Academic literature on the topic 'Leveling Mathematical models'

In order to calculate the parameters of roller leveling process, the 3D mathematical models of plate leveling based on the curvature integral by elastic-plastic differences were set up. The calculation results by the models showed a good correlation with the measured data from a plate mill which adopts the advanced control system by SMS. The analytic models can be developed which analyzed the leveling process so efficiently that it can be used for process controlling. Additionally, the plastic deformation ratio was analyzed which can account for the leveling phenomenon, and the model was regressed which can be used easily for engineering calculation.

During rolling and cooling at cooling beds, section bars get general and local curvatures, to correct which, leveling at roller leveling machines (RLM) is used. Calculation of leveling parameters of section bars at RLM is based on hypothesis of isotropy and homogeneity of the deformed metal. Besides the calculation is based also on assumptions of a linear distribution of penetration coefficient of plastic deformation along the rolled product thickness at alternating bending, point character of roller and rolled product surface contact, vertical direction of leveling force for all rollers of RLM. Application of those hypothesizes considerably deteriorates the accuracy of technological parameters calculation for rolling and leveling operations. A mathematical model presented for leveling parameters of section bars at RLM calculation. The novelty of the model is an accurate determination of the border between elastic and plastic zone Z0, which is accomplished by an iterative method. The information about exact value of Z0 is necessary for calculation of stress distribution along the piece section, as well as sag and curvature calculation after the leveling. In traditional models the Z0 value is determined approximately and does not meet the today’s requirements. Stress distribution diagrams along the rolled product section at bending under RLM rollers presented for rectangular, square, channel, Z-section profiles of rolled products, as well as for I-beam and rail, necessary for calculation of residual stresses. The comparison was done of P65 rail sag in the plane of maximum rigidity at the six-roller RLM of Kuznetsk steel-works and their value, obtained by the mathematical model application. The discrepancy between actual and calculated data is only 4.5%, which speaks about conformity of the elaborated mathematical model.

Body tilt is typically unavoidable for agricultural vehicles or platforms when operated over tough terrain in agricultural production, and, therefore, it is not possible to guarantee the operation performance. Current leveling methods mainly focus on wheeled vehicles or adjustment for single working parts rather than the vehicle body, and few of them could be applied to crawler vehicles. The objective of this research was to put forward an adaptive leveling system for combine harvesters based on the development of a new four-point lifting adjustable crawler chassis. The working principle of the proposed adjustable mechanism was studied on the basis of the analysis of adjustment characteristics under multiple posture adjustment conditions in a RecurDyn environment. The design relies on the combination of the attitude detection of the leveling system and adjustment calculation of driving hydraulic cylinders according to the established mathematical models. Within the designed adjustable extent (including adjustment range of vehicle height 0–87.8 mm, lateral inclination ±3.98° and longitudinal inclination −2.9–5.2°), the leveling performance of lateral and longitudinal inclination was then tested separately. The experiment showed that the leveling system could achieve automatic leveling with an accuracy of ±0.4° and could provide technical support for the development of crawler vehicles.

Generally, pressures resulted from roller during leveling process in selective laser sintering has the effect of densification of powder materials. But extra frictions due to them become the forces which always deteriorate the surface of the part and mark it with several lines trace. Sometimes, the manufacturing can even not continue if these forces accumulate to a large extent to move the whole part. Therefore, the whole forming process will be obliged to stop owing to the displacement of part from above mentioned damage. In this work, the emerging reason and related variation factors of these forces were studied mathematically, the mathematical and physical model of friction force was also built to describe the connections between the leveling process parameters and them. How to control the influence factor of friction to abate their damages to surfaces and promote the forming quality were also discussed based on these models. This will provide a common reference for the application of selective laser sintering technology.

The development of the Earth Gravitational Model 2008 (EGM2008) model is a significant contribution for modeling the Earth's gravity and geoid. Recently, it can be confidently used versus geometric models following a simple refinement procedure. Several studies show that, EGM2008 can reach the accuracy of regional or local geoid models after modeling the differences between the GPS-leveling geoid heights and EGM2008 derived geoid heights at identified control points. The study focuses on a corrector surface fitting (CSF) approach based on radial basis functions (RBF) as improvement procedure for EGM2008. A detailed mathematical model and solution algorithm of the proposed model is given, and it has been applied in different test areas covering the city borders of Bursa, Konya, Denizli and Gaziantep in Turkey. Accuracy of the improved model was evaluated in scattered check points within test regions. The geoid heights of all check points obtained by GPS-leveling measurements were compared with the geoid heights obtained from improved model. The discrepancies between the calculated and measured geoid heights were analyzed and discussed.

This paper discusses various sources of information related to the issue of determining heights by GNSS-leveling. Implementation of the GNSS leveling method requires the presence of geoid or quasi-geoid heights, which today can be obtained from the corresponding models. In recent decades, scientists from around the world have developed many global, regional and local models of geoid and quasigeoid. This has contributed to the emergence of numerous publications on GNSS leveling. The purpose of the work is to perform the analysis of modern models of reference surfaces on the basis of materials of scientific publications according to the criteria that have a significant impact on research in the field of determining the height by GNSS-leveling. Method. The paper considers 44 publications published in the period 2001–2021. Among the research in this direction, there are three types of work: 1) 13 publications on methods of constructing the models themselves; 2) 12 works on their accuracy analysis and 3) 19 works on “adjustment” of model heights. At the first stage of the research the analysis was performed according to criteria related to geoid and quasi-geoid surface modeling, including Stokes and Molodensky theory, mathematical methods of data analysis and processing, tidal systems, zero-order geoid undulation and scale levels of geoid and quasi-geoid models. In the second stage, the frequency of publications by years was analyzed and the activity of publications of existing geoid and quasigeoid models on the sample of countries, which was made on the basis of all selected works in this study, was established. At the third stage, a quantitative analysis of official published models of geoid and quasi-geoid on the frequency of publications for the study period. The ratio of the accuracy of the heights of global geoid models in relation to the magnitude of the degree and order of their calculation is established. Results. In 58 % of the analyzed works, the authors use Stokes’ theory in their research, and in 42 % – Molodensky’s theory. Among the mathematical methods of data analysis and processing, 27 % use the method of mean square collocation, 20 % use the least squares method, the “delete-restore” method and the method of modifying Stokes’ formula with least squares (or KTH-method). The Fast Fourier transform method was used in 13 % of the works. Publications on the creation of global models of the Earth mostly use the parameters of the tide free tidal system in their calculations – a total of 40 % works. No less important criterion (33 % of works) should be taken into account the parameter of undulation of the geoid of zero order (“zero degree term”). In total, 41 % of research is aimed at creating and analyzing quasi-geoid models on a regional scale. During the study period, most works were published in 2012 and 2018. Leading countries in the development of quasi-geoid models are Canada, Poland, Sweden and the United States, and global geoid models are Germany, the United States and China. For the period 2001–2021, 99 global geoid models of various degree and order were officially presented, among which GOCO, EIGEN and EGM series models are most often used for research. Also during this period, 177 quasi-geoid models were presented, the most of which were published in 2019. Based on these data, the relationship with the frequency of publications in 2008–2021 can be traced. The accuracy of global geoid models in relation to the degree and order of their calculation is systematic in the range of 0.52–1.92 m, 0.38–0.50 m, 0.23–0.38 m and 0.12–0,14 m for models 60-220, 220-260, 260-720 and 720-2190 degree and order respectively. Scientific novelty. It is shown that the analysis of modern models of reference surfaces on the basis of materials of scientific publications in the field of GNSS-leveling method allows establishing the existing advantages and disadvantages of research in this field. Practical significance. The data of such analysis can be used to solve key problems in determining the height of the GNSS-leveling method, which require further research and to find modernized solutions.

The article is devoted to comparison of methods of calculating the approximate elevations of nodal points when adjusting leveling networks by strict and non-strict methods. Ensuring geomechanical monitoring of the mutual influence of constructed and operated objects is important in the intensive development of underground space of megacities, the construction of unique objects and structures. In the course of the research, mathematical models of level networks were developed and presented in the form of a closed loop and a set of open polygons. Analysis of modeling allows to determine the feasibility of applying the knot method by Professor V.V. Popov instead of the parametric method of adjustment. It is established that the quality of the results of strict equalization depends entirely on the quality of measurements, since deviations from the true values do not exceed the measurement error. The research has shown that it is possible to simplify the processing of monitoring data and evaluation of various configuration options for leveling networks, using algorithms for calculating approximate marks of nodal points. This makes it easier to process monitoring results and evaluate various network configuration options while ensuring the required level of measurement accuracy.

Building deformation models consistent with reality is a crucial step for time-series deformation monitoring. Most deformation models are empirical mathematical models, lacking consideration of the physical mechanisms of observed objects. In this study, we propose an improved time-series deformation model considering rheological parameters (viscosity and elasticity) based on the Kelvin model. The functional relationships between the rheological parameters and deformation along the Synthetic Aperture Radar ( SAR) line of sight are constructed, and a method for rheological parameter estimation is provided. To assess the feasibility and accuracy of the presented model, both simulated and real deformation data over a stretch of the Lungui highway (built on soft clay subgrade in Guangdong province, China) are investigated with TerraSAR-X satellite imagery. With the proposed deformation model, the unknown rheological parameters over all the high coherence points are obtained and the deformation time-series are generated. The high-pass (HP) deformation component and external leveling ground measurements are utilized to assess the modeling accuracy. The results show that the root mean square of the residual deformation is ±1.6 mm, whereas that of the ground leveling measurements is ±5.0 mm, indicating an improvement in the proposed model by 53%, and 34% compared to the pure linear velocity model. The results indicate the reliability of the presented model for the application of deformation monitoring of soft clay highways. The estimated rheological parameters can be provided as a reference index for the interpretation of long-term highway deformation and the stability control of subgrade construction engineering.

Purpose The purpose of this paper is to propose an integrated model for allocation and leveling of human resources in IT projects. Design/methodology/approach A single case study was conducted in a large company of IT outsourcing services, which were assessed the management of 14 projects. The survey was conducted through interviews with project managers, and digital files and internal documents of the organization related to these projects. Findings In the analysis, it was identified that the critical path is not identified in all projects, and even when this happens, resources are not allocated in the first tasks in that path. A committee controls the allocation of resources with the assessment of skills, but there is no control of all resource constraints. Research limitations/implications The main limiting factors for this study are: use of data of one company in the IT industry, making it difficult to generalize the model for other sectors companies; it was noted during interviews that the project managers interviewed do not always know in detail all the company’s processes for allocation and resource leveling, due to the large number of processes and different management activities of these professionals. Practical implications A model and actions for this implementation was proposed, such as training for the use of the technique of critical path; allocation and leveling done simultaneously; decisions of the management committee based on information of availability, key skills, holidays, days off of human resources; development of a software tool that integrates this information, generating graphical interfaces that are not provided by project management software with the use of an allocation factor. Social implications The characteristics of the proposed model, as well as the use of the allocation factor, can help managers to validate their allocation models and leveling of human resources in an integrated manner. Originality/value The study explains that the granularity of analysis of resource allocation increases by decomposition of the duration of each activity in fixed time segments. It is suggested to use the mathematical concept of the allocation factor (Fa).

Relevance. When the hydraulic fluid is operated for several cycles, the impact on hydraulic performance and longevity is greatly increased. So, there are several ways to fix this problem. To increase the efficiency of the hydraulic system, it is necessary to study the working processes, the hydraulic systems of the quick-change equipment of the machine with a lawn of the kshp are made as a whole, and the equipment of the machine is attached to the suspension device. The complexity of these processes lies in the fact that they allow experimental research and verification of results using mathematical models. Aim. The purpose of the experimental study in this dissertation is to study the effect of forces acting on the hydraulic system when excavating the hydraulic system of a multipurpose machine and substantiate the parameters by assessing power use efficiency. Methods. Checking the suitability of the working fluid during earthworks, as well as the mathematical model. In this case, we studied the hydraulic system of a single-bucket excavator, the device of quick-change equipment for a universal machine. Results. The theoretical work performed has been verified and the confirmation of the operation of a multipurpose machine designed with earth and dozer equipment. The installation of equipment based on TTZ-80 made it possible to carry out experimental research with the most energy-intensive workflow, determining energy efficiency indicators for excavation and leveling. Conclusion. Comprehensive tests made it possible to conclude that the characteristics of the developed design and the characteristics of the engine of the base machine - the TTZ-80.10 - KM-1 tractor, overcome the resistance encountered during technological operations of a multipurpose machine.

The main milestones of the formation and development of astronomical science in Kharkiv during 1883–1945 are reconstructed on the example of the activities of the astronomical observatory of Kharkiv University. During this period, the outstanding worldview science in Kharkiv has achieved significant success: the works of Kharkiv astronomers have received world recognition; a well-known scientific planetary school has been established at the Observatory; the scientific community highly appreciated the research on the physics and chemistry of the Moon, the giant and small planets of the Solar System. The primary goal of the research is to inscribe the history of the university Observatory into the European and world context. Its purpose is to summarize the results of a comprehensive historical ad scientific study of the development of astronomical research in Kharkiv at the end of the 19th century – the first half of the 20th century and identification of ways of further scientific research. The completed research, which continues the problems of works devoted to the study of the history of astronomical science in Ukraine, focuses on expanding the well-known source base by attracting new retro-information resources. In particular, the monograph used a significant array of archival primary sources from almost twenty archival and library institutions of different countries. Most of them were introduced into scientific circulation for the first time, which allowed to determine and specify the sequence of stages of development of astronomical science in Kharkiv during the research period, to clarify and identify the little-known circumstances of the observatory life. The methodological basis of the study is the principles of historism, objectivity and a systematic approach to studying the problem. To solve specific problematic tasks in the monograph, general scientific and specially historical methods were used which allowed to study, analyze and summarize the presented factual material in a complex manner. The main sections of the monograph represent the dynamics of replenishment of the instrumental base of the university observatory, the chronology of the construction of the observatory complex of buildings at the location of the modern Scientific Research Institute of Astronomy of the V. N. Karazin Kharkiv National University. According to the author’s periodization, the stages of formation of subjects and directions of scientific work of university astronomers have been analyzed, including: seismic observations with the help of horizontal Rebeur-Paschwitz pendulums, research of the activity of the Sun, astrometric observations on the Repsold meridian circle of for the purpose of compiling a catalog of zodiac stars, studying lunar eclipses and meteor showers. The participation of university astronomers in the creation of the plan of the city of Kharkiv and its connection with the general network of precise geometric leveling of the Military Topographic Department of the General Staff; the organization of observations by an expedition of Kharkiv astronomers of the total Solar eclipse of 1914 in Henichesk; the creation of the School-workshop of precision mechanics at the Faculty of Physics and Mathematics of Kharkiv University were considered; information on the participation of Kharkiv astronomers in the events of the civil war during the Ukrainian Revolution was documented. The scientific research activity of Kharkiv astronomers during 1920-1930-s which was devoted to carrying out important astrometric works on meridian observations of star declinations by absolute methods and observations of Kopf-Rentz stars according to the programs of the International Astronomical Union; the initiation of the creation of the Catalog of faint stars; research in astrophysics aimed at studying the physical conditions on the Moon and the Sun, planets and the interstellar environment; performing long series of spectrophotometric observations of the Moon, Jupiter, Mars and Saturn under different conditions of observation; study of the kinematics of stellar systems of different order, the physical parameters and evolution of stars, the morphology of the Galaxy, the nature of the stellar subsurfaces and atmospheres, dust and gas nebulae, new stars and the variability of stars have been considered; the directions of solid works carried out in the field of celestial mechanics, devoted to the dynamics of the minor planets of the Jupiter group, the definition and improvement of the orbits of minor planets have been clarified. The development of amateur astronomy in Kharkiv, in particular, the functioning of circles and societies that directed their activities to the dissemination of astronomical knowledge, was highlighted; the participation of their representatives in astronomical observations at the Kharkiv Astronomical Observatory was emphasized. Reconstructed the development of historical events in the 1930s related to the involvement of Soviet and Western astronomers in the processes of political confrontation between the USSR and the Western world; investigated the course of circumstances that prevented the implementation of the project of creating a new modern astronomical center of national importance – the central Ukrainian observatory in Kharkiv; the participation of an expedition of Kharkiv astronomers in the observation of the «great Soviet eclipse» – the total solar eclipse of 1936 – in the North Caucasus is highlighted; established the facts of political «purges» and repressions by the People’s Commissariat for Internal Affairs ( the NKVD) in the Kharkiv Astronomical Observatory. The activity of the Kharkiv Astronomical Observatory has been documented and authentic biographical information about its representatives during the Nazi occupation of 1941–1943, the period of the German-Soviet war, has been presented; the unpopular facts of the forced collaboration of some scientists are highlighted; the process of recovery and reconstruction of the Kharkiv Astronomical Observatory after the liberation of the city is characterized. With the aim of researching the personal history of Kharkiv astronomy of the studied period, the monograph presents the results of a historical and biographical study of facts of life and scientific heritage of scientists who fully devoted themselves to Science, laid the foundations for the future development of many directions of modern astronomical research, made a significant contribution to the treasury of the national and European astronomical science, whose activities were connected with the Kharkiv Astronomical Observatory, in particular: Grigory Levytsky, Ludwig Struve, Mykola Evdokymov, Otto Struve, Mykola Barabashov, Boris Gerasimovich, Vasil Fesenkov, Oleksiy Razdolsky, Boris Ostashchenko-Kudryavtsev, Nicholas Bobrovnikov, Paraskovia Parkhomenko, Mstislav Savron, Boris Semeykin, Kostyantyn Savchenko and others (25 biographical essays are presented). A significant part of the mentioned factual material was also introduced into scientific circulation for the first time. A separate section of the monograph provides chronologically structured information that reflects the sequence of research work of the Kharkiv Astronomical Observatory employees during the period under study: from astrometric observations of stars and seismic research to spectrohelioscopic and spectroheliographic observations of the Sun and the initiation of the Kharkiv school of planetary science. It is assumed that the materials of the monograph will be used in research work devoted to the study of the process of institutionalization of astronomical research in Kharkiv at the end of the 19th century – the first half of the 20th century.

Efficient and accurate GNSS data post-processing can greatly improve the efficiency of mapping work, this paper outlines the mathematical model of GNSS control network data processing and solving process, uses the data processing software GGO of Guangzhou Gio Electronic Technology Co. The results of the baseline solution and the difference between the baseline solution and the solution of the Leica LGO and COSA software are compared. The results show that the baseline solution and net leveling solution can be correctly performed with the software of this framework, and the error of baseline solution is within 3 mm in each direction compared with LGO, and the error of net leveling result is within 2 mm compared with COSA, which is sufficient to meet the requirements of engineering practice.

The four-point leveling hydraulic system (FLHS) is a key component of high-precision hydraulic press. To meet the development trend of leveling system of hydraulic press, such as large stroke, anti-bias load ability, big leveling torque, principle of passive FLHS with four axis synchronous controlling has been proposed, using four high-precision displacement sensors and four high-response servo-proportional valves (HSPV). Because the HSPV has a certain predictive opening, during the process of passive leveling operating, linearization of the mathematic model at operating point is necessary. In this paper, a simulation model of the system, which uses the average type synchronous control strategy, is built with ADAMS and MATLAB / Simulink, as well as the operational parameters of the model. The result of the simulation shows that the system using the average type synchronous control strategy is able to ensure the synchronization error among the four axis of the leveling system. It also suggests that the proposed leveling and the control strategy are reasonable, effective and feasible.

Calculations (with a 10-room and a simpler 3-room simulation of the large house fire) of temperature and smoke levels in several rooms of a structural fire are possible with the CFAST computer code. The accuracy and applicability of the results is greatly enhanced though the comparison of the calculations with experimental data. Experimental work thereby assists in understanding fire behavior in structural fires. Temperature measurements at different locations during a house fire provide necessary data for the development of mathematical models, which attempt to simulate the fire on a computer. In this paper, a large 170 square meter single-level house was subject to a complete experimental burn, with temperature measurements and fire observations during the entire burn, and subsequent modeling via a detailed 10-room simulation and a simpler 3-room simulation. The CFAST (Consolidated Model of Fire Growth and Smoke Transport) computer code is used to calculate temperatures and smoke levels in the various rooms of the house during the burn (with 10 different rooms). Four fire scenarios are considered in the simulation, with increasing realism regarding the actual fire specification. A simpler calculation (with 3 different rooms) has also done to see if the similar results would be shown with the 10-room simulation. It was found that results for smoke temperature and smoke layer heights were very similar, leading to the conclusion that a 3-room simulation of a 10-room building gives adequate modeling capability of the real structural fire. Computation results give the expected trends (deduced from local point temperature measurements) of initial temperature surge and decay, peak and leveling off temperatures, especially with respect to the northwest bedroom with a closed door. The effect of whether a door of a room would have been open was investigated computationally, with results illustrating far more dangerous smoke temperature and smoke level in the room when its door is open.

The article assesses the level of economic security of an agro-industrial complex using an indicative method. The design criteria (indicators) for assessing the level of economic security of an agrarian formation have been determined. A mathematical model has been drawn up to calculate the deviations of indicator indicators from the threshold values. The main threats to the economic security of the pilot enterprise have been identified, for leveling the impact of which the main stages of the anti-crisis program are outlined.

As a method for simultaneously increasing efficiency of energy use and stability of energy supply in commercial buildings, we have proposed Totalized Hydrogen Energy Utilization System (THEUS) that uses hydrogen as a high potential for energy carrier. The hydrogen storage method used by this system adopts metal hydride that excels in volumetric storage density. In this paper, as the model case for electric power load leveling operation, the optimum design and optimum operation method for multiple metal hydride tanks are described with a mathematical model which can simulate operation of the metal hydride tank and experimental equipment. As a result, the combination of tank specifications and operating conditions that produce the effective simultaneous utilization of 1) hydrogen, 2) metal hydride and 3) heat are identified. Furthermore, an operating method to make the most of the metal hydride tank flexibility with respect to tank selection is determined.