Mathematical Model For Calculation Research Articles

Математическая модель, алгоритм формирования вектора состояния и техническая реализация многокоординатного задающего органа внутрикамерных манипуляторов

The purpose of the study is a development of a mathematical model and an algorithm for the calculation of the state vector of a multi-axes delta-type control joystick for moving special purposes arm manipulators by a human operator in the loop. Research methods. The paper considers the existing methods of remote control of intrachambers special purpose arm manipulators with a human operator in the control loop, identifies the advantages and disadvantages of existing solutions. The task of synthesizing the optimal control stick to ensure driving of the manipulator in 3D-space was set. Today, nuclear industry enterprises widely use hermetic chambers in which copy-type electromechanical manipulators are installed. The manipulation system includes an arm manipulator installed directly in a sealed chamber, and its kinematically similar control arm. The operator manually moves the control arm, the trajectory of which is repeated inside the chamber by the arm manipulator. Taking into account moral and physical obsolescence, the introduction of modern approaches to the human-machine interaction is required. The paper proposes a mathematical model for calculation the state vector (linear and angular coordinates) of a delta-type control stick from measured information about the relative angular position in its rotational kinematic pairs. Results of the study. An algorithm for calculating the coordinates of the handle of the control stick is synthesized based on a priori information about the relative position of the elements in the delta-mechanism. Taking into account the additional discrete and proportional controls located on the handle of the control stick, the proposed algorithm and its practical implementation make it possible to introduce effective manipulator control modes. Conclusion. The main results of the work include a mathematical model and an algorithm for generating the state vector of the delta-type control stick, which allows the operator to form the linear and angular velocity vectors of the arm manipulator and its gripper movement by one hand. The technical implementation of the control stick and algorithm, as well as its test operation with a dual arm manipulator system, showed the high efficiency of the proposed solutions.

Optimization Analysis of Meshing Worm Drive Structure with Roller Enveloping Ring Surface

Based on the meshing theory of the worm drive with the roller enveloping ring surface and the mathematical model of transmission efficiency of transmission mechanism, the mathematical calculation model of transmission efficiency for simultaneous meshing of multiple teeth has been set up; the geometrical parameters of transmission countershaft, the influence of friction parameters on transmission efficiency of transmission pair have been analyzed. The analysis and optimized results are that the transmission efficiency is negatively correlated with friction parameters and with other structural geometric parameters and positively correlated with the center distance in the structural geometric parameters. Thereinto, friction parameters and throat-neck coefficient have a great influence on transmission efficiency, and the roller radius and center distance have little influence on it. After structure optimization, the transmission efficiency is improved by 3.86% compared with before optimization.

An Analytical Framework for Error Propagation Effects in Multiprocess Manufacturing

Analysis of multisource errors accompanying process execution and study of the propagation effects of the corresponding multiprocess manufacturing process are the basic prerequisites for optimizing the generation process and improving the quality of the product. This paper proposes an analytical framework for error propagation effects in multiprocess manufacturing, which completely covers error source analysis, mathematical calculation of error propagation accumulation, and description of error propagation effects, which can provide better support for error traceability, error propagation monitoring, and error dissipation in manufacturing production. First of all, establish the process state model into the features of the manufacturing level, analyze the type of multisource error, and its mode of action when executing the process operation; second, establish the mathematical calculation model of error propagation accumulation based on state space equation is established, so as to realize calculation and analysis of error propagation; and finally, establish the link graph and link matrix of error propagation influence in multiprocess manufacturing process are established to further reveal the scope and path of error propagation influence. In this section of the case study, a plate cover part had been taken as an example, the multisource error in its manufacturing was analyzed, and the propagation and accumulation of these error values are obtained by state space and state transition theory. On this basis, the link graph and its corresponding link matrix were used to explicitly describe the error propagation effects during the multiprocess manufacturing of the example part. The example analysis illustrated the proposed error analysis framework could analyze and calculate the multisource error of multiprocess manufacturing and visually describe the error propagation effects, which showed the effectiveness and feasibility of the proposed method framework.

A high-resolution upwind numerical scheme for solving transient multiphase flow in wellbore

The identification of gas-liquid interface is the basis for accurate calculation of wellbore flow parameters after gas invasion, which plays an important role in the safety and reliability of drilling engineering. At present, most petroleum engineering uses a simple difference algorithm to calculate the wellbore multiphase flow, this scheme can not capture the gas-liquid interface accurately, and the numerical accuracy is low. Therefore, this paper proposes a mathematical and numerical calculation model for transient multiphase flow in wellbore during gas invasion. Using second-order Runge-Kutta method and OMUSCL2 method, a high-precision and high-resolution upwind AUSMV numerical scheme is constructed to capture the gas-liquid interface. The research shows that the high-precision and high-resolution upwind AUSMV scheme can accurately capture the gas-liquid interface, and thus accurately solve the multiphase flow parameters in wellbore during the gas invasion.

GLOBAL CLIMATE: THE PLANET AS A THERMODYNAMIC SYSTEM

The Purpose of the Study is to theoretically substantiate the problem of studying the planet as a thermodynamic system in the context of the global climate. The Research Methodology. Methods of analysis, modeling, description and generalization of data were used to study the problem of global climate and formulate conclusions. The Scientific Novelty of the research lies in the integrated focus on the global climate problem and the actualization of the complex study through the creation of mathematical-physical calculation model. The Conclusion. Joint efforts of scientists and society are necessary for a comprehensive study of the global climate problem. Modern research should use an integrated approach and be based on a mathematical and physical calculation model.

Simple and effective mathematical models for cellulose water content calculation from absorbance/wavenumber shifts in NIR spectrum

This study presents the evaluation of the near infrared (NIR) spectroscopy utility in the quantitative analysis of the moisture content in cellulose (from 0.5 to 11.0 wt.%). Being the first statistic-based work examining the relations between the wavenumber/absorbance and moisture content, this research innovatively describes the variations in the X- and Y-coordinates of 9 absorption bands plotted as a function of water amount established with Karl-Fischer titration. Simple linear, semilogarithmic and power models have been investigated. While model exhibited R2>90%, the standard error of calibration (SEC) has been shown and an external validation was carried out. Power model has been successfully applied to describe the changes in the intensity of the peak situated from 5400 to 5000 cm−1 (R2 = 90%) with a standard error of prediction of approx. 17.2%. Furthermore, absorption bands that wavenumber shifts could provide significant information on the behaviour of the active centres in cellulose have been favourably defined.

Gas dynamics features of physico-chemical processes in the SRM large-sized charges at open firing

The problem of utilization of solid rocket motors (SRM) with large-sized charges is a relevant objective. This is due to the decommissioning of SRM that failed or were rejected during production and operation, as well as with the implementation of strategic arms reduction treaties. Comparative analysis of SRM with large-sized charge utilization methods showed that the simplest, most productive, and relatively safe technique is open firing. At the same time, the information on the dynamics of harmful substances emission into the environment is needed to conduct quantitative assessment of the concentrations of environmentally hazardous combustion products formed during open firing. The calculation of intraballistic parameters in SRM makes it possible to estimate the consumption parameters of harmful gaseous and condensed combustion products entering the atmosphere. Also, it allows analyze the spatial and temporal course of the concentrations of these substances and optimize ways to reduce environmental hazards. The mathematical model and results of gas dynamics parameters calculation at the open firing of large-sized SRM with the demounted nozzle unit and forward bottom are submitted. The key features of realized flow modes are marked: significant pressure differentials along the length of the SRM in the initial stage of its activity; transonic velocities of intrachannel flow; erosion effects on the initial stages of burning rate.

Study on the Optimal Operation of Indoor Heating Considering the Envelope Structure in the Context of Time-Sharing Tariff

In this paper, a mathematical model of building heat transfer calculation is established, and the heat storage capacity of the building envelope model is tested and applied under the background of time-of-use electricity price. The building envelope in the context of time-of-use tariff in the process of simulating the temperature environment is considered, and the optimal solution derived by comparing the optimized operation scheme on a typical load day is adopted. Through the comparison of common schemes, the scheme proposed in this paper can effectively avoid energy waste, save electricity, improve the operation scheme of indoor heating in buildings, and provide theoretical reference for the optimal operation of building energy saving and consumption reduction.

Application of Virtual Network Mapping Algorithm Based on Optimal Subnet in Enterprise Cost Accounting Platform

The price of the product has a great impact on the market competitiveness of the product. The manager can adjust the operation strategy according to the cost information of the product, cut costs, adjust the market decision and make the product more competitive in the market. Therefore, the research of product costing method has a very important significance. Considering that the physical resources in the processing of the virtual network mapping (VNM) fragment embedded in the request are rejected, and the problem of physical resource usage is weakened, a VNM algorithm based on the optimal subnet edge matching algorithm is proposed. After the VNM request is coarsened to the subnet, the breadth-first search algorithm is used to create the physical subnet candidate set, and the constraints of the virtual node and the coarsening network topology are complied with. The simulation results show that the proposed algorithm reduces the number of link mapping hops and can improve the acceptance rate and cost-benefit ratio of virtual networks. First of all, this paper analyzes the research background of manufacturing cost calculation and the research situation at home and abroad, discusses the advantages and disadvantages of standard cost calculation and studies and analyzes the principles, advantages and disadvantages of standard cost calculation in daily business activities. Second, design a new mathematical accounting model based on the mathematical model of standard cost calculation in daily business activities. This combines the advantages of standard costing and time-based activity costing, and provides theoretical support for manufacturing companies to use this accounting method. Finally, the research results of this paper are summarized, and the shortcomings of this paper are analyzed. Cost accounting method needs to be further studied.

Application of optimization methods to minimize noise in quantum key distribution systems integrated into fiber-optic communication lines using dense wavelength division multiplexing

Subject of study. This study examined the applicability of the simulated annealing optimization algorithm to the search for optimal configurations of quantum and information channels required for a successful quantum key distribution session considering grids with different frequency spacings between channels, such as 12.5, 25, 50, and 100 GHz. Aim of study. This study was aimed at optimization of a search for configurations of quantum and information channels for a grid corresponding to dense wavelength division multiplexing standards using optimization methods based on analysis of the channel noise effect on quantum key distribution sessions and investigation of these methods. Method. Naturally, quantum signal powers are significantly lower than those of classic signals. Therefore, noise from information channels for a configuration where they propagate in the same fiber with quantum channels results in considerable reduction of quantum key distribution system performance. This problem can be mitigated by reducing the noise level in the channel via the selection and use of an optimal spectral channel allocation. The search for such channel allocation schemes, which are further referred to as configurations, can be implemented via several methods, such as the educated guess method and the approach entailing optimization using the simulated annealing optimization algorithm, which are the subjects of this study. The results obtained using this method were compared with similar results obtained using the educated guess method. Descriptions of the methods and their interpretation for the context of the objectives of the study are presented together with mathematical models for calculation of noise resulting from spontaneous Raman scattering, four-wave mixing, and linear channel crosstalk. Optimal allocation schemes of quantum and information channels in the grid with dense wavelength division multiplexing (configurations) obtained using the two methods are described. The configurations were considered optimal when the total value of all channel noise types considered in the mathematical model was minimal. Main results. Optimal configurations obtained using methods of simulated annealing and educated guess are described in this study. We demonstrated that the educated guess method is applicable when the spontaneous Raman scattering is the primary contributor to the total losses. In this case, the information channels should be arranged according to the Raman scattering cross-section graph. However, when the contribution of four-wave mixing is comparable with or exceeds that of spontaneous Raman scattering, the simulated annealing algorithm is preferrable to search for the optimal configurations. In this case, information channels should be located at a distance from the quantum channel: the smaller the grid spacing, the further the information channels are positioned from the quantum channel to obtain optimal configurations. Increase in the number of channels results in reduction in this separation distance inside the grid with fixed channel spacing. Practical significance. Currently, practical implementations of fiber-optic communication lines are inextricably connected with multiplexing technologies, particularly, dense wavelength division multiplexing, to satisfy the constantly growing demand in increasing information capacity of communication channels and constructing quantum networks. Assignment of separate fibers for quantum key distribution systems is not optimal; thus, existing technologies of channel multiplexing must be integrated into the quantum key distribution systems. However, a rapid increase in the quantum bit error rate occurs owing to the presence of undesirable channel noise in fiber-optic communication lines, which eventually results in the impossibility of performing a successful quantum key distribution session. Therefore, accurate and profound analysis of the contributions of channel noise types is required to minimize this noise via the selection of an optimal configuration of classical and quantum channels on the frequency grid.

Reducing the technosphere impact of agricultural machines by expanding the low-temperature applicability of alternative fuels

The subject of the study was alternative fuels used in agricultural machines. As an alternative fuel, a mixture consisting of diesel fuel, rapeseed oil and a targeted additive was considered. The main task was to develop a method for expanding the limits of low-temperature properties of alternative fuels used in tractors of agricultural machines. Because of the studies, a mathematical calculation model for determining the clouding temperature of an alternative fuel with the addition of a targeted additive was developed, the obtained calculation mathematical model was tested with experimental data, which showed 96 % convergence of theoretical calculations with experimental data. The low-temperature applicability of alternative fuel has been expanded by 9 degrees, and it has been proven that for normal operation of a diesel engine in low temperature conditions on fuel with rapeseed oil additives, it is advisable to use a multifunctional additive DIFRON H372 up to 2 %, which allows reducing the level of technospheric impact on the environment.

A mathematical model for a rapid calculation of the urban canyon albedo and its applications

Urban canyon albedo (UCA) is a primary indicator used to evaluate the impact of urban geometry on radiation absorption. A rapid and effective theoretical calculation for the UCA is helpful in urban design. This research establishes a simplistic but robust mathematical model for calculating the UCA. The model was validated using prior observational studies showing that the maximum root mean square error (RMSE) is 0.03, and the minimum Pearson correlation coefficient (r) is 0.63. The model was then used to evaluate the influence of urban canyon geometry and materials on UCA. The results show that the canyon aspect ratio controls the UCA, especially when the canyon aspect ratio is less than 4. Furthermore, high-albedo facades can effectively increase UCA, and high-albedo pavements are recommended only if the urban canyon aspect ratio is less than 1. Finally, the solar performance of urban canyons on an urban scale was estimated by combining our model with digital elevation model (DEM) data. This study can be used in urban planning to estimate the radiation performance of an urban canyon quickly before full-scale urban thermal environment simulation.

Программа для ЭВМ как инновационный подход в оценке качества и организации косметологической помощи

INTRODUCTION: Injections of botulinum toxin preparations are the most popular cosmetic procedure. However, in practice, sufficient cosmetic effect is not always noted. Study, analysis and improvement of botulinum therapy by a doctor, familiarization of the patient with the correction plan including long-term monitoring, are necessary measures to increase the compliance and the extent of satisfaction with the results, which will permit to further improve the quality of medical care. Despite numerous developments in the field of organization and quality management in healthcare, this problem remains relevant today. The article describes a clinical example of using a computer program for evaluation of the evidence of facial mimic wrinkles after botulinum therapy in different follow-up periods, and evaluation of the effectiveness of botulinum therapy using mathematical model for calculation of the integral quality coefficient and visibility graphs. CONCLUSION: The program helps a practicing cosmetologist evaluate the effectiveness of the procedure, master the skills of quality expertise and improve organization of medical care in the field of esthetic medicine.

Results of validation and cross-verification of the ROK/B design code on the problem of loss of cooling in the spent fuel pool *

The procedures of validation and cross-verification of the newly developed computational code ROK/B are described. The main problem solved using the ROK/B code is the substantiation by calculation of the coolant density in the spent fuel pool (SFP) and the temperature regime of the fuel assemblies during a protracted shutdown of the cooling systems (break in the supply of cooling water). In addition to the above, it is possible to use the ROK/B code to carry out calculation of an accident with the discharge of the coolant from the SFP with simultaneous prolonged shutdown of the cooling systems. The ROK/B code allows carrying out calculations for various types of designs of the fuel assemblies and VVER reactors, in particular, VVER-1000, VVER-1200 and VVER-440 power units with single- and two-tiered fuel assembly arrangement, with clad pipes in racks (for compacted assemblies storage) and pipes without cladding, with cased assemblies and caseless ones. During fuel reloading, a high level of the coolant is maintained, which makes it possible to do “wet” transportation of the assemblies from the reactor to the SFP. The mathematical model for heat and mass transfer calculation, including the boiling coolant model, implemented in the ROK/B code, includes: the motion equation, equations for calculating the enthalpy along the height of the fuel section of a fuel assembly with natural circulation of coolant within the channel containing the fuel assembly (lifting section) and in the inter-channel space (lowering section), the equation of mass balance between the channels of the racks with assemblies and in the inter-assembly space and the amount of evaporated (and outflowed) water, the heat balance equation for a fuel rod in a steam environment. The system of equations is supplemented by closing relations for calculating the thermal physics properties of water and steam, fuel and cladding materials, as well as the coefficients of heat transfer from the wall to the steam, hydraulic resistance and density of the steam-water mixture in the channels, and the heat released in the reaction of steam with zirconium. Validation of the computational code was carried out on the basis of the data of the ALADIN experiment performed by German specialists and the data of JSC OKB Gidropress. Cross-verification of the ROK/B code was carried out in comparison with the results of calculation using the KORSAR/GP and SOKRAT/B1 codes. Based on the results of the validation, it has been concluded that the deviation of the ROK/B results from the experimental data is not more than 2 to 10% (10% for the option with a fuel rod power of 20 W). Based on the results of cross-verification, it has been concluded that the discrepancy between the ROK/B results and the calculation results for the KORSAR/GP and SOKRAT/B1 codes is not more than 0.5% (for SOKRAT/V1) and less than 10% (for KORSAR/GP).

Estimating Lost Gas Content for Shales Considering Real Boundary Conditions during the Core Recovery Process.

Shale gas has become an important natural gas resource in recent years as the conventional oil and gas resources are depleting. Shale gas content is one of the most important parameters for reserve calculation and sweet-spot prediction. The traditional core recovery method is widely used to determine gas content. However, the estimation of lost gas content is the main factor of error and difficulty. Large errors and uncertainties occur when using the widely used methods, such as the United States Bureau of Mines (USBM) method. Hence, a more accurate method is required. In this work, a full-process model is developed in COMSOL Multiphysics to describe the lost gas with time during the core recovery process as well as the desorption stage after the core is covered. In this method, by setting the initial gas pressure and flow parameters and matching the desorbed gas volume and considering variable diffusivity with respect to temperature, the initial gas content and the gas lost with respect to time are calculated. Overall, 10 field data are tested using this full-process model, and the USBM method is also applied to compare the results. It is found that if the ratio of lost gas volume estimated using the USBM method to the desorbed gas volume of the field data is lower than 2.0, the USBM method underestimates the lost gas compared to the full-process method; if the ratio is about 2.0, the results from the USBM and the full-process methods are comparable; and if the ratio is close to 3.0, the USBM method tends to overestimate the lost gas. The modeling results indicate that this proposed full-process method is more theoretically sound than the USBM method, which has high uncertainties depending on the number of desorbed gas data points used. Nevertheless, this proposed method requires a large number of parameters, leading to the difficulty in finding true parameters. Therefore, an optimization algorithm is required. In summary, this study provides theoretical support and a mathematical model for the inversion calculation of lost gas during shale core recovery. It is helpful to evaluate the resource potential and development economics of shale gas more accurately.

Mathematical model of linear and non-linear proppant concentration increase during hydraulic fracturing – a solution for sequential injection of a number of proppant types

It is known that much of the technology aimed at intensifying fluid inflow by means of hydraulic fracturing involves the use of proppant. In order to transport and position grains in the fracture, a uniform supply of proppant with a given concentration into the fracturing fluid is ensured. The aim of the operation is to eliminate the occurrence of distortions in the injection program of proppant HF. A mathematically accurate linear increase of concentration under given conditions is possible only if the transient concentration is correctly defined. The proposed approach allows to correctly form a proppant HF work program for both linear and non-linear increase in proppant concentration. The scientific novelty of the work lies in application of a new mathematical model for direct calculation of injection program parameters, previously determined by trial and error method. A mathematical model of linear and non-linear increase of proppant concentration during HF was developed. For the first time, an analytical solution is presented that allows direct calculation of parameters of the main HF stages, including transient concentrations for given masses of the various types of proppant. The application of the mathematical model in formation of a treatment plan allows maintaining correct proppant mass distribution by fractions, which facilitates implementation of information and analytical systems, data transfer directly from a work program into databases. It is suggested to improve spreadsheet forms used in production, which would allow applying mathematical model of work program formation at each HF process without additional labour costs. The obtained mathematical model can be used to improve the software applied in the design, modelling and engineering support of HF processes.

Numerical Simulation and Experimental Verification of Phase Change Buoyancy Control System

Phase change buoyancy control systems (PBCS) driven by phase change materials have unique advantages over conventional hydraulically actuated buoyancy control systems, especially in their high adaptability for deep-sea exploration and seamless interaction with humans. Studying the heat transfer process and working mechanism of PBCS is helpful to research the precise control mode of the phase change buoyancy regulation system. In this study, we chose paraffin wax as the phase change material for PBCS. A buoyancy generator for phase change buoyancy regulation is designed and manufactured. By studying the relation between its expansion volume and heating time and heat input, the mathematical model of the volume change of PBCS is established. We obtain the calculation results of the PBCS working process by using the computer-aided software MATLAB. Experimental results show that the theoretical volume expansion velocity and volume expansion rate of paraffin are almost consistent with the experimental results. The mathematical calculation model is available and has a significant reference value for further research on the theoretical basis of the diving depth control of PBCS.

Groundwater Dynamic Characteristics with the Ecological Threshold in the Northwest China Oasis

Suitable groundwater level is an important foundation for the stability of the ecological environment, and the healthy development of the social economy, in the arid area of Northwest China. The Manas River Basin is a typical oasis in an arid area, where the problems of salinization and desertification are prominent. By analyzing the variation characteristics of groundwater in the study area from 2013 to 2019 combined with remote sensing technology—according to the theory of capillary water rise and phreatic evaporation—a mathematical calculation model of the ecological threshold is established to determine the ecological groundwater level. The results show that (1) the groundwater level in the study area fluctuates by 0.2–18 m throughout the year, and the variation of groundwater drawdown is 5–35 m from 2013 to 2019; (2) the upper threshold of the ecological groundwater level is 0.82–4.05 m and the lower threshold is 3.35–10.23 m; (3) the ecological water shortage area in the study area is 9755.36 km2, and the groundwater ecological deficit is 105.741 × 108 m3. This study can provide a theoretical basis for the determination of the ecological groundwater level, the optimal allocation of water resources, and ecological environment management in the arid area of Northwest China.

Advanced Mathematical Calculation Model of Single-Stage RCG

Aiming at the slow calculation speed of the finite-element-analysis (FEA) method of the single-stage reluctance coil gun (RCG) and considering that the existing mathematical analysis method is not mature enough and the accuracy is low, this article constructed and summarized an advanced mathematical calculation model as a mathematical block diagram and implement the model in MATLAB/Simulink that can be used to optimize some circuit parameters of a coil launcher. On the one hand, the model switching from resistance–inductance–capacitance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> ) to resistance–inductance circuit according to the actual application of the coil gun is established; on the other hand, the advantages of the FEA method are used to calculate the inductance, and a dynamic correction of inductance and inductance gradient according to the current value is proposed. The method is used to correct the deviation caused by the magnetic saturation problem. A comparison with the calculation data of the FEA method shows that the calculation of the constructed mathematical calculation model is basically correct and more efficient, and the expansion of the algorithmic function is easy to realize.

Research on quality inspection model of spot welding of equal-thickness three-layer sheets based on ultrasonic A-scan

To judge the spot welding quality automatically and effectively, this thesis uses the conventional ultrasonic A-scanning to study the mathematical model of nugget diameter for equal-thickness three-layer sheets. The finite element simulation model of the spot welding ultrasonic nondestructive (NDT) testing for equal-thickness three-layer low carbon sheets is established. The calculated values of the nugget diameter between different laminates are studied. Finally, the experiment of the spot welding ultrasonic nondestructive testing is carried out. This thesis verifies the correctness of the finite element simulation and the mathematical calculation model. The research results are of great significance to ultrasonic automatic inspection technology of spot welding.