Approximate Calculation Method Research Articles

Pixel-wise parallel calculation for depth from focus with adaptive focus measure

Depth-from-focus methods can estimate the depth from a set of images taken with different focus settings. We recently proposed a method that uses the relationship of the ratio between the luminance value of a target pixel and the mean value of the neighboring pixels. This relationship has a Poisson distribution. Despite its good performance, the method requires a large amount of memory and computation time because it needs to store focus measurement values for each depth and each window radius on a pixel-wise basis, and filtering to compute the mean value, which is performed twice, makes the relationship among neighboring pixels too strong to parallelize the pixel-wise processing. In this paper, we propose an approximate calculation method that can give almost the same results with a single time filtering operation and enables pixel-wise parallelization. This pixel-wise processing does not require the aforementioned focus measure values to be stored, which reduces the amount of memory. Additionally, utilizing the pixel-wise processing, we propose a method of determining the process window size that can improve noise tolerance and in depth estimation in texture-less regions. Through experiments, we show that our new method can better estimate depth values in a much shorter time.

Bias in Zipf\u2019s law estimators

The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be computationally intractable. A more computationally efficient method of approximate Bayesian computation (ABC) is explored. This method is shown to have less bias for data generated from idealised rank-frequency Zipfian distributions. However, the existing estimators and the ABC estimator described here assume that words are drawn from a simple probability distribution, while language is a much more complex process. We show that this false assumption leads to continued biases when applying any of these methods to natural language to estimate Zipf exponents. We recommend that researchers be aware of the bias when investigating power laws in rank-frequency data.

Approximate Calculation Method for Noncentral t-Distribution Quantile

In the process of structural design and structural performance evaluation, the inference of the reliable life of the structure and the representative value of the material strength is a necessary work. The determination of material strength is the presumption of the quantile of the normal distribution, and the determination of the confidence level of the quantile of the normal distribution involves the noncentral t-distribution function. However, the calculation of the quantile is very complicated and is often provided in the form of a numerical table, which often involves multiparameter interpolation calculation, so it is not convenient to apply. The existing approximate calculation methods for noncentral t-distribution quantiles have strict application conditions, and the calculation process is relatively cumbersome. It is still difficult to meet actual needs in terms of fitting accuracy, application range, and convenience. In this paper, a new calculation method for noncentral t-distribution quantiles is proposed by introducing new probability expressions and related approximate distributions, based on theoretical derivation and numerical fitting. The comparative analysis results show that the method not only is convenient for calculation but also has the advantages of higher accuracy and wider application range, and it is more in line with the actual needs of engineering.

Benchmark multi-layer simulations for residual stresses and deformation in small additively manufactured metal parts

Scan pattern dependent (multi-track) residual stress buildup over multiple layers in the powder bed fusion process is governed by coupled thermo-mechanics. The high computational cost associated with these simulations has resulted in the general adoption of approximate computational methods. The numerical or thermo-mechanical accuracy of assumptions made in these computational methods is not fully characterized. If benchmark multi-track simulations for small size multi-layer parts are available, including temperatures, strain fields and deformation results, it will be possible to scientifically develop new approximation schemes or modify existing ones to improve their accuracy. Present work develops a suggestive benchmark using full multi-track thermomechanical simulations, with comparison to various approximate methods. The target configurations are simple prismatic geometries with 30 layers and up to 120 mm 3 volume, illustrating the influence of domain size on the approximate results. Anticipating the future challenges of measuring stresses and deformation in these small benchmark geometries, an experimental setup based on sheet metal forming principals is demonstrated numerically. The proposed setup will provide a methodology to experimentally validate these benchmarks.

Mathematical Model for the Kinetics of Heterogeneous Reaction of Carbonates Dissociation in the Process of Roasting in the Presence of Temperatures Gradients in Phosphate Raw Material

The paper deals with the investigation of the parameters for the structural and kinetic rate equation of the carbonates dissociation reaction, in accordance with the obtained results of the nonisothermic experiment, in the conditions of gradient temperature presence in the investigated samples. The most significant is the study of physicochemical transformations kinetic laws, which degree of completeness effects the quality of intermediate products directly, that is decarbonization and sintering. The main part of the process, when phosphorites are heated, takes place in a solid phase. The feature of topochemical reactions is their localization in the aria between a solid phase surface of the initial substance and the reaction products. This surface is formed and changed, as a result of chemical and power technological process for roasting, determining the dependence of the reaction rate on time. The method of thermal analytical experiments is used. The reverse kinetic problem is solved in the temperatures range of the chemical–technological process for roasting phosphate raw materials on conveyor indurating machines. The authors propose a method of approximate calculation for the parameters of kinetic equations which allows to reduce errors, caused by the heat exchange processes in a measuring cell, significantly. The obtained results and their accuracy are suitable for the practical application.

METHOD FOR APPROXIMATE CALCULATION OF FUNCTIONAL CHARACTERISTICS OF GAS PUMPING UNITS

Is described the method of approximate calculation of the functional characteristics of gas-pumping units and the method of diagnostics of the value of the impairment of the working wheel of the central center of the main gas pipelines is described. It is clear that the deposits are inflated with the impairment of productivity and productivity, and that is efficiency factor of superchargers. The architecture of the program complex is described, as well as the necessary system and technical facilities for carrying out the transfer for fragmentation at the warehouse of the automatic transmission system of the gas transmission system. Experimentally, the accuracy of the value of the radial prominence in the gaps of the working wheel on the buttstock of the "Demag" 655 P2 type was verified. The revision of the growth rates from the results of the straight lines to the open flow part was not shifted 0.15 mm. Descriptions of the method of implementation by a complex of programs, allow to carry out the development of the main indicators of the functional and technical mill of the VCN GPA: vitreous-pressure, forceful, polytropic KKD characteristics. These indicators are used for the purpose of determining the overall performance of the energy efficiency of the robotic skin GPU: the effective effort of the gas turbines, the vitrates of the fired gas from the of the coated gas pump, which is displayed in the real demand. The economics of the robotics of compressor stations, the supply of the pumped gas, the confirmation of the plans for the supply of gas to the residents and the safe functioning of the gas transportation system (GTS) of Ukraine, a significant world of possessing the functional To this, it is of particular importance to build up the development of new methods and to provide diagnostics, to ensure that the actual FCS possesses an assessment. At present, there is evidence of the actual state of possession of a more efficient operation of the plant in the transition from a traditional technical service to a resource-saving one. The obtained results show that the calculation of the actual characteristics of the VCN using the proposed method allows to take into account the influence of seal wear on the actual parameters of the regime over the entire range of workloads of single-stage and multistage superchargers.

Development of Methodology for Calculation of Discontinuous Circular Welds in Torsion

The main criterion for the performance of welds is the strength. The least durable ones are the corner joints used to perform various types of welded joints. In the literature, the methods of calculating the strength of welded joints with solid welds are considered in sufficient details. Methods of calculation of connection interrupted sutures absent. In this case, the greatest difficulty is the calculation of connections using circular intermittent welds, which are often performed in welded drums and pulleys; they work on torsion. Therefore, the development of methods for calculating circular intermittent welds for torsion is quite important.Shear stresses in welds from torque are determined depending on the value of the polar moment of resistance of its dangerous section. When determining the polar moment of resistance of the dangerous section of a circular discontinuous weld, it was represented by a set of sections in the form of a sector of a circular ring. The method of calculation of the polar moment of resistance of the rotated dangerous section of a circular discontinuous weld, which takes into account the relative length of the weld areas and their number, as well as the method of accurate and approximate calculation of shear stresses in the weld.

МЕТОД ФИКТИВНЫХ РЕАКЦИЙ В МОДЕЛИРОВАНИИ КОНТАКТНОЙ ПОВЕРХНОСТИ НА ПРИМЕРЕ ФЛАНЦЕВЫХ СОЕДИНЕНИЙ

An iterative method for calculating flanged connections in the finite element formulation is proposed. The essence of the proposed method is to separate the contact problem into a separate localized process that depends only on the initial distribution of forces from the main load on the flange connection. In the initial matrix of stiffness of unrelated bodies, a binding matrix of contact with elements of high rigidity is added. The calculation is performed in two phases: the first phase determines the movement of the actual loads on the second, through a vector of dummy reactions, iterative specified voltage at the contact surfaces. The results obtained by the proposed method are compared with the experimental results and with the approximate calculation method.

ОПТИМИЗАЦИЯ ФЕРМЕННЫХ КОНСТРУКЦИЙ С ПОЯСАМИ СТУПЕНЧАТО-ПЕРЕМЕННЫХ СЕЧЕНИЙ ИЗ ПРЯМОУГОЛЬНЫХ ТРУБ

The article describes the regularity of the optimization calculation of unification zones in relation to beam chords of step-variable cross-sections with the determination of their design coefficients. The rationality of the formation of these chords in truss structures made of rectangular pipes is shown due to the difference not in the heights of the sections, but in their thicknesses with welded joints on the longitudinal slits.The engineering method for calculating such joints, as well as their load-bearing capacity, has been tested by tensile strength tests of the samples.The universality of the technical solution of welded joints with slits ensures their use in structures made of tubular and rolled profiles, and it preserves the accepted layout of standardized trusses with assemblies and flanged connections. The significant reduction in structural material (steel) in standardized trusses made of bent-welded profiles was revealed when chords of uniform cross-sections were replaced with chords of step-variable cross-sections. The article also gives the comparative calculation of the design coefficients and the averaged coefficients of chord elements use when the lengths of the unification zones and the belt panels coincide. Sufficient correctness of the approximate calculation method for solving optimization problems and variant design of load-bearing structures is confirmed.

Quantum simulation of the ground-state Stark effect in small molecules: a case study using IBM Q

As quantum computing approaches its first commercial implementations, quantum simulation emerges as a potentially ground-breaking technology for several domains, including biology and chemistry. However, taking advantage of quantum algorithms in quantum chemistry raises a number of theoretical and practical challenges at different levels, from the conception to its actual execution. We go through such challenges in a case study of a quantum simulation for the hydrogen (H $$_2$$ ) and lithium hydride (LiH) molecules, at an actual commercially available quantum computer, the IBM Q. The former molecule has always been a playground for testing approximate calculation methods in quantum chemistry, while the latter is just a little bit more complex, lacking the mirror symmetry of the former. Using the variational quantum eigensolver method, we study the molecule’s ground state energy versus interatomic distance, under the action of stationary electric fields (Stark effect). Additionally, we review the necessary calculations of the matrix elements of the second quantization Hamiltonian encompassing the extra terms concerning the action of electric fields, using STO-LG-type atomic orbitals to build the minimal basis sets.

Identification for Recycling Polyethylene Terephthalate (PET) Plastic Bottles by Polarization Vision

The recycling of disposed PET plastic bottles has significant meaning for environmental pollution control and resource recycling. The reuse value heavily depends on the purity of the recycled PET. In order to improve the purity of PET recycling, a new means of material identification of PET plastic bottle based on polarization vision is proposed. To identify PET plastic bottles on conveyor belt, an effective region segmentation method for plastic bottle location and feature extraction has been put forward. The polarization of the scattered light on the surface of the object contains the information of its material. To obtain robust material characteristics of the PET plastic bottle, an approximate refractive index calculation method based on the degree of polarization and phase angle is introduced. The mean, standard deviation and coefficient of variation of the approximate refractive index and intensity distribution are used to construct the feature vector. The support vector machine (SVM) algorithm was used for PET identification. The experimental results show that the mean accuracy of PET plastic bottles material identification of recycled bottles is up to 92.06%.

An Optimized Method of Packet Loss Rate under Backup Path Protection in OBS Network

In order to calculate the packet loss rate in OBS network, this paper proposes a method, which performs good in both accuracy and rapidity, based on Erlang B formula to estimate the packet loss probability in OBS network using backup path protection mechanism. This method can be used to optimize the design of OBS network protocol, and it also provides an accurate and efficient approximate calculation method of packet loss rate in OBS network and can be conductive to the study of using copy transmission to enhance the network survivability. Based on the formula of Erlang B, this paper briefly introduces the derivation process and principle of this method. The basic experimental principles of simulation and estimation processes are designed in this paper, and the experimental results of the proposed method under a typical network topology (ARPA network) with no protection mechanism and 1 and 2 backup paths protection mechanisms are analyzed to verify its rapidity and accuracy. The results of experiments show the accuracy and efficiency of this method.

Approximate calculation method for angular acoustic scattering by non-analytic objects with use of Green functions

Approximate calculation method for angular acoustic scattering by non-analytic objects with use of Green functions

Benchmark Data Sets of Boron Cluster Dihydrogen Bonding for the Validation of Approximate Computational Methods.

The success of approximate computational methods, such as molecular mechanics, or dispersion-corrected density functional theory, in the description of non-covalent interactions relies on accurate parameterizations. Benchmark data sets are thus required. This area is well developed for organic molecules and biomolecules but practically non-existent for boron clusters, which have been gaining in importance in modern drug as well as material design. To fill this gap, we have introduced two data sets featuring the most common non-covalent interaction of boron clusters, the dihydrogen bond, and calculated reference interaction energies at the "golden standard" CCSD(T)/CBS level. The boron clusters studied interact with formamide, methanol, water and methane at various distances and in two geometrical arrangements. The performance of the tested approximate methods is variable and recommendations for further use are given.

The Maximum Entropy Method for Bilevel Stochastic Programming

Bi-level stochastic programming is a process of taking the optimal value of the lower level as the feedback to the upper level, and the constraint that the lower level has one single optimal solution can be relaxed in calculation. Using the maximum entropy method, the present study proposed an approximate calculation method for stochastic programming. The proposed method constructs a maximum entropy function for lower-level programming to approximately express the lower-level optimal value function, converts the bi-level stochastic programming problem into a single-level stochastic programming program, and hence obtains a calculation method for an approximation optimal solution (ε-optimal solution) of the bi-level stochastic programming problem.

On Calculation of Means of SDE with Drift

The numerical method of approximate calculation of mean of a stochastic differential equation with a drift was constructed. The proposed method is based on the so called weak method of approximations and does not require simulations of trajectories of the solutions.

МОДЕЛИРОВАНИЕ НЕСТАЦОНАРНОГО ТЕРМОНАПРЯЖЕННОГО СОСТОЯНИЯ ЛОПАТКИ ГТУ

The paper proposes a method of approximate calculation of the temperature field of the turbine blade in non-stationary mode by means of CFD-modeling. The academic version of the ANSYS-Fluent software package was used as a modeling tool. The local values of the heat transfer coefficient along the contour of the blade profile were calculated in the work. Previously, the gas flow velocity in the curved interscapular channel was calculated to determine the distribution of the gas flow velocity along the convex and concave surfaces of the blade. Comparison of the data thus obtained with the result of processing the experience conducted on the turbine, shows that in the conditions of the real rotating installation, the heat transfer to the surface of the blade was approximately 2 times higher. The most probable reason for this discrepancy is the earlier beginning of the transition to the turbulent boundary layer on the surface of the blade in real conditions of high turbulence of the oncoming flow. Calculations show that in the case of a sharp change in gas temperature, the largest temperature difference in the blade occurs after a few seconds and reaches 50 ... 90% of the change in gas temperature, and in blades with thin edges - close to this value. Increasing the thickness of the edges can significantly reduce the uneven temperature in the blades with sharp changes in gas temperature. In order to identify the nature of the stress state of the blades at different modes of operation of the gas turbine unit, the temperature stresses in the blade were calculated. The calculation was performed for Mises averaged stresses s in the cross section of an unevenly heated blade. When starting the installation, the maximum force occurred 30 ... 40 seconds after the start of the rotation of the rotor almost simultaneously with the maximum temperature difference between the edges and the central part of the section. The highest stress values occurred in the region of the inlet edge, where they exceeded 680 MPa per compression. In the future, the temperature stresses decreased and even changed sign due to the cooling process of the blade, overheated when throwing the gas temperature. Keywords: CFD-model, solid-state modeling, temperature field, blade, heat transfer, gas turbine installation.

Determination of thermal diffusivity of the material by numerical-analytical model of a semi-bounded body

A mathematical description of the material thermal diffusivity aт in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as the Fourier number Fo ≤ Foк (Foк ≈ 0.04–0.06). It is assumed that the temperature distribution over cross-section of the heated layer of the plate R is sufficiently described by a power function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating aт in the time interval ∆τ from the dynamics of temperature change T(Rп , τ) of a plate surface with thickness Rп heated under boundary conditions of the second kind. Temperature of the second surface of the plate T(0, τ) is used only to determine the time of the end of experiment τк. The moment of time τк, in which the temperature perturbation reaches the adiabatic surface x = 0, can be set by the condition T(Rп , τк) – T(0, τ = 0) = 0,1 K. The method of approximate calculation of dynamics of changes in depth of the heated layer R by the values of Rп , τк , and τ is proposed. Calculation of a т for the time interval ∆τ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of a т calculation was made by the test (initial) temperature field of the refractory plate with the thickness Rп = 0.05 m, calculated by the finite difference method under the initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rп) at radiation-convective heating. The heating time was 260 s. Calculation of aт, i was performed for 10 time moments τi + 1 = τi + Δτ, τ = 26 s. Average mass temperature of the heated layer for the whole time was T = 302 K. The arithmetic-mean absolute deviation of aт(T = 302 K) from the initial value at the same temperature was 2.8 %. Application of the method will simplify the conduct and processing of experiments to determine the thermal diffusivity of materials.

Filtration Bypassing Retaining Hydraulic Structures

Concrete dams that are part of river waterworks are integrated with earthworks or with banks using coastal abutments. If the soil of cost or earthen dam is permeable, then in the zone of contiguity water filtration occurs around the coastal abutment. Calculation of filtration bypassing the coastal abutment at specified water levels in the upper and lower pools is performed with the aim of constructing an encircling curve of depression and determining a gradient of filtration flow that controls the filtration strength of the soil beyond the abutment. This problem has no theoretical solutions – in view of its complexity, approximate calculation methods have been developed for individual calculation schemes. For the case when the soil behind the coastal abutment is homogeneous and isotropic, groundwater inflow from the coast is absent or insignificant and can be neglected, and the coastal abutment is located on a water bed and approximate methods by V. P. Nedrigi and R. R. Chugaeva are proposed in the paper. The experience of surveying a number of Belarusian hydropower stations has shown that the absence of a justified prediction pertaining to the position of groundwater levels beyond the estuary leads to a decrease in the strength and stability of the coastal abutment and its possible destruction. An experimental verification of the approximate method for calculation filtration bypassing the coastal abutment developed by R. R. Chugaev has been carried out in laboratory conditions. According to the obtained experience a depression curve encircling the abutment has been constructed which show good agreement between experimental and calculated data that allows to use this method for reasonable design of coastal abutment structures ensuring their reliable operation.

Determination of efforts from temperature and humidity exposure in walls

The construction of large-panel buildings has more than half a century of history, during which space-planning and design solutions have been improved, methods of calculation have been developed and the regulatory and technical base has been updated. For this period, accurate and approximate calculation methods, both of individual structural elements and the structural systems of buildings on the whole, have been harmonised and verified, the technologies and techniques of automated calculation methods and software systems for their implementation have been developed. One of the features of the life cycle of the housing stock of large-panel buildings is that over the long period of their operation, the regulatory and technical base on which they were designed periodically underwent changes. In terms of ensuring constructive safety from the effect of power loads on buildings, a system of fixed coefficients of working conditions supports the continuity of development of design standards. The affection of temperature and humidity exposure is determined according to the requirements for the temperature difference between the outer and inner surfaces of the outer walls. Based on the accumulated experimental data for the past years between the design period and the current period of operation, the numerical standard values of the heat transfer coefficients of the inner and outer surfaces of the enclosing structures have changed in relation to the previous standards by which these structures were designed. This necessitates a re-evaluation of efforts caused by temperature and humidity exposure in order to make a decision on the need to strengthen structures.