-body animal imaging. The DM is eight detector units (DU) in a row. Each DU contains 12×12 lutetium-yttrium oxyorthosilicate (LYSO) crystals having a 1.05 mm pitch read by 4×4 silicon photomultipliers (SiPM) having a 3.2 mm pitch. A small-footprint, highly-multiplexing readout employing only passive electronics is devised to produce six outputs for the DM, including two outputs derived from SiPM cathodes for determining event time and active DU and four outputs derived from SiPM anodes for determining energy and active crystal. Presently, we have developed two DMs that are 1.28×10.24 cm2 in extent and approximately 1.8 cm in thickness, with their outputs sampled at 0.7 GS/s and analyzed offline. For both DMs, our results show successfully discriminated DUs and crystals. With no correction for SiPM nonlinearity, the average energy resolution for crystals in a DU ranges from 14% to 16%. While not needed for preclinical imaging, the DM may support 300-400 ps time-of-flight resolution.

On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics

When two particles interact primarily through gravity and follow the laws of quantum mechanics, the generation of entanglement is considered a hallmark of the quantum nature of the gravitational interaction. However, we demonstrate that entanglement dynamics can also occur in the presence of a weak quantum interaction and non-linear corrections to local quantum mechanics, even if the gravitational interaction is classical or absent at short distances. This highlights the importance of going beyond entanglement detection to conclusively test the quantum character of gravity, and it requires a thorough examination of the strength of other quantum forces and potential non-linear corrections to quantum mechanics in the realm of large masses.

Nonlinear high-order harmonics correction for phase measuring profilometry

Gamma nonlinearity severely affects the accuracy of phase measuring profilometry (PMP). Through averaging two phase maps with inverse errors, conventional methods including double phase-shifting (DPS) and Hilbert transform (HT) only compensate the fundamental harmonic while leaving high-order harmonics. To address this issue, this paper presents an efficient high-order harmonics correction (HHC) method. The averaged phase is encoded into factitious fringes on the computer. Then we directly apply HT on these factitious fringes to generate transformed fringes, while the addition of the ideal phase and residual harmonics is converted to multiplication. Finally, the residual high-order harmonics are suppressed, and the corrected phase is calculated using the phase-shifting algorithm. In comparison to conventional DPS and HT methods, the proposed HHC method can efficiently correct the residual high-order harmonics, thereby enhancing the measuring accuracy.

Optical link encoding based simultaneous correction for crosstalk and nonlinearity in multi-site optical converged networks.

This paper reports a correction scheme to address the problem of modulation nonlinearity and optical switch crosstalk simultaneously for the multi-site optical converged network. Based on the optical link encoding and exclusive-or operation for the received signal, the present spectrum usage can be obtained among the confusion with interferences containing the modulated harmonic distortion and the crosstalk leakage from other sites. The proof-of-concept experiment is performed on various interferences involving the linear frequency modulated (LFM) waveform and the quadrature amplitude modulation (QAM) signal. The corrected spectrum has realized an improved signal-to-noise ratio (SNR) of over 22 dB compared to the uncorrected counterpart. Furthermore, it consistently maintains a superior SNR, surpassing the single impairment-corrected scenario by an impressive margin of at least 15.9 dB. Besides, the implementation would not introduce additional noise, making the corrected result agree well with the ideal case. Without any increase in hardware complexity, the presented scheme provides an effective technique to meet the correction challenge of large-scale and complicated optical networks with multiple optoelectronic devices.

Solitary Vortex Dynamics of 2D Bose-Einstein Condensates with Higher-Order Nonlinear Interactions

For study of Continuous matter waves in Bose-Einstein condensates in nonlinear and quantum atom optics, the two-dimensional Gross-Pitaevskii equation (GPE) is chosen as the reliable model for studying the dynamics of vortices in the framework of mean-field theory. In related problems in several recent studies showing that higher-order interrelationships are an indispensable component of the GPE even at the mean-field level, by numerically estimating the vortex dynamics variables. In this paper, derive the vortex soliton solutions using the variational method and investigate the effect of higher-order nonlinear corrections on the behavior of the vortex dynamics, which are shown to have an important impact on the vortex dynamics behavior.

On adaptive identification of systems having multiple nonlinearities

Objectives. The solution to the relevant problem of identifying systems with multiple nonlinearities depends on such factors as feedback, ways of connecting nonlinear links, and signal properties. The specifics of nonlinear systems affect control systems design methods. As a rule, the basis for the development of a mathematical model involves the linearization of a system. Under conditions of uncertainty, the identification problem becomes even more relevant. Therefore, the present work sets out to develop an approach to the identification of nonlinear dynamical systems under conditions of uncertainty. In order to obtain a solution to the problem, an adaptive identification method is developed by decomposing the system into subsystems.Methods. Methods applied include the adaptive identification method, implicit identified representation, S-synchronization of a nonlinear system, and the Lyapunov vector function method.Results. A generalization of the excitation constancy condition based on fulfilling the S-synchronizability for a nonlinear system is proposed along with a method for decomposing the system in the output space. Adaptive algorithms are obtained on the basis of the second Lyapunov method. The boundedness of the adaptive system trajectories in parametric and coordinate spaces is demonstrated. Approaches for self-oscillation generation and nonlinear correction of a nonlinear system are considered along with obtained exponential stability conditions for the adaptive system.Conclusions. Simulation results confirm the possibility of applying the proposed approach to solving the problems of adaptive identification while taking the estimation of the structural identifiability (S-synchronization) of the system nonlinear part into account. The influence of the structure and relations of the system on the quality of the obtained parametric estimates is investigated. The proposed methods can be used in developing identification and control systems for complex dynamic systems.

Prediction of urban airflow fields around isolated high-rise buildings using data-driven non-linear correction models

When it comes to predicting urban airflow, steady Reynolds-averaged Navier-Stokes (SRANS) models that rely on Reynolds stress often face a challenge called the closure problem. This problem involves unresolved structural flaws and uncertainties in the closure coefficients used in the models. Previous attempts to recalibrate coefficients for specific urban flows without breaking the linear constitutive relation have resulted in simulation results constrained by the baseline turbulence model. Therefore, this study aims to enhance the performance of SRANS models by addressing these structural flaws. To achieve this, a novel data-driven framework is proposed. It leverages the deterministic symbolic regression algorithm to discover explicit algebraic expressions for a non-linear Reynolds stress correction model. The robustness of the correction model is ensured by maintaining the linear eddy viscosity model for iterative calculations while keeping the non-linear component frozen. The proposed framework is evaluated using three isolated building cases with varying geometric configurations and inflow boundary conditions. Findings demonstrate that computational fluid dynamics (CFD) predictions incorporating the data-driven non-linear correction model consistently align closer to wind tunnel experimental results compared to both standard and non-linear versions of the k-ε turbulence model. This improvement is reflected in reduced reattachment lengths and more accurate mean velocity distributions in the wake of buildings. However, it should be noted that there is a possibility of overpredicting wind velocity in the windward area. This study introduces valuable insights and additional strategies to enhance the prediction accuracy of SRANS models in urban airflow simulations.

Design method for a small F-number two-material uniform dispersion immersion grating imaging spectrometer.

Immersion gratings have high dispersion efficiency and have important application value in miniaturized imaging spectrometers, but its serious dispersion nonlinearity causes difficulties in calibration and image processing, which limits its application range. To solve this, this paper presents a design method for a two-material linear dispersion immersion grating device design method, and a compact small F-number immersion grating spectrometer based on it. First the vector form dispersion equation of the two-material immersion grating is derived and the linear spectral dispersion immersion grating design process is given, then a compact small F-number uniform dispersion imaging spectrometer is given as a design example using the proposed method. The results show that when the operating band of the system is 1590-1675 nm, the spectral resolution is better than 0.25 nm, and F-number can achieve better than 2. Compared with traditional single-material immersion grating imaging spectrometer, the designed imaging spectrometer dispersion linearity is significantly improved. Finally, the influence of prism materials, structure parameters and grating parameters on dispersion nonlinearity is analyzed. Design and analysis results show that the proposed two-material immersion grating device has much better spectral dispersion nonlinearity correction ability, and its design method can provide reference to the compact spectrometer design based on immersion gratings.