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Journal articles on the topic 'Process control Dynamics Mathematical models'
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1
Al Salaimeh, Safwan. "MATHEMATICAL MODELS FOR COMPUTERIZED CONTROL SYSTEM." Gulustan-Black Sea Scientific Journal of Academic Research 48, no. 05 (July 5, 2019): 119–23. http://dx.doi.org/10.36962/gbssjar119.
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The software is a set of mathematical methods, and algorithms of information processing, which used in creating the control system. When designing control systems, Initial data for the design of control system. The tasks of the computerized control system are understood as a part of the computerized functions of the computerized control system characterized by the outcomes and outputs in specific form. control function is: commutative action for computerized control system, aimed to achieve a criterion goal. Depending on the properties of the process and their mathematical description can be combined into different classes; This paper shows the designing the mathematical models which need to computerized control systems (models (3) – (8)). In the same time this paper shows the main methods which were used to formulate the mathematical models as: • Stochastic and deterministic; • One dimensional and multidimensional; • Linear and nonlinear; • Static and dynamic; • Stationary and non – stationary; • With distributed and lumped parameters.
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ZAVADSKY, SERGEY V., DMITRI A. OVSYANNIKOV, and SHENG-LUEN CHUNG. "PARAMETRIC OPTIMIZATION METHODS FOR THE TOKAMAK PLASMA CONTROL PROBLEM." International Journal of Modern Physics A 24, no. 05 (February 20, 2009): 1040–47. http://dx.doi.org/10.1142/s0217751x09044486.
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Mathematical models of the structural parametric optimization of plasma dynamics are discussed. Optimization approach to plasma dynamic is based on the consideration of trajectory ensemble. This ensemble describes transient process in tokamak subject to the initial data and external disturbances. In the framework of this approach the optimization of dynamics of the trajectory ensemble in ITER tokamak is given. The trajectories of this ensemble are perturbed at the initial point set and the set of external disturbances.
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Barrios Sánchez, Jorge Manuel, Roberto Baeza Serrato, and Marco Bianchetti. "Design and Development of a Mathematical Model for an Industrial Process, in a System Dynamics Environment." Applied Sciences 12, no. 19 (September 30, 2022): 9855. http://dx.doi.org/10.3390/app12199855.
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This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency domain based on the Laplace transform. The conventional control engineering technique is used to present and reduce the dynamic system in a block diagram as a mechanism for determining the structure of the system. The direct path equation and the feedback equation are determined to obtain mathematical models that explain the trajectory of the behavior of each state variable through a transfer function in response to the different inputs of the system. The research proposal is based on presenting an alternative of analytical validation for more robust decision-making to systems dynamics models, based on the explanation of the system structure through a transfer function and its analysis of stability and external controllability for the system dynamics model under study. The results are visually analyzed in a root diagram.
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Vukobratović, M. K., V. F. Filaretov, and A. I. Korzun. "A unified approach to mathematical modelling of robotic manipulator dynamics." Robotica 12, no. 5 (September 1994): 411–20. http://dx.doi.org/10.1017/s0263574700017963.
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SUMMARYA new method for computer forming of dynamic equations of open-chain mechanical robot configurations is presented. The algorithm used is of a numeric-iterative type, based on mathematical apparatus of screw theory, which has enabled elimination of the unnecessary computations in the process of dynamic model derivation. In addition to conventional kinematic schemes of robotic manipulators, the branched kinematic chains which have recently found their application in the locomotion of robotic mechanisms were also treated. Both the inverse and direct problems of dynamics were addressed. A comparative analysis was carried out of the numerical complexity of various existing algorithms of numeric-iterative type dealing with the problems of spatial active mechanisms dynamics. It has been shown that the proposed method regardless of its generality, approaches by its models complexity symbolic models, which are valid for particular robotic mechanisms only where they achieve a high degree of efficiency.
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Jia, Xiao Yi, Yu Tian Lin, Hui Bin Lin, Ling Gao, Jian Qun Lin, and Jian Qiang Lin. "Mathematical Modeling of CSTR Bioreactor Control for Production of Recombinant Protein." Advanced Materials Research 894 (February 2014): 311–15. http://dx.doi.org/10.4028/www.scientific.net/amr.894.311.
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Fermentation process using recombinant strain for production of recombinant protein is widely used in commercialization of the biotechnologies. The continuous stirred tank reactor (CSTR) is a typical microbial cultivation method, has the major advantage of high productivity. Mathematical modeling and simulation is useful for analysis and optimization of the CSTR fermentation process. Most of the mathematical models developed for CSTR are black box models without information of the intracellular dynamics and regulations. In this research, a mathematical model is built based on gene regulation for recombinant protein production using CSTR, and simulation is made using this model.
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Kochuk, Serhii, Dinh Dong Nguyen, Artem Nikitin, and Rafael Trujillo Torres. "Identification of UAV model parameters from flight and computer experiment data." Aerospace technic and technology, no. 6 (November 29, 2021): 12–22. http://dx.doi.org/10.32620/aktt.2021.6.02.
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The object of research in the article is various well-known approaches and methods of structural and parametric identification of dynamic controlled objects - unmanned aerial vehicles (UAVs). The subject of the research is the parameters of linear and nonlinear mathematical models of spatial and isolated movements, describing the dynamics and aerodynamic properties of the UAV and obtained both from the results of flight experiments and using computer object-oriented programs for 3-D UAV models. The goal is to obtain mathematical models of UAV flight dynamics in the form of differential equations or transfer functions, check them for reliability and the possibility of using them in problems of synthesis of algorithms for automatic control systems of UAVs. Tasks to be solved: evaluation of the analytical (parametric), direct (transient), as well as the identification method using the 3-D model of the control object. Methods used structural and parametric identification of dynamic objects; the determination of static and dynamic characteristics of mathematical models by the type of their transient process; the System Identification Toolbox package of the MatLab environment, the Flow Simulation subsystem of the SolidWorks software and the X-Plane software environment. The experimental parameters of UAV flights, as well as the results of modeling in three-dimensional environments, are the initial data for the identification of mathematical models. The following results were obtained: the possibility of analytical and computer identification of mathematical models by highly noisy parameters of the UAV flight was shown; the mathematical models of UAVs obtained after identification is reliable and adequately reproduce the dynamics of a real object. A comparative analysis of the considered UAV identification methods is conducted, their performance and efficiency are confirmed. Conclusions. The scientific novelty of the result obtained is as follows: good convergence, reliability and the possibility of using the considered identification methods for obtaining mathematical models of dynamic objects to synthesize algorithms for automatic control systems of UAVs is shown.
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Alzbutas, R., and V. Janilionis. "THE SIMULATION OF DYNAMIC SYSTEMS USING COMBINED MODELLING." Mathematical Modelling and Analysis 5, no. 1 (December 15, 2000): 7–17. http://dx.doi.org/10.3846/13926292.2000.9637123.
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The new approach to the problems of dynamic systems simulation is proposed. The analytical and imitation modelling of non‐linear complex dynamic systems which comprise simulation of continuous and discrete processes with constant and variable parameters, are investigated. The aggregate mathematical modelling scheme [1] and the method of control sequences for discrete systems specification and simulation are used as well as the dynamic mathematical modelling scheme for continuous process formalization and modelling. According to them the investigated systems are presented as the set of interacting piecewise linear aggregates, which can include processes described with differential equations. The above mentioned approach is used in developing software for the construction and research of the models. The modelling of the dynamic systems’ control is also analyzed and developed software for the dynamic systems’ simulation is presented. It is related to the proposed combined modelling methodology. The developed dynamical simulation system ADPRO (Automatic Differentiation PROgram) extends applicability of the system SIMAS (SIMulation of the Aggregate Systems) [2] with dynamical simulation means realized with APL2 (A Programming Language 2) and based on automatic differentiation [3]. The created model of service process and its control can be used as a base for other models of wide class complex dynamics’ systems [4], the parts of which are described with differential equations.
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Korniyenko, Bogdan, and Andrii Nesteruk. "Mathematical modelling of granulation process in fluidised bed (overview of models)." Proceedings of the NTUU “Igor Sikorsky KPI”. Series: Chemical engineering, ecology and resource saving, no. 2 (June 30, 2022): 51–59. http://dx.doi.org/10.20535/2617-9741.2.2022.260349.
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One of the most common methods of making mineral fertilizers is granulation. Fertilizers in the form of granules have a number of advantages over conventional fertilizers in the form of powder or liquid, namely, ease of transportation, well absorbed and less susceptible to weathering from the soil, convenient to use. To obtain solid particles from liquid starting material such as solutions, emulsions or suspensions, the following processes are used: crystallization, granulation, spray drying. Depending on the focus of the study, the fluidized bed granulation process can be modeled at different levels of abstraction. The dynamics of individual particles is modeled on a microscopic scale. The interaction of a particle with a liquid, equipment or other particles is considered. The next rougher level of abstraction is the mesoscale. Here the particles are divided into classes according to their characteristics. It is assumed that the particles of the class have the same properties and dynamics. On a macroscopic scale, the roughest level of approximation, attention is focused on the integral behavior of the whole set of particles. As a result, the selected characteristic values describe the state of the particle layer. There are different approaches to modeling for each scale. It is proposed to describe the microscopic scale using the hydrodynamics model, the mesoscale using the balance model, and the macroscopic scale using the moments method or the Lagrange-Euler model. A combined balance-hydrodynamics model and a multi-chamber balance model that can be used for the tasks of building information technology for fluidized bed granulation process control technology are also considered.
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Ritonja, Jožef, Andreja Goršek, Darja Pečar, Tatjana Petek, and Boštjan Polajžer. "Dynamic Modeling of the Impact of Temperature Changes on CO2 Production during Milk Fermentation in Batch Bioreactors." Foods 10, no. 8 (August 5, 2021): 1809. http://dx.doi.org/10.3390/foods10081809.
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Knowledge of the mathematical models of the fermentation processes is indispensable for their simulation and optimization and for the design and synthesis of the applicable control systems. The paper focuses on determining a dynamic mathematical model of the milk fermentation process taking place in a batch bioreactor. Models in the literature describe milk fermentation in batch bioreactors as an autonomous system. They do not enable the analysis of the effect of temperature changes on the metabolism during fermentation. In the presented extensive multidisciplinary study, we have developed a new mathematical model that considers the impact of temperature changes on the dynamics of the CO2 produced during fermentation in the batch bioreactor. Based on laboratory tests and theoretical analysis, the appropriate structure of the temperature-considered dynamic model was first determined. Next, the model parameters of the fermentation process in the laboratory bioreactor were identified by means of particle swarm optimization. Finally, the experiments with the laboratory batch bioreactor were compared with the simulations to verify the derived mathematical model. The developed model proved to be very suitable for simulations, and, above all, it enables the design and synthesis of a control system for batch bioreactors.
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Zamula, Alina, and Sergii Kavun. "Complex systems modeling with intelligent control elements." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (January 10, 2017): 1750009. http://dx.doi.org/10.1142/s179396231750009x.
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The approach to managing complex systems through the usage of fuzzy technology in combination with the system-dynamic modeling is improved. The methods of system dynamics and artificial intelligence represented the research subject. Object of study includes process operation of complex systems. For the experiment selected banking system (BS) and commercial bank (CB) as its subsystem. The mathematical models of the BS and CBs are developed; elements of intelligent control are formalized. The knowledge base in the form of production rules is designed in the paper. Functions of fuzzy variables and their parameters are selected for building fuzzy models using Mamdani and Sugeno algorithms. The control impact and the functioning of intellectual decision support system for the prediction task are studied. The efficiency of scientific research on the example of the Ukrainian BS is evaluated.
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Nguyen, Nhu Tuong An, Vinh Quang Do, The Thinh Pham, and Tuan Tran Nguyen. "Application of different control algorithms on a ‘home-made’ temperature control lab kit." Can Tho University Journal of Science 14, no. 1 (March 30, 2022): 62–73. http://dx.doi.org/10.22144/ctu.jen.2022.007.
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Providing enough facilities for students to do laboratory activities is important. An existing useful kit was proposed for students learning a variety of control engineering topics. A temperature control lab kit is made from scratch using common electronics components as a replacement for the original TCLab introduced by Hedengren (Hedengren et al., 2019). Mathematical models of the system derived from theoretical and experimental methods are simulated in Matlab/Simulink to verify their accuracy to the physical kit. Different control algorithms such as: On/Off, PID, Fuzzy are then applied on the Kit as well as its mathematical models to illustrate their control feasibility. Human machine interface (HMI) is also designed using Matlab GUI allowing an operator to select a control algorithm, tune control parameters and monitor parameters of the process. Experimental results show that the derived models can reflect quite well dynamics of the physical kit with temperature deviation among them in the range of ±3°C. This confirms that the kit is well-suited for teaching different control topics such as system modelling, system identification, classical control and advanced control algorithms.
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Khvostov, A. A., A. A. Zhuravlev, E. A. Shipilova, R. S. Sumina, G. O. Magomedov, and I. A. Khaustov. "Simulink models of technological systems with perfect mixing and plug-flow hydrodynamics." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 3 (December 20, 2019): 28–38. http://dx.doi.org/10.20914/2310-1202-2019-3-28-38.
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The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. The process of synthesis of the dynamic matrix mathematical model was considered by the example of a sugar syrup cooler, the quality indicator of the finished product are selected as sucrose crystals and their portion in the total volume of caramel mass. Taking into account the dependence of syrup viscosity on temperature, thermal effects as a result of the process of crystallization of sucrose from syrup, design features of a typical caramel machine made it possible to clarify the dynamics of the process of syrup cooling. The model developed with this approach allows to obtain real-time estimates of temperatures at the outlet of the cooler, which makes it possible to study the dynamics of the technological process and synthesize the control system. The presented approach allows to implement mathematical models of ideal reactors in Simulink system and to move to matrix ordinary differential equations, which makes it possible to convert them into Simulink blocks. The approach is also applicable to other models of ideal reactors, which allows to form libraries of typical ideal reactors of Simulink system for synthesis of heat and mass exchange equipment. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.
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Dyvak, Mykola, Andriy Melnyk, Andriy Pukas, and Libor Dostalek. "Control of mathematical modeling process of dynamics of harmful substances concentrations on the basis of ontological approach." Computational Problems of Electrical Engineering 12, no. 1 (June 2, 2022): 7–16. http://dx.doi.org/10.23939/jcpee2022.01.007.
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The problem of building a mathematical model of the dynamics of nitrogen dioxide concentrations at different parts of the city is considered in the paper. The peculiarities of the construction of such models on the basis of periodic measurement of concentrations of harmful substances and identification on the basis of the measurements obtained are considered. This paper also proposes an ontological approach as a control tool that greatly simplifies the systematic standardized methods of the models storage, the process of their construction and appropriate usage in practice. The use of the ontological model allows formalizing the process of obtaining, storing and using relevant knowledge and is suitable for more intelligent systems, such as identification of obviously erroneous solutions based on the model, predictive control of the model, optimization of the decision-making process based on knowledge and modeling of an appropriate technological flow chart. This paper also describes the features of the construction of the corresponding ontological model, the pattern of choice of a nonlinear model with "switching" to different conditions. Relevant experimental studies have also been conducted to confirm the effectiveness of the proposed approach.
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Shmalko, Elizaveta, Yuri Rumyantsev, Ruslan Baynazarov, and Konstantin Yamshanov. "Identification of Neural Network Model of Robot to Solve the Optimal Control Problem." Informatics and Automation 20, no. 6 (November 18, 2021): 1254–78. http://dx.doi.org/10.15622/ia.20.6.3.
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To calculate the optimal control, a satisfactory mathematical model of the control object is required. Further, when implementing the calculated controls on a real object, the same model can be used in robot navigation to predict its position and correct sensor data, therefore, it is important that the model adequately reflects the dynamics of the object. Model derivation is often time-consuming and sometimes even impossible using traditional methods. In view of the increasing diversity and extremely complex nature of control objects, including the variety of modern robotic systems, the identification problem is becoming increasingly important, which allows you to build a mathematical model of the control object, having input and output data about the system. The identification of a nonlinear system is of particular interest, since most real systems have nonlinear dynamics. And if earlier the identification of the system model consisted in the selection of the optimal parameters for the selected structure, then the emergence of modern machine learning methods opens up broader prospects and allows you to automate the identification process itself. In this paper, a wheeled robot with a differential drive in the Gazebo simulation environment, which is currently the most popular software package for the development and simulation of robotic systems, is considered as a control object. The mathematical model of the robot is unknown in advance. The main problem is that the existing mathematical models do not correspond to the real dynamics of the robot in the simulator. The paper considers the solution to the problem of identifying a mathematical model of a control object using machine learning technique of the neural networks. A new mixed approach is proposed. It is based on the use of well-known simple models of the object and identification of unaccounted dynamic properties of the object using a neural network based on a training sample. To generate training data, a software package was written that automates the collection process using two ROS nodes. To train the neural network, the PyTorch framework was used and an open source software package was created. Further, the identified object model is used to calculate the optimal control. The results of the computational experiment demonstrate the adequacy and performance of the resulting model. The presented approach based on a combination of a well-known mathematical model and an additional identified neural network model allows using the advantages of the accumulated physical apparatus and increasing its efficiency and accuracy through the use of modern machine learning tools.
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Gallego, Antonio J., Manuel Macías, Fernando de de Castilla, and Eduardo F. Camacho. "Mathematical modeling of the Mojave Solar Plants." Energies 12, no. 21 (November 3, 2019): 4197. http://dx.doi.org/10.3390/en12214197.
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Competitiveness of solar energy is one of current main research topics. Overall efficiency of solar plants can be improved by using advanced control strategies. To design and tuning properly advanced control strategies, a mathematical model of the plant is needed. The model has to fulfill two important points: (1) It has to reproduce accurately the dynamics of the real system; and (2) since the model is used to test advanced control strategies, its computational burden has to be as low as possible. This trade-off is essential to optimize the tuning process of the controller and minimize the commissioning time. In this paper, the modeling of the large-scale commercial solar trough plants Mojave Beta and Mojave Alpha is presented. These two models were used to test advanced control strategies to operate the plants.
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Wolkenhauer, O., S. N. Sreenath, P. Wellstead, M. Ullah, and K. H. Cho. "A systems- and signal-oriented approach to intracellular dynamics." Biochemical Society Transactions 33, no. 3 (June 1, 2005): 507–15. http://dx.doi.org/10.1042/bst0330507.
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A mathematical understanding of regulation, and, in particular, the role of feedback, has been central to the advance of the physical sciences and technology. In this article, the framework provided by systems biology is used to argue that the same can be true for molecular biology. In particular, and using basic modular methods of mathematical modelling which are standard in control theory, a set of dynamic models is developed for some illustrative cell signalling processes. These models, supported by recent experimental evidence, are used to argue that a control theoretical approach to the mechanisms of feedback in intracellular signalling is central to furthering our understanding of molecular communication. As a specific example, a MAPK (mitogen-activated protein kinase) signalling pathway is used to show how potential feedback mechanisms in the signalling process can be investigated in a simulated environment. Such ‘what if’ modelling/simulation studies have been an integral part of physical science research for many years. Using tools of control systems analysis, as embodied in the disciplines of systems biology, similar predictive modelling/simulation studies are now bearing fruit in cell signalling research.
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Slivinskas, Kastytis, Vladimir Gichan, Vytautas Striška, and Algimantas Juozas Poška. "Optimization of Transport Movement Parameters of the Transfer Manipulator for the Quenching Bath According to the Technological Process Requirements." Solid State Phenomena 164 (June 2010): 411–18. http://dx.doi.org/10.4028/www.scientific.net/ssp.164.411.
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The paper analyzes problems related to optimal selection and possible control of parameters of transport movements of the manipulator serving galvanizing and quenching baths. Evaluation of the acceleration and braking processes as well as minimization of the deflection during oscillations of the suspended loading are considered. Mathematical models of the transfer manipulator together with the loading unit were developed, which enable dynamic evaluation of transporting movements. Calculations of the dynamics of the model and simulations of the transfer process were performed. The obtained research results allow to improve the quality of the processing and reduce the emission of pollutions.
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Kovalenko, O. Ye, and V. L. Kosolapov. "Stability model of agent-based situational control system." Mathematical machines and systems 3 (2020): 93–104. http://dx.doi.org/10.34121/1028-9763-2020-3-93-104.
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While managing complex systems, it is advisable to use mathematical models adequate to real systems, which can be used for generalized model analysis of different solutions in systems of situational man-agement (SSM). Such mathematical models are an important component of the SSM in the process of supporting the adoption of important strategic and operational decisions at various levels of government. Implementation of SSM in the form of a multi-agent system, due to its characteristics, is an adequate approach to solving the problems of situational management (SM). According to the context of SM, the behavior of the SSM is described as the dynamics of movement from a certain point in the phase space, that corresponds to some state of the managed system under the influence of the ensemble of SSM agents. During the operation of the SSM, its agents use knowledge that corresponds to the context of the situation. The agent's knowledge is a fragment of the field of knowledge on the target problem of SM. Knowledge of the problem area of the SM is a key element of the SM model. The convergent agents’ ensemble of SSM is characterized by a certain level of intelligence, which is represented as an entropic force that uses the free energy of the dissipative system to maintain its stability. An agent-oriented approach to the study of the stability of a dynamic stochastic system in the process of situa-tional management as a target project activity is proposed. Within the scope of the proposed approach, the stability model of agent SSM as a dynamic stochastic system is considered using the Lyapunov sta-bility criterion in the form of a system of ordinary differential equations. Support of modeling functions by agents of agent-oriented system allows to form adequate behavior in the process of situational man-agement in the conditions of changes in the environment. Developed models for integrating behavioral and coordination aspects of knowledge-based agents can be used in the development of situational man-agement systems and technologies.
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Feldblium, I. V., V. G. Akimkin, A. V. Alimov, M. V. Piterskiy, Yu A. Zakharova, Yu A. Mikhaylenko, N. I. Markovich, and A. A. Zakharov. "NEW APPROACHES TO ASSESSING AND FORECASTING MORBIDITY WITH ENTEROVIRUS (NON-POLIO) INFECTION IN THE RUSSIAN FEDERATION USING MATHEMATICAL MODELS." Health Risk Analysis, no. 3 (September 2021): 108–17. http://dx.doi.org/10.21668/health.risk/2021.3.10.
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At present it is impossible to develop epidemiologic surveillance and control over any infection regarding studies on dynamics of morbidity, seasonality and periodicity without using mathematical modeling techniques. Our research goal was to study regularities in manifestations of epidemic process for enterovirus (non-polio) infection (EVnI) in the Russian Federation over 14 years (2006–2019) using mathematical models (linear, logarithmic, power, and exponential approximation).An optimal mathematical model was selected using three statistical parameters, namely determination coefficient, Fischer’s exact test, and standard error. Periodicity of rises and falls in morbidity was calculated with Fourier one- dimensional spectral analysis. Intra-year dynamics of morbidity with EVnI was estimated basing on monthly spread of the disease cases on the RF territory. Classic seasonal decomposition, Census I technique, was applied to analyze time series of monthly morbidity. It was determined that EVnI epidemic process was unevenly spread over years in the RF in the examined period of time (2006–2019) and there were two opposite trends in it; the first one lasted from 2006 to 2010 when morbidity was declining and the second was from 2010 to 2019 when it was growing. Having analyzed manifestations of EVnI epidemi- ologic process in long-term dynamics given its uneven spread as per years, we established that it was advisable to use mathematical models approximated as per separate time periods. Average long-term morbidity with EVnI amounted to 8.09 0/0000 in the RF in 2010–2019 with growth rate being equal to 17.7 %. Maximum value was registered in 2017 (16.32 0/0000). An unfavorable prediction for further epidemic situation development was revealed for the examined pe- riod. The epidemic process was characterized with 4-year periodicity and summer-autumn seasonality with peaks usually occurring in August and September. Rates that characterized intensity of the trends in long-term morbidity dynamics and were calculated with mathematical models differed authentically from those obtained via conventional calculations of average values (χ=11.08; d.f.=1; p=0.0009).
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Feldblium, I. V., V. G. Akimkin, A. V. Alimov, M. V. Piterskiy, Yu A. Zakharova, Yu A. Mikhaylenko, N. I. Markovich, and A. A. Zakharov. "NEW APPROACHES TO ASSESSING AND FORECASTING MORBIDITY WITH ENTEROVIRUS (NON-POLIO) INFECTION IN THE RUSSIAN FEDERATION USING MATHEMATICAL MODELS." Health Risk Analysis, no. 3 (September 2021): 108–17. http://dx.doi.org/10.21668/health.risk/2021.3.10.eng.
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At present it is impossible to develop epidemiologic surveillance and control over any infection regarding studies on dynamics of morbidity, seasonality and periodicity without using mathematical modeling techniques. Our research goal was to study regularities in manifestations of epidemic process for enterovirus (non-polio) infection (EVnI) in the Russian Federation over 14 years (2006–2019) using mathematical models (linear, logarithmic, power, and exponential approximation).An optimal mathematical model was selected using three statistical parameters, namely determination coefficient, Fischer’s exact test, and standard error. Periodicity of rises and falls in morbidity was calculated with Fourier one- dimensional spectral analysis. Intra-year dynamics of morbidity with EVnI was estimated basing on monthly spread of the disease cases on the RF territory. Classic seasonal decomposition, Census I technique, was applied to analyze time series of monthly morbidity. It was determined that EVnI epidemic process was unevenly spread over years in the RF in the examined period of time (2006–2019) and there were two opposite trends in it; the first one lasted from 2006 to 2010 when morbidity was declining and the second was from 2010 to 2019 when it was growing. Having analyzed manifestations of EVnI epidemi- ologic process in long-term dynamics given its uneven spread as per years, we established that it was advisable to use mathematical models approximated as per separate time periods. Average long-term morbidity with EVnI amounted to 8.09 0/0000 in the RF in 2010–2019 with growth rate being equal to 17.7 %. Maximum value was registered in 2017 (16.32 0/0000). An unfavorable prediction for further epidemic situation development was revealed for the examined pe- riod. The epidemic process was characterized with 4-year periodicity and summer-autumn seasonality with peaks usually occurring in August and September. Rates that characterized intensity of the trends in long-term morbidity dynamics and were calculated with mathematical models differed authentically from those obtained via conventional calculations of average values (χ=11.08; d.f.=1; p=0.0009).
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Khusainov, Denis, Andrey Shatyrko, Alexey Bychkov, Bedrick Puza, and Veronika Novotna. "INVESTIGATION OF THE IMPACT OF DELAY IN ONE MATHEMATICAL MODEL OF WORLD DEVELOPMENT DYNAMICS." Journal of Automation and Information sciences 6 (November 1, 2021): 47–54. http://dx.doi.org/10.34229/1028-0979-2021-6-5.
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There is a large number of works devoted to the dynamics of world development. But very few of them have clear abstract mathematical models of the corresponding processes. This work is devoted to further deepening and mathematical abstraction of the study of world development process. The qualitative analysis of linear and modified nonlinear model in the form of systems of inhomogeneous differential equations is carried out. Their steady states are calculated, explicit analytical solutions are presented. For the first time, a model taking into account the time delay factor is proposed, which is written in the form of functional-differential equations with argument deviation. It is shown that with such an introduction to the model of a delayed argument, the system can be reduced to a system of linear inhomogeneous differential equations with constant coefficients without delay, and the stability of the steady state of the system equilibrium under study will be affected only by linear terms of equations without argument deviation. This fact well correlates with the socio-economic interpretation of this problem. In the future, the work will focus on studying the influence of not one but several factors of time lag, when the model is presented as a system of functional-differential equations with several different deviating arguments in equations responsible for the dynamics of a particular process dynamics of world development.
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Kotov, B. I., V. O. Hryshchenko, S. P. Stepanenko, Y. I. Pantsir, and I. D. Gerasimchuk. "Mathematical model of system dynamics for heat utilization from ventilation emissions with intermediate heat carrier as an object of automation." Mehanization and electrification of agricultural, no. 14(113) (2021): 88–97. http://dx.doi.org/10.37204/0131-2189-2021-14-9.
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Annotation Purpose. Formulation of a mathematical description of the non-stationary thermal regime of the heat utilization system of ventilation emissions on the basis of a heat exchanger with an intermediate heat carrier for industrial premises. Methods. The specificity of the object under study determines the analytical method of research, which is based on the analysis of the thermal balance of the elements of the studied system and the heat and energy connections between them. Results. A mathematical description of the dynamics of the thermal process in a recuperative heat recovery unit with an intermediate heat carrier is formulated taking into account the variable parameters of ventilation air, both exhaust and supply air and the presence of condensation on the surface of the heat exchanger. Given the possibility of automatic control of the operation of the disposal system by changing the flow of intermediate coolant (which makes the system of equations nonlinear), a linearized mathematical model of the dynamics of the studied system is proposed. Conclusions 1. The obtained mathematical models allow to determine the dynamic characteristics of the system of waste heat utilization in transient modes, as well as to evaluate the efficiency of the system itself and to optimize the parameters of heat exchangers. 2. The linearized model of the thermal utilizer allows to synthesize the system of automatic control of the operating mode and to investigate its parameters. Keywords: waste heat utilization, heat exchanger recuperator, intermediate heat carrier, dynamic mode, mathematical model, production room.
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Ibrir, Salim, and Ruxandra Botez. "Robust Stabilization of Uncertain Aircraft Active Systems." Journal of Vibration and Control 11, no. 2 (February 2005): 187–200. http://dx.doi.org/10.1177/1077546305041366.
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Often, dynamical aircraft systems cannot always be accurate because some approximation assumptions, imprecisions or uncertainties may have been introduced or imposed during the modeling process. Mathematical models of aircraft systems always contain uncertain elements, which model the designer’s lack of knowledge about some parameter values, disturbances and unmodeled dynamics. Using both Lyapunov’s direct method and the linear matrix inequality approach, we develop the controller design procedure, and give a definite feel for stability analysis and robust control for aircraft systems with significant uncertainty. An example of an uncertain thrust vectoring aircraft is studied to illustrate our control design strategy.
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Zhuchenko, Anatolii, Ruslan Osipa, Liudmyla Osipa, and Lesia Ladieva. "Algorithm for controlling the process of buffer wastewater neutralization." Proceedings of the NTUU “Igor Sikorsky KPI”. Series: Chemical engineering, ecology and resource saving, no. 3 (September 29, 2021): 27–35. http://dx.doi.org/10.20535/2617-9741.3.2021.241028.
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In Ukraine, the condition of surface water near industrial enterprises is extremely critical. The operation of enterprises leads to intensive water pollution with industrial and domestic wastewater. Therefore, improving the quality of treatment facilities through the introduction of automated control systems is an urgent problem.
For the operation of automated control systems for typical cleaning processes, a software package is required, which is developed on the basis of appropriate algorithmic software and mathematical models of processes. To obtain them, methods of mathematical and simulation modeling and block diagram method of algorithmization were used.
In order to assess the quality of the developed algorithm for controlling the process of buffer wastewater neutralization during operation, a comparison of control system operation based on this algorithm with the most successful foreign variants of neutralization control systems was made. Simulation for the average values of operating parameters Q = 75 m3 / h, CP = 75 g / l, and Ck = 2 g / l at minimum b = 0.02 g / l pH and maximum buffer value b = 0.47 g / l pH, and also with unidirectional extreme combination of parameters Q = 50 m3 / h, CP = 100 g / l, b = 0,02 g / l pH and Q = 100 m3 / h, CP= 50 g / l, for minimum b = 0.02 g / l pH and maximum buffering value b = 0.47 g / l pH shows that the best quality of transient processes is for the control system operating on the basis of the developed algorithm. For any combination of parameters, the transients for this control system provide better quality transients. Studies have shown that the control system based on the developed algorithm in comparison with the previously proposed systems provides better process control by reducing the time of transients and reducing the dynamic deviation of the output parameters, which improves the quality of wastewater treatment.
Given the non-stationary process and high requirements for the cleaning parameters, manual control of this process is beyond the power of even an experienced operator. The developed mathematical model describing the dynamics of the wastewater neutralization reactor with buffer properties and the process control algorithm made it possible to proceed to the development of the control system software, which is necessary for the automated control of this process.
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Madear, Gelu, and Camelia Madear. "Environmental modelling - a modern tool towards sustainability." MATEC Web of Conferences 342 (2021): 03013. http://dx.doi.org/10.1051/matecconf/202134203013.
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One way to solve environmental problems is through modelling. Humankind developed a series of models, from mental models, physical models to computer simulation models. Building a model assumes abstraction, simplifying the natural system by considering only the essential details and discarding irrelevant ones. Mapping the real worlds to the world of models is done by choosing an abstraction level and the corresponding modelling tool. The right abstraction level is paramount for any modelling project, depending on the real problem being analysed. In modern simulation modelling, there are three methods, each having a particular range of abstraction levels: system dynamics, discrete event (process-centric modelling) and agent-based models. Ecosystems and generally any environmental problems (real world) are complex dynamics that challenge our comprehension. Understanding the significant environmental challenges is vital to adopt adequate policies for a sustainable environment through modelling and simulation. Since our cognitive abilities are limited, we need a simulation of the environmental systems to see the dynamic patterns and how humans interact with the environment. Environmental modelling helps us understand complex systems by building mathematical models and running simulations using a high abstraction level. The system dynamics method of modelling and simulation is used to clarify the representation of the stocks and flows and the feedback process that control the flows and describe the dynamic behaviour (growth, decay, or oscillations) of complex systems over time. Modelling for prediction, understanding across time and spatial scales, and environmental systems disciplines is key for a sustainable future.
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Arif Mammadov, Arif Mammadov, Nizami Ismayilov Nizami Ismayilov, Mukhtar Huseynov Mukhtar Huseynov, and Faiq Guliyev Faiq Guliyev. "SOME ASPECTS OF MATHEMATICAL MODELING OF ELECTRIC STEEL MELTING PROCESS." PAHTEI-Procedings of Azerbaijan High Technical Educational Institutions 14, no. 03 (March 21, 2022): 04–12. http://dx.doi.org/10.36962/pahtei14032022-04.
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The article discusses some aspects of mathematical modeling of the process of melting electric steel on the basis of innovative metallurgical technologies. It was noted that the production of electric steel mainly consists of three stages - preparation of the charge, melting and casting of liquid steel. The most important of these stages is the mathematical modeling of the melting process, especially the physicochemical processes that take place during melting. All physicochemical processes controlled in order to obtain the required chemical composition of electric steel for modeling are combined into two main groups, such as metal refining and alloying. Possibilities of mathematical modeling of electric steel melting processes have been identified: to successfully solve different types of problems without conducting pro¬duc¬tion experiments; to ensure optimal modes of melting in specific production conditions. The problems to be solved by mathematical modeling have been identified: con¬struc¬tion of a model for specific conditions that allow to achieve the required value of any parameter of the solution; possibility to purchase electric steel in specific conditions; minimum cost of material, time, labor and energy and required chemical composition, temperature and mass melting of steel; automatic control of all parameters of the solution. To solve these problems, the characteristics of static, dynamic and mixed mathematical models have been identified. It has been shown that a deterministic mathematical model can be applied to a system of equations expressing the functional relationships between the parameters of the solution and the factors affecting them. The mixed mathematical model includes equations expressing functional correlations. This model is actually a deterministic static model. Depending on the problem, the expediency of using appropriate models in the melting of electric steel is justified. In general, the creation of a mathematical model of melting processes of electric steel includes: dividing the melting into elementary physicochemical processes within the limits of each period, ie decomposing the melting process; to give a quantitative description of each elementary process, ie to describe the process mathematically; write a mathematical model of each cycle of melting by combining the quantitative characteristics of the parameters and elementary processes controlled on the basis of the equations of material and heat balances; to obtain a mathematical model of the solution as a whole by combining mathematical models of different periods. As an example of the application of mathematical modeling in electroplating processes, the amount of pores formed during the steel melting process in the main braided electric arc furnace was calculated using scrap metal. Keywords: electroplating steel, mathematical modeling, static model, dynamic model, deterministic model, mixed model, functional relationships.
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Wong, Wee, Ewan Chee, Jiali Li, and Xiaonan Wang. "Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing." Mathematics 6, no. 11 (November 7, 2018): 242. http://dx.doi.org/10.3390/math6110242.
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The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to increase profitability, reduce waste and extend product ranges. Model predictive control (MPC) can be applied to enable this vision by providing superior regulation of critical quality attributes (CQAs). For MPC, obtaining a workable system model is of fundamental importance, especially if complex process dynamics and reaction kinetics are present. Whilst physics-based models are desirable, obtaining models that are effective and fit-for-purpose may not always be practical, and industries have often relied on data-driven approaches for system identification instead. In this work, we demonstrate the applicability of recurrent neural networks (RNNs) in MPC applications in continuous pharmaceutical manufacturing. RNNs were shown to be especially well-suited for modelling dynamical systems due to their mathematical structure, and their use in system identification has enabled satisfactory closed-loop performance for MPC of a complex reaction in a single continuous-stirred tank reactor (CSTR) for pharmaceutical manufacturing.
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Moldabekov, Meirbek, Suleimen Yelubayev, Kuanysh Alipbayev, Anna Sukhenko, Timur Bopeyev, and Darya Mikhailenko. "Stability Analysis of the Microsatellite Attitude Control System." Applied Mechanics and Materials 798 (October 2015): 297–302. http://dx.doi.org/10.4028/www.scientific.net/amm.798.297.
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The problem of development of the microsatellite attitude control system on the base of reaction wheels positioned along its principal central axes of inertia is considered in this article. As difference from the classical mathematical models describing the microsatellite motion, this article includes the mathematical model of reaction wheel which is controlled by the input voltage of the electric motor. PD-controller is used as the basis for the development of the control law for microsatellite attitude. The stability analysis of the microsatellite attitude control process was carried out with the help of Lyapunov function method. This analysis allowed to prove that obtained attitude control law provides the asymptotic stability of the microsatellite rotational motion. Further, the function of control voltage for the reaction wheel’s electric motor with account of its technical specifications was obtained based on the derived mathematical model of the reaction wheel’s dynamics. The results of performed simulation showed the effectiveness of developed control. Obtained results of the study provide a base for the use of presented approach to the development of attitude control system for microsatellites with various missions.
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Xuan, Shaoyong, Shenping Hu, Zhuang Li, Wei Li, and Boyin Li. "Dynamics Simulation for Process Risk Evolution on the Bunker Operation of an LNG-fueled Vessel with Catastrophe Mathematical Models." Journal of Marine Science and Engineering 7, no. 9 (August 31, 2019): 299. http://dx.doi.org/10.3390/jmse7090299.
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Liquefied nature gas (LNG) is a green energy. LNG-fueled vessels are extremely complex engineering systems. In view of the inherent hazardous properties of LNG fuel, LNG fueling is not only an important part, but it is also full of high risks in the operation of LNG-fueled vessels (LNGFVs). Therefore, it is necessary to study the risk factors, and the intrinsic relationship among them between the LNG and the vessel, and to simulate the system dynamics in the process of LNGFV operation. During the process of fueling of LNGFV, at every moment the vessel interacts with the energy and information of the surrounding environment. First, the impact of the three interactions of the fueling operation process, ship factors, and environmental factors were analyzed on the risk of fueling operation, and a complete node system was proposed as to the complex system dynamics mode. Second, by analyzing the boundary conditions of the system, the relationship of factors was established via the tools of system dynamics (SD). Based on the catastrophe theory (CA), the dynamics model for the fueling of LNG is set up to study the system’s risk mutation phenomenon. Third, combined with the simulation results of the case analysis, the risk evolution mode of the LNGFV during the fueling process was obtained, and constructive opinions were put forward for improving the safe fueling of the LNGFV. Application examples show that formal description of risk emergence and transition is a prerequisite for the quantitative analysis of the risk evolution mode. In order to prevent accidents, the coupling synchronization of risk emergence should be weakened, and meanwhile risk control should be implemented.
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Oriola, David, Hermes Gadêlha, and Jaume Casademunt. "Nonlinear amplitude dynamics in flagellar beating." Royal Society Open Science 4, no. 3 (March 2017): 160698. http://dx.doi.org/10.1098/rsos.160698.
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The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
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Rakhmanov, S. R. "Dynamics of exit section of automatic mill of pipe rolling line." Ferrous Metallurgy. Bulletin of Scientific , Technical and Economic Information 77, no. 2 (February 25, 2021): 175–86. http://dx.doi.org/10.32339/0135-5910-2021-2-175-186.
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Nonuniformity of pipe wall thickness is one of significant indices, determining quality of hot-rolled seamless pipes. One of the reasons of increased nonuniformity arising is dynamics of exit section mechanisms of pipe rolling line (PRL). Results of study of mandrel holding mechanism dynamics of PRL presented. Dynamic models of exit section, accounting parameters of technological process and inertia of a rolled hollow billet elaborated, which enabled to determine the character of dynamic processes at the exit section of PRL automatic mill. Differential equations of exit section elements motion at the exit section of PRL automatic mill were made up. The solution of the differential equations system was obtained in a numerical form by application of Runge‒Kutta method for correspondent dynamic models of exit section based on the example of calculations for ТПА-350 automatic mill. The pattern of dynamic processes arising at the exit section was specified at realization of the whole technological process of a hollow billet rolling at automatic mill, taking into consideration alternative action from the side of deformation center and mass of the rolled hollow billet. It was shown, that the specified solution of the task for three advanced dynamic models of mechanical system considerably differs from those of the known mathematical models. It was established, that the dynamics of the mandrel holding mechanism of ТПА-350 automatic mill equivalently form the mechanism of finished pipes geometry forming. Analysis of dynamic models of the mill exit section enabled to select the necessary technological and dynamic parameters of the mechanical system, to determine stable modes of hollow billets rolling at the ТПА-350 automatic mill. Results of the study of dynamics of exit section ТПА-350 automatic mill presented. A scheme of modernization of the exit section ТПА-350 automatic mill proposed, which enables to realize rational modes of operation accounting level of mechanical system dynamics and to control quality (geometric parameters) of the rolled pipes.
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Rezchikov, A. F., V. A. Kushnikov, V. A. Ivaschenko, D. S. Fominykh, A. S. Bogomolov, and L. Yu Filimonyuk. "Controlling the Welding Process in Robotic Te chnological Complexes by the Criterion of Product Quality." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 1 (January 15, 2019): 29–33. http://dx.doi.org/10.17587/mau.20.29-33.
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The solution of the problem of controlling the arc welding process by robotic technological complexes by the quality criterion of the produced products is proposed in this paper. The statement of the problem is given, the criterion of the quality in the form of the goal function is described. The mathematical models based on the principles of J. Forrester’s system dynamics is developed. The main indicators that affect the quality of the welding process in RTC and their relationships are identified as system levels. The external factors that depend on the indicators and affect them are also defined. The functional dependencies of the indicators were obtained as a result of approximation of statistical data based on long-term observations of the process. A system of the differential equations that describe the cause-effect relationships between the indicators and the factors is developed. Based on the mathematical model, an algorithm for the search for control actions, the implementation of which minimizes the goal function was developed. The developed models and the control algorithms might significantly improve the quality of the arc welding process. The proposed software is testing as a part of the RTC Kawasaki technical control system at OJSC "Transmash" (Engels, Russia).
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Kabanov, S. A., B. A. Zimin, and F. V. Mitin. "Development and Research of Mathematical Models of Deployment of Mobole Parts of Transformable Space Construction. Part I." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 1 (January 14, 2020): 51–64. http://dx.doi.org/10.17587/mau.21.51-64.
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The process of deployment elements of constructions and adjustment of the radio-reflecting network of large-sized transformable space-based reflector with the use of a cable-stayed form maintenance system is considered. The deployment process can be broken down into separate phases. At each stage, the movement is due to the impact on the design of the actuator — the element of the control system. Energy for the deployment of the reflector elements is produced by drives, in particular an electric machine. The use of this type of actuator allows you to control the process of disclosure. Due to the fact that currently achieved a huge process in computer technology that allows you to perform three-dimensional computing operations in a short time, it is particularly important to use optimal control algorithms. When deployment the reflector for two types of motion — rotational and translational — mathematical models based on Lagrange equations of the II-kind are obtained. These mathematical models take into account such parameters as dissipation, the presence of longitudinal and transverse deformation. The models provide for the presence of a stop and a lock, as an Executive element in the deployment selected brushless DC motor. All the observations made allow us to formulate a smooth statement disclose items on the stop with minimum oscillation of the structure. The developed models allow to analyze the n-th number of natural oscillation frequencies. Modeling with different parameters of the model is carried out. The parameters of the transition process of the spoke at the opening of the first link with the other links embedded in it and at the fully covered spoke are analyzed. It is shown that depending on the mass-dimensional parameters there is a significant change in the dynamics. For the spoke extension stage, the weight and size characteristics have little effect on the opening dynamics. The smaller the Young’s modulus and density of the material, the greater the damped longitudinal oscillations.. The simulation of this stage with a spoke made of different materials is carried out. Various methods are proposed to reduce the opening time at all stages and minimize transverse and longitudinal oscillations. The possibility of application of the developed mathematical models for a wide range of tasks is shown.
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Botros, K. K., P. J. Campbell, and D. B. Mah. "Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine." Journal of Engineering for Gas Turbines and Power 113, no. 2 (April 1, 1991): 300–311. http://dx.doi.org/10.1115/1.2906563.
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Dynamic simulation of the operation of a compressor station requires mathematical modeling of the dynamic behavior of the compressor unit and various piping elements. Such models consist of large systems of nonlinear partial differential equations describing the pipe flow together with nonlinear algebraic equations describing the quasi-steady flow through various valves, constrictions, and compressors. In addition, the models also include mathematical descriptions of the control system, which consists of mixed algebraic and ordinary differential (mad) equations with some inequalities representing controllers’ limits. In this paper a numerical technique for the solution of the gas dynamics equations is described, based on the transfer matrix formulation relating the state vector time difference at one side of an element to that on the other side. This approach facilitates incorporation of all element transfer matrices into an overall transfer matrix according to the system geometric connectivity. The paper also presents simulation results and comparison with actual field measurements of three case histories: (1) simulation of a compressor surge protection control process; (2) unit startup; and (3) slow transient of a compressor station responding to changes in the discharge pressure set point. Good agreement between simulation results and field measurements is demonstrated.
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Baratchart, Etienne, Chen Hao Lo, Conor C. Lynch, and David Basanta. "Integrated computational and in vivo models reveal Key Insights into macrophage behavior during bone healing." PLOS Computational Biology 18, no. 5 (May 13, 2022): e1009839. http://dx.doi.org/10.1371/journal.pcbi.1009839.
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Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes.
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Ayesa, E., G. Oyarbide, L. Larrea, and J. L. Garciía-Heras. "Observability of reduced order models - application to a model for control of alpha process." Water Science and Technology 31, no. 2 (January 1, 1995): 161–70. http://dx.doi.org/10.2166/wst.1995.0094.
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This paper describes the theoretical basis and some applications of a identifiability/observability test for state-space models based on the recursive calculation of the numerical condition of the observability matrix. This test evaluates the possibility of estimating the unknown states and parameters of a mathematical model under defined experimental conditions and available information. The numerical value of the proposed “observability parameter” is also an index of uncertainty propagation through the model. As examples of the utility of the proposed test, the paper presents the analysis of a reduced-order model for two wastewater treatment plant configurations (D-N and Alpha process), evaluating the on-line information that is theoretically indispensable in distinguishing each one of the unknown states and parameters under steady or dynamic conditions.
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Kulik, Anatoliy Stepanovich, and Vitalii Geogiiovich Dzhulgakov. "RATIONAL CONTROL OF OBJECTS WITH UNCERTAIN DYNAMICS." Aerospace technic and technology, no. 3 (July 15, 2019): 4–14. http://dx.doi.org/10.32620/aktt.2019.3.01.
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The reasons causing uncertainty in the dynamics of objects are considered on the example of aerospace engineering. Objects of automatic control, consisting of control objects, servo drives, and sensors, are subjects to the influence of indefinite external and internal disturbing influences, which destabilize their performance. Classical methods of automatic control of such objects do not allow obtaining the desired quality indicators. For the rational control of such objects with uncertain dynamics, a new approach has been proposed, which is based on a deep diagnosis of the causes of destabilization and flexible restoration of working capacity. The main provisions of the method of rational control are described. A new class of mathematical models called diagnostic is presented. In-depth diagnostic procedures are formed using formalized and weakly formalized models of the processes of regular and abnormal operation of the control system. For the formation of a priori and a posteriori knowledge of the causes of malfunctioning, structures of developing dichotomous trees are used, representing a kind of product knowledge bases with a design in nodes “if ... then ...”, with logical rules for obtaining a diagnosis of the causes of destabilizing effects. A method for solving diagnostic problems for objects with uncertain dynamics is described. To restore the performance of objects with uncertain dynamics, the use of redundant means has been proposed: signal and parametric adjustment, reconfiguration of algorithms and hardware. The process of parrying destabilization, which was diagnosed, is formed using the second method A. M. Lyapunov. This method ensures the stability of the system and the specified quality control. Rational adaptation to destabilizing effects is based on the use of intelligent procedures for in-depth diagnosis of the causes of a malfunction of the control system and a flexible restoration of working capacity in real time. Such procedures allow for productive training in order to preserve the efficiency of the control system throughout the entire life cycle. The results of applying the method of rational control to a number of model samples of aircraft are given.
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Makarov, V. A., and F. A. Korolev. "The leak detection process modeling." Journal of Physics: Conference Series 2373, no. 2 (December 1, 2022): 022033. http://dx.doi.org/10.1088/1742-6596/2373/2/022033.
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Abstract The paper describes formalized description concept of the expiration gas process through product manufacturing defects in the control of tightness: Model Internal description based on the use of parameters of circuit theory and mathematical model of the external description made by means of functional expansions obtained on the basis of mathematical models experimental research of the implemented software package external description. A dynamic model of the outflow of gases through product defects is presented by the Wiener-Voltaire equations. The proposed method for studying the outflow of gases through product defects consists a simulation object whose input is subjected to an external action with constant other variable parameters and registration of the output signal. The experimental data are compared with the results of theoretical calculations based on the molecular model of the outflow process.
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Tergeussizova, Aliya. "MATHEMATICAL MODELING OF THE PROCESS OF DRAWING AN OPTICAL FIBER USING THE LANGEVIN EQUATION." Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska 9, no. 2 (June 21, 2019): 64–67. http://dx.doi.org/10.5604/01.3001.0013.2551.
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In order to design stochastic pulse frequency systems for automatic control of objects with delay, this article shows how we obtained their models in the form of stochastic differential equations. The method of dynamic compensation of objects with delay is considered. A stochastic differential system in the Langevin form is obtained.
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Jiang, Shu Juan, Fei Fei Yu, and Mao Zheng Fu. "Dynamical Identification Model of Laser Cladding Width in Metal Parts Laser Shaping Process." Advanced Materials Research 820 (September 2013): 216–19. http://dx.doi.org/10.4028/www.scientific.net/amr.820.216.
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The dynamical model of laser cladding width is identified by the method of step response experiments. Mathematical models between the cladding width and the laser power, the scanning speed, or the powder flowrate are established respectively according to corresponding experimental results. Simulating experiment results verify the validity of these models. The dynamical identification lays foundation for the closed loop control in laser shaping process so as to improve the quality of the laser formed parts.
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Zhang, N., D. K. Liu, J. M. Jeyakumaran, and L. Villanueva. "Modelling of dynamic characteristics of an automatic transmission during shift changes." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 216, no. 4 (June 1, 2002): 331–41. http://dx.doi.org/10.1177/095965180221600403.
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This paper describes modelling of the transient dynamics of an automatic transmission during gear changes. A brief introduction to the automatic transmission system and the dynamic characteristics of the transmission components during the gear changes are presented. Then, detailed mathematical models of a four-speed automatic transmission manufactured by BTR Automotive, Australia, are developed. A mode description method is used to describe the transient shifting process and a modular structure of the transmission system, which consists of a torque converter module, geartrain module, hydraulic system module and modules of clutches and bands, is presented. As an application, the developed simulation system is applied to investigate the transient performance of the automatic transmission during the 1–2 shift process. The output torque profiles predicted by the model simulation correlate very well with the experimental data measured from vehicle tests.
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Keller, André A. "Reaction-diffusion systems in natural sciences and new technology transfer." Journal of the Mechanical Behaviour of Materials 21, no. 3-4 (December 1, 2012): 123–46. http://dx.doi.org/10.1515/jmbm-2012-0024.
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AbstractDiffusion mechanisms in natural sciences and innovation management involve partial differential equations (PDEs). This is due to their spatio-temporal dimensions. Functional semi-discretized PDEs (with lattice spatial structures or time delays) may be even more adapted to real world problems. In the modeling process, PDEs can also formalize behaviors, such as the logistic growth of populations with migration, and the adopters’ dynamics of new products in innovation models. In biology, these events are related to variations in the environment, population densities and overcrowding, migration and spreading of humans, animals, plants and other cells and organisms. In chemical reactions, molecules of different species interact locally and diffuse. In the management of new technologies, the diffusion processes of innovations in the marketplace (e.g., the mobile phone) are a major subject. These innovation diffusion models refer mainly to epidemic models. This contribution introduces that modeling process by using PDEs and reviews the essential features of the dynamics and control in biological, chemical and new technology transfer. This paper is essentially user-oriented with basic nonlinear evolution equations, delay PDEs, several analytical and numerical methods for solving, different solutions, and with the use of mathematical packages, notebooks and codes. The computations are carried out by using the software Wolfram Mathematica®7, and C++ codes.
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Jiang, Shu Juan, and Ai Zhong He. "Dynamical Identification Model of Laser Cladding Height in Metal Parts Laser Shaping Process." Advanced Materials Research 591-593 (November 2012): 1050–53. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1050.
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The metal parts laser shaping process dynamical identification is fulfilled by the method of experiment. Through step response experiments, mathematical models between the cladding height and the laser power, the scanning speed, or the powder flowrate are established respectively. Simulating experiments validate these identification models. From the identification models, the metal parts laser shaping process is understood, which is the basement for designing closed loop control in forming process and is significant to improve the quality of formed parts.
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Gabdrakhmanova, Nailia, and Maria Pilgun. "Intelligent Control Systems in Urban Planning Conflicts: Social Media Users’ Perception." Applied Sciences 11, no. 14 (July 17, 2021): 6579. http://dx.doi.org/10.3390/app11146579.
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The relevance of this study is determined by the need to develop technologies for effective urban systems management and resolution of urban planning conflicts. The paper presents an algorithm for analyzing urban planning conflicts. The material for the study was data from social networks, microblogging, blogs, instant messaging, forums, reviews, video hosting services, thematic portals, online media, print media and TV related to the construction of the North-Eastern Chord (NEC) in Moscow (RF). To analyze the content of social media, a multimodal approach was used. The paper presents the results of research on the development of methods and approaches for constructing mathematical and neural network models for analyzing the social media users’ perceptions based on their digital footprints. Artificial neural networks, differential equations, and mathematical statistics were involved in building the models. Differential equations of dynamic systems were based on observations enabled by machine learning. Mathematical models were developed to quickly detect, prevent, and address conflicts in urban planning in order to manage urban systems efficiently. In combination with mathematical and neural network model the developed approaches, made it possible to draw a conclusion about the tense situation around the construction of the NEC, identify complaints of residents to constructors and city authorities, and propose recommendations to resolve and prevent conflicts. Research data could be of use in solving similar problems in sociology, ecology, and economics.
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Roeva, Olympia, and Elena Chorukova. "Metaheuristic Algorithms to Optimal Parameters Estimation of a Model of Two-Stage Anaerobic Digestion of Corn Steep Liquor." Applied Sciences 13, no. 1 (December 23, 2022): 199. http://dx.doi.org/10.3390/app13010199.
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Anaerobic Digestion (AD) of wastewater for hydrogen production is a promising technology resulting in the generation of value-added products and the reduction of the organic load of wastewater. The Two-Stage Anaerobic Digestion (TSAD) has several advantages over the conventional single-stage process due to the ability to control the acidification phase in the first bioreactor, preventing the overloading and/or the inhibition of the methanogenic population in the second bioreactor. To carry out any process research and process optimization, adequate mathematical models are required. To the best of our knowledge, no mathematical models of TSAD have been published in the literature so far. Therefore, the authors’ motivation is to present a high-quality model of the TSAD corn steeping process for the sequential production of H2 and CH4 considered in this paper. Four metaheuristics, namely Genetic Algorithm (GA), Firefly Algorithm (FA), Cuckoo Search Algorithm (CS), and Coyote Optimization Algorithm (COA), have been adapted and implemented for the first time for parameter identification of a new nonlinear mathematical model of TSAD of corn steep liquor proposed here. The superiority of some of the algorithms has been confirmed by a comparison of the observed numerical results, graphical results, and statistical analysis. The simulation results show that the four metaheuristics have achieved similar results in modelling the process dynamics in the first bioreactor. In the case of modelling the second bioreactor, a better description of the process dynamics trend has been obtained by FA, although GA has acquired the lowest value of the objective function.
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Fominykh, Dmitry, Vadim Kushnikov, and Alexander Rezchikov. "Prevention unstable conditions in the welding process via robotic technological complexes." MATEC Web of Conferences 224 (2018): 01045. http://dx.doi.org/10.1051/matecconf/201822401045.
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The article presents the statement of the problem, models and algorithms for controlling the welding process via robotic technological complexes in conditions of the risk of unstable states. The system dynamics model was used to describe the technological process. As system levels the basic indicators influencing quality of the made production chosen on the basis of experience of operation of the robotic technological complexes are taken. Functional dependences between indicators and their dependences on external factors are determined by approximation of statistical data. The procedure of identification of unstable states for the mathematical model on the example of the Rossler’s attractor is developed. An algorithm for preventing the system from falling into unstable states in the process control is proposed
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Baraniuk, Roman, and Welf-Guntram Drossel. "Simplification of the Model of Piezoelectric Actuator Control Based on Preliminary Measurements." Actuators 9, no. 3 (September 18, 2020): 90. http://dx.doi.org/10.3390/act9030090.
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This article describes a mathematical model simplification, designed to automate the iterative process of non-circular drilling with a precise shape. This model has been optimized for systems that already have experimental data for processing and analysis. Additionally, using optimization steps, the model can be used for systems with insufficient experimental data with a self-learning opportunity. The high-end model can be used for drilling systems represented as a “black box” without knowing of any parameters of the system. The simplification and assumptions algorithm is based on controlling the input signal for non-circular drilling in the cylinders of internal combustion engines using a drilling machine controlled by 8 piezoelectric actuators. The total dynamics of this system is unknown and consists of the dynamics of electrical converters, piezo-kinematics, and mechanics. Simplification is carried out starting from the methods of diacoptics for a complex system with different process-flow rates, and ending with one or the sum of linear models valid for a given system of assumptions.
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Kulik, Anatoliy, Konstantin Dergachov, and Sergey Pasichnik. "THE MODELS OF A HOLDING-BALANCE TWO-WHEELED EXPERIMENTAL SAMPLE PLANAR MOTION." International Scientific Technical Journal "Problems of Control and Informatics 67, no. 4 (September 1, 2022): 18–34. http://dx.doi.org/10.34229/2786-6505-2022-4-2.
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The subject is the process of holding-balance two-wheeled experimental sample (HTES) planar motion models formation. The goal is to develop an approach to the formation of flat motion models of the HTES as an automatic controlled object. The problems: to form a physical model of a holding-balance two-wheeled experimental sample; to develop a nonlinear mathematical description of the forward and angular HTES motion on the plane using the Lagrangian formalism; to make a description of the controlled object in the frequency domain using Laplace transforms; to obtain a linearized mathematical description of the automatic controlled object in the state space; to form graphic models of the HTES as a control object using structural diagrams in the time and frequency domains; to form the conditions for using mathematical descriptions as mathematical models of the automatic control object. The methods applied are: Lagrange method, analytical linearization, state space, Laplace transformation. The following results were obtained: dynamic models of mechanical and electromechanical processes of forward and angular HTES movements on a plane were formed. Using the Lagrangian approach, a nonlinear mathematical model of the holding-balance two-wheeled experimental sample movement was developed. Using the method of analytical linearization, a mathematical model of linear approximation in the form of differential equations with constant coefficients was obtained. The mathematical models of local movements in the frequency domain in the form of transfer functions have been formed. A structural diagram of the transformation processes in holding-balance two-wheeled experimental sample has been created. The possibility of constructing mathematical models in the space of states in both vector-matrix form and structural diagrams form for solving specific problems of analysis and synthesis is shown. Conclusions. The scientific novelty consists in the formation of an approach to obtaining models of translational and angular movements of holding-balance two-wheeled experimental sample on a plane, which differs from the known ones in the completeness of accounting for acting forces and moments.
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Musin, Artur R. "Economic-mathematical model for predicting financial market dynamics." Statistics and Economics 15, no. 4 (September 4, 2018): 61–69. http://dx.doi.org/10.21686/2500-3925-2018-4-61-69.
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Study purpose.Existing approaches to forecasting dynamics of financial markets, as a rule, reduce to econometric calculations or technical analysis techniques, which in turn is a consequence of preferences among specialists, engaged in theoretical research and professional market participants, respectively. The main study purpose is developing a predictive economic-mathematical model that allows combining both approaches. In other words, this model should be estimated using traditional methods of econometrics and, at the same time, take into account the impact on the pricing process of the effect of clustering participants on behavioral patterns, as the basis of technical analysis. In addition, it is necessary that the created economic-mathematical model should take into account the phenomenon of existing historical trading levels and control the influence they exert on price dynamics, when it falls into local areas of these levels. Such analysis of price behavior patterns in certain areas of historical repeating levels is a popular approach among professional market participants. Besides, an important criterion of developing model’s potential applicability by a wide range of the interested specialists is its general functional form’s simplicity and, in particular, its components.Materials and methods. In the study, the market of the pound sterling exchange rate against the US dollar (GBP/USD) for the whole period of 2017 was chosen as the considered financial series, in order to forecast it. The presented economic-mathematical model was estimated by classical Kalman filter with an embedded neural network. The choice of these assessment tools can be explained by their wide capabilities in dealing with non-stationary, noisy financial market time series. In addition, applying Kalman filter is a popular technique for estimation local-level models, which principle was implemented in the newly model, proposed in article.Results. Using chosen approach of simultaneous applying Kalman filter and artificial neural network, there were obtained statistically significant estimations of all model’s coefficients. The subsequent model application on GBP/USD series from the test dataset allowed demonstrating its high predictive ability comparing with added random walk model, in particular judging by percentage of correct forecast directions. All received results have confirmed that constructed model allows effectively taking into account structural features of considered market and building good forecasts of future price dynamics.Conclusion. The study was focused on developing and improving apparatus of forecasting financial market prices dynamics. In turn, economic-mathematical model presented in that paper can be used both by specialists, carrying out theoretical studies of pricing process in financial markets, and by professional market participants, forecasting the direction of future price movements. High percentage of correct forecast directions makes it possible to use proposed model independently or as a confirmatory tool.
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Bulavatsky, Volodymyr. "CLOSED FORM SOLUTIONS OF SOME BOUNDARY VALUE PROBLEMS OF FRACTIONAL-DIFFERENTIAL CONSOLIDATION DYNAMICS OF GEOPOROUS MEDIA." International Scientific Technical Journal "Problems of Control and Informatics 67, no. 3 (June 1, 2022): 77–86. http://dx.doi.org/10.34229/2786-6505-2022-3-6.
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The modern geotechnologies that aimed to operate in complex mining and geological conditions requires further development and refinement of existingmathematical models and methods for modeling the dynamics of geomigrationprocesses. At the same time, significant progress in the field of mathematicalmodeling of geomigration processes under difficult conditions of their course associated with the use of the formalism of integro-differentiation of the fractionalorder. Usually, the mathematical modeling of the dynamics of geomigration processes performed under conditions of geoporous media saturation with pure water, but currently, due to the growing man-made impact on the nature, researchin modeling of the dynamics of these processes when the geoporous media saturated by saline solutions is particularly actual. This is largely due to a number ofecological problems, including the protection of soils and groundwater fromcontamination by toxic contents of surface storage of industrial and domestic effluents. In this paper, exact solutions of some one-dimensional boundary valueproblems of fractional-differential consolidation dynamics of saline solutions ofclay geoporous media saturated with salt solutions are obtained under conditionsof simultaneous consideration of both space and time non-locality of the geomigration process. Particularly a fractional-differential mathematical model of thedynamics of non-local in time and space of the filtration-consolidation process ispresented, which contains the derivatives of the Caputo time variable and theRiemann–Liouville geometric variable. Within the framework of this model, theformulation is given and the exact solution of the direct consolidation dynamicsproblem of a geoporous finite thickness massif saturated with saline solution isobtained. The problem of consolidation dynamics of a finite thickness massif inthe inverse formulation with respect to the definition of unknown source functions that depend only on the geometric variable under the corresponding additional (final) conditions is also considered. The conditions for the existence ofregular solutions of the considered problems are given.