Element Error Research Articles

Verification of Phase Shifter Measurements of a Reflective Array Antenna

Introduction. Large-size phased antenna arrays (PAA) frequently incorporate optical excitation schemes, whose main elements include the feed and the reflective aperture. In turn, the reflective aperture consists of several tens of thousands of radiators and phase shifters. Major distortions of the radiation pattern in reflective arrays occur due to phase errors, leading to a decrease in the gain and an increase in the side lobes of the radiation pattern. In the millimeter wavelength range, ferrite phase shifters can have an initial phase from 0 to 360 °, thus requiring measurements of the array elements following their assembly.Aim. To develop a method for evaluating errors in measurements of the parameters of phase shifters incorporated in an antenna array by comparing theoretical and experimental data.Materials and methods. A convenient method for determining the parameters of phase shifters is probing, in which a movable probe is connected in series with each array element. In cases where a PAA element represents a single structure consisting of a ferrite segment and a dielectric radiator, measurements are carried out using a probe in the form of a segment of a round waveguide moving towards the radiator. In order to evaluate the measurement error of such a scheme, a mechanically controlled reference phase shifter was used.Results. Measurement errors for the probe structure used were calculated based on the assumption of the phase error arising from the vector addition of the controlled and uncontrolled reflected signals at the input of the PAA element, in the section of the reference plane at the input of the probe. In addition, the S-parameters of the superposition section were calculated. The extrema of the error function were used to determine the maximum errors in measuring the phase and amplitude.Conclusion. The performed analysis confirmed the validity of the proposed method for measuring the parameters of phase shifters using a waveguide probe. The measurement error of the PAA elements according to the proposed scheme was found to be about 3 o, which is commensurate with that of recording devices.

Mathematical models for calculating the quantitative characteristics of the optimal quantization of information

Various additional mathematical aspects related to solving the problem of optimal information quantization in the sense of filling are considered, such as control of quantum elements, accounting for errors of quantum elements, determining the amount of information during quantization, and determining the numerical values of fractals of distributions represented as a sequential fractal distribution. The purpose of the article is to consider additional questions based on a specific "heavy" probability distribution the normal distribution. The considered questions are made in order to facilitate the solution of applied problems for researchers dealing with the problem of information quantization.

Анализ вероятностных характеристик электрических параметров широкополосного балансного смесителя частот СВЧ радиосигналов на базе резонансно-туннельных диодов и оценка его надежности

The object of research is the broadband balanced SHF mixer (BM) based on resonant-tunneling diodes (RTDs). The research goals are to perform the statistical analysis of BMs design parameters technological errors impact on its electrical characteristics scatter, and to analyze the kinetics of these characteristics under the destabilizing factors influence. The ranging of BMs design parameters technological errors impacts on its electrical characteristics scatter revealed that the biggest impact is made by the technological errors of the BMs non-linear elements I-V characteristics. The BMs reliability study revealed that to ensure the studied BMs reliability during operation under high temperatures impact the design and technological optimization of the BMs electrical characteristics is required.

Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading

The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in the discrete formulation due to a relaxation of the divergence constraint which means that they are not pressure-robust. A recent reconstruction approach for classical methods recovers this invariance property for the discrete solution, by mapping discretely divergence-free test functions to exactly divergence-free functions in the sense of {varvec{H}}({text {div}}). Moreover, the Stokes solution has locally singular behavior in three-dimensional domains near concave edges, which degrades the convergence rates on quasi-uniform meshes and makes anisotropic mesh grading reasonable in order to regain optimal convergence characteristics. Finite element error estimates of optimal order on meshes of tensor-product type with appropriate anisotropic grading are shown for the pressure-robust modified Crouzeix–Raviart method using the reconstruction approach. Numerical examples support the theoretical results.

Path Planning and Trajectory Tracking Strategy of Autonomous Vehicles

With the development of global urbanization and the construction of regional urbanization, residents around urban cities are increasingly making demands on urban public transportation system. A new kind of modern public transportation vehicle named Multi-Articulated Guided Vehicle based on Virtual Track (MAAV-VT) with the advantages of beautiful, smart energy conservation and environmental protection is proposed in this paper, which aims at optimizing the public transportation system between and within urban areas. Therefore, concentrating on the general design and control strategy, the main contents of this paper are as follows. At first, the design concepts and key technologies of MAAV-VT are introduced. It is the fusion of urban rail transit operation mode and advanced automotive technologies, which have the characteristics of 100% low-floor, medium to high velocity, medium to big capacity, and low construction cost. Then, as the core subsystem, to guarantee the properties of self-guiding and trajectory tracking of the new vehicle, this paper is focused on the control system based on the dynamics and kinematics model of the whole multi-articulated vehicle. The multi-trace-points cooperative trajectory tracking control strategy on the basis of the circulation of feasible path generation method is proposed and the lateral controller is designed for trajectory tracking. The process of feasible path generation is conducted once the tracking error exceeded. A simulation platform is built considering the mechanical properties of each vehicle element and the characteristic of articulated mechanism. Finally, the function of control system is validated. The tracking error of each vehicle elements would be reduced to make sure the whole multi-articulated vehicle moves along the preset virtual track.

Sparse tensor product high dimensional finite elements for two-scale mixed problems

We develop the essentially optimal sparse tensor product finite element method for solving two-scale mixed problems in both the primal and dual forms. We study the two-scale homogenized mixed problems which are obtained in the limit where the microscopic scale tends to zero. These limiting problems are posed in a high dimensional tensorized product domain. Using sparse tensor product finite elements, we solve these problems with essentially optimal complexity to obtain an approximation for the solution within a prescribed accuracy. This is achieved when the solutions of the high dimensional two-scale homogenized mixed problems possess sufficient regularity with respect to both the slow and the fast variable at the same time. We show that this regularity requirement holds when the two-scale coefficient and the forcing satisfy mild smoothness conditions. From the finite element solutions for the two-scale homogenized mixed problems, we construct numerical correctors for the solutions of the original two-scale mixed problems. We prove an error estimate for these correctors in terms of both the homogenization error and the finite element error. Numerical examples confirm the theoretical results.

Determination of the Content of Impurity Elements in Aluminum Alloy by XRF Analysis

Aluminum alloy is one of the most widely used metal materials in today’s society. Measurement and analysis of its impurity elements can effectively improve the performance of aluminum alloy. Energy dispersive X-ray fluorescence spectrometry (EDXRF) was used to analyze the types and contents of impurity elements in aluminum alloys, and the best working conditions for the EDXRF analyzer to measure impurity elements in aluminum alloys were determined. The absorption and enhancement effect of Al, Zn, Cu on impurity elements in Ti, Cr, Mn, Fe, Cu, Zn in aluminum alloy was discussed, and the empirical coefficient method was used to correct it. The analytical precision of EDXRF was evaluated. The data show that the average relative errors of the impurity elements in the aluminum alloy are Ti: 7.50%, Cr: 2.48%, Mn: 0.99%, Fe: 3.49%, Cu: 0.44%, Zn: 0.14%, respectively. It shows that the XRF measurement method is feasible and the accuracy meets the requirements of engineering design.

Determination of the errors first component in the tolerance field structure of the inter-transition size for the transformation of geometric elements in the structure of the initial blanks

To determine the errors first component in the tolerance field structure of the inter-transition size the knowledge base of the production technological preparation by seven levels of its basic objects of functionally different types is used. The task is solved in the working space of working machines, in the structure of which two technological schemes are built: for basing the initial blanks in working machines and for basing form elements in working machines and their geometric forming on working machines. Technological schemes for basing the initial blanks into working machines in the general case have a significant impact on the geometric and dimensional errors (the considered component) of the shape elements to be converted in the technological schemes for basing form elements into working machines and their geometric forming on working machines. It is shown that the determination of the errors first component in the tolerance field structure of the inter-junction size must be carried out by means of specialized intelligent control and measuring systems, embedding them in the structure of working machines. Determination of the first component in the tolerance field structure of the inter-transition size is relevant, has scientific novelty and practical significance. Keywords technological preparation of production; cutting processing; system analysis; information technology; modeling solutions; systems technology

球域上椭圆方程有效的有限元方法和误差分析

球域上椭圆方程有效的有限元方法和误差分析

Quasi-Monte Carlo Finite Element Analysis for Wave Propagation in Heterogeneous Random Media

We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of wave propagation modeled by the Helmholtz equation in a bounded region in which the refractive index is random and spatially heterogenous. Our focus is on the case in which the region can contain multiple wavelengths. We bypass the usual sign-indefiniteness of the Helmholtz problem by switching to an alternative sign-definite formulation recently developed by Ganesh and Morgenstern Numer. Algorithms, 83 (2020), pp. 1441--1487. The price to pay is that the regularity analysis required for QMC methods becomes much more technical. Nevertheless we obtain a complete analysis with error comprising stochastic dimension truncation error, finite element error, and cubature error, with results comparable to those obtained for the diffusion problem.

Moving Least Squares Interpolation Based A-Posteriori Error Technique in Finite Element Elastic Analysis

The performance of a-posteriori error methodology based on moving least squares (MLS) interpolation is explored in this paper by varying the finite element error recovery parameters, namely recovery points and field variable ... | Find, read and cite all the research you need on Tech Science Press

New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints

We study first-order necessary optimality conditions and finite element error estimates for a class of distributed parabolic optimal control problems with pointwise state constraints. It is demonstrated that, if the bound in the state constraint and the differential operator in the governing PDE fulfil a certain compatibility assumption, then locally optimal controls satisfy a stationarity system that allows to significantly improve known regularity results for adjoint states and Lagrange multipliers in the parabolic setting. In contrast to classical approaches to first-order necessary optimality conditions for state-constrained problems, the main arguments of our analysis require neither a Slater point, nor uniform control constraints, nor differentiability of the objective function, nor a restriction of the spatial dimension. As an application of the established improved regularity properties, we derive new finite element error estimates for the dG(0) − cG(1)-discretization of a purely state-constrained linear-quadratic optimal control problem governed by the heat equation. The paper concludes with numerical experiments that confirm our theoretical findings.

Fabrication-error analysis of injection-molded aspheric elements using typical aberration terms in transmitted wavefront with Shack–Hartmann wavefront-sensing measurement

Aspheric lenses help meet the most demanding optical requirements while the precision injection molding technique hits the target for precision and cost. We developed a method of analyzing aberration terms in the transmitted “wavefront measurement,” determined by Shack–Hartmann wavefront sensing to estimate the fabrication errors of injection-molded aspheric elements. Considering aspheric element fabrication using a small training data set and F-measure fuzzy cluster analysis, an unsupervised learning method was applied to extract typical aberration terms from the wavefront polynomial. The experimental results suggest that these aberration terms, which are related to spherical (third-, fifth-, and seventh-order) and coma (third-order) aberration terms in the transmitted wavefront polynomial expansion, can be employed to estimate the surface error and decenter, respectively, of a lens from a specific mold cavity. The sampling lenses evaluated in the proposed measuring process were collected from different mold cavities according to their total working performance in the modulated transfer function measurement for the whole camera module. The performances of the typical aberration terms were discussed by comparing to the ones obtained from an interferometer and a profilometer. The proposed method could provide high detection efficiency and can thus be applied for the quality control of aspheric elements for mobile phones, where the existing errors are mainly spherical, coma, and astigmatism aberrations.

Calculation of Uncertainties in Operating Strapdown Inertial Navigation Systems on Mobile Objects

The calculation of errors of the main elements of algorithms in the operation of a strapdown inertial navigation system on moving objects is undertaken. Four coordinate systems have been treated, in which the necessary equations for the projections of vectors on the axis of coordinate systems have been obtained for their further use in the construction of system algorithms. The transition matrices for different coordinate systems are compiled, and the dependences of these systems on each other are obtained. When determining the speed of a moving object, the equations of the orientation errors of the object have been compiled. Errors in the operational algorithms of a strapdown inertial navigation system have been simulated, which consist of errors in determining the speeds, coordinates, and orientation of an object. A structural diagram of the navigation system is compiled demonstrating the formation of errors. It is shown that the errors considered depend on the accuracy of the sensitive elements—gyroscopes and accelerometers. A relationship between the specified accuracy of the navigation system and the requirements for the accuracy of sensitive elements is revealed.

An iterative rectification procedure analysis for historical timber frames: Application to a cultural heritage Chinese Pavilion

The paper deals with the challenging problem of the rectification of leaning 3D historical timber frames. A prestigious case study is analyzed, namely the Feiyun Pavilion, PRC. Detailed onsite investigations on geometry, out-of-verticality, damages, material properties and building details are carried out. A finite element (FE) trial and error numerical procedure of rectification is then proposed in a general framework, basing on a discretization into FEs of the frame in its deformed configuration and on the application of horizontal displacements at the nodes belonging to the external box edges. The procedure is automatized in Ansys commercial code; beams, pillars and braces are modeled with an elasto-plastic orthotropic material, whereas for joints non-linear translational and rotational springs are utilized, with non-linear constitutive relationships deduced from suitable experimentation. The following phases define the core of the rectification algorithm: (i) application of the anti-displacements that equal the experimentally measured out-of-verticality values to produce corrective forces, (ii) strengthening of the joints and elements to improve structural stiffness, e.g. with hooping steel belts and reinforcing plate, (iii) removal of the corrective forces and consequent elastic return of the structure to a new position that still exhibits deviation, (iv) re-application of anti-displacements equal to the residual deviation found in (i)+(iii), (v) repetition of phase (i), (iii) and (iv) until the residual deviation is eliminated. The corrective displacements can be obtained by the superposition of anti-displacements applied in each cycle. The procedure is successfully applied in a single benchmark and -using an approximate but effective way- to the complex leaning structure under consideration which requires huge restoration. The approach shows excellent rectification capabilities in the idealized case, as well as a fairly good performance in the case of the existing structure considered as case study, where different deterioration phenomena are taken into account.

Prediction-Based Error Correction for GPU Reliability with Low Overhead

Scientific and simulation applications are continuously gaining importance in many fields of research and industries. These applications require massive amounts of memory and substantial arithmetic computation. Therefore, general-purpose computing on graphics processing units (GPGPU), which combines the computing power of graphics processing units (GPUs) and general CPUs, have been used for computationally intensive scientific and big data processing applications. Because current GPU architectures lack hardware support for error detection in computation logic, GPGPU has low reliability. Unlike graphics applications, errors in GPGPU can lead to serious problems in general-purpose computing applications. These applications are often intertwined with human life, meaning that errors can be life threatening. Therefore, this paper proposes a novel prediction-based error correction method called Prediction-based Error Correction (PRECOR) for GPU reliability, which detects and corrects errors in GPGPU platforms with a focus on errors in computational elements. The implementation of the proposed architecture needs a small number of checkpoint buffers in order to fix errors in computational logic. The PRECOR architecture has prediction buffers and controller units for predicting erroneous outputs before performing rollback. Following a rollback, the architecture confirms the accuracy of its predictions. The proposed method effectively reduces the hardware and time overheads required to correct errors. Experimental results confirm that PRECOR efficiently fixes errors with low hardware and time overheads.

Finite element error analysis on transmission shaft parts and application of local mesh refinement

In view of the strength problem of the transmission shaft parts in the swinging and punching structure of the forging press, based on the finite element analysis theory and the mesh refinement method, the accuracy of the finite element calculation in the whole mesh refinement process is analyzed by comparing the element strain energy error and the energy percentage error of different node numbers. The results show that the edge length of the discretized element is reduced and the calculation accuracy is improved correspondingly, but the calculation amount of the whole mesh refinement is large.Therefore, local mesh refinement is applied to improve the calculation accuracy. The results show that the error of energy percentage tends to be 10%, and the calculation accuracy is high. The accuracy analysis method and the application of local grid refinement provide the theoretical basis for the structural optimization of mechanical products.

First-principles calculation of higher-order elastic constants using exact deformation-gradient tensors

We propose a general and easy-to-use method of the ab initio calculation of the higher-order elastic constants, which is based on the analytical formulas for the deformation-gradient tensors as functions of the Lagrangian strain. The method allows for elimination of the truncation errors in the Taylor expansion series of the deformation gradients and is particularly useful to calculate the fourth-order elastic constants, where large strains have to be applied. It also facilitates the calculation of the Lagrangian stress, which is helpful in determination of the strain-stress relations. To demonstrate the application of our approach, we derive the analytic formulas for the deformation gradients as functions of the Lagrangian strain tensors, which are used in calculations of the third-order elastic constants in trigonal crystals and the fourth-order elastic constants in cubic crystals. Then, we perform the ab initio calculations of the fourth-order elastic constants in face-centered-cubic aluminum. We discuss the results obtained using the strain-energy and strain-stress relations and analyze the errors of the fourth-order elastic constants which would be incurred when approximating the deformation gradients by the Taylor polynomials. We show that the relatively small truncation errors in the Taylor expansion series of the deformation gradients can cause significant deviations of the fourth-order elastic constants. This effect is larger for the strain-energy method than for the strain-stress approach. We find that in both methods, the deviations are particularly significant for the ${C}_{1155}$, ${C}_{1266}$, ${C}_{4455}$, ${C}_{1255}$, and ${C}_{1456}$ elastic constants and are mainly caused by the truncation errors in the nondiagonal elements of the Taylor expansion series of the deformation gradients.

Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics.

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures.

A refractive phase corrector optics is proposed for the compensation of fabrication error of X-ray optical elements. Here, at-wavelength wavefront measurements of the focused X-ray beam by knife-edge imaging technique, the design of a three-dimensional corrector plate, its fabrication by 3D printing, and use of a corrector to compensate for X-ray lens figure errors are presented. A rotationally invariant corrector was manufactured in the polymer IP-STM using additive manufacturing based on the two-photon polymerization technique. The fabricated corrector was characterized at the B16 Test beamline, Diamond Light Source, UK, showing a reduction in r.m.s. wavefront error of a Be compound refractive Lens (CRL) by a factor of six. The r.m.s. wavefront error is a figure of merit for the wavefront quality but, for X-ray lenses, with significant X-ray absorption, a form of the r.m.s. error with weighting proportional to the transmitted X-ray intensity has been proposed. The knife-edge imaging wavefront-sensing technique was adapted to measure rotationally variant wavefront errors from two different sets of Be CRL consisting of 98 and 24 lenses. The optical aberrations were then quantified using a Zernike polynomial expansion of the 2D wavefront error. The compensation by a rotationally invariant corrector plate was partial as the Be CRL wavefront error distribution was found to vary with polar angle indicating the presence of non-spherical aberration terms. A wavefront correction plate with rotationally anisotropic thickness is proposed to compensate for anisotropy in order to achieve good focusing by CRLs at beamlines operating at diffraction-limited storage rings.