Design Of Mathematical Model Research Articles

THEORETICAL CALCULATION AND EXPERIMENTAL TESTING OF IMPROVED BELT TRANSMISSION FOR COTTON CLEANING MACHINES

The article considers the object of belt transmission driving all the drums of the USK cotton[1]cleaning unit, most commonly used in the cleaning shop of cotton-cleaning plants, and theoretically calculates the improved design of belt transmission consisting of two pulleys and a belt. Traction power of belt and belt transmission according to experimental methods is characterized by dependence of belt relative slip and efficiency on transmission resistance coefficient. A mathematical model of new belt transmission design has been developed, which allows theoretical estimating of belt tensile strength and rational operating mode in elastic slipping zone; the design has been installed at the machinery of the cotton-cleaning plant, a part of unitary enterprise “Real Agro Cotton”. The results of the experiment were analyzed.

String stepped screen design and main parameters

Introduction. Obtaining energy is the most important problem of mankind. Coal-fired generation has solved, and will solve this problem in the foreseeable future due to its extensive resource base and relatively stable and low price. At the same time, the efficiency of the generating enterprises depends on the quality of the fuel supplied. For generating enterprises and domestic household using a layered method of burning fuel, it is very important to use high-grade coal, which increases the efficiency of their work. Obtaining high-grade coal, i.e. its separation by size classes is carried out by gravity screens. The advantages of the gravity screens are simple design and the absence of a drive during the sorting operation. Low sorting quality is the disadvantage. Therefore, the creation of new gravity screen designs and the development of existing ones to improve the sorting quality is of great importance. Methods of research. The Siberian Federal University has developed a design of a string stepped screen which uses a gravitational method of sorted material separation by size classes. To introduce it to industry, it is important to know the basic design parameters inherent in the proposed design. The article offers a mathematical model for calculating string stepped screen parameters and presents the results of calculating screen dimensions depending on other changing parameters. Mathematical modeling (construction of a mathematical calculation model) and analysis for string stepped screen design have been carried out to determine its basic parameters. Research results. A string stepped screen design is presented. A mathematical model for basic parameters calculation has been developed. Graphs have been constructed showing the dependence of the changing screen dimensions on other changing values. The string stepped screen design has been analysed. Conclusion. Based on the conducted research, a mathematical model for string stepped screen parameters calculation is constructed. The dependences of length and height on the front wall and screening section angles are constructed. The obtained dependences will allow to determine the string stepped screen parameters for the specified values of the screened material size.

Application of modular mathematical modeling in intelligent design of 3D digital substation

Abstract The construction of modular digital smart grid, as a result, the complexity of the power grid is increasing and new technologies and schemes are emerging, more sophisticated design means are needed. Therefore, the author puts forward the research on the intelligent design of three-dimensional digital substation. The emergence of 3D design has changed the status quo of difficult collaboration among multiple disciplines under the traditional design mode, and improved the level of substation design from the perspective of life-cycle management. Firstly, the characteristics of digital collaborative design are analyzed, the construction of 3D model library of equipment is explained, and the intelligent auxiliary control system of substation is described, taking a project as an example, after checking the electrification distance, it can be found that the electrification distance between the camera arranged in the 220kV power distribution unit area and the lightning arrester of the outgoing line does not meet the requirements, and the number of equipment is 3, the application of three-dimensional design is described from the aspects of video monitoring system, automatic fire extinguishing system, etc, its application in the front end equipment layout, model retrieval, collision inspection between safety distance and foundation, buried pipe design, material statistics and other dimensions of these systems were shown in detail, the method of 3D design is deeply studied and applied to the practical engineering design of high voltage substation. The space characteristics of 3D design can be used to realize complex underground pipeline layout, cable optimal layout, collision inspection, construction simulation, visual display, etc.

A multi-objective memetic algorithm for automatic adversarial attack optimization design

The phenomenon of adversarial examples has been revealed in variant scenarios. Recent studies show that well-designed adversarial defense strategies can improve the robustness of deep learning models against adversarial examples. However, with the rapid development of defense technologies, it also tends to be more difficult to evaluate the robustness of the defensed model due to the weak performance of existing manually designed adversarial attacks. To address the challenge, given the defensed model, the efficient adversarial attack with less computational burden and lower robust accuracy is needed to be further exploited. Therefore, we propose a multi-objective memetic algorithm for auto adversarial attack optimization design, which realizes the automatic search for the near-optimal adversarial attack towards defensed models. Firstly, the more general mathematical model of auto adversarial attack optimization design is constructed, where the search space includes not only the attacker operations, magnitude, iteration number, and loss functions but also the connection ways of multiple adversarial attacks. In addition, we develop a multi-objective memetic algorithm combining NSGA-II and local search to solve the optimization problem. Finally, to decrease the evaluation cost during the search, we propose a representative data selection strategy based on sorting cross entropy loss values of images output by models. Experiments on CIFAR10, CIFAR100, and ImageNet datasets show that our method can efficiently find near-optimal adversarial attacks with lower robust accuracy and less time cost, which can provide more reliable and efficient robustness evaluation for defensed models.

Privacy risks of whole-slide image sharing in digital pathology

Access to large volumes of so-called whole-slide images—high-resolution scans of complete pathological slides—has become a cornerstone of the development of novel artificial intelligence methods in pathology for diagnostic use, education/training of pathologists, and research. Nevertheless, a methodology based on risk analysis for evaluating the privacy risks associated with sharing such imaging data and applying the principle “as open as possible and as closed as necessary” is still lacking. In this article, we develop a model for privacy risk analysis for whole-slide images which focuses primarily on identity disclosure attacks, as these are the most important from a regulatory perspective. We introduce a taxonomy of whole-slide images with respect to privacy risks and mathematical model for risk assessment and design . Based on this risk assessment model and the taxonomy, we conduct a series of experiments to demonstrate the risks using real-world imaging data. Finally, we develop guidelines for risk assessment and recommendations for low-risk sharing of whole-slide image data.

Integration of blockchain-enabled closed-loop supply chain and robust product portfolio design

Blockchain technology is one of the latest financial concepts influencing international trades, which contributes to speeding the supply chains by managing faster and more accurate financial transactions. Moreover, the product portfolio is highly effective on the financial flow of the supply chain. Accordingly, in this research, a comprehensive framework is proposed to design a blockchain-enabled closed-loop supply chain (BCSC), considering the role of the product portfolio. First, a mathematical model for robust product portfolio design is proposed. Next, a closed-loop supply chain network is designed where the financial flow via blockchain is of concern. To optimize this supply chain, the change in equity, as well as satisfaction from the blockchain network, is maximized. An exact solution method using GAMS software is applied to optimize the proposed mathematical model. The results obtained by implementation and analysis of this proposed framework indicate that by designing a product portfolio based on a robust model, BCSC would achieve the ideal value for its financial indexes, the change in equity in specific. Comparison of this newly proposed framework with the integrated portfolio-supply chain model reveals a 0.33% average error and a 1.5% reduction in lost revenue. It is concluded that this proposed framework assists supply chain managers in reducing their inaccurate decisions in both the physical and financial flow considerably.

A mathematical model for vaccine cold chain network design considering social sustainability

Breakages that may occur in the cold chain cause serious economic, environmental, and social costs, as well as a substantial risk for human and public health. Therefore, it is necessary to design an effective, robust, and strong vaccine cold chain network. Sustainable Development Goal 3 titled “Good Health and Well Being” emphasizes children's health and specifies reducing the mortality rate for under five ages. In this study, we consider the Expanded Programme on Immunization (EPI) vaccine cold chain in Türkiye and develop a linear programming model for a multi-product, multi-period, multi-stage vaccine cold chain network in light of Sustainable Development Goal 3. The study aims to maximize fully immunized children for up to five years and propose a framework for a vaccine cold chain network design. The proposed model is applied to a real case. Finally, various scenario analyzes are applied to show the results of the model under different conditions.

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

A mathematical model of catalyst combination design and temperature control in the preparation of C4 olefins through ethanol coupling.

The preparation of C4 olefins through ethanol catalytic coupling is a crucial area of study. According to the experimental data obtained by a chemical laboratory for different catalysts at different temperatures, three mathematical models were developed to provide insights into the relationships among ethanol conversion rate, C4 olefins selectivity, yield, catalyst combination, and temperature. The first model is a nonlinear fitting function that analyses the relationships among ethanol conversion rate, C4 olefins selectivity, and temperature under varying catalyst combinations. Two-factor analysis of variance was employed to determine the influence of catalyst combinations and temperatures on ethanol conversion rate and C4 olefins selectivity. The second model is a multivariate nonlinear regression model that describes the relationships among the yield of C4 olefins, catalyst combination, and temperature. Finally, an optimization model was derived based on the experimental conditions; it provides a solution for the selection of the optimal catalyst combinations and temperatures to achieve the maximum yield of C4 olefins. This work has significant implications for the field of chemistry and the production of C4 olefins.

SNC BASED NETWORK LAYER DESIGN FOR UNDERWATER COMMUNICATION USED IN OPEN OCEAN FISH FARMING

Aquaculture is gradually moving toward Open Ocean Fish Farming (OOFF) in recent times because of the huge environmental impacts caused by onshore fish farming. Although Offshore fish farming has a lot of benefits over onshore fish farming it has its threats as well. Harmful Algae Blooms (HAB) are one such threat to Offshore fish farming. HAB is the formation of algae in groups that are toxic. The HAB can significantly affect the health of the fish that are being cultured. To prevent and act on HAB, monitoring of different environmental parameters is done in the field that is of concern. Traditionally for these kinds of monitoring human drivers are employed. But involving human drivers for monitoring in offshore conditions is cost expensive and difficult. Technology-enabled autonomous monitoring is needed in an offshore environment. Here comes underwater Wireless Sensor Networks (UWSN) which can be used for inspection of underwater fish farms for the detection of HAB. In UWSN loss is one of the main parameters that affect the Quality of Service. So this research focuses on the development of a Stochastic Network Calculus (SNC) based mathematical model of the network layer design for underwater communication that can be used in OOFF. In this work, we introduced the loss factor parameter into SNC and derived the loss bound for underwater communication, and the same is evaluated using discrete event simulation.

Development of mathematical model for design of vehicle steering system

The vehicle steering system is one of the most important systems on the vehicle, both in terms of safety and performance. Based on the geometry of the steering trapezoid, the geometry of the suspension system, the alignment angles of the wheels, as well as the characteristics of the tires, a mathematical model for the design of the formula student vehicle "Road Arrow" steering system was developed. Based on the dynamic state of the vehicle, the mathematical model provides information on the stress of the steering system, the torque on the steering wheel and the slip angles of the steered wheels. The mathematical model was developed using the MATLAB software, and validation of the results was performed by comparing the results with the ones obtained by simulations in MSC ADAMS. Analysing the obtained results, it is possible to conclude that the average value of relative error of the stress is approximately 15%, for slip angles of the steered wheels is approximately 7%, and the error for torque on the steering wheel is approximately 6%.

A food bank network design examining food nutritional value and freshness: A multi objective robust fuzzy model

One main reason for food scarcity is its improper and uneven distribution amongst those who require aid. To overcome this issue, charities and food banks serve as the connection between beneficiaries and donors. They are mostly nonprofit organizations but they incur operational costs for storage and delivery of the donated food items. The donated food items are either canned and cold, or hot meals from over production of businesses; and therefore their freshness, inventory and shelf-life bring about additional operational challenges in distribution and logistics. The uncertainty of demand and supply is another challenge to overcome, which necessitates a robust plan. This article proposes a multi-objective mathematical programming model for a food bank network design to optimize the cost, food freshness and its nutritional value. A robust fuzzy counterpart of the model is developed together with three solution methods including ϵ-constraint, MOGWO and NSGA II. The MOGWO algorithm shows a better performance in our numerical experiment with large instances. Its application on a case study resulted in a supply network with lower cost, smaller fleet size and higher food quality, although less fresh distributed foods compared to the benchmark network. The trade-off between the cost and freshness of food is depicted here by examining shelf-life of products and vehicle capacity. The long lasting products incur less transportation cost due to compactness of packaging, and similarly, higher capacity vehicles lead to more cost efficient dispatch with longer routes which decrease the freshness of food. According to our numerical results, higher uncertainty rate in the network increases total cost, but also overall nutritional value of the distributed food over the network due to greater supply of food.

Mathematical design and meshing analysis of a new internal gear transmission based on spatial involute-helix curve

We present a new internal gear transmission based on spatial involute-helix curve in this article. Firstly, the generation principle of spatial involute-helix curve is proposed according to gear geometry theory. Mathematical design model of the spatial conjugate involute-helix curves is provided through establishing the meshing relationship solved by relative velocity and specific normal vector at contact point. The equations of conjugated spatial involute-helix curve and line of action of contact curves are derived, respectively. Secondly, tooth profiles construction with spatial involute-helix curve pair is carried out by isometric offsetting and kinematics methods. General tooth profiles form and numerical example are proposed in terms of given design parameters. Furtherly, meshing analysis of generated tooth profiles are discussed. Center distance separability and axial errors action are discussed according to the theoretical derivation and simulation process. Contact stress analysis and the comparison are studied by finite element method. Finally, the experimental test of the new gear pair manufactured by CNC technology is provided and general transmission efficiency results and contact conditions of tooth profiles under different error conditions are displayed. Research conclusions show that the new internal gear drive has well transmission property and further study on the contact dynamic and error analysis will be carried out.

Power distribution network design considering dynamic and differential pricing, buy-back, and carbon trading

The increase in energy demand and the effect of traditional energy generation supported by the penetration of technological advancements in renewable energy generation calls for an integrated power distribution network design. In this study, a power distribution network design with the establishment of distributed renewable energy resources and involvement of prosumers in energy system to generate, buy, and supply carbon-free energy is considered. The dynamic prices that cope with the dynamic demand of both prosumers and customers over the energy planning time horizon and the buy-back price to be paid to the prosumers are also considered. A mathematical model for power distribution network design, including carbon trading and a buy-back policy, was developed. The objective is to determine the generation capacity of the distributed renewable energy resources to be installed at different potential sites, the differential prices offered to prosumers and consumers, and the buy-back price while maximizing the profit of a power plant. A scenario-based stochastic solution approach and fuzzifying fuzzy parameters are provided to address the above problem. The results show that the power plant earns the most profit at a relation factor of 0.8 between the differential prices by offering the highest buy-back price to incentivize the prosumers. With the increase in the relation factor, the net profit of the power company decreases, but the buy-back price increases, while the dynamic prices remain unpredictable. The average buy-back price offered to prosumers was 62.4% of the average selling price.

Robust supply chain design with suppliers as system integrators: an aerospace case study

ABSTRACT Original Equipment Manufacturers (OEMs) have sought new supply chain paradigms that allowed them to focus on core activities, i.e. overall product design and commercialisation. This pursuit led to partnerships with a new generation of tier-1 strategic suppliers acting as integrators. Integrators are not only responsible for system supply, but also for system design. However, critical integrators were not able to live up to their new roles, which led to costly delays in development and production. These failures highlight the ineptitude of current risk management practices employed by OEMs. To support OEMs in implementing a more differentiated and suitable approach to the use of integrators, this paper proposes a mathematical programming model for Supply Chain Design (SCD). Instead of looking at the introduction of integrators as a dichotomous decision, the model suggests the optimal number of integrators, i.e. systems, and individual part suppliers. We propose new measures for integration risk, which build upon current risk assessment practices. Robust optimisation is used to study the effect of uncertainty over baseline risk values. All approaches were tested using both randomly generated instances and real data from a large European OEM in the aerospace industry.

Adaptive design methodology of segmented non-uniform fin arrangements for trans-critical natural gas in the printed circuit heat exchanger

As the core heat transfer equipment of a floating storage regasification unit (FSRU), the printed circuit plate heat exchanger (PCHE) has a significant impact on the gasification performance of liquefied natural gas (LNG). During LNG regasification process, natural gas undergoes a trans-critical process and its thermal properties such as density, viscosity and specific heat capacity vary considerably especially near the pseudo-critical point, which will probably lead to more volatile flow heat transfer mechanism. The traditional design scheme of uniform finned channel is difficult to give full play to the efficiency and compactness of PCHE because of lacking considering the local fluid thermodynamic variation. Therefore, this paper provides a novel design method for optimizing the flow channel profile of PCHE by applying adaptive segmented non-uniform finned micro-channels. Firstly, the entire flow channels are segmented by qualifying the gradient of density with temperature ∂ρ/∂t of trans-critical natural gas. Subsequently, within the constraints of heat exchange requirements, maximum allowable pressure drop, existing manufacturing techniques and structural strength, a mathematical optimization design model considering non-uniform fin arrangements and interlinked thermal states among these segmented channels is established. Then, to comprehensively improve entropy generation number and volume, Pareto solutions covering local flow channel parameters are obtained based on multi-objective genetic algorithm. Finally, the actual performance differences between two optimization methods respectively derived from the conventional uniform fin channels and the proposed non-uniform fin arrangements are compared based on distributed parameter model. The results show that the deviation of the entropy generation number between the optimized and validated values for the non-uniform design is very small at 6.5%, much less than that of 31.4% in the uniform design. Moreover, under the premise of the similar heat transfer efficiency, the volume for the PCHE by the non-uniform design can be reduced by 9.3%. These indicate that the proposed design methodology of segmented non-uniform fin arrangements indeed makes the PCHE more compact and enables the thermal-hydraulic performance better. The current work will serve as a framework for the design and optimization of PCHEs with drastic changes in fluid physical properties.

Methodology of the PEM FC Gas Diffusion Layer Permeability Determination and Its Description Related to the Fuel Cell Flow Field Design

Hydrogen fuel cells represent an important part of the new energy scheme for low emission society. Development of the more efficient, durable and energy dense systems requires precise information on the numerous aspects, especially on the local distribution of physio-chemical quantities inside the fuel cells stacks. It is extremely difficult to obtain such information experimentally. Therefore, the mathematical modelling represents a feasible alternative. It offers an efficient and versatile way for the acquisition of required information. Accuracy of mathematical model, however, is primarily determined by the accuracy and reliability of the experimental data available. In this particular case, permeability of gas diffusion layer for reactants and products is of interest. Permeability values in porous environment are available experimentally. It is, however, important to keep in mind that permeability value is strongly dependent on the material porosity and thus on a degree of its compression inside the stack. Therefore, permeability value is varying with position over the electrode. Suitable approach, making possible to describe smoothly variation of the gas diffusion layer permeability with degree of its compression, is desirable. Traditional approach is to use corresponding semi-empirical equations. It is a purpose of this work to verify applicability of the Kozeny-Carman equation for this particular case and thus to fill in this gap in the current knowledge.Prior the experimental validation of the Kozeny-Carman equation accuracy, methodology of obtaining sufficiently accurate permeability data needs to be developed. In the first step of this process, permeability cells were designed, characterized by the homogeneous gas flow distribution in the channel, used for positioning of the gas diffusion layer sample, to be characterized. A special attention was paid to the absence of any turbulence domains close to the pressure reading ports, which could cause potential error in the observed pressure values. The figure provided documents results of the cell geometry optimization. Mathematical model calculated gas stream lines shown document fulfilling above stated conditions and thus ensuring reliability of the experimental data obtained. The cell lid determined the channel height itself. A series of lids was produced, allowing study of gas diffusion layers permeability at the different degrees of compression, i.e. porosities. The channel depth accuracy was required to be within tolerance of 2 mm. Pressure drop on the channel was determined by varying the streaming gas flow rate. Hydrogen and nitrogen (simulating air) were used as a test gasses. Permeability of gas diffusion layers were determined based on pressure drops using Darcy’s law. This set of data allowed comparing experimental data with Kozeny-Carman equation behavior. The agreement obtained was sufficient to justify the usage of this type of semi-empirical equation for the flow field mathematical modelling. Corresponding conclusion was in the last step of the study verified by means of the model serpentine flow field attached at the gas diffusion layer at the different degrees of compression. Experimental data obtained have shown very good agreement with the model calculations. It can thus be concluded, that Kozeny-Carman provides sufficient approximation of the gas diffusion permeability values to be used in the mathematical models for design of fuel cells and fuel cells stacks for geometry optimization.The work was supported from European Regional Development Fund-Project "Fuel Cells with Low Platinum Content" (No. CZ.02.1.01/0.0/0.0/16_025/0007414). Figure 1

Application of Mathematical Modeling and Computational Tools in the Modern Drug Design and Development Process.

The conventional drug discovery approach is an expensive and time-consuming process, but its limitations have been overcome with the help of mathematical modeling and computational drug design approaches. Previously, finding a small molecular candidate as a drug against a disease was very costly and required a long time to screen a compound against a specific target. The development of novel targets and small molecular candidates against different diseases including emerging and reemerging diseases remains a major concern and necessitates the development of novel therapeutic targets as well as drug candidates as early as possible. In this regard, computational and mathematical modeling approaches for drug development are advantageous due to their fastest predictive ability and cost-effectiveness features. Computer-aided drug design (CADD) techniques utilize different computer programs as well as mathematics formulas to comprehend the interaction of a target and drugs. Traditional methods to determine small-molecule candidates as a drug have several limitations, but CADD utilizes novel methods that require little time and accurately predict a compound against a specific disease with minimal cost. Therefore, this review aims to provide a brief insight into the mathematical modeling and computational approaches for identifying a novel target and small molecular candidates for curing a specific disease. The comprehensive review mainly focuses on biological target prediction, structure-based and ligand-based drug design methods, molecular docking, virtual screening, pharmacophore modeling, quantitative structure–activity relationship (QSAR) models, molecular dynamics simulation, and MM-GBSA/MM-PBSA approaches along with valuable database resources and tools for identifying novel targets and therapeutics against a disease. This review will help researchers in a way that may open the road for the development of effective drugs and preventative measures against a disease in the future as early as possible.

Optimization and Test of Structural Parameters of Flat Hob Chopper

In order to reduce the chopping power consumption of a flat hob chopper (referred to herein as chopper) on the premise of ensuring the chopping effect of the chopper, the mathematical model of optimal design of chopper is established in this paper with the minimum chopping power as the objective. With the help of MATLAB software, the mathematical model is solved. The chopping power curves of each point on the chopper blade edge line before and after the optimization of structural parameters are generated. The results indicate that when the coordinate value of point A on the blade edge line on the Z axis is 0.7 m; the included angle between the bottom surface of the blade and the axis of the cutter roll is 6°. When the radius of the chopper is 0.11 m, the chopper can obtain the theoretical minimum chopping power. The analysis result of chopping power curve is the chopping power after structural parameter optimization is reduced by about 25.50% compared with that before optimization. The choppers before and after the optimization of structural parameters was trial manufactured and sequentially mounted on the performance test bench of the chopping system of the forage ramie harvester. The test results show the standard-length rate of ramie stalk chopped by the choppers before and after the optimization of structural parameters were 92.96% and 92.84%, respectively, which were extremely close to each other, indicating that the optimization of structural parameters has no influence on the chopping effect of the chopper. The chopping power of the chopper is reduced by 22.25% after optimization, which is close to the software analysis value (25.50%), indicating that the optimization result is accurate and reliable. This study can provide parameter foundation and an optimization method for lowering chopping power consumption of the chopper.

Identification of the Optimal Pattern of the Injection and Dosage of DC Immunotherapy Using the Mathematical Models Based on Ordinary Differential Equations.

Mathematical modeling offers the possibility to select the optimal dose of a drug or vaccine. Considerable evidence show that many bacterial components can activate dendritic cells (DCs). Our previous report showed that multiple doses of DCs matured with Listeria monocytogenes led to tumor regression whereas multiple doses of CpG-matured DCs affected tumor reversely. To assess a combined pattern of DC vaccination proposed by a mathematical model for tumor regression. WEHI164 cells were inoculated subcutaneously in the right flank of BALB/c mice. Bone marrow-derived DCs were matured by Listeria monocytogenes and CpG motifs. DCs were injected using specific patterns and doses predicted by mathematical modeling. Effector cell-mediated cytotoxicity, gene expression of T cell-related transcription factors, as well as tumor growth and survival rate, were assessed in different groups. Our study indicated that the proposed mathematical model could simulate the tumor and immune system interaction, and it was verified by decreasing tumor size in the List+CpG group. However, comparing the effect of different treatment modalities on Th1/Treg transcription factor expression or cytotoxic responses revealed no advantage for combined therapy over other treatment modalities. These results suggest that finding new combinations of DC vaccines for the treatment of tumors will be promising in the future. The results of this study support the mathematical modelling for DC vaccine design. However, some parameters in this model must be modified to provide a more optimized therapy approach.