Approximate Calculation Method Research Articles

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.

A method for approximate computation of waveguide scattering matrices

A waveguide occupies a domain in an -dimensional Euclidean space which has several cylindrical outlets to infinity. Three classes of waveguides are considered: those of quantum theory, of electromagnetic theory, and of elasticity theory, described respectively by the Helmholtz operator, the Maxwell system, and the system of equations for an elastic medium. It is assumed that the coefficients of all problems stabilize exponentially at infinity, to functions that are independent of the axial variable in the corresponding cylindrical outlet. Each row of the scattering matrix is given approximately by minimizing a quadratic functional. This functional is constructed by use of an elliptic boundary value problem in a bounded domain obtained by cutting the cylindrical outlets of the waveguide at some distance . The existence and uniqueness of a solution is proved for each of the three types of waveguides. The minimizers converge exponentially fast as functions of , as , to rows of the scattering matrix. Bibliography: 47 titles.

Study on the Comprehensive Method of Crack Control in Engineering Structure

It is a very complex and important problem that cracks of engineering structure are caused by deformation (hydration heat, shrinkage, temperature difference). The author in the accumulation of a large number of construction and crack processing experience and theoretical research, on the basis of combination of existing computer network technology, is proposed based on computer technology of the engineering structure crack control synthesis method, including the approximate calculation method of structural mechanics, structure and foundation interaction, construction technology and the optimization of material, environmental conditions, etc.

Optimizing AC Resistance of Solid PCB Winding

At high frequency, power losses of a winding due to eddy currents becomes significant. Moreover, the skin and proximity AC resistances are influenced by the width of printed circuit board (PCB) conductors and distance between the adjacent tracks which causes many difficulties to design windings with lowest AC resistances. To clarify this phenomenon, this paper focuses on modeling the influence of skin and proximity effects on AC resistance of planar PCB winding, thereby providing guidelines to reduce the winding AC resistance. An approximate electromagnetic calculation method is proposed and it shows that when the winding proximity AC to DC ratio ( F p r o x i m i t y ) is equal to 1 3 the AC on DC ratio caused by skin effect ( F s k i n ) , the winding is optimized and it has lowest AC resistance. 3-D finite element simulations of 3, 7 and 10-Turn windings, which are divided into 3 groups with the same footprint, are presented to investigate the lowest AC resistance when the track width varies from 3 mm to 5 mm and the frequency range is up to 700 kHz. In order to verify the theoretical analysis and simulation results, an experiment with 3 simulated groups, (9 prototypes in total) is built and has a very good fit with simulation results. Experimental results show that at the optimal width, the AC resistance of the windings can be reduced up to 16.5 % in the frequency range from 200 kHz to 700 kHz.

Calculating the first eigenvalues of the spectral problem in the theory of hydrodynamic stability by Orr-Sommerfeld

The difficulties arising in the linear theory of viscous fluid flow stability are to a great extent connected with the mathematical problems of finding eigenvalues of non-self-conjugated differential operators. Finding the eigenvalues of the Orr-Sommerfeld spectral problem is a difficult problem of computational mathematics. The methodology of applying the method of regularized traces for finding eigenvalues of the classical spectral problem of the Orr-Sommerfeld hydrodynamic stability theory is considered in this paper. A new method for approximate computation of the first eigenvalues of spectral problems generated by discrete semi-limited operators has been developed. This method is not iterative in contrast to the known numerical methods for finding eigenvalues of operators. New estimates of the regularized traces of the discrete operator have been obtained in this work. The formulas by which it is possible to calculate the corrections of the necessary order perturbation theory have been found. The computational experiment to calculate the first eigenvalues of the Orr-Sommerfeld spectral problem has been performed.

A method for approximate computation of waveguide scattering matrices

Волновод занимает область в $(n+1)$-мерном евклидовом пространстве с несколькими цилиндрическими выходами на бесконечность. В основном рассматриваются три класса волноводов: квантовые волноводы, электромагнитные волноводы и волноводы теории упругости; они описываются соответственно оператором Гельмгольца, системой Максвелла и системой уравнений теории упругости. Приближением для строки матрицы рассеяния служит минимизатор некоторого квадратичного функционала. Этот функционал строится с помощью эллиптической краевой задачи в ограниченной области, полученной усечением цилиндрических выходов волновода на расстоянии $R$. Для каждого из упомянутых трех типов волноводов устанавливается однозначная разрешимость этой задачи. Доказывается сходимость минимизатора к строке матрицы рассеяния с экспоненциальной скоростью при $R \to \infty$. При этом предполагается, что коэффициенты рассматриваемых задач стабилизируются на бесконечности с экспоненциальной скоростью к функциям, не зависящим от аксиальной переменной в соответствующем цилиндрическом выходе. Библиография: 47 названий.

Partitioning the vibrational spectrum: Fingerprinting defects in solids

Vibrational spectroscopy techniques are some of the most-used tools for materials characterization. Their simulation is therefore of significant interest, but commonly performed using low cost approximate computational methods, such as force-fields. Highly accurate quantum-mechanical methods, on the other hand are generally only used in the context of molecules or small unit cell solids. For extended solid systems, such as defects, the computational cost of plane wave based quantum mechanical simulations remains prohibitive for routine calculations. In this work, we present a computational scheme for isolating the vibrational spectrum of a defect in a solid. By quantifying the defect character of the atom-projected vibrational spectra, the contributing atoms are identified and the strength of their contribution determined. This method could be used to systematically improve phonon fragment calculations. More interestingly, using the atom-projected vibrational spectra of the defect atoms directly, it is possible to obtain a well-converged defect spectrum at lower computational cost, which also incorporates the host-lattice interactions. Using diamond as the host material, four point-defect test cases, each presenting a distinctly different vibrational behaviour, are considered: a heavy substitutional dopant (Eu), two intrinsic point-defects (neutral vacancy and split interstitial), and the negatively charged N-vacancy center. The heavy dopant and split interstitial present localized modes at low and high frequencies, respectively, showing little overlap with the host spectrum. In contrast, the neutral vacancy and the N-vacancy center show a broad contribution to the upper spectral range of the host spectrum, making them challenging to extract. Independent of the vibrational behaviour, the main atoms contributing to the defect spectrum can be clearly identified. Recombination of their atom-projected spectra results in the isolated spectrum of the point-defect.

Study on outage performance gap of two destinations on CR-NOMA network

Non-orthogonal multiple access (NOMA) and cognitive radio (CR) are promising for solving the severe spectral scarcity problem encountered by the next generation of wireless communication systems. This study aims to improve spectral efficiency at two secondary destinations by investigating a CR-NOMA network under situation of the perfect successive interference cancellation (SIC). We also derive the exact outage probability for secondary users. Furthermore, an approximate computation method is applied to indicate more insights. It is confirmed that the performance achieved together with performance gap among two users can be obtained due to different power allocation factors assigned to users.

On powerful exact nonrandomized tests for the Poisson two-sample setting.

In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher's exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

Process capability indices when two sources of variability present, a tolerance interval approach

AbstractThe sound tolerance interval–based method and two Pp–based approximations are compared on the proportion of nonconforming parts. As output distribution of the process, one possible model is examined here: two sources of variations are in a one‐way structure. It was found that the uncertainty of variance components estimates plays the major role in the goodness of the three calculation methods.SummaryStatistical indices – like process capability (CP) or process performance (PP) index – make the relationship between the width of the specification interval and the extent of the process variability illustrative. The latter is characterized by the tolerance interval, which contains the major part of the population with high confidence. In the original concept this tolerance interval is calculated using oversimplified models. In practice this model is not conform with reality. As improvement two sources of variation is assumed in a one‐way structure.The proportion of non‐conforming parts of the population is the quantity of interest. Non‐conforming means that the characteristic is beyond the specification limits. According to this, the quantile of the distribution shall be determined that is equal to the specification limits. Thus, the task is to calculate the tolerance interval for the distribution.In practical cases the variance components are unknown and are to be estimated. To estimate the ratio of non‐conforming parts, two approximate calculation methods which are coherent with the definition of PP are investigated, as well.The aim of this work is to compare the results of the two PP based approximate methods with the tolerance interval based (theoretically sound) calculation method. Two situations from the practice are considered – datasets from process validation and process monitoring environment are evaluated during which the effect of the number of experiments is given. Our study indicated that the main difference of the goodness of the approximations is from the uncertainty of parameter estimates.

某些“积不出”函数的定积分近似计算方法及其原函数的近似曲线

某些“积不出”函数的定积分近似计算方法及其原函数的近似曲线

ВЛИЯНИЕ ПЛАСТИЧЕСКИХ ДЕФОРМАЦИЙ НА ВЫСОТУ НЕСОМКНУТОЙ ОСТАТОЧНОЙ ТРЕЩИНЫ В СЖАТОЙ ЗОНЕ БЕТОНА

A significant part of the territory of Russian Federation refers to seismically dangerous areas. In the current code in design of reinforced concrete buildings for seismic loads the development of plastic strains is supposed. They are taken into account while determining loads by introduction of reducing factor K1, but their influence on the strength of elements is neglected. Plastic strains of reinforcement lead to appearance of residual cracks in compressed zone of concrete and due to this the reduction of bearing capacity of bending elements takes place on following loading cycles. The approximate method of determination of the depth of open cracks and of the residual height of sections when changing the sign of internal forces after reaching the maximum deflection has been proposed. The depth of residual crack is determined from the condition of equilibrium of longitudinal forces with regard to stress-strain state of a section at three stages of loading: at a moment of achievement of maximum plastic strains, at the unloading stage and at a moment of the beginning of crack formation after changing the sign of internal forces. The comparison of results obtained by the approximate method and results of calculation of finite elements model of a beam has been carried out.