Mathematical Model Of System Research Articles

Performance evaluation of ecofriendly R1234ze(E) refrigerant in an automotive air conditioning system

AbstractA mathematical model for an air conditioning system used in five‐seater cars is developed with R1234ze(E) and R134a refrigerants, consisting of real system geometry like an evaporator, compressor, condenser, and thermostatic expansion valve. The mathematical model includes refrigerant properties, heat transfer, and pressure loss correlations for two‐phase and single‐phase regions. The performance parameters of a system like evaporator cooling duty, condenser heat loss, compressor power, refrigerant flow rate, and compressor volumetric efficiency obtained from a mathematical model are validated with the results of an experimental facility developed with R134a. The uncertainty analysis performed for the testing facility showed below 11% deviation. The simulation and experimental results showed an overall 10%–15% difference. It is found that the experimental cooling capacity with R134a and numerical cooling capacity with R134a show a 4%–12% variation, experimental cooling capacity with R134a and numerical cooling capacity with R1234ze(E) show a 7%–20% variation, and numerical cooling capacity with R134a and numerical cooling capacity with R1234ze(E) show a 5%–15% variation for the given range of compressor speed (500–1500 rpm), and condensing temperature (26–45°C). The study concluded that R1234ze(E) could potentially replace R134a because it has similar thermophysical properties and an average performance difference of up to 10% with R134a. Due to the limitations of the electric motor used to drive the compressor, tests in the current study were conducted at modest compressor speeds (500–1500 rpm). Future research will focus on experiments with high compressor speed (in the range of 1500–4000 rpm) and R1234yf and R1234ze(E) refrigerants for performance evaluation of automobile air conditioning systems.

Calibration methods to fit parameters within complex biological models.

Mathematical and computational models of biological systems are increasingly complex, typically comprised of hybrid multi-scale methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. These mechanistic models concurrently simulate detail at resolutions of whole host, multi-organ, organ, tissue, cellular, molecular, and genomic dynamics. Lacking analytical and numerical methods, solving complex biological models requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these models to multiple experimental datasets over time and space presents significant challenges. In this work we undertake the task of reviewing, testing, and advancing calibration practices across models and dataset types to compare methodologies for model calibration. Evaluating the process of calibrating models includes weighing strengths and applicability of each approach as well as standardizing calibration methods. Our work compares the performance of our model agnostic Calibration Protocol (CaliPro) with approximate Bayesian computing (ABC) to highlight strengths, weaknesses, synergies, and differences among these methods. We also present next-generation updates to CaliPro. We explore several model implementations and suggest a decision tree for selecting calibration approaches to match dataset types and modeling constraints.

Nonlinear state feedback-synergetic control for low frequency oscillation suppression in grid-connected pumped storage-wind power interconnection system

Aiming at enhancing the performance of suppressing low frequency oscillation in grid-connected pumped storage-wind power interconnection system (PS-WPIS), the nonlinear state feedback-synergetic control (NSF-SGC) governor is studied. Firstly, the nonlinear mathematical models of grid-connected pumped storage power system (PSPS) and PS-WPIS are established. Then, the NSF-SGC strategy and macro variable determination method are proposed, and the NSF-SGC governor equation is derived. Furthermore, the action mechanism, regulation and damping characteristics of NSF-SGC governor in grid-connected PSPS and PS-WPIS are explored. Finally, the sensitivity and robustness of NSF-SGC governor are illuminated. The results show that, the proposed NSF-SGC strategy is superior to the proportional-integral, NSF and SGC strategies in regulation quality, and can significantly suppress low-frequency oscillation. The stability of grid-connected PSPS can be prominently improved by selecting smaller linear and time parameters, and a larger absolute value of nonlinear parameter of NSF-SGC governor. The NSF-SGC governor with dual macro variables enhances the damping characteristics of grid-connected PS-WPIS. Appropriate parameters of NSF-SGC governor can enhance the regulation performance of grid-connected PS-WPIS. Noise and parameter sensitivity analysis provide a guidance for improving system stability. The NSF-SGC governor has strong robustness under the variations of hydraulic, mechanical and electrical parameters.

The challenges of modeling using fuzzy standard interval arithmetic: A case study in electrical engineering

In this work, the aim is to shed light on the challenges in deriving a mathematical model of dynamical systems when fuzzy standard interval arithmetic (FSIA) serves as a mathematical tool. The challenges in question are investigated through two approaches called the direct and devious approach. Specifically, in the direct approach, the challenges lie in the high complexities of deriving the fuzzy model while maintaining conformity with the laws of physics. Additionally, it is possible that the resulting fuzzy model may not have a solution. Concerning the devious approach, the primary challenge is the potential violation of the physics laws governing the system, which means that the validity of the fuzzy model is not guaranteed. Moreover, in both cases, the UBM phenomenon poses another challenge, preventing the attainment of a unique fuzzy model. As a result, it is demonstrated that FSIA and any related concepts, such as the strongly generalized Hukuhara derivative (SGH-derivative), generalized Hukuhara derivative (gH-derivative), generalized derivative, etc., mainly suffer from the catastrophe of physics laws violation (CPLV), which can be considered the most significant drawback. Furthermore, it is explained that the reason for a fuzzy differential equation under concepts such as the SGH-derivative or gH-derivative having multiple solutions is due to the CPLV. To clarify the CPLV, a simple electrical circuit with uncertain elements is examined as a case study.

Mathematical Modeling of a Fuzzy Logic-Based Car Parking System

This paper presents the mathematical modeling of a fuzzy logic-based car parking system. Many people are facing problems parking vehicles in parking lots in most urban cities. The technology of fuzzy-based systems is necessary for all vehicle users to acquire parking slots in cities. A smart parking system helps in obtaining information about available parking spaces, organizing and processing it, and then placing the car in a certain position. The method adopted makes use of a fuzzy-based smart car parking system to develop the usage of small parking spaces for parking lots to allow the parking of vehicles based on their weight. A set of rules was used in the fuzzy logic to control two sets of parking decisions, namely the vehicle entry decision and the inpark decision, by bearing in mind the weight of vehicles and the availability of parking spaces in the parking mall. The results obtained show that the smart car parking system keeps the availability of parking lots in equilibrium, depending on the entry and exit of vehicles. In conclusion, it was discovered that the total number of vehicles granted entry at each time interval depends on the availability of parking lots on each designated floor.

HYDRO TURBINE SPEED CONTROL SYSTEM

The article presents a mathematical model of an hydro turbine speed control system. In the world and domestic practice of creating hydraulic turbine equipment, there is a clear tendency to create computer-based rotor speed control systems for hydraulic turbines. Computer systems provide an opportunity to implement the introduction of effective algorithms using software that improve the static and dynamic characteristics of the system. This in turn increases the importance of mathematical modeling both at the design stage and during commissioning. The analysis of the performed works devoted to the mathematical description of the elements of the hydraulic drive of the regulator showed that they are reduced to linearized equations without taking into account a number of important factors that will increase the accuracy of the mathematical model. Improvement of static and dynamic characteristics and the system as a whole can be achieved by solving the scientific problem of studying its dynamics based on the development of a more complete mathematical model. To reduce friction and hysteresis, to prevent obliteration, the electrohydraulic converter plunger in the lower part is equipped with a segner wheel. Improving the dynamic characteristics of hydraulic turbine speed controllers requires the development of nonlinear mathematical models with subsequent analysis of transients in the hydraulic drive of the speed controller. Evaluation of the quality of transient processes and subsequent adjustment of parameters allows to achieve a reduction in the duration of transients, increase the speed and accuracy of positioning at small movements of the servo motor. A number of unaccounted factors during the preparation of the mathematical model of the electro-hydraulic converter makes it possible to increase its adequacy to the real object of study and increase the speed of the control system of the rotor speed of the hydraulic turbine.

A novel mechanistic modelling approach for microbial selection dynamics: Towards improved design and control of raceway reactors for purple bacteria

Purple phototrophic bacteria (PPB) show an underexplored potential for resource recovery from wastewater. Raceway reactors offer a more affordable full-scale solution on wastewater and enable useful additional aerobic processes. Current mathematical models of PPB systems provide useful mechanistic insights, but do not represent the full metabolic versatility of PPB and thus require further advancement to simulate the process for technology development and control. In this study, a new modelling approach for PPB that integrates the photoheterotrophic, and both anaerobic and aerobic chemoheterotrophic metabolic pathways through an empirical parallel metabolic growth constant was proposed. It aimed the modelling of microbial selection dynamics in competition with aerobic and anaerobic microbial community under different operational scenarios. A sensitivity analysis was carried out to identify the most influential parameters within the model and calibrate them based on experimental data. Process perturbation scenarios were simulated, which showed a good performance of the model.

Cardiovascular sex-differences: insights via physiology-based modeling and potential for noninvasive sensing via ballistocardiography.

In this study, anatomical and functional differences between men and women in their cardiovascular systems and how these differences manifest in blood circulation are theoretically and experimentally investigated. A validated mathematical model of the cardiovascular system is used as a virtual laboratory to simulate and compare multiple scenarios where parameters associated with sex differences are varied. Cardiovascular model parameters related with women's faster heart rate, stronger ventricular contractility, and smaller blood vessels are used as inputs to quantify the impact (i) on the distribution of blood volume through the cardiovascular system, (ii) on the cardiovascular indexes describing the coupling between ventricles and arteries, and (iii) on the ballistocardiogram (BCG) signal. The model-predicted outputs are found to be consistent with published clinical data. Model simulations suggest that the balance between the contractile function of the left ventricle and the load opposed by the arterial circulation attains similar levels in females and males, but is achieved through different combinations of factors. Additionally, we examine the potential of using the BCG waveform, which is directly related to cardiovascular volumes, as a noninvasive method for monitoring cardiovascular function. Our findings provide valuable insights into the underlying mechanisms of cardiovascular sex differences and may help facilitate the development of effective noninvasive cardiovascular monitoring methods for early diagnosis and prevention of cardiovascular disease in both women and men.

Mathematical Modeling and Experimental Characterization of the Piezoelectric Servo Valve System

Abstract The dynamic performance of the hydraulic system depends on the dynamic characteristics of the servo valve. In this article, the control characteristics of the piezoelectric servo valve are studied theoretically and experimentally. The mathematical model of the system is established by considering the influence of the piezoelectric servo valve, the influence of the pipeline, and the interaction between them. The frequency response characteristics of the system and the influence of the pipeline parameters on the control characteristics of the system are discussed. The simulation results are compared with the experimental results to verify the accuracy and efficiency of the piezoelectric servo valve dynamic model established in this article.

Variational inequalities of multilayer viscoelastic systems with interlayer Tresca friction: Existence and uniqueness of solution and convergence of numerical solution

The mathematical model of multilayer viscoelastic system based on the actual structure of asphalt pavement and the properties of its numerical solutions are studied. Firstly, based on the partial differential equations, the variational inequality model of the multilayer viscoelastic system is derived, and the existence and uniqueness of its solutions are further proved. Then, based on the finite element theory, the convergence property and error analysis of the semi‐discrete numerical solutions of the variational inequalities are further studied. Finally, the convergence and error analysis of the fully discrete numerical solutions of the variational inequalities are derived by the forward difference method. The conclusion of the above error analysis also confirms the feasibility of studying the mechanical response of asphalt pavement based on variational inequality.

Research on the Calculation Model and Control Method of Initial Supporting Force for Temporary Support in the Underground Excavation Roadway of Coal Mine

This paper proposes a temporary support system for improving the efficiency and safety of underground roadway excavation in coal mines. Firstly, this study establishes a calculation model for the initial supporting force of the excavation of roadway temporary support and a gray system-based automatic prediction model for the initial supporting force level, based on the mechanism of temporary support controlling the roof. These models enable the prediction of the required initial supporting force at different locations along the roadway’s temporary support area, thereby providing a basis for controlling the initial supporting force of the temporary support system. To achieve efficient and adaptive control of the initial supporting force of temporary supports at different locations, this study designs a support force controller based on Simulated Annealing Particle Swarm Optimization Proportional-Integral-Derivative (SAPSO-PID). This study establishes a mathematical model for the hydraulic cylinder pressure system controlled by the temporary support overflow valve and conducts a stability analysis and model verification. The study constructs a simulation control system for the initial supporting force based on SAPSO-PID using the combined simulation platform of AMESim and Matlab. The simulation results demonstrate that the proposed support force control system efficiently achieves adaptive control of the initial supporting force of temporary supports. An experimental system in the underground roadway of a coal mine is constructed to validate the results of the simulation analysis.

Assignment of the cutting mode when boring holes on CNC machine

Due to structural limitations, the processes of boring holes are performed in a low-rigidity machining system, which predetermines their susceptibility to vibrations. The article is devoted to the study of the process of boring holes on CNC machines, and the subject of the study is the effect of the cutting mode on the stability of the machining. The mathematical model of the machining system is presented in the form of a two-mass dynamic system, which forms a closed loop structure with negative feedback by elastic displacement. In addition, positive feedback is taken into account through the delay argument function, which represents machining along traces. It has been proven that this process provokes the emergence of regenerative oscillations in the machining system. The application of the system’s approach made it possible to obtain a mathematical model in the form of state variables, which is acceptable for the use of numerical modeling methods in both time and frequency space. An applied engineering program for determining the stability diagram in "cutting depth - spindle speed" coordinates has been created. The program uses a new criterion of stability of systems closed through positive feedback loop with a delay argument function. For the first time, the validity of such a criterion was proved for systems described by differential equations of the fourth order. The importance of taking into account the results of the study in the form of a stability lobes diagram when assigning a cutting mode, especially in the area of high speeds, is proven. Thus, according to the results of the experiments, a change in speed of only 7% from 2150 rpm to 2320 rpm with the same cutting depth of 0.4 mm allows the process to become stable. The use of the created program is possible in the system of automatic control of the online cutting mode when the machine is equipped with vibration sensors with appropriate systems for identifying the dynamic parameters of the machining system, which will significantly increase the machining efficiency.

Investigation of high-energy impact system using a physical model

The aim of the experimental research is to validate the theoretical findings obtained from a mathematical model of a two-mass impact system. The research object is a physical model of a two-mass impact system, designed to prevent the transfer of the reactive component to the tool carrier. The model includes a housing, inertial mass, elastic member and impact part. In the operating position, a compressed elastic member is placed between the inertial mass and the impact part, held together by dogs. The height at which the impact part detaches from the inertial mass is determined by the position of the clamp, which separates the moving impact part and inertial mass during free fall. The study involved the fundamental principles of similarity theory, planning theory and data processing. The height at which the impact part detaches from the inertial mass and the impact part is taken as an independent factor, while the energy of a single impact serves as the response function, determined by the diameter of the cone impression delivered by the impact part onto a wooden base. Based on the analysis of physical laws, similarity criteria for the impact mechanism were established, along with dependent and independent indicators, and transfer equations from real parameters to model parameters were derived. The research findings indicate that the total area of air holes should be at least half of the cross-sectional area of the housing for a physical model. The relationship between the diameter of the cone impression on the wooden base and the impact energy was determined. The adequacy of the mathematical model describing the processes in the impact device was confirmed, with a maximum discrepancy of 18% between the results of mathematical and physical modelling of the operating process for the impact mechanism characterised by an increased energy of a single impact. Therefore, the research results validate the results obtained from the mathematical model of the impact mechanism. Further studies should focus on refining the physical model to record the rebound height of the inertial mass as a function of the parameters of the impact mechanism.

Performance evaluation of underwater vision systems

The article describes a methodology for performance evaluation of vision systems for remotely operated underwater vehicles. The methodology is based on a system approach and uses mathematical models of the aqueous medium where an optical signal propagates, the underwater object image registration system, and the mathematical model of the human visual system. The detection and recognition probabilities of underwater object image at a given registration range are used as performance evaluation indicators of underwater vision systems. The mathematical model of the aqueous medium developed by the authors allows quantitative evaluation of the influence of backscattering interference arising during objects illumination on the underwater vision system performance. The results of numerical experiments presented in the paper illustrate the possibility of using the proposed technique to optimize the underwater object image registration system parameters in order to achieve the required values of detection or recognition probabilities at the given ranges.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems.

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

An effective mathematical model of cardiac electrical activities for Bundle Branch Blocks

In this paper a mathematical model of cardiac induction system is developed. Sinoatrial node (SA), atrioventricular node (AV) and His Purkinje system (HP) are represented by modified Van der Pol-type oscillators (VDP) connected with time-delay coupling. Atrial and ventricular muscles are modeled using modified Aliev-Panfilov equations (AP), with stimulation current from the related pacemakers, to represent the P, QRS, Ta, and T waves. The main aim of this paper is to model bundle branch blocks (BBBs) for right (RBBB) and left (LBBB) branches. In fact, the right and left ventricles are directly affected by these blocks since the HP bundle is composed of right and left bundle branches that provide electrical signals, respectively, to the right and left ventricles. Four VDP oscillators are utilized, one for each of SA, AV, right HP, and left HP. The depolarization of the right and left ventricular muscles are represented by two systems of AP equations to produce right QRS and left QRS waves. The results of the simulation are compared with real normal and pathological electrocardiograms (ECGs) to show the effectiveness and the accuracy of the proposed model. The simulation proves that the model can reproduce the blocks in the HP bundle branches.

The Importance of Studying Markov Processes in the Course of Studying Mathematical Models of a Technical System at the Stages of Diagnostics and Repair

The Importance of Studying Markov Processes in the Course of Studying Mathematical Models of a Technical System at the Stages of Diagnostics and Repair

Experimental and Simulation Study of Solar-Powered Air-Gap Membrane Distillation Technology for Water Desalination.

This work aimed to investigate temperature polarization (TP) and concentration polarization (CP), which affect solar-powered air-gap membrane distillation (SP-AGMD) system performance under various operating conditions. A mathematical model for the SP-AGMD system using the experimental results was performed to calculate the temperature polarization coefficient (τ), interface temperature (Tfm), and interface concentration (Cfm) at various salt concentrations (Cf), feed temperatures (Tf), and flow rates (Mf). The system of SP-AGMD was simulated using the TRNSYS program. An evacuated tube collector (ETC) with a 2.5 m2 surface area was utilized for solar water heating. Electrical powering of cooler and circulation water pumps in the SP-AGMD system was provided using a photovoltaic system. Data were subjected to one-way analysis of variance (ANOVA) and Spearman's correlation analysis to test the significant impact of operating conditions and polarization phenomena at p < 0.05. Statistical analysis showed that Mf induced a highly significant difference in the productivity (Pr) and heat-transfer (hf) coefficients (p < 0.001) and a significant difference in τ (p < 0.05). Great F-ratios showed that Mf is the most influential parameter. Pr was enhanced by 99% and 146%, with increasing Tf (60 °C) and Mf (12 L/h), respectively, at a stable salt concentration (Cf) of 0.5% and a cooling temperature (Tc) of 20 °C. Also, the temperature increased to 85 °C when solar radiation reached 1002 W/m2 during summer. The inlet heat temperature of AGMD increased to 73 °C, and the Pr reached 1.62 kg/(m2·h).

A Novel Equivalent Continuous Metering Control With a Uniform Switching Strategy for Digital Valve System

Pulse number modulation (PNM) combined with pulse width modulation (PWM) control is an effective solution to improve the resolution of digital valve systems. However, the numerous discrete variables that use parallel <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> / <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> valves cause difficult control coordination and uneven switching. To address this issue, this article defines the equivalent spool displacement of the digital flow control unit by the number of PNM-controlled valves and the duty cycle of PWM-controlled valves to replace multiple discrete variables and develops the equivalent continuous metering control method. Furthermore, a uniform switching control strategy is proposed for the PWM-controlled valve using a uniformly distributed permutation for each <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> / <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> valve. The proposed control methods are verified by simulation on the built mathematical model of the equal-coded digital valve system. Experimental results for the displacement control of a hydraulic cylinder at 1 rad/s show that the average error of the equivalent continuous metering control is about 0.236 mm and the dispersion index reaches 20%, while the uniform switching control strategy achieves 80% with an average error of 0.215 mm. Simulated and experimental results demonstrate that the equivalent continuous metering control with a uniform switching strategy can almost evenly distribute switching numbers without compromising the accuracy of the displacement control.

Modelling and Testing the Dynamic Properties in a Submachine Gun-Man System

This work was an attempt at an analysis of the interaction between a firearm and a human, exemplified by a cal. 9 mm submachine gun (SMG), PM-98 GLAUBERYT and a trained, professional shooter - a Police special team operator. The results of the analysis made it possible to develop several guidelines aimed at designing the dynamic performance of SMGs to improve their aiming accuracy. In connection with this work, experimental tests were performed at a firing range, where the process of firearm discharge was recorded using a Phantom slow-motion digital camera. What followed was the analysis of the video record using the Tema dedicated computer software. The SMG’s dynamic performance was adjusted to reduce the hit scatter. Based on the results of the empirical tests at the firing range, physical and mathematical models of the SMG-operator system were formulated. The SMG-operator system was simulated in the Scilab software, which provided time-based variation trends of the kinematic quantities that characterised the movements of individual modelled objects. The variation trends determined included displacement, velocity and acceleration of the SMG, its bolt assembly, and the human operator as a function of time. The results of the theoretical analysis were compared to the empirical test results from the firing range. It was found that in the virtual modelling space, the SMG model had a performance similar to that of its real counterpart. With the theoretical model verified, several performance parameters of the SMG were modified and guidelines were developed that could improve the aim.