Dynamic Mathematical Model Research Articles

Renewable energy sources integration via machine learning modelling: A systematic literature review

The use of renewable energy sources (RESs) at the distribution level has become increasingly appealing in terms of costs and technology, expecting a massive diffusion in the near future and placing several challenges to the power grid. Since RESs depend on stochastic energy sources —solar radiation, temperature and wind speed, among others— they introduce a high level of uncertainty to the grid, leading to power imbalance and deteriorating the network stability. In this scenario, managing and forecasting RES uncertainty is vital to successfully integrate them into the power grids. Traditionally, physical- and statistical-based models have been used to predict RES power outputs. Nevertheless, the former are computationally expensive since they rely on solving complex mathematical models of the atmospheric dynamics, whereas the latter usually consider linear models, preventing them from addressing challenging forecasting scenarios. In recent years, the advances in machine learning techniques, which can learn from historical data, allowing the analysis of large-scale datasets either under non-uniform characteristics or noisy data, have provided researchers with powerful data-driven tools that can outperform traditional methods. In this paper, a systematic literature review is conducted to identify the most widely used machine learning-based approaches to forecast RES power outputs. The results show that deep artificial neural networks, especially long-short term memory networks, which can accurately model the autoregressive nature of RES power output, and ensemble strategies, which allow successfully handling large amounts of highly fluctuating data, are the best suited ones. In addition, the most promising results of integrating the forecasted output into decision-making problems, such as unit commitment, to address economic, operational and managerial grid challenges are discussed, and solid directions for future research are provided.

Study of dynamics of the turning process in pneumechanical spinning in the presence of false torsion

The paper presents the results of a study of the dynamics of the process of torsion of yarn of pneumomechanical spinning in the presence of false torsion. Dynamic mathematical models of the process of torsion of yarn of pneumomechanical spinning in the presence of false torsion in unsteady modes of starting and stopping the forming-twisting device are constructed. By now, the question of yarn twisting in a transient mode of operation in rotor spinning remains unexplored. We have here made an attempt to fill the indicated gap by constructing mathematical models of a forming-twisting device during torsion. In connection with the above-mentioned problem arises to systematize the accumulated information on new methods of forming yarn and constructions of forming and torque devices, to clarify a number of questions of theory and technology, and also to classify methods of forming yarn. The main direction of development of new methods of yarn formation remains the improvement of the high-speed modes of the working organs and, above all, of the forming and turning devices, which raises a number of important problems of both technological and structural nature.

Design and Performance Research of a Novel Iron-Core Permanent Magnet Compensated Pulsed Alternator With Segmental Squirrel-Cage

Compensated pulsed alternator (CPA) can realize transient high current discharge by compressing magnetic field through compensating element, which has important application in pulse power field. The compen- sation shield and short circuit compensation winding are usually used as compensation elements, but the local compensation effect will be affected by the opposite eddy currents or conductor currents under other poles at maximum discharge time. To solve this problem, a novel iron-core permanent magnet CPA (PMCPA) with segmental squirrel-cage is proposed in this paper. At the time of maximum discharge, the bars' current of each segmental squirrel-cage segment will not be affected the bars' currents in opposite direction of other segments, which has better local compensation effect. In addition, the permanent magnet (PM) excitation eliminates the brush and slip ring and improves the reliability of operation. First, the design basis and scheme of the PMCPA are introduced. Second, the dynamic mathematical model of the PMCPA is presented. Third, the finite-element model of the PMCPA is established to analyse. Fourth, the prototype is manufact- ured to test and validate. Through analysis and verification, the superiority of segmental squirrel-cage compensation is proved, which provides a new idea for the optimization and development of compensation elements.

A dynamical behavior of the coupled Broer-Kaup-Kupershmidt equation using two efficient analytical techniques.

The aim of the present study is to identify multiple soliton solutions to the nonlinear coupled Broer-Kaup-Kupershmidt (BKK) system, including beta, conformable, local-fractional, and M-truncated derivatives. The coupled Broer-Kaup-Kupershmidt system is employed for modelling nonlinear wave evolution in mathematical models of fluid dynamics, plasmic, optical, dispersive, and nonlinear long-gravity waves. The travelling wave solutions to the above model are found using the Unified and generalised Bernoulli sub-ODE techniques. By modifying certain parameter values, we may create bright soliton, squeezed bell-shaped wave, expanded v-shaped soliton, W-shaped wave, singular soliton, and periodic solutions. The four distinct kinds of derivatives are compared quite effectively using 2D line graphs. Also, contour plots and 3D graphics are given by using Mathematica 10. Lastly, any pair of propagating wave solutions has symmetrical geometrical forms.

A brief overview of mathematical modeling of the within-host dynamics of Mycobacterium tuberculosis

Tuberculosis (TB), a disease caused by bacteria Mycobacterium tuberculosis (Mtb), remains one of the major infectious diseases of humans with 10 million TB cases and 1.5 million deaths due to TB worldwide yearly. Upon exposure of a new host to Mtb, bacteria typically infect one local site in the lung, but over time, Mtb disseminates in the lung and in some cases to extrapulmonary sites. The contribution of various host components such as immune cells to Mtb dynamics in the lung, its dissemination in the lung and outside of the lung, remains incompletely understood. Here we overview different types of mathematical models used to gain insights in within-host dynamics of Mtb; these include models based on ordinary or partial differential equations (ODEs and PDEs), stochastic simulation models based on ODEs, agent-based models (ABMs), and hybrid models (ODE-based models linked to ABMs). We illustrate results from several of such models and identify areas for future resesarch.

Synthesis of a measurement procedure for estimating the orientation of a small unmanned aerial vehicle under conditions of changing status of measurement results

The problem of processing measurement information with changing status of measurement results of micromechanical sensors of an intelligent on-board measuring system of a small unmanned aerial vehicle is considered. While vehicle is in the air, the measurement results status changes from confirmed to orienting, for example, due to sensor defects, degradation of the measuring channel, the appearance of false measurement output signals of micromechanical sensors due to vibrations and shocks caused by the movement of air masses. As a result, the probability of stability loss of a small unmanned aerial vehicle increases and it is necessary to raise the accuracy of estimating its orientation in conditions of changing status of measurement results. The measuring procedure of the Kalman structure is considered, the equations of which are determined with accuracy to the parameters of the transition and noise matrices of the state, as well as the perturbation vector, characterizing the measuring process. The parameter values are determined by a mathematical model for converting measuring information based on a dynamic mathematical model, which distinguishes the developed measuring procedure from a measuring procedure with a classical transition matrix. A neural network is used to find unknown parameters. A multilayer perceptron was selected as the basis of a neural network, for which an error back propagation algorithm is used to train. Based on the results of mathematical modeling and measurement experiment, it was found that the accuracy of the synthesized measuring procedure based on a dynamic mathematical model is higher than the accuracy of the measuring procedure of the Kalman structure with a classical transition matrix. The results of the study will be useful in the development of intelligent measurement procedures for on-board measurement systems operating under conditions of changing status of measurement results

Mathematical analysis and modeling of fractional order human brain information dynamics including the major effect on sensory memory

Mathematical analysis and modeling of fractional order human brain information dynamics including the major effect on sensory memory

Mathematical Modelling of Malaria Transmission Dynamics with Optimal Control Strategies in Kebri Dehar District, Somali Regional State, Ethiopia

Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female anopheles mosquito. In this study, we present a mathematical model of malaria transmission dynamics with optimal control. We estimated the basic reproduction number for the infected cases in Kebri Dehar district from September 2011 - June 2015 E.C is . The parameters of the model are estimated by using the confirmed malaria cases of Kebri Dehar district, Ethiopia. We formulated the model for malaria and present its dynamics in details. Initially, we present the basic mathematical results and then show briefly the stability results for the model. Further, we formulate an optimal control problem with control functions and obtain the optimal control characterization. The optimal control problem is solved numerically and the results comprised of controls system for different strategies. The controls such as prevention, treatment and insecticide could use the best role in the disease eradication from the community. Our results suggest that the prevention of humans from the mosquitoes, treatment of infected humans and the insecticide spray on mosquitoes can significantly reduce the infection of malaria and may reduce further spread of infection in the community.

Analysis of Age-Structured Mathematical Model of Malaria Transmission Dynamics via Classical and ABC Fractional Operators

Malaria is a complex disease with many factors influencing the transmission dynamics, including age. This research analyzes the transmission dynamics of malaria by developing an age-structured mathematical model using the classical integer order and Atangana–Baleanu–Caputo fractional operators. The analysis of the model focused on several important aspects. The existence and uniqueness of solutions of fractional order were explored based on some fixed-point theorems,such as Banach and Krasnoselski. The Positivity and boundedness of the solutions were also investigated. Furthermore, through mathematical analysis techniques, we analyzed different types of stability results, and the results showed that the disease-free equilibrium point of the model is proved to be both locally and globally asymptotically stable if the basic reproduction number is less than one, whereas the endemic equilibrium point of the model is both locally and globally asymptotically stable if the basic reproduction number is greater than one. The findings from the sensitivity analysis revealed that the most sensitive parameters, essential for controlling or eliminating malaria are mosquito biting rate, density-dependent natural mortality rate, clinical recovery rate, and recruitment rate for mosquitoes. Numerical simulations are also performed to examine the behavior of the model for different values of the fractional-order alpha,and the result revealed that as the value α reduces from 1, the spread of the endemic grows slower. By incorporating these findings, this research helps to clarify the dynamics of malaria and provides information on how to create efficient control measures.

P148 Longitudinal single-cell data informs deterministic modelling of inflammatory bowel disease

Abstract Background Crucial contributions to our understanding of the inflammatory process in inflammatory bowel disease (IBD) have been made using single cell level approaches. Extracting mechanistic details of cell and gene dynamics would be critical to understanding the mechanisms mediating mucosal healing and predicting response to specific therapies. However, this remains challenging. Therefore, our aim was to use ordinary differential equations (ODEs) for mathematical modelling of cell abundance and prediction of biological processes in IBD. Methods We used mathematical modelling of published longitudinal single-cell mRNA sequencing (scRNA-seq) data from DSS colitis in mice to simulate cellular dynamics during IBD. We validated our predictions using pseudo-bulk gene expression analysis and flow cytometry. We also analysed a published microarray dataset from colonic biopsies of 51 IBD patients prior to infliximab treatment. Results Based on the scRNA-seq data, we used our mathematical model to predict the immune dynamics of a different mouse colitis protocol. We validated these predictions experimentally using flow cytometry and found good agreement between model simulation and experimental data (predicted vs. observed, Pearson's rho=0.92). We found that the estimated turnover rates predicted the protein level of the proliferation marker KI-67 (rho=0.88) in DSS colitis. Finally, we wanted to investigate whether our mathematical model reflected processes in human IBD. We reasoned that genes correlated with epithelial cell dynamics might be indicative of mucosal healing after DSS retrieval. We found more highly correlated genes when using simulated epithelial abundance compared to experimentally measured epithelial abundance. Many genes associated with tight junctions (Cldn8, Cftr, Crb3, Jam2) were among the highly positively correlated genes and genes associated with inflammation (Il1b, Jak2, Il10ra) were among the negatively correlated genes with epithelial cell abundance. We then looked for differentially expressed (DE) genes in pre-treatment colon biopsies between responders and non-responders to infliximab. We found a significant overlap of 25 positively correlated genes with upregulated DE genes in responders, i.e. associated with tight junctions, and 73 negatively correlated genes with upregulated genes in non-responders, i.e. associated with inflammatory pathways. Conclusion We demonstrate that mathematical modelling of colonic cell dynamics provides insight into IBD progression and treatment response. Furthermore, our results suggest that pre-treatment barrier integrity may predict and influence response to infliximab treatment.

Desorbent swing adsorption process using ethylene to separate propane and propylene under isobaric conditions

The separation of olefin and paraffin using adsorption technology remains a significant challenge. This study proposes a novel desorbent swing adsorption (DSA) process using an olefin desorbent with a weaker adsorption affinity (C2: ethylene) to separate a paraffin/olefin mixture with a higher adsorption affinity (C3s: propane and propylene) under isobaric conditions, which is the reverse concept of using a desorbent with a stronger affinity in conventional DSA systems. The proposed DSA process effectively separates the C3 mixture because the deteriorating effects caused by the desorbent is minimized. Based on sequential breakthrough experiments with zeolite 13X DSA using ethylene, the efficient separation of a propylene dehydrogenation product (propane:propylene = 60:40 vol%) to produce polymer-grade propylene is achieved. It is confirmed that ethylene desorbent stream pushes out the adsorbed propylene and regenerates the adsorption bed without changing the pressure. The desorption step plays a key role in the separation performance of the proposed DSA process because the regenerated bed offers favorable conditions when filled with the weaker desorbent after the desorption step. The flowrate of the desorbent strongly affects the efficiency of propylene desorption. After validating the dynamic mathematical model using the experimental results, a two-bed DSA process using a six-step sequence that includes rinse export/import and idle steps is shown to achieve a propylene purity above 99.999 % (desorbent-free basis) with a recovery of 99.39 %, a productivity of 4.21 mol∙kg−1∙hr−1, and an ethylene usage of 7.59 mol∙kg−1∙hr−1. This study offers important insights into the development of adsorptive separation designs for olefin/paraffin separation.

Method of Localization of Spatiotemporal Patterns on the Time Sequence of Biomedical Images

A method has been developed for localizing spatiotemporal patterns observed in sequentially recorded biomedical images of laser scanning microscopy and reflecting the dynamics of the biological structures under study. By means of interpolation by radial basis functions of each individual image, a compact mathematical model of the space-time dynamics of the brightness function on a sequence of images is obtained. The subsequent localization of the structures of the sought-for dynamic patterns is carried out by means of the mathematical apparatus of singular spectral analysis. The results of experiments on optical visualization of the activity patterns of the olfactory bulb of a macrosmatic (rat) confirmed the efficiency of the developed method for localizing the reaction to biomarkers of human oncological diseases.

Modeling and simulation analysis of a novel proportional water flow valve with a digital pilot stage

The position straightness of the hydraulic supports is the key factor to the intelligent fully mechanized mining, and the adjacent cylinder is the actuator used to pull the hydraulic support. However, the control component of the adjacent cylinder is electromagnetic on/off valve that cannot control the movement of adjacent cylinder proportionally. Therefore, a novel proportional water flow valve with a digital pilot stage is proposed to control the trajectory of adjacent cylinder precisely. The novel valve consists of a dual active cartridge main valve and a digital pilot valve that includes a high speed on/off valve A (HSV-A) and a throttle valve piloted by the high speed on/off valve B (HV-B). A coupling dynamic mathematical model of the flow valve is formulated and the dynamic characteristics of the valve is analyzed theoretically. The fluctuation of the throttle valve and main spool motion is also analytically calculated. In addition, the influences of the control parameters and key structural parameters on the throttle valve and the main valve's motion are analyzed on the basis of AMESim simulation respectively. The simulation results have demonstrated that the displacement fluctuation of the valve can be reduced by increasing the control frequency. The throttle valve closed-loop displacement fluctuation is about 0.2 mm and 0.1 mm when the control frequency is 100 Hz and 200 Hz. What's more, decreasing the main valve orifice diameter can also effectively lower the main valve displacement fluctuation, while it will diminish the main valve response speed at the same time.

Soft-sensor estimation via parameter fitting and dynamic optimization in an experimental batch butadiene homopolymerization reactor

In this work, we address modeling and experimental tasks to develop an industrial process for the anionic polymerization of butadiene, which is a key compound used in the production of high-performance tires. The aim of this study was to determine the processing conditions that lead to the efficient manufacturing of polybutadiene. Accordingly, an experimental polymer reaction facility was constructed to record both butadiene conversion and temperature profiles. A first-principles dynamic mathematical model was developed to track the measurement variables as best as possible. To improve the tracking of recorded variables, some process variables were deployed as manipulated variables. Because good experimental tracking was not acceptable, we used the soft-sensor approach to estimate some additional degrees of freedom. The estimation task was performed by describing the problem as a dynamic optimization problem. The results clearly show that the optimization and control tasks of butadiene polymerization reaction facilities are demanding and require good experimental information to develop reliable mathematical models that can be leveraged to speed up the development of such industrial polymerization systems.

Mathematical modeling of fluid dynamics in invitro gut fermentation systems: A new tool to improve the interpretation of microbial metabolism.

In vitro systems are widely employed to assess the impact of dietary compounds on the gut microbiota and their conversion into beneficial bacterial metabolites. However, the complex fluid dynamics and multi-segmented nature of these systems can complicate the comprehensive analysis of dietary compound fate, potentially confounding physical dilution or washout with microbial catabolism. In this study, we developed fluid dynamics models based on sets of ordinary differential equations to simulate the behavior of an inert compound within two commonly used invitro systems: the continuous two-stage PolyFermS system and the semi-continuous multi-segmented SHIME® system as well as into various declinations of those systems. The models were validated by investigating the fate of blue dextran, demonstrating excellent agreement between experimental and modeling data (with r2 values ranging from 0.996 to 0.86 for different approaches). As a proof of concept for the utility of fluid dynamics models in invitro system, we applied generated models to interpret metabolomic data of procyanidin A2 (ProA2) generated from the addition of proanthocyanidin (PAC)-rich cranberry extract to both the PolyFermS and SHIME® systems. The results suggested ProA2 degradation by the gut microbiota when compared to the modeling of an inert compound. Models of fluid dynamics developed in this study provide a foundation for comprehensive analysis of gut metabolic data in commonly utilized invitro PolyFermS and SHIME® bioreactor systems and can enable a more accurate understanding of the contribution of bacterial metabolism to the variability in the concentration of target metabolites.

Mathematical modelling of transmission dynamics of Marburg virus with effective quarantine approach

Marburg virus disease (MVD) is a severe infection with an extremely high fatality rate, spread through direct and indirect contact. Recently, there was an outbreak of the deadly MVD disease. We studied the transmission dynamics of MVD through the SEQIR model and determined the basic reproduction number, the local stability, and the global stability of the disease-free equilibrium. This study aims to mathematically model the transmission dynamics of MVD using an effective Quarantine Approach. Building upon existing research, the model introduces a quarantine compartment and analyses the disease-free equilibrium.The results indicate that quarantining exposed individuals effectively curb the transmission of MVD and prevents secondary infections. Additionally, the introduction of treatment in the model ensures the survival of patients. However, it is emphasized that further research is essential to develop specific treatments for MVD, as preventive measures alone may not be sufficient to control the disease's spread.

A dynamical mathematical model for crime evolution based on a compartmental system with interactions

We use data on imprisonment in Spain to fit a system of three ordinary differential equations that describes the temporal evolution of three different groups in the country: offenders that are not in prison, offenders that are in prison, and the rest of people. These remaining people are considered as susceptible, who may become offenders by their relationships. That is, crime is regarded to behave as a social epidemic. We first investigate the dynamics of the model to find out when criminality becomes extinct or endemic in the long run, depending on the basic reproduction number. Then, we estimate the parameters of the model and conduct a sensitivity analysis. Finally, a random error is incorporated, and nonlinear regression is carried out to gather the unexplained variability of the data. Our results report a satisfactory model fitting to the crime data, closely delineating their dynamics.

Research on dynamic calibration and compensation method of strain-gauge type force sensor

Purpose This paper aims to propose an effective dynamic calibration and compensation method to solve the problem that the statically calibrated force sensor would produce large dynamic errors when measuring dynamic signals. Design/methodology/approach The dynamic characteristics of the force sensor are analyzed by modal analysis and negative step dynamic force calibration test, and the dynamic mathematical model of the force sensor is identified based on a generalized least squares method with a special whitening filter. Then, a compensation unit is constructed to compensate the dynamic characteristics of the force measurement system, and the compensation effect is verified based on the step and knock excitation signals. Findings The dynamic characteristics of the force sensor obtained by modal analysis and dynamic calibration test are consistent, and the time and frequency domain characteristics of the identified dynamic mathematical model agree well with the actual measurement results. After dynamic compensation, the dynamic characteristics of the force sensor in the frequency domain are obviously improved, and the effective operating frequency band is widened from 500 Hz to 1,560 Hz. In addition, in the time domain, the rise time of the step response signal is reduced from 0.29 ms to 0.17 ms, and the overshoot decreases from 26.6% to 9.8%. Originality/value An effective dynamic calibration and compensation method is proposed in this paper, which can be used to improve the dynamic performance of the strain-gauge-type force sensor and reduce the dynamic measurement error of the force measurement system.

Mathematical Model of Impact Projectile Flight Dynamics as an Element of its Digital Twin

This paper gives the analysis of the structure and characteristics of the mathematical model of the impact projectile’s flight dynamics. The model is designed for being used as an element of the projectile’s digital twin. The model is based on differential motion equations of a gyro-stabilized solid with an axisymmetric mass distribution. Different types of angle variables were chosen for describing aerodynamics and formulating equations of motion. Non-linear (considering the nutation angle) dependences for aerodynamic coefficients are proposed. They are created by applying proven scientific concepts and research methods in aerodynamics of axisymmetric body and by comparing with known numerical and experimental results obtained in exterior ballistics of gyro-stabilized aviation and artillery projectiles. Special aspects of initial conditions for angles and angular velocity were also studied. Since the impact projectile is considered as an axially symmetric body, its self-rotation angle is not of practical inte rest. Using algebraic manipulations, the differential equation for this angle was eliminated from the set of equations. This has made it possible to significantly reduce stiff of the remaining system of differential equations. The Dormand-Prince method is recommended as a method of numerical integration. The method of the eight-order (with seventh-order uncertainty estimate) allows getting the high accurate solution of the differential equations set under relatively small computing costs. The model allows computing the projectile trajectory under various initial conditions, including the flight with high nutation angles up to 87°—89°. As a result, there is a possibility to determine the nature of the interaction between impact projectiles and typical targets (ricochet, surface effect, after-penetration effect) within a wide range of approach angles to the target’s surface (skin) unattainable during the full-scale tests. The possibility of solving similar problems allows to recommend the designed model as an element of the impact projectile’s digital twin intended for testing its exterior ballistics on the digital (virtual) test range. All testing calculations and final modeling were made by using the "GNU Octave" computational software package.

Methodology for the Synthesis of a Multicopter Controller Acting as a Swarm Agent using the Thermal Motion Equivalent Method

The paper is dedicated to the development of a method for the synthesis of the control system of a swarm multicopter. The motion of the agents in the swarm is organised by the thermal motion equivalent method. The idea of the method is the behavioral similarity of the thermal motion of the atoms by the agents. In the practical implementation of the thermal motion equivalent method, it is important to ensure constancy of velocity and isotropy of agent dynamics. Violating these properties will cause the swarm to fail a mission, such as an area exploration, by reducing the RMS speed of the agents to zero. The proposed solution to these problems is to synthesize a modal controller for the agent-boundaries test system for the slowest control channel, thereby ensuring RMS velocity constancy of the agent. The synthesized controller is used as a filter in the fast-acting channels, the second horizontal channel and the vertical channel. In the fast-acting channels, an additional filter is proposed to bring their dynamics to the slowest channel, thereby ensuring isotropy. The inclusion of a limit on the maximum length of the equivalent field vector ensures isotropy. The synthesis was carried out using a simplified multicopter dynamics mathematical model, obtained with small UAV deviations from the vertical and without considering the Coriolis force. The methodology for the synthesis of a multicopter control system for functioning as part of a swarm is developed using the obtained results. Numerical simulation results of both a single vehicle in closed space and a swarm using a more complete nonlinear dynamic quadcopter model are presented. The proposed method has the advantage of simple synthesis using a linear model. Numerical simulation results confirm the operability of the developed methodology.