Auxiliary Angle Research Articles

Joint parameter estimation algorithm for polarization-sensitive channel compression arrays based on atomic norm minimization

To reduce the complexity of direction-of-arrival (DOA) algorithms in polarization-sensitive arrays and maintain high estimation accuracy while decreasing runtime, this paper proposes a channel compression model based on orthogonal dipole arrays. In addition, a DOA estimation algorithm using atomic norm minimization (ANM) is introduced for this model. This algorithm performs eigenvalue decomposition on the covariance matrix of the data received from the polarization-sensitive channel compressed array. A new observation vector is constructed for the ANM problem under the channel compression model using the obtained eigenvalues and eigenvectors. Subsequently, a Toeplitz matrix is constructed from the optimal solution of the semi-positive definite programming (SDP) problem. The Vandermonde decomposition of the Toeplitz matrix provides estimates of the signal DOA parameters. By combining the vectorization result of the covariance matrix and the least-squares calculation, the polarization auxiliary angle and polarization phase angle information of the incident source are also obtained. Simulation experiments compare the root-mean-squared error (RMSE) of each algorithm at different angular intervals and signal-to-noise ratios (SNR) to confirm the validity of estimating DOA and polarization parameters.

Foliation, topology and nucleon charge profiles in hypersphere soliton model

Abstract In the hypersphere soliton model (HSM), we study the geometrical inner structures and the ensuing charge distributions 
of the nucleons by exploiting the aspect of the HSM where the hypersphere soliton is 
described by an extended object possessing the parameter $\lambda$ $(0\le\lambda<\infty)$ which corresponds 
to the radial distance from the center of $S^{3}$ to the foliation leaves of the hypersphere soliton. To do this, we investigate the foliation and topology related with geometry on a hypersphere described by $(\mu,\theta,\phi)$. Exploiting the so-called scanning algorithm we study geometrical relations between spherical shell foliation leave on a northern hemi-hypersphere $S^{3}_{+}$ and that on a flat equatorial solid sphere $E^{3}$ which contains the center of $S^{3}$. We then elucidate the physical meaning of $\mu$ in $S^{3}$ of radius $\lambda$ by showing that $\mu$ plays the role of an auxiliary angle 
to fix the radius $\lambda\sin\mu$ of the $S^{2}$ spherical shell sharing the center of $S^{3}(=S^{2}\times S^{1})$, at a given angle $\mu$. Next, using the charge density profiles of nucleons with $\mu$ dependence, we construct the nucleon fractional charges of spherically symmetric and nontrivial distributions. We note that the proton and neutron charges do not leak out from the hypersphere soliton, and the positive and negative charges in the neutron are confined inside and outside its core, respectively. Explicitly we predict the fractional volumes and charges of the neutron. The proton and neutron are shown to be described by a topological structure of two 
Hopf-linked M"obius strip type twist circles in $S^{3}$. We also note that the characteristic ratio of the hypersphere volume to the corresponding solid sphere one is given by a geometrical invariant related with hyper-compactness.

Signal Injection Sensorless Control Without Manipulating Convergence Point Based on Symmetrical Auxiliary Angles for Saturated Synchronous Machine

Signal Injection Sensorless Control Without Manipulating Convergence Point Based on Symmetrical Auxiliary Angles for Saturated Synchronous Machine

ALGORITHM FOR PREDICTING THE ROUGHNESS OF THE INNER SURFACE DURING TURNING PROCESS

The article analyzes the main technological factors affecting the quality of parts, specifically the quality of the treated surface or the roughness of the surface of the part. Turning (boring) was considered as an example, and a number of measures aimed at improving the quality of the surface at the design stage were also proposed. A simulation stochastic model of surface roughness shaping during surface turning was proposed. Based on this model, an algorithm and a computer program were developed to calculate the roughness at the design stage. The initial data for modeling are the main angle in the plan φ, the auxiliary angle in the plan φ1, the radius at the tip of the cutter r and the feed S, as factors that most strongly affect the roughness during boring. An experiment was carried out, where not only average values were obtained, but also histograms of the distribution of roughness parameters, the adequacy of this model was proved. When calculating the roughness, additional factors were taken into account, for example, the condition of the machine, which made it possible to correct the simulation stochastic model and introduce vibration components associated with the forces acting during cutting and elastic squeezes of the cutter during boring process. Keywords: turning processing, surface quality, surface roughness, imitating model, stochastic model.

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution.

An indicator preselection based evolutionary algorithm with auxiliary angle selection for many-objective optimization

Many-objective evolutionary algorithms (MaOEAs) have received significant achievements in recent years. Maintaining a balance between convergence and diversity becomes a key challenge for many-objective evolutionary algorithms when the number of optimization objectives increases. To address this issue, we propose a many-objective evolutionary algorithm using the indicator preselection and auxiliary angle selection (PSEA). In PSEA, a unit vector-based indicator is proposed to pre-select the population region for increasing selection pressure and maintaining diversity simultaneously, which is utilized to identify a promising region in the objective space. Due to the poor quality of individuals outside the promising region, these individuals in the current population can be temporarily discarded. Then, to ensure the diversity of the population, a new strategy based on the second auxiliary angle strategy is designed to calculate the neighborhood density. Finally, in the environmental selection, these strategies are employed for selecting individuals with good convergence and diversity from the candidate set one by one to enter the next generation. The experimental results on commonly used benchmark test problems and many-objective traveling salesman problems with objectives varying from 5 to 20 have demonstrated that PSEA outperforms some state-of-the-art approaches.

Improved block sparse Bayesian learning based DOA estimation for massive MIMO systems

Direction-of-arrival (DOA) estimation is crucial for suppressing inter-cell interference in massive multiple-input multiple-output (MIMO) systems. However, conventional algorithms are unsuitable for low signal-to-noise ratio (SNR) and a small number of snapshots. Consequently, in an attempt to achieve fast reconstruction speed while ensuring high accuracy, this study proposes an improved block sparse Bayesian learning-based DOA estimation algorithm for two-dimension massive MIMO systems. Using the sparse characteristics and inherent structure of the signal, the DOA estimation problem is transformed to a joint task of sparse signal reconstruction and parameter optimization. Subsequently, the estimation accuracy is improved through complete excavation and learning of the signal temporal structure. In addition, to avoid the direct solution of the posterior probability distribution, reduce the number of iterations and increase the reconstruction speed, variational inference is used to approximate the Bayesian model and solve the joint problem through parameter learning. Moreover, the auxiliary angle is introduced to avoid extra angle matching, which further reduces the complexity. Simulations are performed to verify the proposed method and the results prove its superiority when applied to massive MIMO systems compared with some existing DOA estimation algorithms.

МАТЕМАТИЧЕСКИЕ МОДЕЛИ СИЛ РЕЗАНИЯ ПРИ ТОЧЕНИИ

This paper considers the predictive determination of the cutting force components for non-free cutting during turning. It has been established that plastic deformation and friction along the rear surfaces adjacent to the main and auxiliary cutting edges of the tool influence the magnitude and direction of the action of the component . The resulting force is defined as the vector sum of the forces that occur on the main and auxiliary cutting edges. The authors propose to determine the direction of the force in non-free cutting as a vector in the chip flow direction relative to the main cutting edge. The chip deviation angle was fixed by photographing the cutting process. The authors confirmed that in free cutting, the chip flow direction is perpendicular to the main cutting edge. The machining of shaped surfaces on lathes with numeric control systems is accompanied by changes in the feed movement direction and, as a result, changes in the kinematic main and auxiliary angles in the plan of the cutting tool. The increasing active length of the main cutting edge leads to an increase in the contact area of the rear surface of the main cutting edge with the machinable surface, and, consequently, an increase in the force component . The experimental measurement of the cutting force components allowed the determination of the impact degree of the force components connected both to the plastic deformation of the machinable material and to the friction on the rear surfaces adjacent to the main and auxiliary cutting edges of the tool. The analytical dependencies express the functional relationship between the elements of cutting modes, the geometric parameters of the cutters, the degree of wear, the shape of the machinable surface, and the physical and mechanical properties of the machinable material. A large set of parameters included in the formulas for determining the cutting force components allows the adequate monitoring the nature of the force interaction of the technological system elements during machining.

Vector Trajectory Method for Obstacle Avoidance Constrained Planetary Landing Trajectory Optimization

Considering the requirement of avoiding obstacles in different planetary landing missions, this article presents a generalized method dealing with the obstacle avoidance constrained landing trajectory optimization problem with vectorized strategy, i.e., vector trajectory method (VTM). By introducing a trajectory direction constraint with vectorized description, the character of the obstacle avoidance trajectory can be more specifically depicted. Moreover, by satisfying proper trajectory direction constraint, the lander’s particular performances, such as the observation to the target or probability of a safe flight, can be improved. To this end, the VTM and relevant theorem are first developed, revealing the relationship between the two aspects of obstacle avoidance constraint (i.e., distance constraint and trajectory direction constraint). Then, both aspects of constraints are uniformly transformed as the auxiliary angle magnitude constraint with the vectorized strategy, which significantly simplifies the solving procedure of obstacle avoidance constrained trajectory optimization problem. Finally, the proposed VTM is illustrated in detail through the examples with the planetary landing background of atmospheric entry and powered descent landing.

Multi-Dimensional Parameter Estimation in Polarimetric ULA with Cross-Distribution Dipole Pairs

This paper investigates the estimation of parameters—including the elevation angle, azimuth angle, polarization auxiliary angle, polarization phase difference, frequency and range of near-field sources in a Polarimetric Uniform Linear Array (P-ULA) with defective electromagnetic vector sensors. The cross-distribution dipole pairs are alternately placed in the xoy plane and yoz plane, respectively, and the whole array is divided into two subarrays, where subarray 1 consists of all of the dipole pairs placed in the xoy plane, while the dipole pairs placed in yoz plane are gathered in subarray 2. Specifically, the polarization auxiliary angle and the polarization phase difference, as well as the elevation and azimuth angles of the sources, are firstly estimated based on the Fourth-Order Cumulant (FOC) matrix in each subarray. Moreover, a decoupling method is developed to obtain the elevation and azimuth. Subsequently, the frequency and range are estimated based on the FOC matrix. Then, the parameter pair matching method is performed in order to match the pairs. Finally, an analysis of the Cramér-Rao Bound (CRB) is provided, and comparisons of the root mean square error with respect to the different input signal-to-noise ratios and number of snapshots, among different estimation methods, are implemented in the environment of additive white gaussian noise. The simulation results are provided in order to verify the effectiveness and feasibility of the proposed method for multi-dimensional parameter estimation.

Research on the Influence of Various Attribute Factors on Passive Interference in UHV Transmission Lines Based on Orthogonal Test

Considering the problem of passive interference caused by electromagnetic scattering effects of transmission lines to neighboring radio stations and other communication equipment, this paper refines the passive interference calculation model for UHV transmission lines. The solution calculation is carried out by the Method of Moments, and the law of passive interference effect of the tower structure, auxiliary angles, and ground roughness under different frequency incident waves, is summarized. By designing an orthogonal test, the degree of influence of the above attributing factors on passive interference results in the established joint model of three towers with two stall distances was explored by using Analysis of Variance. The results demonstrate that both auxiliary angles and rough ground show a pattern of enhanced electromagnetic scattering effect with increasing plane wave frequency in single-factor analysis. When multiple factors are combined, the rough ground has a significant effect on the results. This method effectively evaluates the passive interference influence factor while reducing the modeling and simulation engineering and provides a reference for the passive interference prediction in subsequent practical projects.

Estimation Method for Mixed Near-Field and Far-Field Sources Based on Four-Order Cumulant and Polarization Sensitive Array

A new multidimensional parameters joint estimation method of mixed near-field and far-field sources based on polarization sensitive array, fourth-order cumulant, joint diagonalization technology, and propagator method is presented, which can realize the joint estimation of DOA (Direction of Arrival), range, frequency, polarization auxiliary angle, and polarization phase difference without multidimensional spectral peak searching and parameter pairing, and it is suitable for any additive Gaussian noise environment and effective for reducing the loss of array aperture. The algorithm skillfully constructs the fourth-order cumulant matrix by using the output on the label of specific dipole pairs of the received array, which effectively avoids the matrix rank reduction caused by the far-field sources coexistence situation. In addition, the presented algorithm utilizes the orthogonal propagation algorithm for subspace decomposition and uses the total least square solution to replace the orthogonal solution of singular value decomposition, which effectively reduces the computational complexity. The experiment proved the effectiveness of the proposed algorithm.

Development and Test of Rubber Wheel Full Hydraulic Drill in Coal Mine

In order to solve the problem of moving rig quickly and reducing labor intensity in the mine face with trackless transportation conditions, a solution of rubber wheel drill which meets the working conditions is put forward. The drilling rig adopts the configuration of double power and double system, the power comes from the engine when moving, to achieve walking, steering, braking and temporary stability, relocation and transfer of high efficiency and flexibility, the power comes from the motor when drilling, to achieve rotation, feed and auxiliary Angle adjustment, safe and pollution-free construction. After the assembly and debugging of the whole machine, ground simulation test and underground industrial test were carried out on the rig. The test results show that the rig has strong maneuverability, one person can complete the moving walking, the maximum walking speed is 20km/h, and the steering is flexible and the braking is safe. The maximum depth of drilling hole construction is 318m, the target area hit rate reaches 77.8%, the working performance is stable, the hydraulic system is stable, and all parameters meet the design requirements. The equipment provides new technical equipment for the mine drilling construction with trackless transportation conditions.

Results of revision intramedullary nailing with and without auxillary plate in aseptic trochanteric and subtrochanteric nonunion

PurposeAim of this study was to investigate whether limited open auxiliary angle stable plate fixation has an effect on functional and radiologic outcomes one year after revision intramedullary nailing in aseptic trochanteric and subtrochanteric fracture nonunion.MethodsIn a retrospective analysis, surgically revised aseptic trochanteric and subtrochanteric nonunion was evaluated in a total of 190 consecutive patients ranging from 18 to 94 years between 12/2005 and 10/2018.ResultsOne year after revision intramedullary nailing, nonunion healing was assessed in 129 out of 136 patients (95%) in group 1 without auxiliary plate fixation and in 51 out of 54 patients (94%) in group 2 with auxiliary plating (p = 0.23). In group 1, range of motion (ROM) was unrestricted in 88 patients and still restricted in 48 patients. In group 2, ROM was free in 34 patients and restricted in 20 patients (p = 0.25). The mean Lower Extremity Functional Scale (LEFS) was 56 points in group 1 and 55 points in group 2 (p = 0.55).ConclusionThis study did not demonstrate significant differences in functional and radiologic outcomes following revision intramedullary nailing of aseptic trochanteric and subtrochanteric fracture nonunion. Limited open auxiliary plate fixation might be a reasonable option especially in cases of relevant varus axis deviation and comminuted or atypical fracture configurations, regardless of patients’ age.Retrospectively registered with the German Clinical Trials Register (01/25/2021; ID: DRKS00024112).

Research on machining technology of high speed and ultra-thin wall parts

This paper mainly analyzes and experiments the processing technology of high speed (12000 r/min) and large proportion thin-wall parts (thickness/width = 1:80 and thickness/height = 1:120), so as to guide the machining of closed centrifugal impellers in aerospace. In this process, low melting point alloy is selected as the filling material to increase the rigidity of thin-walled parts and improve the indicated roughness of parts. Different low melting point alloy filling structures are carried out on large proportion of thin-wall sample parts. In addition, an auxiliary angle R is added at the stress concentration of the part itself to reduce the vibration caused by the machining path. For the results of simulation and test, the parts without filling low melting point alloy can not be processed and used at all, while the “tower” filling structure has fine cracks at the top of the thin-walled parts. The “column” filling structure increases the rigidity by about 19.97 % and the roughness by about 50 %.

ПРИМЕНЕНИЕ ИСКУССТВЕННЫХ НЕЙРОННЫХ СЕТЕЙ ДЛЯ ПРОГНОЗИРОВАНИЯ ШЕРОХОВАТОСТИ ПРИ ЧИСТОВОМ И ПОЛУЧИСТОВОМ ТОЧЕНИИ

A technique for the development of artificial neural networks to predict the roughness of the treated surface during finishing and semi-finishing turning is presented. The back-propagation network architecture was adopted, having an input, hidden and output layers, a sigmoidal activation function for the hidden layer and a linear one for the output layer. To form a training sample, empirical expressions in the form of power functions were used, training of networks was carried out according to the Levenberg-Marquardt algorithm, which has fast convergence. Technological modes (cutting speed and depth of cut, tool feed), cutting tool geometrical parameters (main and auxiliary angles in terms of the tool, radius at the tip of the tool, rake angle), physicomechanical properties of the material being processed, each the training sample is formed from thousands of source data combinations. Separate networks have been developed that predict roughness during finishing and semi-turning turning, as well as a combined network that takes into account both types of processing. Analysis of the accuracy of the networks showed good results, the relative error of calculations does not exceed 1%. The proposed neural network models can be used in technological preparation of production, as well as in systems of adaptive control of the cutting process.

Methods for Transformation of Rectangular Spatial Coordinates to Geodetic Coordinates

The article gives a brief analysis of methods and algorithms for the transformation of spatial rectangular coordinates to curvilinear coordinates - geodetic latitude, geodetic longitude, geodetic height. Two algorithms for solving the equation for determining longitude are considered. Three formulas used to calculate the height are analyzed, with an estimate of their errors due to the approximate latitude. The shortcomings of mathematical solutions to these problems are revealed. A study of different approaches and methods for solving the transcendental equation for determining the latitude, based on the theory of separation of the root of the equation, is performed. Using this technique, iterative processes were performed to calculate the reduced latitude , using trigonometric identities, by introducing an auxiliary angle and transforming it to an algebraic quartic equation, which Borkowski solves by the Ferrari's method. The determination of the root isolation interval allowed using the chord method (proportional parts) to determine the latitude. In all cases, estimates of the convergence of the iterative processes that facilitate the comparative analysis of the proposed solutions are obtained. By further decreasing the separation interval of the root, the accuracy of the non-iterative determination of the latitude is improved by the Newton method.

Angle between terminator and meridian: flat geometry versus formulae of solar azimuth and an easy approach to the daylight map

The calculation of the angle between the day-night line on the Earth’s surface, a terminator, and the meridian at a given point, at dawn or at sunset, can easily be performed either by means of flat geometry or, for those familiarized with astronomy, through formulae for the Sun’s azimuth and elevation, both derived from spherical trigonometry. The two procedures are compared. An auxiliary angle obtained in the process of derivation via planar geometry becomes useful to represent the daylight map on a terrestrial planisphere.

High-accuracy device for measuring the twist angle

This paper describes a high-accuracy optoelectronic device for measuring the twist angle, based on an autocollimation method and using a reflector in the form of a unit of right-angle prisms. The device makes it possible to measure the relative twist angle of objects in the range ±2.5° when there is a distance of 2.5–3.5 m between the reflector and the optoelectronic unit of the device. The rms deviation of the measured angle from the true value in this case does not exceed 2′′ in the range ±2.5°, and it does not exceed 1′′ in the range ±10′. A specially shaped mark is used in the device that makes it possible to measure the auxiliary angle between the direction of the edge of the prism reflector and a plane perpendicular to the optical axis of the device. The installation can be used to transfer the azimuthal direction vector.

The Definition of Universal Momentum Operator of Quantum Mechanics and the Essence of Micro-Particle’s Spin——To Reveal the Real Reason That the Bell Inequality Is Not Supported by Experiments

The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.