Element Error Research Articles

Optimal proposal particle filters for detecting anomalies and manoeuvres from two line element data

Detecting the manoeuvres of satellites is an important goal within the broader task of space situational awareness. Moreover, it is advantageous to be able to detect other anomalous behaviour from satellites arising from, for instance, collisions or malfunction. The Two Line Element (TLE) data published by NORAD is the only publicy-available comprehensive source of data for satellite orbits. This paper presents a filtering approach for detecting anomalies in satellite orbits from TLE data. Particle filters are deployed to track the state of the satellites’ orbits. New TLEs that are deemed sufficiently unlikely given one’s belief of the current orbital state are designated as anomalies. The change in the orbits over time is modelled using the SGP4 model. However, it is shown that this model can have large errors in certain elements in some instances. The structure of these errors is analysed and a suitable model uncertainty is derived. The optimal proposal filter is used to further reduce the impact of the errors in the SGP4 model. This strategy improves the proposal distribution from which the particles are drawn before re-weighting, so that the resulting weights are less degenerate. The proposed techniques are evaluated on a benchmark set of 15 satellites for which an externally-obtained ground truth is available, along with simulated orbital data with inserted manoeuvres. Although this benchmark is larger than the evaluation sets used in other published work, it cannot be representative of the full population of satellites and so more emphasis is placed on the simulated data. The proposed techniques are compared against a baseline, which is similar to many previously-proposed techniques for satellite manoeuvre detection. The particle filters are shown to be superior at detecting the subtle in-track and cross-track manoeuvres in the simulated dataset. However, on the benchmark dataset, a simple baseline that focusses on the mean motion can perform equivalently to the best filters. This simple technique is likely overfit to the benchmark.

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb gauge

Abstract Recently, it has been proposed to compute parton distributions from boosted correlators fixed in the Coulomb gauge within the framework of Large-Momentum Effective Theory. This method does not involve Wilson lines and could greatly improve the efficiency and precision of lattice QCD calculations. However, there are concerns about whether the systematic uncertainties from Gribov copies, which correspond to the ambiguity in lattice gauge-fixing, are under control. This work gives an assessment of the Gribov copies’ effect in the Coulomb-gauge-fixed quark correlators. We utilize different strategies for the Coulomb-gauge fixing, selecting two different groups of Gribov copies based on the lattice gauge configurations. We test the difference in the resulted spatial quark correlators in the vacuum and a pion state. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise. This demonstrates that the effect of the Gribov copies can be neglected in the practical lattice calculation of the quark parton distributions.

A deep convolutional neural network for blind element error correction of spatial heterodyne spectrometer using line selective convolutional blocks

The "GF Special Project" is a massive remote sensing technology initiative including a number of satellites and various observation platforms. GF-5 is the satellite with the most payloads, the highest spectral resolution, and the most difficulty in development, and it can monitor a variety of environmental elements using spatial heterodyne spectroscopy (SHS) technology, including atmospheric aerosols, carbon dioxide, methane, terrestrial vegetation, straw burning, and urban heat islands. In this study, a novel blind element error correction technique based on deep learning network is investigated and developed for spatial heterodyne interferograms, as well as the formation mechanism and distribution characteristics of the SHS interferometric data. LSConv-Net, a new CNN model, was created and trained to denoise in the presence of high-density and ultra-high-density blind element errors. We do this by introducing a new line-selective convolutional (LSConv) block. Simultaneously, experimental validation of blind element error correction utilizing laboratory water vapor interferometric data and atmospheric CO2 absorption interferometric data from GF-5, and the change in FWHM before and after the experiment was tested using potassium lamp interferograms. Experiments show that the Deep neural networks trained with this model may successfully suppress the effect of blind element noise on spectra, recover spectra that have been overwhelmed by high-density blind element noise without any effect on other non-blind pixels, and surpass all similar techniques in terms of spectral recovery.

Error analysis of a fully discrete projection method for Cahn–Hilliard Inductionless MHD problems

This article investigates the fully discrete finite element approximation and error analysis for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn–Hilliard equations, Navier–Stokes equations and Poisson equations, which are nonlinearly coupled through convection, stresses, and Lorentz forces. To address this highly nonlinear and multi-physics system, we propose a fully discrete energy stable scheme with the finite element projection method for spatial discretization, in which the velocity and pressure are decoupled. The temporal discretization is a combination of the first-order Euler semi-implicit scheme and a convex splitting energy strategy. We show that the proposed scheme is mass-conservative, charge-conservative and unconditional energy stable. The error estimates for the phase variable, chemical potential, velocity, pressure, current density and electric potential are rigorously established. Finally, several three-dimensional numerical experiments are performed to illustrate the features of the proposed numerical method and verify the theoretical conclusions.

Robust methods for multiscale coarse approximations of diffusion models in perforated domains

For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale numerical methods, this coarse space is spanned by locally discrete harmonic basis functions. Along the subdomain boundaries, the basis functions are piecewise polynomial. The main contribution of this article is an error estimate regarding the H1-projection over the coarse space; this error estimate depends only on the regularity of the solution over the edges of the coarse partitioning. For a specific edge refinement procedure, the error analysis establishes superconvergence of the method even if the true solution has a low general regularity. Additionally, this contribution numerically explores the combination of the coarse space with domain decomposition (DD) methods. This combination leads to an efficient two-level iterative linear solver which reaches the fine-scale finite element error in few iterations. It also bodes well as a preconditioner for Krylov methods and provides scalability with respect to the number of subdomains.

Dynamic Polarization Patterning Technique for High-Quality Liquid Crystal Planar Optics

The Pancharatnam–Berry (PB)-phase liquid crystal (LC) planar optical elements, featuring large apertures and a light weight, are emerging as the new generation optics. The primary method for fabricating large-aperture LC planar optical elements is through photo-alignment, utilizing polarization laser direct writing. However, conventional polarization direct writing suffers from an inertia-induced stopping step during splicing, leading to suboptimal optical effects. Here, we propose a novel highly efficient method for arbitrary polarization patterning, significantly reducing interface splicing errors in these optical elements. (We call it dynamic polarization patterning technology). This process involves simultaneous mobile splicing and real-time generation of different polarization patterns for exposure, eliminating the inertia-related splicing interruption. As a demonstration, we fabricated a lens with an aperture of approximately 1 cm within 30 min at 633 nm. Furthermore, we developed a 100% fill-factor lens array (3 × 3) with an element lens diameter of approximately 7 mm within 1.5 h at 532 nm. Their focal lengths were uniformly set at 30 cm, demonstrating superior convergence capabilities within their designated working wavelengths, alongside commendable performance in converging light across various other wavelengths. Our measurements confirmed the good focusing performance of these samples. The convergence spot size of the lens deviated by approximately 40% from the theoretical diffraction limit, whereas the lens array exhibited a deviation of around 30%. The dynamic polarization direct writing during uniform platform movement reduced splicing errors to a mere 100–200 nm. The enhancement in imaging quality can be primarily attributed to the innovative use of mobile polarization splicing exposure technology, coupled with the inherent self-smoothing properties of LC molecules. This synergy significantly mitigates the impact of seam diffraction interference.

Guided Lamb Wave Array Time-Delay-Based MUSIC Algorithm for Impact Imaging.

Composite materials, valued in aerospace for their stiffness, strength and lightness, require impact monitoring for structural health, especially against low-velocity impacts. The MUSIC algorithm, known for efficient directional scanning and easy sensor deployment, is gaining prominence in this area. However, in practical engineering applications, the broadband characteristics of impact response signals and the time delay errors in array elements' signal reception lead to inconsistencies between the steering vector and the actual signal subspace, affecting the precision of the MUSIC impact localization method. Furthermore, the anisotropy of composite materials results in time delay differences between array elements in different directions. If the MUSIC algorithm uses a fixed velocity value, this also introduces time delay errors, further reducing the accuracy of localization. Addressing these challenges, this paper proposes an innovative MUSIC algorithm for impact imaging using a guided Lamb wave array, with an emphasis on time delay management. This approach focuses on the extraction of high-energy, single-frequency components from impact response signals, ensuring accurate time delay measurement across array elements and enhancing noise resistance. It also calculates the average velocity of single-frequency components in varying directions for an initial impact angle estimation. This estimated angle then guides the selection of a specific single-frequency velocity, culminating in precise impact position localization. The experimental evaluation, employing equidistantly spaced array elements to capture impact response signals, assessed the effectiveness of the proposed method in accurately determining array time delays. Furthermore, impact localization tests on reinforced composite structures were conducted, with the results indicating high precision in pinpointing impact locations.

GIS-BASED REAL-TIME GAS LEAK DETECTION SYSTEM AT BASKENT NATURAL GAS DISTRIBUTION COMPANY

Abstract. Natural gas has been used for heating and production purposes in Turkey since 1987, and every passing year, the natural gas pipeline network continues to expand with investments. The distribution of natural gas within urban areas is achieved through a complex network structure formed by the joining of Polyethylene (PE) and Steel (ST) pipes using various connection elements. This complex structure is susceptible to deformation over time due to various reasons such as corrosion in steel lines, manufacturing errors in connection elements in PE lines, and other factors. As a result, natural gas leaks occasionally occur in these pipelines. The leakage control process in natural gas pipelines is carried out using specially designed equipment and vehicles equipped for this purpose. However, while these systems may be sufficient for collecting the necessary data for leak detection, the complex structure of the distribution network and the necessary data for leak detection, the complex structure of the distribution network and the necessity of performing this process with multiple teams bring about many challenges in terms of tracking, management, and reliability of the operation. At this point, the advancement of GIS (Geographic Information System), mobile, and communication technologies has made it possible to overcome these challenges. In this study, a real-time GIS-supported leak detection system developed using these technologies for Başkent Natural Gas Distrubition Inc. (Başkentgaz), which provides natural gas distribution services in Ankara, has been described. The study discusses the benefits brought by this system to the natural gas leak detection process.

A unified immersed finite element error analysis for one-dimensional interface problems

It has been known that the traditional scaling argument cannot be directly applied to the error analysis of immersed finite elements (IFE) because, in general, the spaces on the reference element associated with the IFE spaces on different interface elements via the standard affine mapping are not the same. By analyzing a mapping from the involved Sobolev space to the IFE space, this article is able to extend the scaling argument framework to the error estimation for the approximation capability of a class of IFE spaces in one spatial dimension. As demonstrations of the versatility of this unified error analysis framework, the manuscript applies the proposed scaling argument to obtain optimal IFE error estimates for a typical first-order linear hyperbolic interface problem, a second-order elliptic interface problem, and the fourth-order Euler-Bernoulli beam interface problem, respectively.

Optimizing Controls to Track Moving Targets in an Intelligent Electro-Optical Detection System

Electro-optical detection systems face numerous challenges due to the complexity and difficulty of targeting controls for “low, slow and tiny” moving targets. In this paper, we present an optimal model of an advanced n-step adaptive Kalman filter and gyroscope short-term integration weighting fusion (nKF-Gyro) method with targeting control. A method is put forward to improve the model by adding a spherical coordinate system to design an adaptive Kalman filter to estimate target movements. The targeting error formation is analyzed in detail to reveal the relationship between tracking controller feedback and line-of-sight position correction. Based on the establishment of a targeting control coordinate system for tracking moving targets, a dual closed-loop composite optimization control model is proposed. The outer loop is used for estimating the motion parameters and predicting the future encounter point, while the inner loop is used for compensating the targeting error of various elements in the firing trajectory. Finally, the modeling method is substituted into the disturbance simulation verification, which can monitor and compensate for the targeting error of moving targets in real time. The results show that in the optimal model incorporating the nKF-Gyro method with targeting control, the error suppression was increased by up to 36.8% compared to that of traditional KF method and was 25% better than that of the traditional nKF method.

Structural method for increasing the accuracy of converting parameters of the complex resistance of traction power supply objects into a time-frequency signal

The article discusses the principles of operation of quasi-balanced bridge converters with closely inductive couplings between the arms, having an extended range and maximum sensitivity by creating a parametric auto-resonant mode by changing the supply frequency of the measuring bridge. To reduce the errors of the conversion elements, a conversion algorithm based on a mathematical model is proposed, and a schematic diagram of a capacitive sensor parameter into code using a microcontroller is given.

Виброактивность электромеханических устройств вследствие наличия технологических погрешностей

This article discusses a theoretical justification for the presence of vibration in operating modes of electromechanical devices due to technological errors occurring during the machining of parts and assembly of products. The reason for the presence of a dense spectrum of vibration caused by technological errors in the structural elements of ball bearings (outer and inner rings, balls, and cage) is also denoted. The analytical dependence of the vibration amplitude on the magnitude of technological errors is shown. It follows from the results of the analysis that for the most effective minimization of the vibration activity of an electromechanical device, it is necessary to use broadband damping, which is liquid–viscous in most cases. In addition to the above, it is advisable to apply damping in the cascade version. When solving the system of vibration equations for an electromechanical device, replacing ball bearings with sliding bearings eliminates the first four terms, which characterize a wide and dense vibration spectrum of the ball bearings in the operating mode of the electromechanical device.

Finite element error analysis of affine optimal control problems

This paper is concerned with error estimates for the numerical approximation for affine optimal control problems subject to semilinear elliptic PDEs. To investigate the error estimates, we focus on local minimizers that satisfy certain local growth conditions. The local growth conditions we consider in this paper appeared recently in the context of solution stability and contain the joint growth of the first and second variation of the objective functional. These growth conditions are especially meaningful for affine control constrained optimal control problems because the first variation can satisfy a local growth, which is not the case for unconstrained problems. The main results of this paper are the achievement of error estimates for the numerical approximations generated by a finite element scheme with piecewise constant controls or a variational discretization scheme. Even though the growth conditions considered are weaker than those appearing in the recent literature on finite element error estimates for affine problems, this paper substantially improves the existing error estimates for both the optimal controls and the states when a Hölder-type growth is assumed.

Bearing‐only motion analysis of target based on low‐quality bearing‐time recordings map

AbstractAccurate bearing‐time recordings play a crucial role in hydroacoustic target motion analysis and situation estimation. The target bearing estimated by vector hydrophone in the interference environment suffers from poor display and low signal‐to‐noise ratio. To solve this problem, a two‐stage bearing‐only motion analysis method is proposed. Firstly, the bearing peak information and bearing dispersion are extracted for each sampling moment of the bearing‐time recording. Custom constraint regions and adaptive parameters are then set based on this information. The order truncate average algorithm is improved to enhance the quality of the low‐quality bearing‐time recording map. Secondly, a bearing‐only target motion model is established based on the bearing‐time recording distribution features, and a bearing‐time recording trust interval is constructed. Then a modified pseudo‐linear estimation algorithm is proposed to solve the target motion situation information, including target abeam time, target abeam bearing, target course, velocity‐to‐initial‐distance ratio, and so forth. Finally, by comparing the solved values of the sea trial data with the automatic identification system calculation results, the enhancement effect of the target bearing‐time recording map is significant and the solving error of the target motion elements meets the needs of engineering applications.

Evaluation of an internal standard-free laser ablation-ICP-OES method for elemental analysis in solid food samples

Although the laser ablation-inductively coupled plasma-optical emission spectrometry (LA-ICP-OES) is a promising method for the elemental screening of solid food materials, the main challenge associated with this technique is the lack of commercial solid standard reference materials to serve as the external standard for quantitative calibration. In this study, a reliable internal standard-free LA-ICP-OES method for direct sampling and analysis of solid food materials was developed. The method relies on the carbon internally-standardized relative sensitivity factor (CIS-RSF) was developed, eliminating the need for calibration curves or matrix-matched external standards once the CIS-RSF has been determined. After careful evaluation of the effect of the instrumental operating parameters on the long-term stability of CIS-RSFs, this method was used to analyze a variety of microelements, including sulfur (S), phosphorus (P), zinc (Zn), iron (Fe), manganese (Mg), magnesium (Mn), copper (Cu), calcium (Ca), strontium (Sr), barium (Ba), sodium (Na), and potassium (K), with the limit of quantitation (LOQ) ranging from 0.06 (Sr) to 400 μg g−1 (S). The accuracy and reproducibility of this proposed method were evaluated through the analysis of three food NIST reference materials and six typical food samples. The results indicated that the relative error of most target elements was less than 20% and the reproducibility (SD, n = 3) more than 10%. This developed LA-ICP-OES screening method has great potential for the high-throughput multielement determination of various solid food materials.

IFISS3D: A Computational Laboratory for Investigating Finite Element Approximation in Three Dimensions

IFISS is an established MATLAB finite element software package for studying strategies for solving partial differential equations (PDEs). IFISS3D is a new add-on toolbox that extends IFISS capabilities for elliptic PDEs from two to three space dimensions. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error estimation, as well as iterative solvers. The package is designed to be useful as a teaching tool for instructors and students who want to learn about state-of-the-art finite element methodology. It will also be useful for researchers as a source of reproducible test matrices of arbitrarily large dimension.

Research on artificial neural networks to accurately predict element concentrations in nutrient solutions

Calcium, potassium, nitrogen, magnesium, and phosphorus, the main elements of the nutrient solution, are absorbed by plants and play an important role in plants. By measuring Ca2+, K+, Mg2+, NH4 +, NO3 −, HPO4 2−, the artificial neural networks (ANNs) were used in this study to accurately calculate the concentrations of these elements. Firstly, the error sources of the calculating element concentration were analyzed based on the data of six-ion measurement experiments. Subsequently, various optimization algorithms were compared to optimize back propagation and radial basis function ANNs. Finally, the results of mean relative errors (MREs) and recovery values show that ANNs can effectively reduce the measurement error of ion sensors. From the perspective of recovery values, the prediction error of all elements can be controlled within 15%. From the perspective of MRE, except for magnesium and phosphorus elements, the improved model prediction errors of other elements were also less than 10%.

Research on Power Decoupling and Parameter Mismatch of Three-Port Isolated Resonant DC–DC Converter Applied Switch-Controlled Capacitor

In order to realize the controllable power decoupling and eliminate the influence of the parameter error of the resonant elements, a three-port DC-DC converter applied switch-controlled capacitor is proposed. The operating principle and transmission power expression of the proposed three-port converter under triple-phase-shift control are analyzed. By adjusting the phase shift angle of the switch-controlled capacitor (SCC) to adjust the resonant frequency of the resonant tanks, the topology-level power decoupling of the circuit at a constant frequency can be achieved. The addition of switch-controlled capacitors provides more freedom for power regulation between ports. Besides, according to the proposed converter, a design method for the parameters of the resonant tank is proposed to eliminate the adverse effects caused by the parameter error of the resonant elements. Then an optimized triple-phase-shift modulation strategy is adopted to achieve the minimum RMS value of the resonant converter. An experimental prototype was designed to verify the correctness of the proposed converter and modulation strategy.

Design and adaptive finite element simulation of conformal transformation optics devices with isotropic materials

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters; then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented; finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material.

An Efficient Finite Element Method and Error Analysis Based on Dimension Reduction Scheme for the Fourth-Order Elliptic Eigenvalue Problems in a Circular Domain

In this paper, we propose an effective finite element method for the fourth order elliptic eigenvalue problems in a circular domain. First, by using polar coordinates transformation and the orthogonal property of Fourier basis functions, the original problem is turned into a series of equivalent one-dimensional eigenvalue problems. Second, according to the properties of Laplace operator in polar coordinate, we deduce the polar conditions and introduce suitable weighted Sobolev space. Based on the polar conditions and weighted Sobolev space, we establish the weak form and the corresponding discrete form. Third, we prove the error estimates of approximation eigenvalues and eigenvectors by means of the spectral theory of compact operators for each one-dimensional eigenvalue system. Finally, we provide some numerical experiments to show the validity of the algorithm and the correctness of the theoretical results.