High-precision Algorithm Research Articles

High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand–Levitan–Marchenko equation

We propose a high precision algorithm for solving the Gelfand–Levitan–Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson’s type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations. To the best of our knowledge, this is the first algorithm to solve this problem with an order of accuracy higher than the second.

Fast nonlinear Fourier transform algorithm for reconstruction of optical data from nonlinear spectra of the Manakov system.

We propose a high-precision algorithm for solving the three-component Gelfand-Levitan-Marchenko equations (GLME) associated with the Manakov system, which describes the behavior of light waves through the optical fibers. The algorithm generalizes the high-order generalized Toeplitz inner-bordering method for solving the two-component GLME associated with the nonlinear Schrödinger equation. Numerical experiments have shown that the proposed algorithm makes it possible to increase the accuracy of solving the GLME associated with Manakov system up to the sixth order.

Optimization of robot manipulator configuration calibration by using Zhang neural network for repetitive motion

High precision and low complexity control algorithm plays an important role in the developing of the end-effector instrumentation of different robot manipulators. In order to reduce the kinetic energy and the high-speed drift phenomenon of the repetitive motion tracking task, the robot manipulator needs to calibrate its configuration. In this paper, we formulate the configuration calibration of the robot manipulator for the repetitive motion task as a future quadratic programming optimization problem constrained with equality constraints, which is also regarded as a fundamental problem in artificial intelligence and modern control engineering. Zhang neural network, which is a canonical method, can be adopted to deal with the continuous form of the future optimization problem, named as temporally dependent quadratic programming problem with equality constraints. In order to overcome the issue of temporally dependent inverse computing, a novel Zhang neural network model and its uncertain disturbance tolerant model, which are termed as filtered reciprocal-kind Zhang neural network model and uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network model, respectively, are proposed by integrating the energy-type cost function and Zhang neural network design formula for solving the temporally dependent quadratic programming problem with equality constraints in this paper. Based on the Euler discrete formula and the models, the discrete filtered reciprocal-kind Zhang neural network and the discrete uncertain disturbance tolerant filtered reciprocal-kind Zhang neural network algorithms are proposed for solving the future quadratic programming problem with equality constraints and the robot manipulator configuration calibration problem of repetitive motion. The convergence properties of the reciprocal-kind Zhang neural network model and its corresponding uncertain disturbance tolerant model are obtained by Lyapunov stability theory of nonlinear system and its corresponding perturbed system, while the convergence property of the filtered reciprocal-kind Zhang neural network model is analyzed by the limit thinking. For the repetitive motion task, three experiments for solving the configuration calibration problem of PUMA560, Kinova Jaco2, and Franka Emika Panda robot manipulators are performed to illustrate the effectiveness, robustness and superiority of our proposed discrete filtered reciprocal-kind Zhang neural network algorithms.

Tangential velocity tracking-based cross-coupled control method with variable feedrate for biaxial parametric curve following

To address the inaccurate contour error calculation problem in traditional cross-coupled control (CCC) methods for biaxial motion systems, this paper presents a novel CCC method based on a recently developed tangential velocity tracking (TVT) strategy. It has the advantage that existing high-precision algorithms for searching the foot point can be directly integrated to obtain the excellent estimation accuracy of contour error. The cumbersome parameter tuning for position controllers of each axis is unnecessary. Moreover, a velocity interpolator for parametric curves is developed to extend the TVT strategy to the variable feedrate case. The stability of the TVT-based CCC system is proved using a quadratic Lyapunov function. Comparative experiments are carried out, and the results indicate that the estimation deviation of contour error in the TVT-based CCC method can be constrained within 1 μm. The maximum contour error is significantly reduced by 65.32% and 50.10% compared with the traditional CCC methods based on tangential and circular approximations, respectively.

New similarity laws reduced from local Mach factors in longitudinal–transverse force theory

The rapid advancement in aeronautics has led to the emergence of intricate dynamic processes and structures, such as vortices, shock waves, flow separation, and turbulence, resulting from the flow around airfoils. Acquiring a profound understanding of these local structures and unraveling the physical mechanisms underlying flow phenomena represents an essential and challenging issue in the field of flight science. In this research, the longitudinal–transverse force theory (L–T force theory), as proposed by previous researchers, is employed to quantitatively assess contributions of local flow structures to aerodynamic forces. Specifically, the research encompasses an analysis of steady and viscous compressible flow over the Royal Aircraft Establishment (RAE)-2822 airfoil, with free-stream Mach number (M∞) ranging from 0.1 to 2.0. We comprehensively estimate longitudinal forces (L-force) and transverse forces (T-force), along with effects of compressibility on aerodynamic forces. Furthermore, recognizing the necessity for high-precision algorithms in the computation of L–T force theory, this investigation utilizes a sixth-order accuracy algorithm for spatial discretization and differencing. Our analysis reveals that the influence of compressibility and the contributions of L-forces to aerodynamic forces become increasingly significant in high M∞ regimes as shearing processes weaken. Additionally, a new similarity law is established to characterize aerodynamic forces acting on the RAE-2822 airfoil based on a novel moderating factor, ζmo, reduced from local Mach factors in the L–T force theory. This coefficient, ζmo, elucidates the degree to which transverse processes are modulated by longitudinal processes. Various angles of attack α and airfoils have also been analyzed, including National Advisory Committee for Aeronautics (NACA)0012 and NACA0006, by introducing a parameter denoted as κ to further validate the universality of the new similarity laws. The results demonstrate a high degree of accuracy in fitting the aerodynamic coefficients.

A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains

An Iterative High-Precision Algorithm for Multi-Beam Array Stitching Method Based on Scanning Hartmann

The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 × 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm’s feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy.

High Precision and Robust Vehicle Localization Algorithm with Visual-LiDAR-IMU Fusion

High Precision and Robust Vehicle Localization Algorithm with Visual-LiDAR-IMU Fusion

Fourth-order high-precision algorithms for one-sided tempered fractional diffusion equations

<p>In this paper, high-order numerical algorithms for two classes of time-independent one-sided tempered fractional diffusion equations were studied. The time derivative was discretized by the backward difference formula, the space tempered fractional derivatives were discretized based on tempered weighted and shifted Grünwald difference operators combined with the quasi-compact technique, and the effective second-order numerical approximations of the left and right third-order Riemann-Liouville tempered derivatives were given, thus the detailed fourth-order numerical schemes of these two classes of equations were derived. With the energy method, we proved rigorously that the numerical schemes were stable and convergent with order $ O(\tau +h^4) $ and were only related to the tempered parameter $ \lambda $. Finally, some examples were given to verify the validity of the numerical schemes.</p>

High-precision algorithm for grain segmentation of thin sections by multi-angle optical-microscopic images

ABSTRACT This paper introduces an algorithm for automating the analysis of petrographic thin-section images of sandstones and siltstones. The images of thin sections are obtained in polarized light at magnifications providing good image quality. In addition, the images for each section are obtained at different angles of rotation of the microscope stage. Augmentation is applied to the obtained photographs: the number of images increases due to rotations, shifts, and rescaling of the image. For training the neural network of the Mask R-CNN architecture, transfer learning is used, with initial weights obtained from a huge variety of nongeological images. The results of image segmentation using Mask R-CNN are compared to the Watershed algorithm results and the U-Net network for two metrics. According to the standard Intersection over Union metric, U-Net for high-quality images and Watershed for blurry images show the best results with a slight superiority. However, according to the Grain Size Metric, which evaluates the accuracy of grain-size measurement, the best accuracy (over 95%) is shown by Mask R-CNN. The grain-size analysis is done, and the porosity of the studied petrographic sections is determined. The use of the proposed approaches in the study of thin sections will significantly reduce the time for obtaining the results of grain-size-distribution analysis and porosity determination. This article is the result of multidisciplinary collaboration between geologists and programmers. This has allowed for the merging of profound knowledge in the field of geology with cutting-edge data processing technologies. By employing the presented methodology, geologists can devote more time to interpreting results rather than obtaining them, which in turn enhances the efficiency of research work. The benefits of using this methodology are not limited to just speeding up the process: it also allows for increased accuracy and reliability of the analysis, minimizing human error.

A review of intelligent coal gangue separation technology and equipment development

ABSTRACT One of the necessary ways to achieve the efficient, clean utilization of coal resources is to reduce the amount of coal gangue in raw coal to ensure the development of clean, low-carbon, and green energy in China. The application of conventional coal gangue separation equipment is severely limited due to the large investment in early construction, high production costs, and large water consumption and waste in production. Intelligent coal gangue separation equipment has the advantages of fast speed, high precision, strong modularity, and integration scalability. It also has the advantages of low operation cost and energy consumption, convenient operation and maintenance, and no water use. All of that could effectively improve the utilization rate of coal resources and expand the economic benefits of enterprises. The application of high-speed, high-precision, and anti-interference online element rapid analysis technology in intelligent coal gangue separation equipment will become an inevitable trend of equipment development in the future with the continuous improvement of coal product demand. Online rapid element analysis technology includes laser-induced breakdown spectroscopy, dual-energy X-ray, and transient neutron activation analysis. Improving and applying more high-speed, high-precision algorithms such as partial least squares and Monte Carlo library least squares in the future are important.

A landscape of complex tandem repeats within individual human genomes

Markedly expanded tandem repeats (TRs) have been correlated with ~60 diseases. TR diversity has been considered a clue toward understanding missing heritability. However, haplotype-resolved long TRs remain mostly hidden or blacked out because their complex structures (TRs composed of various units and minisatellites containing >10-bp units) make them difficult to determine accurately with existing methods. Here, using a high-precision algorithm to determine complex TR structures from long, accurate reads of PacBio HiFi, an investigation of 270 Japanese control samples yields several genome-wide findings. Approximately 322,000 TRs are difficult to impute from the surrounding single-nucleotide variants. Greater genetic divergence of TR loci is significantly correlated with more events of younger replication slippage. Complex TRs are more abundant than single-unit TRs, and a tendency for complex TRs to consist of <10-bp units and single-unit TRs to be minisatellites is statistically significant at loci with ≥500-bp TRs. Of note, 8909 loci with extended TRs (>100b longer than the mode) contain several known disease-associated TRs and are considered candidates for association with disorders. Overall, complex TRs and minisatellites are found to be abundant and diverse, even in genetically small Japanese populations, yielding insights into the landscape of long TRs.

Baseline correction using morphological and iterative local extremum (MILE)

Baseline drift problem usually exists in the spectral analysis due to the detector nonlinearities and temperature variations. Therefore, the baseline must be corrected before accurate data analysis. So, we proposed a novel and high-precise algorithm, baseline estimation using morphological and iterative local extremum (MILE). We first obtained all local extrema of the measured spectrum by derivation. A coarse baseline is then estimated by the PCHIP interpolation method. Subsequently, find the local extrema again of coarse baseline and update by their adjacent data. The update processing iterates multiple times. Finally, the spectrum is corrected by subtracting the estimated baseline. In order to evaluate the performance of our algorithm, we corrected the baseline drift of various spectra, including chromatograms and Fourier Transform Spectrometer spectra. All results achieve a high precision, proving that our algorithm has better accuracy and robustness.

SKIN DISEASE DETECTION USING PYTHON AND DEEP LEARNING

Skin diseases are dangerous and highly contagious especially melanoma, basal cell carcinoma and toxic epidermal necrolysis (TEN). These skin diseases can be cured if detected early. The fundamental problem with this is that only experienced dermatologists can recognize and classify such conditions. Doctors may misclassify the disorder and prescribe the wrong drug for the patient. The paper proposed a skin disease detection tool based on image processing, machine learning and deep learning techniques. The proposed tools are non-invasive, easy-touse and accurate to identify appropriate skin conditions. The patient must provide images of the infected skin area as input. Also, with the help of image model training and high-precision algorithms, skin diseases can be detected with a very low percentage error. In this review, based on the accuracy, we used two different real-time skin detection methods &amp; compared convolutional neural networks (CNN) and random forests (RF). Real-time test results are also displayed.

LightCSPNet: A Lightweight Network for Image Classification and Objection Detection

In recent years, computer vision and convolutional neural networks have been gradually applied in embedded devices. However, due to the limitation of hardware, the inference speed of many high-precision algorithms is very slow, which requires high performance hardware. In this study, a lightweight network called LightCSPNet is proposed for image classification and object detection. LightCSPNet is built by stacking four identical modules, each of which has adopted an improved CSP (Cross-Stage-Partial-connections) structure for channel number expansion. The special inverse residual structure is constructed for feature extraction, and the transformer modules are added in the proposed model. In this study, the typical defect detection in industry is adopted as testing platform, and a defect dataset consisting of 12 categories including cloth, road, bridge, steel and etc., was constructed for image classification. Compared with MobileNetV3, our model has almost the same accuracy, but the number of parameters and GFLOPs (Giga Floating-point Operations Per Second) have been, respectively, reduced to 88% and 36% for ImageNet100 and the dataset we built. In addition, compared with MobileNetV2 and MobileNetV3 for VOC2012 dataset in object detection, LightCSPNet obtained 0.4% and 0.6% mAP (Mean Average Precision) improvement respectively, and the inference speed on CPU was twice as fast.

A high-precision aerosol retrieval algorithm for FY-3D MERSI-II images

The Medium Resolution Spectral Imager-II (MERSI-II) onboard the recently launched Chinese Fengyun-3D (FY-3D) satellite has great capability in detecting global aerosols as it includes aerosol bands similar to Moderate Resolution Imaging Spectroradiometer (MODIS). However, to date, aerosol retrieval based on MERSI-II is still limited to dark target regions and there is no official aerosol products for the MERSI-II. This study focuses on developing a high-precision algorithm to retrieve aerosol optical depth (AOD) suitable for entire land areas (except snow/ice and inland waters) based on MERSI-II measurements. Considering both the accuracy and retrieval efficiency, a new cost function is constructed based on (1) the fact that the AOD (550 nm) retrieved independently from different bands should be the same with the correct aerosol model, and (2) the assumption that the aerosol types are the same in the 5 × 5 km spatial range. The retrieval method based on the new cost function is nearly 50 times faster than most current methods using iterative calculations. To extend the application adaption of the FY-3D MERSI-II AOD retrieval and avoid the errors caused by the surface Lambertian hypothesis, a bidirectional reflectance distribution function (BRDF) database is built using MODIS products. Eight candidate aerosol models in different natural zones of China are constructed based on AERONET aerosol products from 2010 − 2021. The new method is applied to MERSI-II images over China and validated against ground-based measurements at 14 stations from 2020 to 2021. MODIS aerosol products from three operational algorithms are also used for comparison purposes. The results show that MERSI-II AOD retrievals agree well with the ground-based measurements with correlation coefficient (R), root mean square error (RMSE), and relative mean bias (RMB) of 0.913, 0.123, and 0.955, respectively. In addition, 72.19 % of AOD matchups fall within the expected error (EE) envelopes. The MERSI-II retrievals show higher accuracy than that of MODIS dark target (DT) and deep blue (DB) products and comparable accuracy of the MODIS Multi-Angle Implementation of Atmospheric Correction (MAIAC) product. MERSI-II AOD also shows higher stability in terms of spatial and temporal and better performance under heavy aerosol loading conditions than MODIS products. A good AOD agreement with R from 0.777 to 0.863 between MERSI-II and MODIS products is found over the land of China. The new method showing high retrieval efficiency and accuracy has great potential to be operationally applied on AOD retrieval for MERSI-II.

Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes

PurposeIn this paper, a superconvergent patch recovery method is proposed for superconvergent solutions of modes in the finite element post-processing stage of variable geometrical Timoshenko beams. The proposed superconvergent patch recovery method improves the solution speed and accuracy of the finite element analysis of a curved beam. The free vibration and natural frequency of the beam were considered for studying forced vibrations and structural resonance. Beam vibration mode analysis was performed for high-precision vibration mode solutions and frequency values. The proposed method can be used to compute beam vibration modes of beams with different shapes and boundary conditions as well as variable cross sections and curvatures. The purpose of this paper is to address these issues.Design/methodology/approachAn adaptive method was proposed to analyse the in-plane and out-of-plane free vibrations of the variable geometrical Timoshenko beams. In the post-processing stage of the displacement-based finite element method, the superconvergent patch recovery method and high-order shape function interpolation technique were used to obtain the superconvergent solution of mode (displacement). The superconvergent solution of mode was used to estimate the error of the finite element solution of mode in the energy form under the current mesh. Furthermore, an adaptive mesh refinement was proposed by mesh subdivision to derive an optimised mesh and accurate finite element solution to meet the preset error tolerance.FindingsThe results computed using the proposed algorithm were in good agreement with those computed using other high-precision algorithms, thus validating the accuracy of the proposed algorithm for beam analysis. The numerical analysis of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams helped verify that the solutions of frequencies were consistent with the results obtained using other specially developed methods. The proposed method is well suited for the mesh refinement analysis of a curved beam structure for analysing the changes in high-order vibration mode. The parts where the vibration mode changed significantly were locally densified; a relatively fine mesh division was adopted that validated the reliability of the mesh optimisation processing of the proposed algorithm.Originality/valueThe proposed algorithm can obtain high-precision vibration solutions of variable geometrical Timoshenko beams based on more optimized and reasonable meshes than the conventional finite element method. Furthermore, it can be used for vibration problems of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams. The proposed algorithm can be extended for application in superconvergent computation and adaptive analysis of finite element solutions of general structures and solid deformation fields and used for adaptive analysis of more complex plates, shells and three-dimensional structures. Additionally, this method can analyse the vibration and stability of curved members with crack damage to obtain high-precision vibration modes and instability modes under damage defects.

On the Combination of Harmonics and Polynoms in Econometric Modeling of RUB/AZN Exchange Rate

Conducting a combinational polynomial and spectral analysis of time series formed on the basis of daily observations of changes in the RUB/AZN exchange rate with pronounced fluctuations for the period 11.05.2017- 02.11.2018 based on computer econometric modeling.The purpose of the research. The possibility of describing the global rate dynamics by approximation with a combination of a nonlinear polynomial trend and harmonic oscillations of various frequencies relative to this curve; the ability to calculate amplitudes and phases, which can be used to estimate the power spectrum of the Fourier approximation; the ability to develop a high-precision algorithm for predicting exchange rate changes in RUB/AZN.Materials and methodology. The official statistics of the State Statistics Committee of Azerbaijan were used; classical methods of mathematical analysis and economic analysis; methods of econometrics, harmonic (Fourier) analysis, statistical spectral analysis, “Fourier analysis” of the MS Excel add-in, tools of the Eviews 8 application package with the standard deviation and average approximation error being taken into account, the necessary statistical procedures required for identifying and estimating the parameters of the model and checking its adequacy and accuracy.Results. By breaking up the empirical analysis of given time series into time-scale polynomial and time-frequency components. Combinations of the optimal degree of variants of polynomials up to the 11th degree and the number of harmonics of sines and cosines of all possible discrete frequencies were revealed.Conclusion. This result allows us to reconsider the asymmetric impact of RUB/AZN exchange rate pressure on the foreign trade balance between Russia and Azerbaijan. An increase/decrease in exchange rate pressure affects the likelihood of a ruble-manat crisis, while this phenomenon may negatively/positively affect the foreign trade balance and may make it difficult/easier to import resources, goods and services between countries. This, in turn, adds significance to the task of further detailed structuring and analysis of exchange rate changes in RUB/AZN in the face of increased sanction pressures against Russia, thereby actualizing the development of the retrospective part of the study.

High-precision camera calibration based on a 1D target.

In this paper, the problem of camera 1D calibration is well solved by our proposed high-precision algorithm, which can satisfy actual requirements. We present a viewpoint that the closed-form solution can simply achieve high calibration accuracy in the absence of distortion. So, we abandon the habitual strategy of global nonlinear optimization for all intrinsic and extrinsic parameters. The innovations of the proposed algorithm are three-fold: firstly, cyclic distortion correction method is introduced to ensure that the estimated distortion parameters gradually approach the exact values; secondly, a new criterion for the nonlinear optimization of distortion correction is developed; thirdly, we enhance the anti-noise ability of the closed-form solution by optimally weighting the constraint equations. Extensive experiments prove that the proposed algorithm provides the highest calibration accuracy and robustness, which is comparable to 2D calibration. In addition, our proposed algorithm provides a new approach for desirable distortion correction and an idea for 2D calibration of large field of view.

Linear discrete velocity model-based lattice Boltzmann flux solver for simulating acoustic propagation in fluids.

A linear lattice velocity model is developed, and a corresponding lattice Boltzmann flux solver (LBFS) is constructed based on it. This solver calculates the fluxes of the linearized Euler equations (LEEs), which are discretized by the finite volume method (FVM), and can simulate acoustic propagation in fluids. First, the expressions for the distribution function and the lattice velocity of the linear discrete velocity model are constructed using the moment relations in linear form. Second, based on Chapman-Enskog analysis and moment relations, the mesoscopic flux expression can be constructed by comparing the linear lattice Boltzmann equation and LEEs. Finally, the developed scheme is used to calculate the LEE flux term. The developed linear lattice velocity model-based LBFS has the following advantages: (i) It extends the lattice Boltzmann model-based flux solver from solving the macroscopic equations of fluid dynamics to solving linear equations; (ii) it also inherits the advantages of the Boltzmann model-type flux solver. The variables at the interface are calculated from the local solution of the lattice Boltzmann equation, making it more physical. In addition, least-squares-based finite differences and Gaussian integration are used for the FVM to discretize the LEE, making it a high-precision algorithm. Thus, the developed algorithm can accurately capture acoustic propagation in fluids and acoustic scattering in complex geometries. Several numerical cases for propagating acoustics in fluids are simulated to validate the accuracy and robustness of the present algorithm, and an accuracy test shows it approaches fourth-order accuracy.