Mathematical Models In Terms Research Articles

Combining dimensional and statistical analysis for efficient data driven modelling of complex systems

Dimensional analysis is a well-known approach to model building in engineering, because it can contribute to identifying more parsimonious and meaningful equations for describing complex phenomena. Unfortunately, it is not always exploited to the full, because it is typically applied prior to any form of statistical evaluation, often resulting in poor choices of the dimensionless quantities and consequently in suboptimal models. A completely general and data driven technique is proposed, which integrates dimensional and statistical analysis with the help of genetic programming supported symbolic regression and neural computing. The methodology exploits the potential of various machine-learning techniques and allows extracting mathematical models in terms of dimensionless quantities directly from the dimensional databases available. A battery of numerical tests and examples from fluid dynamics and thermonuclear fusion illustrate the unquestionable advantages of the approach for statistical inference and for the interpretation of the large amounts of data produced by modern physics experiments and engineering studies.

State Separate Modular Modeling Methodology of Multioutput DC–DC Converters

Conventional modeling and simulation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -output dc–dc converters requires <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n+1) \times (n+1)$ </tex-math></inline-formula> matrix computations. This approach increases the modeling approach’s complexity and increases the design and simulation time required for the modeling process. A state separate modeling methodology is proposed where each state of the dc–dc converter is considered separately and combined with the help of a multiplexer. The proposed modeling approach is modular and thus improves the scalability to multiple outputs. The proposed methodology aids the designer in designing and modeling multioutput dc–dc converters faster, enabling fast prototyping. The proposed model outperforms the existing mathematical models in terms of computation time. The output voltage variation to duty cycles has a root mean square error in between 0.08 and 0.22 V.

Role of fractional derivatives in the mathematical modeling of the transmission of Chlamydia in the United States from 1989 to 2019.

Nowadays, the mathematical modeling of infectious diseases is a big trend worldwide. The mathematical models help us to forecast future outbreaks of diseases in the presence of present data. In this article, we represent a model of the transmission of Chlamydia in the United States by using data from 1989 to 2019. In the formulation of the model, we used integer and fractional derivatives. Several graphs are plotted for the various possible cases of the given parameters. The aim of this paper is to justify how the mathematical models in terms of fractional derivatives have more degree of freedom to explore disease dynamics for a particular data set and capture memory effects. The separate parameter estimation for each value of the fractional order increases the novelty of this work. The use of a real-data set of Chlamydia in the United States makes this study more visible and important to the literature.

Математичне моделювання процесів в дизель-газотурбінних енергетичних комплексах з термохімічною обробкою палива

This paper discussed the methodological aspects of the study using methods of mathematical modeling of processes in ship power plants with thermochemical fuel treatment. The results of the study of physical and chemical processes in structural and functional blocks, simulating individual links of the thermodynamic cycle, are considered. The combination of blocks with links in the form of material and energy flows makes it possible to model the complete scheme of the mathematical model of the power module. Due to the diversity and complexity of the processes in the combined diesel-gas turbine power complex with a thermochemical fuel treatment system, when modeling, the characteristics of the power equipment were determined separately, followed by merging the results obtained and combining the models with links in the form of material and energy flows. Mathematical models of a gas turbine engine, a recycling circuit, a thermochemical fuel treatment unit were created using the Aspen Plus physical and chemical processes modeling system. Working processes in the internal combustion engine were modeled using the CHEMKIN software package. It has been proven that the universal mathematical models of heat engines, which are part of the power module with thermochemical fuel treatment, require adjustment of the selected basic characteristics. Therefore, mathematical models of structural-functional blocks and groups of blocks contain algorithms for setting up models when they are verified by objective functions. The proposed algorithms provide verification of the developed mathematical models in terms of existing or prospective gas turbine engines and internal combustion engines. These algorithms provide the possibility of correct adjustment of the equipment parameters of diesel-gas turbine power complexes with thermochemical fuel treatment. The mathematical model of the internal combustion engine operating cycle based on the CHEMKIN software package provides an opportunity to conduct a primary assessment of the efficiency of energy conversion in the working cylinder. The results of evaluating the adequacy of the mathematical model of the ICE operating cycle based on the CHEMKIN software package showed a satisfactory agreement between the obtained results and experimental data. The maximum root-mean-square error of the calculated data obtained on the basis of the model is within 8.5%.

Mathematical models for dengue fever epidemiology: A 10-year systematic review.

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading.Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response.Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed.Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

Generalized Differentiability of Continuous Functions

Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Furthermore, the non-differentiability set of such derivatives is proven to be of measure zero. As a second application, the indicial derivative is used in the proof of the Lebesgue differentiation theorem. Finally, the connection with the fractional velocities is demonstrated.

Experimental study of the factors affecting the parameters of emergency braking process for vehicles of category M1

The paper presents the results of an experimental study of the parameters of emergency braking process for vehicles of category M1, wherein disclosed is the influence of a combination of factors such as: actual loading of a vehicle, the presence of ABS, EBD, BAS systems, a trailer of up to 750 kg, condition of the road surface, and seasonality types of tires. As a result of the study, the actual values of the steady-state deceleration jyз and its rise time tвp, were obtained, and their comparative analysis with the recommended standard values was carried out. The paper also presents reliable mathematical models in terms of their practical application during the reconstruction of road traffic accidents.

Investigation of optimal process parameters for laser cutting of Inconel-718 sheet

Precise machining of advance material like Inconel-718 is an emerging need. Selection of an appropriate optimal range of cutting parameters is quite essential to achieve the high-quality cut and is a challenging task within this domain of study. The aim of this research is to develop a robust prediction model, which can suggest the desired range of cutting parameters for accomplishing better cutting quality, precision, and geometrical accuracy. Experiments have been performed on a 300 W (CNC-PCT 300) pulsed Nd: YAG laser cutting system at various levels of input cutting parameters, namely gas pressure, standoff distance, cutting speed, and laser power. Thereafter, response surface methodology has been adopted to develop mathematical models in terms of aforementioned input cutting parameters for geometrical quality characteristics: top kerf width and bottom kerf width. These developed models have been validated by comparing the predicted values with the experimental ones. Further, these models have been optimized using the multiobjective genetic algorithm in order to ascertain the optimal range of cutting parameters pertaining to better quality cut with high precision and geometrical accuracy.

RESPONSE SURFACES FOR PROPERTIES OF CONCRETE WITH CLAY BRICK POWDER AS SUBSTITUTE FOR CEMENT

This study examined the application of pulverize clay brick wastes as alternative constituent for Portland cement replacement in green concrete production using the response surface methodology (RSM). The adopted response surface approach is central composite design (CCD). The statistical models were developed between the concrete constituents (clay brick powder and water cement ratio) and their response variables (slump, compressive and split tensile strength). Relationships were established and mathematical models in terms of actual factors from predicted responses were developed. The influence of the considered factors on the properties of response were visually observed from the contour and response surface plots. The statistical models of experimental values clearly depict that the obtained experimental values are in close agreement with the predicted values, which validates the response surface models with desirability value of 1. The results show that pulverized clay brick waste have significant influence on the properties of concrete than the water cement (w/c) ratio, however, a declining trend was seen for all analyzed concrete properties. In addition, this study showed that the pulverized waste brick can be used as alternative substitute for Portland cement up to 20% in the production of sustainable concrete.

Prediction of optimal cut quality characteristic of Inconel 718 sheet by genetic algorithm and particle swarm optimization

Selection of an appropriate optimal range of cutting parameters during the machining of Inconel-718 is quite essential to achieve the high-quality cut and is a challenging task within this domain of study. The aim of this research is to develop a robust prediction model which can suggest the desired range of cutting parameters for accomplishing better cutting quality, precision, and geometrical accuracy. Experiments have been performed on a 300 W (CNC-PCT 300) pulsed Nd: YAG laser cutting system at various levels of input cutting parameters, viz., gas pressure, standoff distance, cutting speed, and laser power. Thereafter, the artificial neural network technique has been adopted to develop mathematical models in terms of aforementioned input cutting parameters for geometrical quality characteristics: Top Kerf Width, Bottom Kerf Width, and Kerf Taper. These developed models have been validated by comparing the predicted values with the experimental ones. Furthermore, these models have been optimized using a multiobjective genetic algorithm and particle swarm optimization techniques, in order to ascertain the optimal range of cutting parameters pertaining to better quality cut with high precision and geometrical accuracy.

Prediction of geometric quality characteristics during laser cutting of Inconel-718 sheet using statistical approach

Machining of advanced material like Inconel-718 with accuracy and precision is an emerging need. Selection of an appropriate optimal range of cutting parameters is quite essential to achieve high-quality cut and is a challenging task within this domain of study. The aim of this research is to develop a robust prediction model which can suggest the desired range of cutting parameters for accomplishing better cutting quality, precision, and geometrical accuracy. Experiments have been performed on a 300-W (CNC-PCT 300) pulsed Nd:YAG laser cutting system at various levels of input cutting parameters, viz. gas pressure, standoff distance, cutting speed and laser power. Thereafter, response surface methodology has been adopted to develop mathematical models in terms of aforementioned input cutting parameters for geometrical quality characteristics: Top Kerf Width (TKW) and Bottom Kerf Width (BKW). The percentage error in the prediction models has been found as 1.981% and 1.511% for TKW and BKW, respectively. These developed models have been validated by comparing the predicted values with the experimental ones. Further, these models have been used to determine the dependency of responses on input parameters and to ascertain an optimal range of cutting parameters pertaining to better quality cut with high precision and geometrical accuracy. Moreover, it has also been found that the dependency of input parameters on output is non-monotonous in nature.

Supplier selection and order allocation decisions under quantity discount and fast service options

In this study, we first discuss the characteristics of an effective supplier selection approach. Then, we compare the use of Multi-Criteria Decision Making (MCDM) techniques and mathematical models in terms of those characteristics. It is observed that neither of these approaches provides a framework that encompasses all the necessary characteristics. For this reason, a hybrid approach based on fuzzy TOPSIS, trapezoidal type-2 fuzzy AHP and goal programming is developed. Our approach simultaneously considers both qualitative and quantitative criteria, takes case-specific requirements such as capacity constraints, lot size constraints and quantity discounts into account and in the end, it does not only determine the appropriate supplier(s) to work with but also makes the order allocation. We conclude the study by presenting a real life problem and discussing the obtained results. Computational results show that our approach is able to find a tradeoff between conflicting criteria and makes an order allocation that satisfies all the constraints

Sex-structured wild and sterile mosquito population models with different release strategies.

In this paper, we propose sex-structured mathematical models in terms of continuous-time differential equations. We investigate the interactive dynamics of the sex-structured wild and sterile mosquitoes from several aspects including the existence of equilibria and their stability. We consider different strategies of releasing the sterile mosquitoes to control mosquitoes in an effective way. In addition, numerical simulations are provided to illustrate the dynamical features of the models.

Selection of Machining Parameters Using a Correlative Study of Cutting Tool Wear in High-Speed Turning of AISI 1045 Steel

The manufacturing industry aims to produce many high quality products efficiently at low cost, thereby motivating companies to use advanced manufacturing technologies. The use of high-speed machining is increasingly widespread; however, it lacks a deep-rooted knowledge base needed to facilitate implementation. In this paper, response surface methodology (RSM) has been applied to determine the optimum cutting conditions leading to minimum flank wear in high-speed dry turning on AISI 1045 steel. The mathematical models in terms of machining parameters were developed for flank wear prediction using RSM on the basis of experimental results. The high speed turning experiments were carried out with two coated carbide and a cermet inserts using AISI 1045 steel as work material at different cutting speeds and machining times. The models selected for optimization were validated through the Pareto principle. Results showed the GC4215 insert to be the most optimal option, because it did not reach the cutting tool life limit and could be used for the whole range of cutting parameters selected. To quantitatively evaluate the usefulness of the cutting tools, it was proposed the coefficient of use of the tools from the results of the contour graphs. The GC4215 insert showed 100% effectiveness, followed by the GC4225 with 98.4%, and finally, the CT5015 insert with 83%.

Development of the imitation model of the two-stage separation process of oil

In accordance with the law of preservation of the amount of substance, an imitation model for the process of two-stage oil separation has been developed. The creation of this model took into account the features of the operating mode of the horizontally placed separators B-1 and B-2 of the first and second stages of separation. The simulation mathematical model after the identification of parameters was investigated by a numerical method that takes into account the effect of perturbations on the separation process, which is a consequence of the action of a number of physical quantities from the environment on the object. Automated control systems that operate on the principle of negative feedback were used to stabilize the main technological parameters of oil separation. But since the deviation of the regulated quantities from their given values is small, this allowed linearizing the nonlinear model of the two-stage separation process. After studying the simulation model by a numerical method, it is established that the mathematical model of the installation of two-stage separation can be used for the synthesis of effective control systems of the two-stage separation process and the creation of mathematical models in terms of “input-output”. The obtained numerical and graphical result in the form of functional dependencies allows us to establish the relationship of technological parameters, in other words, the change of the value of the parameters at the second stage of separation will depend on the first one and vice versa. Thus, the applied aspect of using the obtained scientific result is the possibility of improving the typical technological process of oil separation.

Symbiotic Sensing for Energy-Intensive Tasks in Large-Scale Mobile Sensing Applications.

Energy consumption is a critical performance and user experience metric when developing mobile sensing applications, especially with the significantly growing number of sensing applications in recent years. As proposed a decade ago when mobile applications were still not popular and most mobile operating systems were single-tasking, conventional sensing paradigms such as opportunistic sensing and participatory sensing do not explore the relationship among concurrent applications for energy-intensive tasks. In this paper, inspired by social relationships among living creatures in nature, we propose a symbiotic sensing paradigm that can conserve energy, while maintaining equivalent performance to existing paradigms. The key idea is that sensing applications should cooperatively perform common tasks to avoid acquiring the same resources multiple times. By doing so, this sensing paradigm executes sensing tasks with very little extra resource consumption and, consequently, extends battery life. To evaluate and compare the symbiotic sensing paradigm with the existing ones, we develop mathematical models in terms of the completion probability and estimated energy consumption. The quantitative evaluation results using various parameters obtained from real datasets indicate that symbiotic sensing performs better than opportunistic sensing and participatory sensing in large-scale sensing applications, such as road condition monitoring, air pollution monitoring, and city noise monitoring.

Statistical models for mechanical properties of UHPC using response surface methodology

One of the main disadvantages of Ultra High Performance Concrete exists in the large suggested value of UHPC ingredients. The purpose of this study was to find the models mechanical properties which included a 7, 14 and 28-day compressive strength test, a 28-day splitting tensile and modulus of rupture test for Ultra High Performance Concrete, as well as, a study on the interaction and correlation of five variables that includes silica fume amount (SF), cement 42.5 amount, steel fiber amount, superplasticizer amount (SP), and w/c mechanical properties of UHPC. The response surface methodology was analyzed between the variables and responses. The relationships and mathematical models in terms of coded variables were established by ANOVA. The validity of models were checked by experimental values. The offered models are valid for mixes with the fraction proportion of fine aggregate as; 0.70-1.30 cement amount, 0.15-0.30 silica fume, 0.04-0.08 superplasticizer, 0.10-0.20 steel fiber, and 0.18-0.32 water binder ratio.

On the Modeling of Surface Roughness and Cutting Force when Turning of Inconel 718 Using Artificial Neural Network and Response Surface Methodology: Accuracy and Benefit

This paper is an attempt to compare artificial neural networks and response surface methodology for modeling surface roughness and cutting force in terms of better coefficient of determination (R2), lower root mean square error (RMSE) and model predictive error (MPE). Models were developed based on three-level Box-Behnken design (BBD) of experiments with 15 experimental runs composed of three center points, conducted on Inconel 718 work material using coated carbide insert with cutting speed, feed rate and depth of cut as the process parameters under dry environment. Results show that the artificial neural network (ANN) compared with RSM is a better reliable and accurate approach for predicting and detecting the non-linearity of surface roughness and cutting force mathematical models in terms of correlation and errors. Indeed, the ANN prediction model provides a maximal benefit in terms of precision of 10.1% for cutting force (Fv) and 24.38% for surface roughness (Ra) compared with the RSM prediction model.

A New Hybrid Approach to Optimize the End Milling Process for Al/SiC Composites using RSM and GA

The centre of research is to optimize the cutting Forces (F R ), surface Roughness (Ra) and Material Removal Rate (MRR) of end milling for Aluminium compositeusing Response Surface Methodology (RSM) and Genetic Algorithm (GA). The RSM L 31 empirical model is conducted with Al/SiC composites of various compositions. The cutting forces and the surface roughness are measured using 3-axis milling tool dynamometer and MarTalk Profilometer respectively. The second order mathematical models in terms of machining parameters are developed for predicting responses with adequacy above 85%. The optimal configuration of end milling are 5 wt. % of reinforcement, 0.3 mm depth of cut, feed rate of 49.3 mm/min and cutting speed of 474.3 rpm to acquire minimum FR, Ra with maximum MRR is done by Genetic Algorithm (GA). From the estimated model, the responses are with the experimental deviation of 11% MRR, 13% Ra and 17% FR for the desirability of 98.7%. The optimization of three machining parameters with a advance hybrid approach brought a new scope for the researchers and manufactures to improve the standard of automated machining.

Heavy metal concentrations in roadside-deposited sediments in Kuwait city

In the present study, roadside-deposited sediment samples collected from Kuwait city district, in Kuwait, were analyzed for specific heavy metals (As, Cr, Cu, Mn, Ni, Pb, and Zn). Contamination assessment status of heavy metals in roadside sediments was made using mathematical models in terms of enrichment factor (EF), geoaccumulation index (I geo), and contamination factor (CF). The sediments showed remarkably high levels of all the metals, except Ni, above background concentrations in the following order (As, Cu, Pb, Zn, Mn, and Cr). CF and I geo revealed overall moderately uncontaminated and moderate contamination, respectively, but the EFs for all metals ranged between moderate and significant enrichment.