Complex Mathematical Models Research Articles

Матрица финансовых потоков — инструмент реализации экономической политики страны

The article discusses a promising and well-proven tool for analyzing economic relations in socio-economic systems, which is actively used all over the world — the matrix of financial flows. The paper identifies the main areas of its application and briefly describes the history of its development in the world and specifically for Russia. The author also features the process of constructing a matrix for 12 economic regions of our country by types of economic activity. In the course of filling with statistical data the problem of assessing the volume of interregional trade was identified, which made it necessary to undertake an additional research, the results of which are presented in the article. In conclusion an example of practical use of the constructed matrix as an independent tool, as well as part of a more complex economic and mathematical model, is demonstrated.

Design of an FPGA-Based Fuzzy Feedback Controller for Closed-Loop FES in Knee Joint Model.

Functional electrical stimulation (FES) device has been widely used by spinal cord injury (SCI) patients in their rehab exercises to restore motor function to their paralysed muscles. The major challenge of muscle contraction induced by FES is early muscle fatigue due to the open-loop stimulation strategy. To reduce the early muscle fatigue phenomenon, a closed-loop FES system is proposed to track the angle of the limb’s movement and provide an accurate amount of charge according to the desired reference angle. Among the existing feedback controllers, fuzzy logic controller (FLC) has been found to exhibit good control performance in handling complex non-linear systems without developing any complex mathematical model. Recently, there has been considerable interest in the implementation of FLC in hardware embedded systems. Therefore, in this paper, a digital fuzzy feedback controller (FFC) embedded in a field-programmable gate array (FPGA) board was proposed. The digital FFC mainly consists of an analog-to-digital converter (ADC) Data Acquisition and FLC sub-modules. The FFC was designed to monitor and control the progress of knee extension movement by regulating the stimulus pulse width duration to meet the target angle. The knee is expected to extend to a maximum reference angle setting (70°, 40° or 30°) from its normal position of 0° once the stimulus charge is applied to the muscle by the FES device. Initially, the FLC was modelled using MATLAB Simulink. Then, the FLC was hardcoded into digital logic using hardware description language (HDL) Verilog codes. Thereafter, the performance of the digital FLC was tested with a knee extension model using the HDL co-simulation technique in MATLAB Simulink. Finally, for real-time verification, the designed digital FFC was downloaded to the Intel FPGA (DE2-115) board. The digital FFC utilized only 4% of the total FPGA (Cyclone IV E) logic elements (LEs) and required 238 µs to regulate stimulus pulse width data, including 3 µs for the FLC computation. The high processing speed of the digital FFC enables the stimulus pulse width duration to be updated every stimulation cycle. Furthermore, the implemented digital FFC has demonstrated good control performance in accurately controlling the stimulus pulse width duration to reach the desired reference angle with very small overshoot (1.4°) and steady-state error (0.4°). These promising results are very useful for a real-world closed-loop FES application.

A neuron fuzzy identification system based on a complex nonlinear mathematical model

A neuron fuzzy identification system based on a complex nonlinear mathematical model

Serial Manipulator Control Optimization Using Ant Colony Algorithm

Serial manipulator is one of robot type that commonly used on industry. The high Degree of Freedom (DoF) of serial manipulator lead to more flexibility on manipulation but at the same time it also lead to more complex mathematical model of serial manipulator. Because of this complexity, we cannot use the common Proportional-Integral-Derivative (PID) tuning method such as Ziegler-Nichols and Cohen-Coon while the parameter on controller is need to be optimal in order to reduce the error during position control and avoid instability which may cause hazard to the operator. Ant colony algorithm proposed to optimize the controller of serial manipulator and result of optimization evaluated through experiment.

Examining the effectiveness of fundamental analysis in a long-term stock portfolio

Over the past decade, a number of modern and sophisticated methods have been developed to optimize the composition of equity portfolios. Most of these methods are based on complex mathematical or financial modelling. Less emphasis has been placed on companies’ internal data, while in recent years external data have become increasingly important. However, for long-term investments, the dominance of external data is not necessarily an efficient way to construct an appropriate portfolio. In this paper, we highlight the phenomenon that complex mathematical models, the based on simpler fundamental indicators can also be an efficient investment tool for in making investment decisions. Our results show that our hypothesis has been confirmed that some basic-based indicators can achieve alpha returns. Our analysis is based on financial reporting data in the form of various financial indicators. We used the S&P500 index as benchmark. A comparative analysis of the stock portfolio created illustrates that basic analysis can be more effective than a chosen market-based stock index. By the end of the period under review, the portfolio based on the selected five core financial indicators had a market capitalization 1.68% higher than the benchmark. The alpha return achieved also demonstrates that even simpler models can be efficient and effective in creating an equity portfolio.

Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number R_{0} > 1; a disease-free equilibrium E_{0} and a disease endemic equilibrium E_{1}. The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number R_{0} <1, we show that the endemic equilibrium state is locally asymptotically stable if R_{0} > 1. We also prove the existence and uniqueness of the solution for the Atangana–Baleanu SIR model by using a fixed-point method. Since the Atangana–Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.

In the Lab: Research and Development in the Field of (Renewable) Gas Processing Technology at DBI Group

DBI Group’s field of activity covers the complete process development of chemical processes, starting with the process balancing and testing of catalysts including the determination of catalyst-specific reaction kinetics, up to lifetime investigations, ageing tests and other reaction engineering investigations. With the data obtained, complex mathematical models can be generated which can be used for the design of reactors or the optimisation of operating regimes. In addition, the company also applies its know-how in the field of mathematical models in application-oriented simulations of thermal processing plants, heat exchangers and gas treatment plants. On the basis of these models, it designs demonstration plants which provide important design fundamentals and technical-scientific correlations for large-scale applications.

Sobolev trained neural network surrogate models for optimization

Neural network surrogate models are often used to replace complex mathematical models in black-box and grey-box optimization. This strategy essentially uses samples generated from a complex model to fit a data-driven, reduced-order model more amenable for optimization. Neural network models can be trained in Sobolev spaces, i.e., models are trained to match the complex function not only in terms of output values, but also the values of their derivatives to arbitrary degree. This paper examines the direct impacts of Sobolev training on neural network surrogate models embedded in optimization problems, and proposes a systematic strategy for scaling Sobolev-space targets during NN training. In particular, it is shown that Sobolev training results in surrogate models with more accurate derivatives (in addition to more accurately predicting outputs), with direct benefits in gradient-based optimization. Three case studies demonstrate the approach: black-box optimization of the Himmelblau function, and grey-box optimizations of a two-phase flash separator and two flashes in series. The results show that the advantages of Sobolev training are especially significant in cases of low data volume and/or optimal points near the boundary of the training dataset—areas where NN models traditionally struggle.

RESEARCH OF APPROACHES TO CONSTRUCTING PREDICTIVE MODELS OF THE SPREAD OF VIRAL DISEASES

The article is devoted to the analysis of the available mathematical models in epidemiology and the possibility of their modification. We note that the situation with the COVID-19 virus pandemic is characterized by several features not comprehensively studied in the existing models. For a rational response to existing challenges, it is necessary to have a predictive and analytical apparatus in the complex (national and regional scale) mathematical models with a planning horizon of 2 years (the expected period of mass production of vaccines). The article discusses the existing approaches to predicting the spread of the COVID-19 virus in Russia based on mathematical models of epidemics. The possibilities and limitations of the proposed approaches are considered. In the conditions of the Russian Federation, transport connectivity at the interregional and intraregional levels plays an important role, and for megalopolises - transport flows within large agglomerations and the age structure of the population. In contrast to previous pandemics and epidemics, public policy plays a significant role. The approach, which consist in building multi-agent models that combine the advantages of compartment models and models based on the Monte Carlo method (individually oriented) is proposed by the authors. It is planned to use compartment models to assess the dynamics of the process and individually-oriented models - at the level of individual territories and districts.

МОДЕЛЮВАННЯ ПРОЦЕСІВ ЕНЕРГОПЕРЕТВОРЕННЯ В СИСТЕМІ РЕКУПЕРАЦІЇ ЕНЕРГІЇ КОЛИВАНЬ ТРАНСПОРТНИХ ЗАСОБІВ

The article presents a complex mathematical model of the energy recovery system for mechanical vibrations of vehicles moving in difficult road conditions. Such a system is an auxiliary power supply system that enhances the functionality of modern vehicles. The mathematical model takes into account the entire set of processes for converting the energy of mechanical vibrations in the following sequence: mechanical energy of the reciprocating oscillatory motion of the vehicle chassis - mechanical energy of the rotational motion of the electric generator shaft - electrical energy of the alternating current of the generator - direct current electrical energy of the battery. The modes of operation of the system are investigated, which provide efficient processes of charging the battery. For a specific example, data on the charging time of a truck battery is given. References 9, figures 7.

A method to assess the robustness of complex mathematical models used for quantitative interpretation of experimental data by nonlinear regression analysis: application to high-affinity binding models.

Nonlinear regression is widely used to fit experimental data to a specific mathematical model to extract numerical values for parameters representing the studied process. However, assessing the degree of precision that can be expected from such an analysis for a given parameter can be quite challenging for complex mathematical models. To address this issue, we propose here a method based on the analysis of a large number of data sets generated in such a way to mimic specific experimental conditions. Applying this methodology to high-affinity binding models, we report here a quantitative analysis of the robustness of such models, and how the precision on the fitting parameters can be expected to vary based on, e.g., the initial experimental conditions, the number or distribution of experimental points, or the experimental variability. We also show that these models, although widely used, are intrinsically limited by the fact that the two main fitting parameters, one representing the concentration of the studied species and the other its affinity, are inversely correlated, but demonstrate that this limitation can be overcome by global analysis of multiple data series generated at different concentrations of the titrated species.

ANALYTICAL MODEL OF PACKET TRANSMISSION OF SPEECH AND DATA IN HF RADIO CHANNELS IN A COMPLEX SIGNAL-INTERFERENCE ENVIRONMENT

The author has carried out an analytical simulation of the process of signal formation and processing in the HF channel during packet transmission of speech and data in a complex signal-interference environment. The totality of the result obtained can be the basis for the development of complex mathematical models of HF channels.

Optimum power transfer in RF front end systems using adaptive impedance matching technique

Matching the antenna’s impedance to the RF-front-end of a wireless communications system is challenging as the impedance varies with its surround environment. Autonomously matching the antenna to the RF-front-end is therefore essential to optimize power transfer and thereby maintain the antenna’s radiation efficiency. This paper presents a theoretical technique for automatically tuning an LC impedance matching network that compensates antenna mismatch presented to the RF-front-end. The proposed technique converges to a matching point without the need of complex mathematical modelling of the system comprising of non-linear control elements. Digital circuitry is used to implement the required matching circuit. Reliable convergence is achieved within the tuning range of the LC-network using control-loops that can independently control the LC impedance. An algorithm based on the proposed technique was used to verify its effectiveness with various antenna loads. Mismatch error of the technique is less than 0.2%. The technique enables speedy convergence (< 5 µs) and is highly accurate for autonomous adaptive antenna matching networks.

Complex mathematical model of the underwater robot operation

The article is devoted to a complex mathematical model of the functioning of an underwater robot that allows solving the problem of operational correction of a service task directly during its execution. The successful usage of UAV largely depends on the quality of preparation and programming of the UAV mission, including the current factors of the water environment. Since UAV works in an aquatic environment, the modeling of its functioning should be carried out taking into account both the environment itself and the dynamics of changes in its properties. The developed mathematical model was implemented in the form of a computer model and confirmed its operability within the declared ranges of initial conditions and initial data. The proposed complex mathematical model can be used for planning of assignments given available energy on board the UAV and allows to evaluate the energy for the operation of the on-board equipment after performing the UAV maneuver in the operating zone and the necessary reserves for the ascent of the unit, its detection and receiving aboard the carrier.

The Rater Performance Categorization System (RPCS) for Intensive English Programs

There are several student performance are assessed in Intensive English Programs (IEP) worldwide in each academic year. These student performances are mostly graded by human raters with a certain degree of error. However, the accuracy of these performance assessment is of utmost importance because they feed data into some high stakes decisions about the students and such performance assessments constitute a large number of students’ scores. Therefore, the accuracy of these performance assessments should be given priority by the IEPs. However, when the current rater performance monitors systems which can help the administrators of IEPs to monitor rater performance in performance assessment are away from practicality because they require the use of complex mathematical models and specialized software. A practical and easy to maintain rater performance categorization system is proposed in this paper and it was accompanied by a sample study Its benefits to the administrators of IEPs and their raters are also discussed besides its practical considerations.

A Guidance method for robustness surrogate assisted multi-objective evolutionary algorithms

In the real world, multi-objective problems(MOPs) are relatively common in optimization in the areasof design, planning, decision support... In fact, problemsinclude two or many objectives, there is a class of problemscalled expensive problems that are problems with complexmathematical models, large computational costs,... Theycan not be solved by normal techniques, they are usually tobe solved with techniques such as simulation, decomposing,problem transformation. In particular, using a surrogatemodel with Kriging, neuron networks techniques in combination with an evolutionary algorithm is a subtle choice,with many positive results, being studied and applied inpractice. However, the use of a surrogate model withKriging, neuron networks combining selection strategy,sampling... can reduce the robustness of the algorithmsduring the search. This paper analyzes the issues affectingthe robustness of the multi-objective evolutionary algorithms (MOEAs) using surrogate models and suggests theuse of a guidance technique to increase the robustness ofthe algorithm, through analysis, experiment and results arecompetitive and effective to improve the quality of MOEAsusing a surrogate model to solve expensive problems.

A Study on Greedy Technique in Container Loading Problem and Knapsack Problem

The main aim of the paper is to use application of greedy algorithm in container loading problem and Knapsack problem. Greedy method gives an optimal solution to the problem by considering the inputs one at a time, checking to see if it can be included in the set of values which give an optimal solution and then check if it is the feasible solution. The Greedy algorithm could be understood very well with a well-known problem referred to as container loading problem and Knapsack problem. The basic Container Loading Problem can be defined as the problem of placing a set of boxes into the container respecting the geometric constraints: the boxes cannot overlap and cannot exceed the dimensions of the container. The knapsack problem is in combinatorial optimization problem. It appears as a sub problem in many, more complex mathematical models of real world problems.

Determining the optimal maintenance period in order to minimize the life cycle cost and maximize the performance and reliability index of the bridge

Population growth and development of economic relations have led to increase utilization of transportation infrastructures. The bridge is one of the important components of road construction that always needs special attention during the whole period of design, execution and operation. To ensure that the stairs are regularly inspected, evaluated and operated, management is needed to meet this need in the stairs by performing appropriate maintenance and repairs. Therefore, in this study, a three-objective optimization model includes minimization of maintenance costs, maximization of bridge performance index and reliability of bridges. For this purpose, a complex integer mathematical programming model has been developed. In order to solve the problem, a multi-objective particle mass optimization algorithm has been developed. From the solution of the proposed algorithm, different Pareto answers are obtained so that the decision makers can choose the answer from the obtained Pareto answers that is their priority.Also, after performing a sensitivity analysis on the parameters of failure rate and failure rate during the effect, it has been observed that by increasing the scenario number in two cases, which indicates an increase in failure rate and failure rate during the effect, the amount of costs increases and The overall performance of the system has been declining, which seems natural and correct.

Using a General Algebraic Formula to Identify the Primary Mechanical Properties Impacting Blood Loss Capacity

The physiological response to hypovolemia is conventionally characterized in terms of clinical symptoms rather than fundamental homeostatic mechanisms. It is well understood how complex changes in the mechanical properties of the ventricles and the vasculature are coordinated to regulate arterial pressure and cardiac output. However, these mechanical properties in animal models are difficult to measure and control. Although complex mathematical models of the cardiovascular system have been developed to predict how changes in mechanical properties affect hemodynamic variables, solutions require assumption of a specific set of parameter values that characterizes each subject. Unlike complex mathematical models, however, equations characterizing simple closed-loop cardiovascular models can be solved algebraically, which provides general algebraic formulas applicable to all mammals in health and disease. Therefore, the purpose of the present work is to use a simple closed-loop model to develop an algebraic formula for maximum blood loss in terms of the mechanical properties of the cardiovascular system. First, the standard minimal closed-loop model was assumed, consisting of four vascular compartments, two ventricles, and two resistances. Second, to solve the set of eight model equations algebraically, the ventricular end-diastolic pressure-volume relationships were linearized. Third, the impact of the baroreflex was assumed to be limited by a maximum heart rate and cardiac contractility, as well as a maximum change in unstressed vascular volumes. Fourth, the blood loss capacity was assumed to be exhausted when mean arterial pressure and cardiac output have reached their minimum levels following failure of homeostatic mechanisms. For healthy adults, it was found that the mechanical properties having the greatest impact on blood loss capacity are venous compliances, ventricular diastolic stiffness, and the maximum change in vascular unstressed volume. This algebraic formula is a novel tool for clinical investigators to address challenges as diverse as comparing experimental results across mammalian species, identifying risk factors for adverse outcomes, and exploring new clinical strategies to extend blood loss capacity.

Active system for reduction of noise parameters of car muffler with the use of pressure sensors based on silicon microcrystals

Purpose: The article contains the results of research and development of a system for active noise damping of an automobile engine. The proposed system of active noise suppression can significantly reduce the sound pressure level in the frequency band up to 500 Hz. The robotic principle of the developed system is based on the addition of an additional buffer tank with a variable volume in the silencer system. The use of high-temperature sensors with strain gauges based on silicon microcrystals to obtain information on the parameters of sound vibrations arising during the exhaust gas outflow made it possible to create a control system for changing the volume of the buffer tank. The results of testing the proposed system of active noise suppression of an internal combustion engine are presented. Design/methodology/approach: The active noise suppression system based on the Helmholtz resonator used tools to control general noise levels, experimental tests, complex mathematical modelling of acoustic processes in Solidworks, taking into account the conditions of propagation and attenuation of sound energy by intermediate closed volumes. Findings: The use of an additional resonator chamber with variable volume in the exhaust muffler of the internal combustion engine allowed to reduce the resonant phenomena in the zone of low-frequency pulsations of exhaust gas pressure from 57 Hz to 43 Hz at frequency drift in the range of 310… 350 Hz, which significantly improved its noise characteristics. Research limitations/implications: For further research, to improve the characteristics of the active noise suppression system, it is advisable to consider the use of several inadditional cameras of the Helmholtz resonator and to clarify the algorithm of the controller in transient modes of engine operation. Practical implications: The developed design of active noise reduction is simpler in comparison with analogs and allows reducing the noise of exhaust gases in a low-frequency range. Originality/value: To reduce the noise, a variable-volume Helmholtz resonator was used, the efficiency of which is provided by high-temperature sensors of the original design.