Reliable Mathematical Model Research Articles

Mass Transfer Characteristics of Haemofiltration Modules-Experiments and Modeling.

Reliable mathematical models are important tools for design/optimization of haemo-filtration modules. For a specific module, such a model requires knowledge of fluid- mechanical and mass transfer parameters, which have to be determined through experimental data representative of the usual countercurrent operation. Attempting to determine all these parameters, through measured/external flow-rates and pressures, combined with the inherent inaccuracies of pressure measurements, creates an ill-posed problem (as recently shown). The novel systematic methodology followed herein, demonstrated for Newtonian fluids, involves specially designed experiments, allowing first the independent reliable determination of fluid-mechanical parameters. In this paper, the method is further developed, to determine the complete mass transfer module-characteristics; i.e., the mass transfer problem is modelled/solved, employing the already fully-described flow field. Furthermore, the model is validated using new/detailed experimental data on concentration profiles of a typical solute (urea) in counter-current flow. A single intrinsic-parameter value (i.e., the unknown effective solute-diffusivity in the membrane) satisfactorily fits all data. Significant insights are also obtained regarding the relative contributions of convective and diffusive mass-transfer. This study completes the method for reliable module simulation in Newtonian-liquid flow and provides the basis for extension to plasma/blood haemofiltration, where account should be also taken of oncotic-pressure and membrane-fouling effects.

Numerical modeling of the performance of a well with an arbitrary piecewise-smooth external boundary in an anisotropic heterogeneous reservoir

The extraction of oil and gas from productive reservoirs of complex geological structures is constantly increasing. Thus, it is obvious that reliable mathematical models able to manage such porous media are of particular interest. In this paper, a model of filtration flow to a well located in an anisotropic heterogeneous soil formation, with a piecewise-smooth external contour, is numerically studied. The permeability of soil, as a porous medium, is characterized by a second-rank tensor. Soil heterogeneity is modeled by a power function of one of the coordinates. We consider a particular case with a positive exponent. The solution of the stated boundary problem of well operation in a porous reservoir causes significant mathematical difficulties associated with the complicated form of the basic equation. The formulation of the problem is reduced to a canonical form, which greatly simplifies the solution. To do this, we turn on the auxiliary plane using homeomorphic (affine) transformation. The problem is reduced to a system that includes a Fredholm type integral equation and an integral relation. The results were obtained using the discrete singularity method. It was found that the algorithm convergence is slightly better under weak anisotropy. The influence of anisotropy and heterogeneity of the soil on the production in the case of the productive reservoir with a rectangular boundary was assessed. The anisotropy can greatly change the production rate compared to the rate of a well in an isotropic soil. Permeability tensor components are located on the main diagonal and have a major impact on the rate of the flow in the anisotropic and heterogeneous soil. This method can be used to solve different problems of fluid filtration in an anisotropic porous medium.

Mathematical model of functional reliability of avionics, taking into account their predicted technical condition

Mathematical model of functional reliability of avionics, taking into account their predicted technical condition

The Grain Cleaning Production Lines’ Energysaving Operation Modes of Electromechanical Systems

Abstract The research was aimed at reducing the power consumption for grain cleaning by using energy-saving modes in the electromechanical systems of grain cleaning units. Specific consumption of active energy per production unit was adopted as a criterion for assessing energy-saving operation modes. The applied method of mathematical experiment planning (MEP) reduced the number of experiments to a minimum to obtain a reliable mathematical model of the research object. To determine the optimal specific power consumption, a theoretical method was developed to rebuild the mathematical model. Thus, the minimum specific power consumption of grain cleaning production lines was obtained, which allowed developing science-based rates of power usage that allow energy savings up to 8-10%.

Modelling, analysis and experimental verification of air disc brake used in heavy duty vehicles

This paper proposes a reliable mathematical model that can be used for design stage of new air disc brake (ADB) development projects. All three phases of braking mechanism (brake apply, brake release and automatic adjustment) are modelled by Matlab Simulink in consideration of hysteresis and adjuster performance experiments. Firstly, mathematical relations of each friction interfaces of air disc brake components are derived and mathematical equations adapted to the Simulink model. To ensure the accuracy of ADB system model, hysteresis and adjuster performance experiments are conducted on a prototype disc brake mechanism supported by a test fixture. This prototype single piston disc brake mechanism is fitted to wheel size in 17.5″ used in heavy commercial vehicles. The predicted clamping force, mechanical ratio, brake efficiency and adjuster rate results are verified by using experimental data. The maximum deviation in hysteresis results is 3.08%. Besides, the maximum deviation in adjuster performance results is 7.15%. The numerically and experimentally obtained hysteresis and adjuster performance results show good agreement. The proposed model is modified in consideration of mechanism supported by a brake calliper for predicting actual performance of single piston brake mechanism on the brake level. The hysteresis and the adjuster performance analyses are conducted by using modified ADB model to calculate the hysteresis based brake efficiency and the adjuster rate. The brake efficiency of new single piston brake design provides similar efficiency as the twin piston disc brake used in heavy commercial vehicles.

Models for evaluating the maximum power produced by a Photovoltaic generator

The size of a photovoltaic system up to determine the necessary number of the installed solar panels photovoltaic to adopt a PV system sufficient to meet the needs of the load at any moment and the carrying capacity of the battery, ​it is necessary that the mathematical model used to calculate the power delivered by the solar panel is more practical. In this work, we presented several mathematical models for calculating the maximum power at the output of a photovoltaic module depending of conditions meteorological (Illumination solar and temperature). A comparative study based on Lu Lin 2004 essays was made for the purpose of deducing the most reliable mathematical model, which can be used to calculate the power delivered by a photovoltaic panel.

Модель надежности многопроцессорных аппаратно-программных комплексов систем управления реального времени с мультиверсионным программным обеспечением

Reliability is a critical parameter of real-time control systems. In practice, the reliability of hardware and software complexes included in such systems, is ensured by creating redundancy of hardware components and a multi-version approach to software development. But the redundant reservation of hardware devices and too many versions of software can lead to unjustified growth in the cost of creating and operating the projected control system. A rational approach to the design requires the creation of a model, which allows evaluating the reliability of different hardware and software complex configurations at the design stage. We proposed a mathematical reliability model of hardware and software complexes of real-time control systems, built with the use of mathematical apparatus of the queueing theory, which is a system of differential equations for the probability of finding states in the system, in which one or another component of the hardware and software complex is faulty. From the system of differential equations, the system of linear algebraic equations for probabilities of states in a steady-state mode was obtained. An analytical solution of this system is given, which allows us to evaluate the reliability of multiprocessor hardware-software complexes with multi-version software without significant expenditure of computational resources. Possibilities of using the results obtained to optimize the reliability of multiprocessor hardware-software complexes with multi-version software are presented and directions for further research are proposed

Mathematical model of heating system before the melting of the metal suspension upper half in the manufacture of turbine blades GTE

The article presents the developed mathematical model of heating system before the upper half of the metal suspension melting during the technological process of manufacturing the turbine blades in a discrete-continuous casting plant. The relevance of this research is connected with the lack of reliable mathematical model that can predict the distribution of temperature fields and heat flows inside the plant, which have a direct impact on the quality of formed macro - and microstructure in the castings of turbine blades. The currently existing methods of indirect indicators’ estimation carry significant errors in the selection of optimal technological modes of the blade casting process. The developed model makes it possible to predict more accurate the distribution of temperature fields and heat fluxes in the corresponding zones of the casting plant. Thanks to this, it is possible to predict with maximum accuracy the production of blades with a given internal structure, as well as to estimate the amount of volumetric shrinkage and deformation of the casting. The developed mathematical model in production conditions will make it possible to predict casting defects in the form of captivity and failure, reduce labor capacity and increase the productivity of the blade casting process.

Multiple Analytical Models to Evaluate the Impact of Carbon Nanotubes on the Electrical Resistivity and Compressive Strength of the Cement Paste

Cement paste is the most common construction material being used in the construction industry. Nanomaterials are the hottest topic worldwide, which affect the mechanical properties of construction materials such as cement paste. Cement pastes containing carbon nanotubes (CNTs) are piezoresistive intelligent materials. The electrical resistivity of cementitious composites varies with the stress conditions under static and dynamic loads as carbon nanotubes are added to the cement paste. In cement paste, electrical resistivity is one of the most critical criteria for structural health control. Therefore, it is essential to develop a reliable mathematical model for predicting electrical resistivity. In this study, four different models—including the nonlinear regression model (NLR), linear regression model (LR), multilinear regression model (MLR), and artificial neural network model (ANN)—were proposed to predict the electrical resistivity of cement paste modified with carbon nanotube. Furthermore, the correlation between the compressive strength of cement paste and the electrical resistivity model has also been proposed in this study and compared with models in the literature. In this respect, 116 data points were gathered and examined to develop the models, and 56 data points were collected for the proposed correlation model. Most critical parameters influencing the electrical resistivity of cement paste were considered during the modeling process—i.e., water to cement ratio ranged from 0.2 to 0.485, carbon nanotube percentage varied from 0 to 1.5%, and curing time ranged from 1 to 180 days. The electrical resistivity of cement paste with a very large number ranging from 0.798–1252.23 Ω.m was reported in this study. Furthermore, various statistical assessments such as coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), scatter index (SI), and OBJ were used to investigate the performance of different models. Based on statistical assessments—such as SI, OBJ, and R2—the output results concluded that the artificial neural network ANN model performed better at predicting electrical resistivity for cement paste than the LR, NLR, and MLR models. In addition, the proposed correlation model gives better performance based on R2, RMSE, MAE, and SI for predicting compressive strength as a function of electrical resistivity compared to the models proposed in the literature.

An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.

Comprehensive multiscale techniques to estimate the compressive strength of concrete incorporated with carbon nanotubes at various curing times and mix proportions

Concrete as a building material is classified as either normal or high strength based on its compressive strength. The compressive strength of conventional concrete ranges somewhere around 20–40 MPa. The incorporation of high-performance nanomaterials, such as carbon nanotubes (CNT), into the concrete mix, is gaining popularity to produce multifunctional composite materials with improved mechanical, physical, and electrical properties. However, the compressive strength of normal concrete (NC) increased with the addition of CNT to the mix design. Therefore, a reliable mathematical model is required to estimate the amount of CNT to gain the necessary compressive strength. In this research, five different models were proposed to forecast the compressive strength of conventional concrete modified with carbon nanotubes, including the artificial neural network model (ANN), M5P tree model, nonlinear regression model (NLR), multilinear regression model (MLR), and linear regression model (LR). For this purpose, 282 data were collected from the literature review to examine and develop the models. During the model development, the most powerful parameters influencing concrete's compressive strength were found, i.e., curing time ranged from 1 to 180 days, cement varied between 250 and 475 kg/m3, water to binder ratio ranged from 0.4–0.87, coarse aggregate 498–1466.8 kg/m3, fine aggregate 175.5–1285 kg/m3, and carbon nanotube varied between (0–10%). Based on statistical assessment parameters such as coefficient of determination R2, mean absolute error (MAE), root mean square error (RMSE), scatter index (SI), and objective (OBJ), the ANN model execute better performance in predicting the compressive strength of NC modified with CNT.

Numerical Simulation and Experimental Observation of Charged Particles Trajectories in Roll-Type Electrostatic Separators

Accurate prediction of the effects of the various factors that might influence the outcome of novel electrostatic separation process requires reliable physical and mathematical models for the numerical simulation of particle trajectories. The major objective of this article was to demonstrate that the use of a high-speed camera for recording particle trajectories could be instrumental in refining the understanding of the complex physical phenomena that occur in these electrostatic devices and in improving their operating conditions, based on valid numerical simulation results. The experiments were carried out with spherical conductive particles, using a roll-type corona-electrostatic separator. The particles trajectories were recorded using a high-speed camera at acquisition frame rate of 200 fps. The electrical field computation and the resolution of the differential equation of motion of the particles under the action of electrical and mechanical forces exerted on them enabled the prediction of the outcome of the separation process. The study was carried out for particles of different sizes, for different high voltages applied to the electrodes and for different electrode positions. The simulation results were in good agreement with the experimental data.

FRACTAL TREELIKE FRACTURE NETWORK MODEL FOR HYDRAULICALLY AND MECHANICALLY INDUCED DYNAMIC CHANGES IN THE NON-DARCY COEFFICIENT DURING THE PROCESS OF MINE WATER INRUSH FROM COLLAPSED COLUMNS

An accurate and reliable mathematical model for water inrush can help ensure operational safety in coal mines. In this study, a numerical model for water inrush caused by collapsed columns that couples mechanical rock deformation with flow in porous media based on a fractal treelike fracture network was developed. In particular, the proposed model considers collapsed columns and mining damage zones as fractal dual-porosity media. The model incorporates Darcy’s law, the Brinkman equation, and the Navier–Stokes equation to govern the groundwater flow. The Brinkman equation was adopted to simulate the groundwater flow in collapsed columns, for which the non-Darcy coefficient can be derived based on damage criteria for the fracture zone. To simulate the dynamics of water inrush in collapsed columns, the finite element method was used to solve the governing equations for the groundwater flow, solid mechanics, and rock damage. The proposed model was validated against two sets of field data, and the results showed that dynamic changes in the non-Darcy coefficient could be used to identify the occurrence of water inrush, which can be employed to improve mining safety.

In-situ adjustable nonlinear passive stiffness using X-shaped mechanisms

A desired structural or material stiffness is critical in many engineering systems for structural stability, vibration control, energy saving and manipulation efficiency. However, passive low-cost high-efficiency in-situ adjustable stiffness systems have not yet been well explored, due to uncertain and unexpected nonlinear behavior within materials and structures, difficulty or limitations in manufacturing or implementation, and various demanding requirements. To address these challenges, we present an efficient stiffness-manipulation method using a flexible and compact X-shaped structure (or mechanism). The resulting nonlinear stiffness systems can be conveniently realized and are capable for achieving various desired stiffness (positive, negative, zero or quasi-zero, multi-stable-equilibria). The inherent nonlinearity of such nonlinear stiffness systems is completely controllable and predictable with simple and reliable mathematical modelling, compared to many other metal materials or foldable mechanisms/structures. Due to the advantages of linkage mechanisms, the X-shaped structure (or mechanism) approach offers superior in-situ adjustability which can be easily achieved via various and simple pre-extension/distance/length/height adjustable mechanisms in practical mechanical designs. The stiffness-manipulation methods demonstrated in this study have also advantages including simplicity and efficiency in manufacturing and assembly, high-quality nonlinearity control and in-situ adjustability, and low-cost part production, without stability issues, manufacturing difficulty and strict material restriction, leading to revolutionary or upgrading technologies to existing engineering systems. Theoretical analysis and experimental validation (or case studies) demonstrate the advantages, effectiveness, and great potential of this new approach for exploiting nonlinearities in various engineering applications.

Statistical Optimization of a Hyper Red, Deep Blue, and White LEDs Light Combination for Controlled Basil Horticulture

This study aims to optimize artificial LEDs light conditions, for “Genovese” basil germination and growth in an indoor environment suitable for horticulture. Following a previous study on the synergic effect of LEDs light and a tailored fertilizer, in this study, the effect of white LED in combination with hyper red and deep blue, as well the plants–lights distance, was correlated to 14 growth and germination parameters, such as height, number of plants, etc. A design of experiments approach was implemented, aiming to derive mathematical models with predictive power, employing a restrained number of tests. Results demonstrated that for the germination phase, it is not possible to derive reliable mathematical models because almost the same results were found for all the experiments in terms of a fruitful germination. On the contrary, for the growth phase, the statistical analysis indicates that the distance among plants and lights is the most significant parameter. Nevertheless, correlations with LED light type emerged, indicating that white LEDs should be employed only to enhance specific growth parameters (e.g., to reduce water consumption). The tailored models derived in this study can be exploited to further enhance the desired property of interest in the growth of basil in horticulture.

Surface roughness effect on fatigue strength of aluminum alloy using revised stress field intensity approach

The fatigue strength of a component is known to highly depend on its surface quality, and it is thus necessary to develop a reliable and appropriate mathematical model for fatigue strength assessment that consider the effect of surface roughness. In this paper, different underlying physical mechanisms of the roughness effect at different regions of specimens were studied by fatigue testing of 7N01 aluminum alloy. For a quantitative analysis of the surface roughness effect, a revised stress field intensity approach for a fatigue strength assessment of microsized notches was proposed as a theoretical support. In the new model, a new form of weight function was built to adapt the characteristics of microsized notches. In addition, the effect of the field radius was fundamentally weakened on solution of the stress field intensity and the difficulty of fatigue failure region definition in the traditional method was overcome correspondingly in the proposed model, which made the calculated field strength accurate and objective. Finally, to demonstrate the validity of the revised approach quantitatively, specimens with conventionally sized notches were subjected to stress field intensity calculations. The results showed that the revised approach has satisfactory accuracy compared with the other two traditional approaches from the perspective of quantitative analysis.

Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

Copper recovery from waste printed circuit boards by the flotation-leaching process optimized using response surface methodology

ABSTRACT Recycling of waste printed circuit boards (PCBs) receives increasing attention due to abundant metallic resources and significant environmental threats. This work proposes a process for copper recovery from PCBs by froth flotation and oxidation leaching. Copper grade is improved from 38.70% to 68.34% with the recovery of 88.76% by froth flotation, and froth flotation is significantly influenced by copper liberation and particles dispersion of PCB powders. Process variables of oxidation leaching are examined by response surface methodology (RSM). A reliable mathematical model is obtained to predict the response as a function of independent variables and their interactions. Oxidation leaching is remarkably influenced by experimental variables, and the interactions between sulfuric acid and hydrogen peroxide are significant. Optimum conditions are achieved as sulfuric acid 1.0 mol/L, hydrogen peroxide 17%, temperature 50°C, and time 234 minutes, and the maximum leaching ratio of Cu is up to 99.94%, indicating that oxidation leaching is an effective method for Cu recovery from PCBs. Implications: Recycling of waste printed circuit boards (PCBs) receives increasing attention due to abundant metallic resources and significant environmental threats. This work proposes a novel process for copper recovery from PCBs by froth flotation and oxidation leaching. Froth flotation is efficient to enrich copper in metal fractions. Process variables of oxidation leaching are examined by response surface methodology (RSM). A reliable mathematical model is obtained to predict the response as a function of independent variables and their interactions. The froth flotation-oxidation leaching process is practicable and effective for copper recovery from waste printed circuit boards. This study significantly contributes to recycling metal resources from waste PCBs. We believe that this work will attract a broad readership and lead others to follow our approach.

Sliding behavior of high speed ball bearings based on improved nonlinear dynamic model

To accurately predict the dynamic behaviors of high speed ball bearings, an investigation on the sliding behavior of balls at high and low speeds, and light and heavy loads is necessary. However, existing nonlinear dynamic models fail to consider comprehensively key factors such as asperity and hydrodynamic tractions, time-varying friction coefficient and time-varying lubricant mode. In this work, these influencing factors are integrated into the nonlinear dynamic model to make it suitable for the working conditions of high and low speeds and light and heavy loads. The dynamic analysis provides the relation of angular speeds of balls with spin and sliding at light and heavy loads, also it reveals the number of pure rolling point under the combined effect of differential sliding and spin sliding. Research results provide a reliable mathematical model and theoretical bases for further studying the dynamic behaviors of high speed ball bearings.

Parameters Influencing Gene Delivery Efficiency of PEGylated Chitosan Nanoparticles: Experimental and Modeling Approach

Experimentation of nanomedicine is labor‐intensive, time‐consuming, and requires costly laboratory consumables. Constructing a reliable mathematical model for such systems is also challenging due to the difficulties in gathering a sufficient number of data points. Artificial neural networks (ANNs) are indicated as an efficient approach in nanomedicine to investigate the cause‐effect relationships and predict output variables. Herein, an ANN is adapted into plasmid DNA (pDNA) encapsulated and PEGylated chitosan nanoparticles cross‐linked with sodium tripolyphosphate (TPP) to investigate the effects of critical parameters on the transfection efficiencies of nanoparticles. The ANN model is developed based on experimental results with three independent input variables: 1) polyethylene glycol (PEG) molecular weight, 2) PEG concentration, and 3) nanoparticle concentration, along with one output variable as a percentage of green fluorescent protein (GFP) expression, which refers to transfection efficiency. The constructed model is further validated with the leave‐p‐out cross‐validation method. The results indicate that the developed model has good prediction capability and is influential in capturing the transfection efficiencies of different nanoparticle groups. Overall, this study reveals that the ANN could be an efficient tool for nanoparticle‐mediated gene delivery systems to investigate the impacts of critical parameters in detail with reduced experimental effort and cost.