Mathematical Model Of System Research Articles

Hydrodynamic response analysis of the aquaculture net under the combined action of irregular waves and currents

ABSTRACT The hydrodynamic response of fishing nets is crucial in aquaculture. During service, due to severe sea states and collisions with large fish, potentially resulting in net damage. Analyzing this damage is complex due to the large number of net meshes. This study establishes a mathematical model of the net system under wave-current coupling based on the rigid-body kinematics and the lumped-mass method. An analysis was conducted to investigate how various environmental conditions and types of damage affect net deformation and force. Results indicate that maximum force occurs at the connections to the rigid frame and the midpoint of the net. Among various types of net damage, the nodes motion increased exclusively around the periphery of the damaged area, while the netting twine force significantly decreased only in the direction of the damage. Notably, damage to the upper net has the greatest impact on both netting twine force and deformation.

Error Analysis and Optimization of Structural Parameters of Spatial Coordinate Testing System Based on Position-Sensitive Detector.

For the research on real-time accurate testing technology for the explosion point spatial coordinate of munitions, its currently commonly used methods such as acoustic-electric detection or high-speed imaging are limited by the field conditions, response rate, cost, and other factors. In this paper, a method of spatial coordinate testing for the explosion point based on a 2D PSD (position-sensitive detector) intersection is proposed, which has the advantages of a faster response, better real-time performance, and a lower cost. Firstly, a mathematical model of the spatial coordinate testing system was constructed, and an error propagation model for structural parameters was developed. The influence of the position of the optical axes' intersection as well as the azimuth angle and pitch angle on the test accuracy of the system was simulated and analyzed, thus obtaining the distribution and variation trend of the overall error propagation coefficient of the system. Finally, experiments were designed to obtain the test error of the system for validation. The results show that the system test accuracy is high when the azimuth angle is 20°-50°, the overall error propagation coefficient does not exceed 48.80, and the average test error is 56.17 mm. When the pitch angle is -2.5°-2.5°, the system has a higher test accuracy, with the overall error propagation coefficient not exceeding 44.82, and the average test error is 41.87 mm. The test accuracy of the system is higher when the position of the optical axes' intersection is chosen to make sure that explosion points fall in the region of the negative half-axis of the Zw-axis of the world coordinate system, with an overall error propagation coefficient of less than 44.78 and an average test error of 73.38 mm. It is shown that a reasonable selection of system structure parameters can significantly improve the system test accuracy and optimize the system deployment mode under the long-distance field conditions so as to improve the deployment efficiency.

Fuzzy Modelling Algorithms and Parallel Distributed Compensation for Coupled Electromechanical Systems

Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system’s components, thermal effects, mechanical vibrations, electrical noise, and the dynamic and transient impacts of electrical loads. In this study, we introduce a fuzzy modelling identification approach utilizing the Takagi–Sugeno (T–S) structure, wherein model and control parameters are optimized. This methodology circumvents the need for deriving a mathematical model through energy balance considerations involving thermodynamics and the non-linear representation of the electric generator. Initially, a non-linear mathematical model for the electrical power system is obtained through the fuzzy c-means algorithm, which handles both premises and consequents in state space, utilizing input–output experimental data. Subsequently, the Particle Swarm Algorithm (PSO) is employed for optimizing the fuzzy parameter m of the c-means algorithm during the modelling phase. Additionally, in the design of the Parallel Distributed Compensation Controller (PDC), the optimization of parameters pertaining to the poles of the closed-loop response is conducted also by using the PSO method. Ultimately, numerical simulations are conducted, adjusting the power consumption of an inductive load.

The optimal polynomial decay in the extensible Timoshenko system

AbstractIn this paper, we derive the equations that constitute the nonlinear mathematical model of an extensible thermoelastic Timoshenko system. The nonlinear governing equations are derived by applying the Hamilton principle to full von Kármán equations. The model takes account of the effects of extensibility, where the dissipations are entirely contributed by temperature. Based on the semigroups theory, we establish existence and uniqueness of weak and strong solutions to the derived problem. By using a resolvent criterion, developed by Borichev and Tomilov, we prove the optimality of the polynomial decay rate of the considered problem under the condition (65). Moreover, by an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we show the non‐exponential stability of the same problem; but strongly stable by following a result due to Arendt–Batty. In the absence of additional mechanical dissipations, the system is often not highly stable. By adding a damping frictional function to the first equation of the nonlinear derived model with extensibility and using the multiplier method, we show that the solutions decay exponentially if Equation (85) holds.

Research on Mathematical Modeling of Naval Gun Servo System

Abstract Tracking performance of naval gun servo system is very important to the whole combat function of naval gun weapon system. Therefore, it is very important to construct accurate mathematical model to improve the performance of servo system. This paper analyzed the structure of naval gun servo system in detail and established the transfer function of each component according to its working principle. Finally, the complete mathematical model of naval gun servo system is established through the organic combination of all parts. Then the stability of the mathematical model of naval gun servo system is judged by Rouse criterion. When the original servo system is unstable, it is necessary to modify the model of servo system by designing lead-lag correction to achieve stable control of the servo system, which lays a foundation for further research on control performance optimization based on mathematical model of naval gun servo system.

Оптимизация региональных планов адаптации к изменению климата в Арктической зоне России на основе прогностического моделирования

Based on the Russian Arctic example, an attempt was made to update the developed regional plans for adaptation to climate change, taking into account currently available scientific knowledge, observational data, climate scenarios and the results of mathematical modeling of natural and socio-economic systems — recipients of climate risks. The authors using the developed methods have calculated the geocryological risk index for the macro-regions of the Russian permafrost zone, as well as the vulnerability index of economic systems for municipalities of the Russian Arctic.

Mathematical Modelling of a Single Magneto-Rheological for Car Suspension System Using Modified Bouc-Wen Model

Magneto-Rheological (MR) automotive suspension represents the most advanced technology currently available for enhancing passenger comfort through intelligent fluid behaviour. This work employed a Modified Bouc-Wen model to create a mathematical representation of a single MR vehicle suspension and compared its ride performance to that of passive suspension systems. The model was formulated and solved using second-order linear differential equations, with MATLAB software utilized to visualize the results. The maximum vertical displacement for the single MR mathematical model in this work was 0.031 m, while the minimum was -0.0124 m. At the minimum position, the vertical displacements for the passive model were 0.0532 m and -0.0133 m. The results demonstrated that the vertical displacement variation was similar for both the mathematical model and the passive system. All displacements obtained from the mathematical modeling of the single MR system were close to its mean of 0.000875 m (nearly zero). There was reduced vibration when zero displacement was achieved. It was concluded that MR damper significantly improved car suspension performance compared to passive solutions. This paper developed a single MR vehicle suspension system using the Modified Bouc-Wen model in a Proton Preve.

Towards a modelling, optimization and predictive control framework for smart irrigation

Smart irrigation scheduling is a promising approach for improving the efficiency and sustainability of agricultural water use, especially in arid and semi-arid lands. In this paper, we present a design and simulation of a model predictive controller for smart irrigation scheduling. The proposed controller is based on a mathematical model of the irrigation system, which is used to predict the future states of the system and determine the optimal irrigation schedule for a given crop and field. This study further evaluates the impact of the predictive control framework on crop yield, water use efficiency (WUE), and water savings in tomato production. Three control strategies, including manual control, open-loop control, and model predictive control (MPC), were compared using a Completely Randomized Design (CRD) methodology. Results indicate that MPC outperforms the other strategies, yielding the highest average crop yield of 20 t/ha and demonstrating superior WUE at 10.4 kg/m3. Additionally, MPC significantly reduces water consumption, achieving a 29 % and 8 % savings compared to manual and open-loop control, respectively. These findings underscore the efficacy of MPC in optimizing crop yield, conserving water resources, and promoting sustainable agriculture practices. The proposed controller has the potential to address the global water scarcity challenge and contribute to the sustainability of agriculture in arid and semi-arid lands.

ANN based optimization of nano-beam oscillations with intermolecular forces and geometric nonlinearity

In this study, we investigate the effect of Van der Waals and Casimir forces on the mathematical model of nano-electromechanical systems (NEMS) such as nano-beam actuators that contain cantilever and double cantilever beams. The singular nonlinear boundary value problem governing the beam-type actuators, including geometric nonlinearity is solved by using an intelligent strength of feedforward artificial neural networks (ANNs) and hybridization of optimization algorithms such as arithmetic optimization algorithm (AOA) and active set algorithm (ASA). The proposed ANN-AOA-AS algorithm is employed to quantify the effect of changes in applied voltage, dispersion forces, geometric nonlinearity parameters, and initial axial strain on the deflection of the beam. Furthermore, to validate the results obtained by the proposed algorithm, statistical analyses are conducted to compare the approximate solutions with state-of-the-art methodologies available in the latest literature. In addition, performance indicators are defined such as mean square error (MSE), Nash–Sutcliffe efficiency (NSE), mean absolute deviations (MAD), root mean square error (RMSE), and Error in Nash–Sutcliffe efficiency (ENSE) to study the accuracy and efficiency of the solutions. The results show that these indicators’ mean percentage values lie around 10−4 to 10−6 which reflects the perfect modeling of the approximate solutions.

A Modified ADRC Scheme Based on Model Information for Maglev Train

During the operation of maglev trains, they are subjected to various disturbances. The presence of these disturbances presents a significant challenge for attaining high-performance control and even poses the risk of system instability. To further enhance the anti-disturbance capability of maglev trains, this paper proposes a model information-assisted modified active disturbance rejection control (MADRC) approach. A mathematical model of the single-point suspension system of maglev trains is constructed for the design of the extended state observer (ESO), which is a modified extended state observer (MESO), and a nonlinear mechanism is incorporated to boost the performance of the ESO. Owing to the introduction of model information, the estimated quantity of disturbances by MESO no longer considers the system model deviation as a disturbance. Hence, the linear feedback control law is modified accordingly. The MESO is regarded as an ESO with time-varying gain using the equivalent gain method, and its stability is proven using the Lyapunov method. The tracking and anti-disturbance performances of different controllers are compared via simulation experiments. Suspension and anti-disturbance experiments are conducted on the single-point suspension experimental platform, verifying that the proposed MADRC has a more potent suppression ability for load disturbances in the suspension system.

PCR virtual temperature sensor design based on system modeling and identification

The reaction results of Polymerase chain reaction (PCR) are highly sensitive to temperature accuracy, but the reaction liquid temperature is hard to be measured directly. In this paper, a virtual temperature sensor is creatively designed to directly obtain the reaction liquid temperature using a model-switching approach. This study first establishes the mathematical models of the temperature control system and obtains precise system models for the heating and cooling stages. Based on this, a virtual sensor is constructed, and a closed-loop fuzzy PID control system is established. Furthermore, the accuracy of the designed virtual temperature sensor is verified through simulation and experimentation. Simulation results show that the fuzzy PID control method has higher temperature accuracy, with a deviation of 0.23 °C, making it more suitable for Peltier systems, as Peltier systems suffer from inconsistent temperature rise and fall models. The experimental results show that the control method using the virtual sensor achieves higher precision in liquid temperature control, with an accuracy of ±0.21 °C. Finally, standard PCR procedures are performed for designed chip, and the results indicate that the temperature sensor and control system designed in this study exhibit significantly higher amplification efficiency, approximately 16 times greater than traditional control methods.

On the Physical Consistency of an Open Quantum Region with a Classical Reservoir in Molecular Simulation

AbstractThe possibility of treating a molecular liquid in an open region at ab initio electronic resolution embedded in a classical reservoir of energy and particles, is investigated. Because of its challenging properties and its relevance in many field of current research, the system chosen as prototype of molecular liquid is water at room conditions. A numerical protocol based on the mathematical model of open particle system is applied and the results are compared with results of a full ab initio simulation of reference. The key conclusion is that one can claim the existence of a mandatory minimal size of the quantum region in which structural and electronic properties reproduce those of reference and, at the same time, the exchange of molecules with the environment takes place as expected. This work provides a proof of concept about the possibility to systematically define a physically well founded open quantum system embedded in a classical environment. In turn, the proof of concept is a key information for the design of numerically efficient algorithms for ab initio molecular dynamics simulations of open systems.

The 1D model of hybrid heat pump system designed and prototyped for electric vehicles

In this paper, a one-dimensional mathematical model of a hybrid heat pump system was developed to improve the driving range of electric vehicles considering energy consumption. The generated one-dimensional model was performed in four different heating modes under various scenarios to satisfy the heating demand considering both the driving range and the target temperature. This model was run in recirculation mode in all analyses for energy efficiency. The electric heater capacity can be reduced to prevent overheating in the cabin. The fastest proposed cases reached the target temperature in 300 s. In this case, the vehicle range was lowest and varied between 72.3 % and 77.5 %. The highest vehicle range varied between 81.3 % and 86.1 % and provided sufficient heating in approximately 900 s. In addition, the effect of preheating by different capacities electric heaters, it was observed that preheating with a low-capacity electric heater had advantages. As a result, the present study shows that the dynamic behavior of the hybrid heat pump systems allows researchers to improve electric vehicles thermal management system which had a crucial role. The results of the model were in good agreement with the experimental data presented with similar boundary conditions in available literature.

Optimal scheduling of multiple entities in virtual power plant based on the master-slave game

As the energy market evolves into a dynamic and interactive landscape, the distributed nature of virtual power plant (VPP) becomes increasingly significant. This shift highlights the limitations of traditional centralized optimization approaches in capturing the complex interplay among various stakeholders. In response, this article introduces a novel multi-entity distributed collaborative optimization strategy for an integrated energy system (IES) that incorporates a VPP, electric vehicles, and carbon capture technologies, under the Stackelberg master-slave game framework. Within this framework, the VPP operator (VPPO) assumes the role of the leader, while the energy supply aggregator (ESA), customer side residential load aggregator (CSRLA), electric vehicles aggregator (EVA), and carbon treatment system aggregator (CTSA) are positioned as the followers. The paper delves into the development of interaction strategies for each entity, aiming at achieving optimal objectives. The study undergoes by presenting the mathematical model of the VPP-integrated energy system, which is seamlessly integrated into the master-slave game structure. This integration facilitates the creation of a distributed multi-entity cooperative optimization model featuring a single leader and multiple followers, with the uniqueness of the Stackelberg equilibrium being rigorously established. Therefore, the research employs a hybrid nutcracker optimization algorithm and quadratic programming (NOA-QP) method to address the engineering challenge of optimizing operator energy pricing. The case study conducted demonstrates that the proposed scheduling methodology improves the VPP system profit by 10.80%, increases the aggregation profit by up to 1317.22%, optimizes the carbon emissions by 15.59%, and significantly improves the solution efficiency of the VPP by 99.29%.

A mathematical modelling for solar irradiance reduction of sunshades and some near-future albedo modification approaches for mitigation of global warming

To address the global warming problem, one of the space-based geoengineering solutions suggests the construction of an occluding disc that can work as a solar curtain to mitigate solar irradiation penetration to the earth atmosphere. A widely discussed concept needs the construction of a large-scale sunshade system near the Sun–Earth L1 equilibrium point in order to control the average global temperature. However, to improve the accuracy of theoretical estimations, more consistent modeling of the Sun-Curtain-Earth system and solar irradiance reduction rate are required. This study revisits the mathematical modeling of the solar irradiance reduction system and considers the fundamentals of shading physics. Simplified mathematical modeling of solar irradiance reduction rate is derived based on the solar flux density. For the climate control, controllability of the reduction rate by using some physical parameters (e.g., flux reflection rate and angle of the curtain) is discussed. Based on the results of this model, the technical challenges and feasibility of constructing a sunshade system at L1 Lagrange point are evaluated. Some technologically feasible, near-future options for the warming problem are discussed briefly.

Problems and corrections of classical mathematical model for piecewise linear system

Due to the existence of gaps or backlash, many mechanical systems can be simplified into piecewise linear models. The dynamic study on mechanical systems should be based on reliable mathematical models. So that it is very important to determine the contact point and separation point between the primary system and the auxiliary spring system (ASS) in a piecewise linear system. In most existing literature, the contact point and separation point of the mathematical model are fixed at the gap. But in this paper, it is found that the contact point and separation point actually change with the system parameters when the ASS contains a damper, which implies the most existing mathematical models are incorrect. It is firstly demonstrated through numerical solution that the primary system will prematurely separate from the ASS before reaching the gap under harmonic excitation, which shows the incorrectness of the classical mathematical models. Then, based on the mechanical model and engineering practice, two corrected mathematical models are proposed. And the motions of the primary system and ASS after premature separation in the corrected models are studied. Finally, through comparisons of the contact points, separation points, amplitude-frequency curves and motion states between the corrected models and the classical mathematical model, it can be concluded that the corrected models are more reasonable. And comparisons with the experimental data imply that the corrected models can better reflect the engineering practice. These results will be helpful to the study and design of the piecewise linear system.

Comparison study of two control strategies for the small pressurized water reactor

The control strategy has a significant impact on the control performance of the reactor system. This paper investigates the feedwater flow and steam flow control strategies for small pressurized water reactors. First, the mathematical model of the SPWR Nuclear Steam Supply System is introduced. Second, a dual-constant control strategy was proposed, and the feedwater flow rate and steam pressure control systems under the two control modes were designed. Moreover, a steam bypass control system was designed to avoid excessive steam pressure under the feedwater flow control mode, and the reactor power and pressurize control systems were introduced. Simulation results indicate that the two control modes both meet the SPWR control requirements. However, the feedwater flow control mode has better reactor coolant temperature and steam pressure control performances during the load rejection transient, owing to the timely discharge of heat from the reactor coolant system through the steam bypass system.

Devising a calculation method for modern structures of current-conducting elements in large electric machines in a three-dimensional statement

The jumpers of rotor pole-to-pole connections are highly stressed elements in a hydraulic generator structure. These assemblies often fail due to deformation that exceeds the size of an air gap. Existing methods do not take into account the thermal component and attempts to improve the design are not based on mathematical models that make it possible to perform calculations with an accuracy of more than 50 %. The method devised in this work makes it possible to obtain boundary conditions of the third kind on the basis of three-dimensional mathematical modeling of the ventilation system of the hydraulic unit without simplifications. The method accuracy is explained by taking into account the spatial thermal component. The heat transfer coefficient determined by this method in the pole-to-pole connections area was ~250 W/(m2·K). Using FEM, mathematical modeling of the thermal stress state of pole-to-pole connections was carried out, taking into account mechanical and thermal factors. This made it possible to design the improved connection structure with additional fastening elements, which make it possible to reduce the displacement to 0.03 mm, and the stress to 53 MPa at the rotor rotation frequency of 880 rpm. This design makes it possible to enable reliable operation of the hydraulic unit under the condition of increasing the rotor rotation frequency to overspeed with disconnected combinatorial dependence, provided that the actual stresses are 0.95 % of the material yield strength. The convergence of the values obtained by the proposed method and by the HSS method exceeded 99 %. The practical result is the proposals for the hydraulic generator design modernization

A review of recent advances in drug loading, mathematical modeling and applications of hydrogel drug delivery systems

A review of recent advances in drug loading, mathematical modeling and applications of hydrogel drug delivery systems

МОДЕЛЬ ОПТИМІЗАЦІЇ ФУНКЦІОНУВАННЯ МІКРОМЕРЕЖІ З СЕС ТА УСТАНОВКОЮ ЗБЕРІГАННЯ ЕНЕРГІЇ

The article provides a description of the microgrid function optimization model for solving the problem of reducing the cost of electricity purchases by the owner of such a microgrid on the retail electricity market. The objective function of minimizing the cost of electricity purchase has been formalized. Approaches to determining the coefficients of penalty functions designed to cut off technically unacceptable modes of the microgrid have been determined. A mathematical model of an energy storage system (ESS) is proposed, in which the functions of calculating the technological costs of electricity are formalized. A system of constraints for the problem of minimization of the cost of electricity purchase is given. Approaches to solving the problem of evaluating the effect of SPP and ESS operation in microgrids using optimization results are determined. Examples of microgrid operation optimization for an enterprise with its own SPP and ESS are presented. The need for additional control of the economic expediency of involving ESS in the regulation of electricity balances at the enterprise was noted. References 17, figures 3, table 1.