Mathematical Model Research Articles

NONLINEAR DYNAMICS METHODS APPLICATIONS TO PRODUCT LIFECYCLE MANAGEMENT

The research being carried out is aimed at applying nonlinear dynamics methods in product life cycle management to improve communication between processes and achieve environmental sustainability. The purpose of the article is to create a nonlinear mathematical model for analysing product lifecycle management. Chaotic nonlinear dynamical processes of product lifecycle are deterministic but have the property that even small uncertainties in initial conditions lead to exponentially growing errors in the management that limit long-term forecasts. The emergence of chaotic behaviour in processes of product lifecycle was explored, focusing on fluctuations. The study employed methods such as systems analysis, correlation analysis, nonlinear dynamics, and the Surrogate model of chaotic Lorenz waterwheel. It was identified that sharp technological innovations as the primary drivers of short-term fluctuations impacting fixed efficiency and effectiveness of product life cycle process development. The resulting nonlinear dynamic model allowed for flexible operation, transitioning between equilibrium, periodic, and chaotic states based on coefficient values for asset growth rates and time constants reflecting product life cycle process dynamics. The research results are valuable for companies seeking to reduce their environmental impact and implement circular economy principles.

NON-ANALYTICAL DESIGN OF THE PI CONTROLLER OPTIMAL PARAMETERS FOR A CONTINUOUS LINE

The multiple motor drives are complex and coupled MIMO nonlinear systems. Due to the complexity of their mathematical models the development of effective control systems is quite complicated task. This paper presents the design of optimal control based on the quadratic optimality criterion for the central section of the continuous production line using soft computer methods when fuzzy model of the controlled system has been used. In this case, the proposed method demonstrates non-analytical design of the optimal parameters of PI controller with emphasis on minimal knowledge on the controlled system. The realized experimental measurements on a continuous line laboratory model confirmed the effectiveness and the good dynamic properties of the optimal continuous line controller and also its applicability to others MIMO nonlinear dynamic systems.

Mathematical Modeling and Analysis of the Freezing Process of Drainage Channels in Cold Region Tunnels

Mathematical Modeling and Analysis of the Freezing Process of Drainage Channels in Cold Region Tunnels

A mathematical model to study low-dose metronomic scheduling for chemotherapy

Metronomic chemotherapy refers to the frequent administration of chemotherapeutic agents at a lower dose and presents an attractive alternative to conventional chemotherapy with encouraging response rates. However, the schedule of the therapy, including the dosage of the drug, is usually based on empiricism. The confounding effects of tumor-endothelial-immune interactions during metronomic administration of drugs have not yet been explored in detail, resulting in an incomplete assessment of drug dose and frequency evaluations. The present study aimed to gain a mechanistic understanding of different actions of metronomic chemotherapy using a mathematical model. We have established an analytical condition for determining the dosage and frequency of the drug depending on its clearance rate for complete tumor elimination. The model also brings forward the immune-mediated clearance of the tumor during the metronomic administration of the chemotherapeutic agent. The results from the global sensitivity analysis showed an increase in the sensitivity of drug and immune-mediated killing factors toward the tumor population during metronomic scheduling. Our results emphasize metronomic scheduling over the maximum tolerated dose (MTD) and define a model-based approach for approximating the optimal schedule of drug administration to eliminate tumors while minimizing harm to the immune cells and the patient’s body.

Prediction of external corrosion rate for buried oil and gas pipelines: a novel deep learning with DNN and attention mechanism method

Buried pipelines is easily subjected to external corrosion affected by complex underground environment, such as soil resistivity, pH, dissolved ion concentration, water content and coatings condition. Therefore, external corrosion rate prediction is essential to ensure pipelines intrinsic safety. Generally numerous researches focused on mathematical models and degradation analysis are limited to considering comprehensive corrosion factors. In this work, a novel proposed deep learning method involves a deep neural network (DNN) and attention mechanism which has good robust generalization ability. DNN was used to predict external corrosion rate of buried pipelines with extracting corrosion characteristics data, and attention mechanism is carried on weighting operations of corrosion factors furtherly. The results show that main controlling factors are pipeline age and soil bulk density, sulfate ion concentration and redox potential have less effect by analyzing external corrosion factors dataset, and data reduction and standardization of DNN-attention mechanism model are carried out. The external corrosion rate value predicted by the DNN-attention mechanism model is the closest prediction with the real truth, which the evaluation index root mean square error (RMSE) is 0.0064, and prediction accuracy is 91.91% compared with convolutional neural network (CNN), CNN-residual, DNN. It proves that it is reasonable to use DNN-attention mechanism to predict the pipeline corrosion rate by using publicly pipeline corrosion dataset.

A nonlocal photoacoustic effect with variable thermal conductivity of semiconductor material subjected to laser heat source

This study explores the behavior of laser-exposed photo-excited carriers, investigating the propagation of photoacoustic waves in the thermoelastic domain. It also delves into the theoretical generation of surface acoustic waves in semiconductors through photo-thermoelastic processes. The research considers the interaction between thermomechanical and acoustic waves in a nonlocal medium with temperature-dependent thermal conductivity. Unlike relying on electron–phonon or electron-hole thermalization processes, photoacoustic waves here result from thermoelastic stress induced by the laser-induced temperature increase. The investigation accounts for the optical, mechanical, and thermoelastic properties of nanoscale semiconductor materials. Predictions of photoacoustic signals are derived by solving a combined thermal diffusion issue and a thermoelastic problem, using Laplace and Fourier transforms in the mathematical model. Numerical solutions encompass various physical fields within the time domain using the inversion technique of Laplace and Fourier transforms, such as thermal, acoustic, mechanical, and carrier density diffusion. The study evaluates and compares the influences of thermal memory and thermal conductivity presenting visual representations.

Radiation Dose-Volume-Response Relationships for Adverse Events in Childhood Cancer Survivors: Introduction to the Scientific Issues in PENTEC

At its very core, radiation oncology involves a trade-off between the benefits and risks of exposing tumors and normal tissue to relatively high doses of ionizing radiation. This trade-off is particularly critical in childhood cancer survivors (CCS), in whom both benefits and risks can be hugely consequential due to the long life expectancy if the primary cancer is controlled. Estimating the normal tissue-related risks of a specific radiation therapy plan in an individual patient relies on predictive mathematical modeling of empirical data on adverse events. The Pediatric Normal-Tissue Effects in the Clinic (PENTEC) collaborative network was formed to summarize and, when possible, to synthesize dose-volume-response relationships for a range of adverse events incident in CCS based on the literature. Normal-tissue clinical radiation biology in children is particularly challenging for many reasons: (1) Childhood malignancies are relatively uncommon-constituting approximately 1% of new incident cancers in the United States-and biologically heterogeneous, leading to many small series in the literature and large variability within and between series. This creates challenges in synthesizing data across series. (2) CCS are at an elevated risk for a range of adverse health events that are not specific to radiation therapy. Thus, excess relative or absolute risk compared with a reference population becomes the appropriate metric. (3) Various study designs and quantities to express risk are found in the literature, and these are summarized. (4) Adverse effects in CCS often occur 30, 50, or more years after therapy. This limits the information content of series with even very extended follow-up, and lifetime risk estimates are typically extrapolations that become dependent on the mathematical model used. (5) The long latent period means that retrospective dosimetry is required, as individual computed tomography-based radiation therapy plans gradually became available after 1980. (6) Many individual patient-level factors affect outcomes, including age at exposure, attained age, lifestyle exposures, health behaviors, other treatment modalities, dose, fractionation, and dose distribution. (7) Prospective databases with individual patient-level data and radiation dosimetry are being built and will facilitate advances in dose-volume-response modeling. We discuss these challenges and attempts to overcome them in the setting of PENTEC.

Optimising power of PV module using modified MPPT for standalone load

The maximum power point tracking (MPPT) has been common terminology among the researchers for those who deal with solar energy. A lot of techniques involving MPPTs have been investigated, evolved and proposed by researchers. But those techniques have got some advantages and suffer from limitation to some extent. The gravity of limitations varies from case to case. In current work, it has been investigated the MPPT based Boost Converter without and with MPPT which is perturb and observe (P&O) type. After observing its limitation, this method of MPPT is modified so as to make it suitable for extracting the maximum power from PV unit at all different load conductance’s. In order to validate this concept, the mathematical model is developed using a MATLAB/Simulink environment and this Modified MPPT technique is implemented. The whole model is simulated and compared with conventional method. This concept is quite new and the proposed one exhibits better performance as compared to conventional methods.

Long-term performance analysis of operational efficiency of a grid-connected solar power plant under Mauritania climate

This work examines a solar power plant connected to the Nouakchott electricity grid in Mauritania. Operating since 2013, the 15 MWp plant's reliability and energy yield have been evaluated using a performance index. The assessment involves three phases. First, the plant's meteorological environment and technical indicators are presented. In the second phase, mathematical performance models specified by the International Energy Agency (IEA) are applied to calculate performance indices using data from the data acquisition system (SCADA). The third phase compares actual production data for 2015, 2017, and 2020 with results simulated for PVsyst for the same years. The obtained results are thoroughly analyzed to highlight relevant physical phenomena. The analysis focuses on the plant's 7-year operating period and its impact on performance indicators for electricity production fed into the grid. This study provides insights into the solar power plant's reliability and energy yield, aiding future operational enhancements. It underscores the importance of performance monitoring and assessment in optimizing solar power generation systems.

Review on Sanskrit Sandhi Splitting using Deep Learning Techniques

A procedure called sandhi is used in Sanskrit to join short words (morphemes) to create compound words. A composite word are broken down into their component morphemes by a process known as sandhi splitting. This study focuses on several performance technologies and methodologies used to perform the above operation on Sanskrit sentences. Various approaches were identified for the problem from the literature survey. Initial approaches involved use of Finite State Transducers. Earlier the approaches introduced to increase accuracy include use of mathematical models and various optimality theories. Graph based approaches and parser based techniques were introduced later. With the advancement of deep learning techniques Recurrent Neural Networks, Long-Short Term Memory models and Double decoder models were adopted which involved training machine learning models through neural networks and classifier algorithms. Bidirectional LSTM models with attention mechanism, transformer based models and large language models like BERT were the most recent methodologies adopted and proved to be of higher accuracy and performance.

Drone direction estimation: phase method with two-channel direction finder

This scientific article presents a block diagram of a two-channel radio direction finder that effectively uses the phase method to determine the direction of the signal source. The main attention is paid to the mathematical model of the formation of the cardioid radiation pattern of biconical antennas, which have unique directivity characteristics. These features significantly affect the accuracy and reliability of the bearing determination process. The developed algorithm aims to accurately determine the direction of motion of an unmanned aerial vehicle, especially in the context of a two-channel radio receiver and a five-element antenna system. This antenna system provides unique capabilities for increased resolution and directional accuracy. The article also touches on the issue of software implementation of the developed algorithm, which is aimed at increasing the number of generated bearing estimates in conditions of limited time for observing an unmanned aerial vehicle. Thus, the proposed method is of interest in the field of precision direction finding in the context of small unmanned vehicles.

Survival modelling of infectious human norovirus and surrogates for high-pressure inactivation in strawberry puree

Berries contaminated with human norovirus (HuNoV) have been frequently identified as a cause of foodborne gastroenteritis. To prevent virus transmission while preserving sensory and quality parameters, non-thermal treatments, such as high-pressure processing (HPP), can be applied to the berries and products thereof. Here, strawberry purees contaminated with HuNoV genogroup I (GI.3[P13]) and II (GII.4 Sydney [P16]), along with murine norovirus (MNV) and Tulane virus (TV) serving as surrogates, were exposed to HPP at several pressure-time combinations. Virus inactivation was assessed by cell culture, including the novel human intestinal enteroids (HIE) model for HuNoVs. The infectivity results showed TV more resistant than MNV to HPP, as also confirmed by kinetic mathematical modelling. Results indicated that a holding pressure of 450 MPa and an exposure time of ≥5 min are reliable operational conditions for HPP process to successfully control viral contamination. In addition, the inactivation models deduced from MNV and TV viruses were challenged with experimental HuNoV GII.4 infectivity resulting in bias factors <1 for all treatment conditions. This finding validates the proposed models for the conservative estimation of HuNoV inactivation. Our work offers a blueprint for moving forward with inactivation studies using the HIE system, which provides useful practical information on optimum treatments for the best public health outcomes.

Speed control for traction motor of urban electrified train in field weakening region based on backstepping method

Tractor motors always operate in the speed region higher than rated speed, but is limited to the module of the stator current, stator voltage vectors. Additionally, mathematical model of traction motor has shown nonlinearity through the product of the state variables 𝑖𝑠𝑑, 𝑖𝑠𝑞 with the input variable 𝜔𝑠:𝜔𝑠𝑖𝑠𝑞, 𝜔𝑠𝑖𝑠𝑑. Therefore, this paper focuses on the study of speed control of traction motors in weakening field region while optimizing torque control, and choosing the backstepping method in designing speed–flux controller in order to solve the nonlinear structure. The simulation results of the responses: speed, torque, power, and flux performed on MATLAB/Simulink software with parameters collected from metro Nhon-Hanoi Station, Vietnam have proven the correctness in theoretical research.

A deterministic mathematical model with non-linear least squares method for investigating the transmission dynamics of lumpy skin disease

Lumpy skin disease (LSD) is an economically significant viral disease of cattle caused by the lumpy disease virus (LSDV) which is primarily spread mechanically by blood feeding vectors such as particular species in flies, mosquitoes and ticks. Despite efforts to control its spread, LSD has been expanding geographically, posing challenges for effective control measures. This study develops a Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) model that incorporates cattle and vector populations to investigate LSD transmission dynamics. The model considers the waning rate of natural active immunity in recovered cattle, disease-induced mortality, and the biting rate. Using a standard dynamical system approach, we conducted a qualitative analysis of the model, defining the invariant region, establishing conditions for solution positivity, computing the basic reproduction number, and examining the stability of disease-free and endemic equilibria. We employ a non-linear least squares method for model calibration, fitting it to a synthetic dataset. We subsequently test it with actual infectious cases data. Results from the calibration and testing phases demonstrate the model’s validity and reliability for diverse settings. Local and global sensitivity analyses were conducted to determine the model’s robustness to parameter values. The biting rate emerged as the most significant parameter, followed by the probabilities of infection from either population and the recovery rate. Additionally, the waning rate of LSD infection-induced immunity gained positive significance in LSD prevalence from the beginning of the infectious period onward. Simulation results suggest reducing the biting rate as the most effective LSD control measure, which can be achieved by applying vector repellents in cattle farms/herds, thereby mitigating the disease’s prevalence in both cattle and vector populations and reducing the chances of infection from either population. Furthermore, measures aiming to boost LSD infection-induced immunity upon recovery are recommended to preserve the immune systems of the cattle population.

From Nash Q-learning to nash-MADDPG: Advancements in multiagent control for multiproduct flexible manufacturing systems

The emergence of flexible manufacturing systems (FMS) capable of processing multiple product types is a result of the growing demand for product customization and personalization. Such multiproduct systems are characterized by a higher level of uncertainty and variability when compared to traditional manufacturing systems. This paper proposes a Nash integrated multiagent deep deterministic policy gradient method (Nash-MADDPG) to control the mobile robots’ assignment in a multiproduct FMS to enable intelligent decision-making, interaction, and dynamic learning capabilities. A mathematical model of a multiproduct FMS from a previous study is described, and system dynamic property is characterized by permanent production loss (PPL). Then, by observing PPL of the system and market demand for each product type, the multi-agent control scheme is developed to assign mobile robots to load/unload various product types at various machines. First, a Nash game is developed among the mobile robots and to improve the cooperation, a collaboration cost is defined. This collaboration cost is then used in the reward function of the multiagent deep deterministic policy gradient (MADDPG) algorithm. Second, the actions are jointly defined based on the action values of MADDPG, and the mobile robots’ strategies in the Nash game, which update the environment to a new state. The performance of the proposed method is verified by comparing it with conventional Nash Q-learning, vanilla MADDPG, Q-learning based single agent reinforcement learning (SARL) and a first-come-first-serve (FCFS) based control. The results demonstrate that the multi-agent control scheme under the proposed Nash-MADDPG is effective in dealing with cooperative FMS environment that involves complicated dynamics and uncertainties.

NUMERICAL TREATMENT OF LINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATIONS USING VARIATIONAL ITERATION ALGORITHM WITH COLLOCATION

To numerically solve the linear Volterra integro-differential equation, this study employs fourth-kind Chebyshev polynomials and the variational iteration algorithm with collocation, which is a combination of the variational iteration strategy and collocation technique. By applying fourth-kind Chebyshev polynomials to the variational iteration method with collocation for solving Volterra integro-differential equations, mathematical problems with a broad range of multidisciplinary applications are addressed, and numerical techniques that produce more accurate and efficient results are developed. The recommended method is then used, and the fourth-kind Chebyshev polynomials generated for the given integro-differential equation serve as the trial functions for the approximation. As a result, the suggested method's significance probably goes beyond a particular equation or application, as it contributes to the larger field of mathematical modeling and numerical analysis. Research methods employing a variational iteration algorithm with collocation aim to provide general techniques that can be applied to a wide range of problems. Additionally, numerical examples were provided to highlight the applicability and dependability of the proposed methodology. The mathematical computations were carried out using the Maple 18 software.

An innovative dry-lab test rig for mechanical-hydraulic power take-off of wave energy conversion system

A dry-lab test rig is a powerful means to reduce costs in the design process of a wave energy conversion system (WECs). A dry-lab test rig technique allows the use of real components inside a simulation of a mathematical model. This paper presents the development of an innovative dry-lab test rig for the mechanicalhydraulic power take-off (MHPTO) unit of WECs. The development of a drylab test rig of MHPTO involves several processes, such as three-dimension (3D) modelling, component purchasing, structure fabrication, component installation, and operational testing. The developed dry-lab test rig consists of two main parts, such as the simulated wave emulator plant and the real MHPTO unit plant. The simulated wave emulator plant was developed in this test rig to replicate the interaction motion between the ocean wave motion and the wave absorber device. The developed dry-lab test rig was tested using five different irregular wave input conditions to ensure it could perform under the five different wave input conditions. The overall results demonstrate that the developed dry-lab test rig was successfully performed in all sea states. From the results, the profile of electrical power produced by the real MHPTO unit can be clearly obtained in each sea state.

A Multi-Stage Framework for Coordinated Scheduling of Networked Microgrids in Active Distribution Systems Considering Economic and Environmental Impact of Hydrogen Refueling and Charging Stations

Due to the increase in electric energy consumption and the significant growth in the number of electric vehicles (EV) at the level of the distribution network, new networks have started using new fuels such as hydrogen to improve environmental indicators and at the same time better efficiency from the excess capacity of renewable resources. In this article, the services that can be provided by hydrogen refueling stations and charging electric vehicles in the optimal performance of microgrids have been investigated. The model proposed in this paper includes a two-stage stochastic framework for scheduling resources in microgrids, especially hydrogen refueling stations and electric vehicle charging. In this model, two main goals of cost minimization and greenhouse gas emissions are considered. In the proposed framework and in the first stage, the service range of microgrids is determined precisely according to the electrical limitations of distribution systems in emergency situations. Then, in the second stage, the problem of energy management in each microgrid will be solved centrally. In this situation, various indicators including the output energy of renewable sources, smart charging of hydrogen and electric vehicle charging stations (EV/FCV) and flexible loads (FL) are evaluated. The final mathematical model is implemented as a multivariate integer multiple linear problem (MILP) using the GUROBI solver in GAMS software. The simulation results on the modified IEEE 118-Bus network show the positive effect of the presence of flexible loads and smart charging strategies by charging stations. Also, the numerical derivation shows that the operating costs of the entire system can be reduced by 4.77% and the use of smart charging strategies can reduce greenhouse gas emissions by 49.13%.

DSFworld: A flexible and precise tool to analyze differential scanning fluorimetry data.

Differential scanning fluorimetry (DSF) is a method to determine the apparent melting temperature (Tma) of a purified protein. In DSF, the raw unfolding curves from which Tma is calculated vary widely in shape and complexity. However, the tools available for calculating Tma are only compatible with the simplest of DSF curves, hindering many otherwise straightforward applications of the technology. To overcome this limitation, we designed new mathematical models for Tma calculation that accommodate common forms of variation in DSF curves, including the number of transitions, the presence of high initial signal, and temperature-dependent signal decay. When tested these models against DSFbase, an open-source database of 6235 raw, real-life DSF curves, these models outperformed the existing standard approaches of sigmoid fitting and maximum of the first derivative. To make these models accessible, we created an open-source software and website, DSFworld (https://gestwickilab.shinyapps.io/dsfworld/). In addition to these improved fitting capabilities, DSFworld also includes features that overcome the practical limitations of many analysis workflows, including automatic reformatting of raw data exported from common qPCR instruments, labeling of data based on experimental variables, and flexible interactive plotting. We hope that DSFworld will enable more streamlined and accurate calculation of Tma values for DSF experiments.

A Mamdani fuzzy inference system with trapezoidal membership functions for investigating fishery production

Seas, marine ecosystems, and coastal regions are crucial components of our environment. Numerous scientific strategies have been adopted to boost fisheries and aquaculture productivity. This study proposes a fuzzy-logic-based model to produce fisheries in India, which ranks fourth worldwide for fisheries production. Five input variables, such as fish seed, export, post-harvesting, released fund, and temperature, are considered inputs, and the production of fisheries is taken as the output variable. A Mamdani-type fuzzy inference system with trapezoidal membership functions is prepared with 243 rules in the IF-THEN format. This mathematical model investigates the impacts of input parameters on the production of Indian fisheries. We fit the model with the real-world data and show that fish seed, export, released fund, and post-harvesting facilities positively impact fisheries production. However, a very high temperature is unsuitable for high production, even if all other parameters lie at their desired level.