Reliable Mathematical Model Research Articles

A Design of Experiment (DoE) Approach to Model the Yield and Chemical Composition of Ajowan (Trachyspermum ammi L.) Essential Oil Obtained by Microwave-Assisted Extraction.

Ajowan (Trachyspermum ammi L.) is a spice traditionally used in Middle Eastern medicine and contains a valuable essential oil (EO) exploited in different fields, such as pharmaceutics, agrochemicals and food additives. This EO is mostly characterized by the thymol to which most of its biological properties are related. Given the economic value of ajowan and its increasing demand across the globe, the extraction method used for its EO is of paramount importance in terms of quality and quantity of the final product. In the present study, we used the design of experiment (DoE) approach to study and optimize the extraction of the ajowan EO using the microwave-assisted extraction (MAE), a novel extraction technique with high efficiency, low energy consumption, short process length and low environmental impact. A two-step DoE (screening followed by surface response methodology) was used to reduce the number of experiments and to improve the cost/benefit ratio. Reliable mathematical models, relating the more relevant EO features with the extraction conditions, were obtained and used to identify the best experimental conditions able to maximize the yield and thymol concentration. The optimized MAE procedure assures an EO with a higher yield and thymol amount compared with the standard hydrodistillation procedure.

On the development of mathematical models for the reliability evaluation of aircraft operation in combat conditions

The authors of this study propose a methodological approach to modelling the reliability evaluation of aircraft operation in combat conditions. When developing recommendations on operational and strategic requirements for promising aircraft, a very important aspect is the elicitation of the requirements for their reliability, namely no-failure operation. Reliability as a parameter of any equipment should be set in the technical specifications for development together with other operational requirements in the form of reasonable quantitative indicators – reliability standards. The establishment of specific reliability standards stimulates its growth and creates the basis for rational design, taking into account the requirements of reliable operation. The analysis showed that different models can be used to simulate aircraft reliability. In this case, for example, the final values of mean time to failure (MTTF) would be different. The test results show that the methods and mathematical models used to substantiate the values of time and probability of trouble-free operation of aircraft do not fully correspond to the actual processes of changing their state during the use in the military. This is confirmed by a significant discrepancy in the values of reliability indicators implemented in practice. This was due to the fact that the acquainted mathematical models of aircraft reliability do not take into account the combat conditions in which they are supposed to operate. In addition, the reliability indicators used do not take into account possible changes (decrease) in these indicators during the period of aircraft operation. In general, the shortcomings inherent in the methods and mathematical models currently used to describe the aircraft reliability reduce the accuracy of the results obtained, and also do not quite adequately reflect the features of the corresponding process. When using different models, the cost of time to failure differs significantly. The more factors are taken into account, the greater the operating time to failure will be. This means that when designing aircraft, it is necessary to set the value of this indicator greater than indicated in the form. Taking into account additional factors complicates the model, but at the same time makes it more accurate.

Overview of the Constitutive Model and Numerical Calibration by FEM to Compute Bearing Capacity and Embankment-Core Deformability

Numerical modeling is a powerful tool to determine the stress-strain relationships of structures. However, for a reliable application, physical and mathematical models must be calibrated and validated. This paper presents an overview of numerical calibration through the finite element method and plate-load tests in an embankment. Additionally, an analysis of the constitutive models used in soils is performed, and the elastic-plastic constitutive model of Mohr-Coulomb was selected since it is the best suited for this study. The results from three test areas within a refinery project that the Cuban government undertook in the province of Cienfuegos are used. The numerical model used in this study was calibrated by means of the error theory and the non-parametric hypothesis tests from Mann-Whitney U. From the practical point of view, this study gives two procedures to calibrate the numerical model with experimental results.

Development and research of a model for differential diagnosis of latent late syphilis and false-positive serological reactions on immunochips with a panel of 12 Treponema pallidum antigens

The aim - to find the optimal attributing rules to distinguish groups of latent stages of syphilis and false positive serological tests of using multivariate discriminant analysis
 Material and methods. The objects of the study were serum samples from patients with late latent (N=34) syphilis and false positive serological tests (N=31).
 The samples were studied to determine IgG and IgM levels using indirect immunofluorescent reaction with immunochip containing recombinant antigens T. pallidum
 Results The mathematical model allows to differentiate with a high degree of confidence patients with late latent syphilis and with false-positive serological reactions to syphilis.
 Conclusions. . Multivariate discriminant analysis makes possible to create reliable mathematical models to classify patients with late latent syphilis and with false-positive serological reactions to syphilis.

Co-hydrothermal carbonization of sewage sludge and banana stalk: Fuel properties of hydrochar and environmental risks of heavy metals

This study investigated co-hydrothermal carbonization (co-HTC) of sewage sludge (SS) and banana stalk (BS), mainly focusing on the variations in hydrochar fuel properties and migration behavior of heavy metals (HMs) responding to different reaction temperature and SS/BS mixing ratios. This work established reliable mathematical models to integrate discrete experimental points and further obtain continuous response surfaces. Moreover, coupling with the two-way analysis of variance, the relationship between hydrochar properties and process parameters could be intuitively described. Statistical analysis (P-value) revealed that the mixing ratio was the most dominant factor affecting various hydrochar characteristics. The synergistic effects, mainly induced by Maillard and Mannich reactions, would contribute to superior hydrochar yield, C and N contents, higher heating value, and energy yield compared with their calculated values. Thermogravimetric analysis indicated that co-HTC with BS was a viable avenue to improve hydrochar combustibility index S to an acceptable level, with figures elevating from 1.34–1.58 to 27.71 (10−7×min−2×℃−3). Additionally, co-HTC of SS and BS could generate efficient synergistic HMs immobilization effects, promoting the transformation of HMs from direct/potential eco-toxic fractions to non-toxic fraction, thereby largely reducing ecological risks of hydrochar. These findings provided referential information for harmless and resource utilization of SS and BS.

The study of the reliability of the hardware part of the office cluster

The study of measures of reliability of the hardware part of the office cluster was carried out on the example of the cluster SKIF-GEO-Office RB (further as “cluster”) developed within the framework of scientific and technical program "SKIF-NEDRA" (2015-2018, Program of the Union State of Russia and Belarus). The cluster components are located in a small rack on the basis of full Tower "Aerocool Expredator Black" type case.The basic architectural principles implemented in the cluster, the composition, structural and functional scheme of the cluster are given. The methodological support for calculating the reliability of the cluster, based on previous studies of the authors, and its structural scheme of reliability is justified. The choice of the main measures of reliability of the cluster core and the set of computing facilities is justified and formulas of calculation of these measures are given. The analysis of the consequences of failures of component parts of the cluster is carried out.A mathematical model of reliability (state graph) of the set of computing facilities of cluster is proposed, which allows to derive formulas for calculating the average value of the time-to-failure and time-to-interruption of cluster. The estimation of the reliability of the cluster as a whole, based on the calculation of measures of reliability on the reference data on the reliability of components as well as on the operation of supercomputers of the family SKIF. The measures of reliability of the cluster are calculated.

Experimental Methods for Measuring the Viscous Friction Coefficient in Hydraulic Spool Valves

In hydraulic components, nonlinearities are responsible for critical behaviors that make it difficult to realize a reliable mathematical model for numerical simulation. With particular reference to hydraulic spool valves, the viscous friction coefficient between the sliding and the fixed body is an unknown parameter that is normally set a posteriori in order to obtain a good agreement with the experimental data. In this paper, two different methodologies to characterize experimentally the viscous friction coefficient in a hydraulic component with spool are presented. The two approaches are significantly different and are both based on experimental tests; they were developed in two distinct laboratories in different periods of time and applied to the same flow compensator of a pump displacement control. One of the procedures was carried out at the Fluid Power Research Laboratory of the Politecnico di Torino, while the other approach was developed at the University of Parma. Both the proposed methods reached similar outcomes; moreover, neither method requires the installation of a spool displacement transducer that can significantly affect the results.

Estimating the optimal parameters of solid oxide fuel cell‐based circuit using parasitism‐predation algorithm

The process of constructing a reliable mathematical model of solid oxide fuel cell (SOFC) is a challenge due to its complex nature. This paper proposes a new methodology incorporated a recent meta-heuristic algorithm named parasitism-predation algorithm (PPA) to estimate the optimal parameters of SOFC equivalent circuit. Two experiments are conducted in this work; the first one comprises four measured datasets for a commercial enhanced cylindrical SOFC manufactured by Siemen Energy. While the second series consists of five measured datasets for a theoretical dynamic SOFC stack with 96 connected cells. The collected datasets are measured at different operating conditions. An excessive comparative study is presented with other optimizers of comprehensive learning particle swarm optimization (CLPSO), improved PSO with difference mean with perturbation (DMP_PSO), heterogeneous CLPSO (HCLPSO), locally informed PSO (LIPS), modified CSO with tri-competitive mechanism (MCSO), opposition-based learning competitive PSO (OBLCPSO), ranking-based biased learning swarm optimizer (RBLSO), competitive swarm optimizer (CSO), hybrid Jaya with DE (JayaDE), and social learning PSO (SLPSO). Furthermore, statistical analyses of the ranking tests, multiple sign tests, Friedman tests, and ANOVA are performed. The obtained results confirmed the proposed PPA's competence in constructing a reliable model of SOFC as it provides the least mean square error (MSE) between the measured and estimated characteristics of 2.164e−6 in the first series of experiments at 1073 K, in contrast, the most peer (CLPSO) provides 5.57e−6. Similarly, in the second series of experiments, PPA achieves lease MSE of 7.17e−2 at 973 K; meanwhile, the most peer (CLPSO) attains 5.44e−1.

Semi-Markov modeling for assessing reliability of road construction machines in the process of their operation

The article provides a theoretical description of the processes of changing the technical state of road-building machines to assess their reliability at the stage of operation based on semi-Markov models. Reliability is the most important property of machines and characterizes their ability to perform their functions during normal operation. Reliability covers all stages of the life cycle of equipment-its design, manufacture, and operation. The operation stage is the longest in time and the costliest to ensure reliability. This explains the relevance of developing a mathematical model of operational reliability of road-building machines. During the operation of technical objects, their technical condition changes under the influence of objective and subjective factors. As a result, quantitative indicators that characterize the technical condition of machines vary widely and are random in nature. Road-building machines may be in one of the following technical states during operation: perfect, imperfect, upstate, down state. At the same time, a perfect machine is always upstate, and an imperfect one can be either upstate or down state. The transition from one technical state to another is random and can be considered instantaneous with a sufficient degree of accuracy. The probability of any technical state in the future depends only on the state of the process in the present and does not depend on when and how the process was in this state. This makes it possible to use the theory of semi-Markov processes when formalizing the process and developing a mathematical model. Based on semi-Markov modeling, the article shows the sequence of constructing a graph of states and transitions from one state to another for a road construction machine during operation; matrices of transitions and probabilities of transitions from one state to another; systems of differential equations for determining the limiting probabilities of finding a machine in a particular technical state during operation. The developed method of semi-Markov modeling allows estimating the operational reliability of equipment with the reliability allowed by probability theory.

Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures’ first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.

The interaction between two electrohydrodynamics phenomena when an electric field affects a two-phase immiscible liquid

Electrohydrodynamic (EHD) phenomena in two-phase immiscible liquids—droplet electrodeformation and electrical coalescence—underpin several technologies, e.g., electrostatic phase separation of water-oil emulsions. The corresponding devices' development calls for a deeper understanding of the underlying physics and reliable mathematical and numerical models. However, another EHD phenomenon that has to take place under the same conditions and can affect the results is unfairly overlooked. The phenomenon is the emergence of near-interface dissociation–recombination layers and EHD conduction pumping inside the dielectric phase. The present paper considers the electrical deformation of a conducting droplet suspended in a low-conducting liquid. A numerical simulation is used to show an EHD conduction pumping (like that emerging near an electrode in low-conducting fluid) to emerge near the interface of two immiscible liquids when one of them is a low-conducting medium. The space charge that causes this EHD flow also affects the Coulomb force applied to the interface and therefore changes droplet electrodeformation. Moreover, both the increase and decrease of electrodeformation are possible outcomes, which can be explained by a concurrent effect on the electric field distribution of charged layers emerging near both the interface and electrodes.

Investigation on the Mathematical Relation Model of Structural Reliability and Structural Robustness

Structural reliability and structural robustness, from different research fields, are usually employed for the evaluative analysis of building and civil engineering structures. Structural reliability has been widely used for structural analysis and optimization design, while structural robustness is still in rapid development. Several dimensionless evaluation indexes have been defined for structural robustness so far, such as the structural reliability-based redundancy index. However, these different evaluation indexes are usually based on subjective definitions, and they are also difficult to put into engineering practice. The mathematical relational model between structural reliability and structural robustness has not been established yet. This paper is a quantitative study, focusing on the mathematical relation between structural reliability and structural robustness so as to further develop the theory of structural robustness. A strain energy evaluation index for structural robustness is introduced firstly by considering the energy principle. The mathematical relation model of structural reliability and structural robustness is then derived followed by a further comparative study on sensitivity, structural damage, and random variation factor. A cantilever beam and a truss beam are also presented as two case studies. In this study, a parabolic curve mathematical model between structural reliability and structural robustness is established. A significant variation trend for their sensitivities is also observed. The complex interaction mechanism of the joint effect of structural damage and random variation factor is also reflected. With consideration of the variation trend of the structural reliability index that is affected by different degrees of structural damage (mild impairment, moderate impairment, and severe impairment), a three-stage framework for structural life-cycle maintenance management is also proposed. This study can help us gain a better understanding of structural robustness and structural reliability. Some practical references are also provided for the better decision-making of maintenance and management departments.

Computer simulation of processes of changing the reliability characteristics of systems with recoverable and non-recoverable elements based on the Simulink Dynamic Simulation Package

The paper presents a methodology and software package of mathematical and computer simulation of changes in the reliability characteristics and integrated indicators of system reliability during operation using Simulink. The software package is an application (Toolbox) to the standard Simulink package. The theoretical basis of the proposed algorithms is the method of analyzing structural diagrams of system reliability. The author proposes an original diagram of building a mathematical model of reliability with both non-recoverable and recoverable elements. The diagram involves a broad interpretation of the concepts of a “recoverable element” and a “recoverable element failure”. This approach found reflection in the wide range of proposed simulation tools. The advantage of the proposed products is the unification and relative ease of building models of systems of a sufficiently high level of complexity, and a wide range of intermediate simulation results available for analysis. The methodology and software package can be used during the system design stage to predict their reliability performance. The paper presents some simulation results.

Screening and identification of soybean varieties with high phosphorus efficiency at seedling stage

In order to simplify the workload and find a reliable method for screening soybeans with different phosphorus (P) efficiencies, 47 soybean varieties were screened from 90 varieties according to yield under normal phosphorus, and 10 indicators including root phenotype, phosphorus utilization efficiency at the seedling stage and yield were measured. Through single-index cluster analysis, the performance value and relative value of the above-mentioned indexes under low-phosphorus conditions were analyzed, and then, the combined indexes were analyzed by principal components method. The membership function method and the cluster analysis method was used to calculate and analyze the comprehensive score value. Three indexes of root P utilization efficiency (X1), relative value of root P utilization efficiency (X2), and root volume (X3) under low P at the seedling stage were selected as the most consistent with the yield screening results under low P condition, and the mathematical model of the comprehensive score value was obtained: D ​= ​1.218X1+ 0.320X2+ 0.007X3-0.664 (P ​= ​0.000, R2 ​= ​1.000). The comprehensive score can screen and identify the P efficiency of soybeans with fewer indexes in the early growth stages, which provides a more rapid and reliable mathematical model for screening and identifying a larger number of germplasm resources for P efficiency.

A Back-of-Queue Model of a Signal-Controlled Intersection Approach Developed Based on Analysis of Vehicle Driver Behavior

In smart cities, it is expected that transport, communication as well as the movement of people and goods will take place in the shortest possible time while maintaining a high level of safety. In recent years, due to the significant increase in the number of passengers and vehicles on the road and the capacity limitations of transport networks, it has become necessary to use new technologies for intelligent control and traffic management. Intelligent transport systems use advanced technologies in the field of data gathering, information processing, and traffic control to meet current transport needs. To be able to effectively control and manage road traffic, it is necessary to have reliable mathematical models that allow for a faithful representation of the real traffic conditions. Models of this type are usually the basis of complex algorithms used in practice in road traffic control. The application of appropriate models reflecting the behavior of road users contributes to the reduction of congestion, the vehicles travel time on the transport network, fuel consumption and the emissions, which in turn support broadly understood energy savings. The article proposes a model that allows for the estimation of the maximum queue size at the signal-controlled intersection approach (so-called: maximum back-of-queue). This model takes into account the most important traffic characteristics of the vehicles forming this queue. The verification allowed for the conclusion that the proposed model is characterized by high compliance with the actual traffic and road conditions at the intersections with signal controllers located in built-up areas in Poland. The obtained compliance confirms the possibility of using the model for practical applications in calculating the maximum back-of-queue at signal-controlled intersections located in built-up areas in Poland.

Availability Measures for 4-Component system by using Markov Process

G.Sarithaet al.,International Journal of Advanced Trends in Computer Science and Engineering, 10(1), January –February 2021, 340 -344340ABSTRACTAvailability depends on both reliability and maintainability. To predict systemavailability, both the failure and repair probability must be considered. Markov process is employed to build the Mathematical models of reliability and availability for the repairable systems. In this paper, availability is computed for repairable systemconsisting of 4-components by using Markov process.

Mathematical Models for Predicting Covid-19 Pandemic: A Review

The catastrophic outbreak of the Novel Corona virus (Covid-19) has brought to light, the significance of reliable predictive mathematical models. The results from such models greatly affect the use of non-pharmaceutical intervention measures, management of medical resources and understanding risk factors. This paper compares popular mathematical models based on their predictive capabilities, practical validity, presumptions and drawbacks. The paper focuses on popular techniques in use for the predictive modeling of the Covid-19 epidemic. The paper covers the Gaussian Model, SIRD, SEIRD and the latest θ-SEIHRD techniques used for predictive modeling of epidemics.

4E analysis and multiple objective optimizations of a cascade waste heat recovery system for waste-to-energy plant

Owning to its advantage in waste reuse, waste-to-energy technology, has become the most popular way to deal with the increasingly municipal solid waste. However, the energy efficiency of waste-to-energy plant is limited because of the huge heat loss. In this study, a novel waste heat recovery system, consisting of a supercritical CO2 cycle, an organic Rankine cycle, and an absorption refrigeration cycle, is proposed to improve both the thermal efficiency and economic performance of the waste-to-energy plant. A comprehensive thermodynamic analysis is performed to study the energy and exergy efficiency of the system by establishing a reliable mathematical model. Net present value analysis is carried out to study the final net profit and dynamic investment payback period. Besides, the levelized cost of electricity and ecological efficiency of the waste-to-energy plant are investigated. Based on the results of parameter sensitivity analysis of the system, multiple objective optimizations is carried out by using non-dominated sorting genetic algorithm-II. The results show that the combined system obtains the highest economic benefit in winter. The energy efficiency of the waste-to-energy plant can be up to 75.07% after adding the waste heat recovery system, with an increment of 54.58%. And the maximum net present value and minimum dynamic payback period are 23.22 M$ and 4.11 years, separately. Compared with the original waste-to-energy plant, the levelized cost of electricity and ecological efficiency are decreased by 68% and increased by 16%, respectively. From the results of sensitivity analysis, the isentropic efficiency of turbine of supercritical CO2 cycle, the evaporator pressure of organic Rankine cycle, and the generator temperature of absorption refrigeration cycle are the most sensitive factors for the thermal efficiency and economic performance of the system. The exergy destruction analysis shows that the exergy destruction rate of the boiler declines to 48.41% after adding the waste heat recovery system, but the condensers need further improvement for their lowest exergy efficiency. In conclusion, the waste-to-energy plant can provide electricity, heating and cooling simultaneously after adding the waste heat recovery system and the proposed system is theoretically feasible from the results of thermodynamic, economic and environmental analysis.

Simulation of the insulation monitoring system of the high-voltage electrical network of a vehicle with a hybrid power plant

The paper presents the results of mathematical and simulation modeling, as well as calculated and experimental dependencies, which make it possible to evaluate the operation of the insulation resistance monitoring system of the high-voltage power grid of a hybrid vehicle. The work also provides circuits for measuring insulation resistance, a mathematical model in the MATLAB Simulink environment, and the peculiarities of the operation of the software and hardware simulation complex. The aim of the work is to obtain the most reliable mathematical and physical model of insulation resistance, to determine the architecture of a high voltage battery with the IRM system included in it, to identify the key functions and characteristics of the IRM system, to test the simulation system. The introduction justifies the importance of the IRM system and provides references to standards that govern the requirements for measuring and identifying utility faults. The block diagram of the high voltage battery control system is presented. The composition of its main elements is described. The functions and key characteristics of the IRM system are considered, typical characteristics of insulation monitoring systems are given. A schematic diagram of determining the insulation resistance of conductors and an electric circuit is clearly considered. An equivalent circuit of a differential DC amplifier with a unipolar power supply is presented, which is used to amplify small differential voltages on a shunt when changing large common-mode voltages, which is part of the measuring circuit. Mathematical and simulation modeling was carried out to evaluate the method for calculating the insulation resistance according to the well-known scheme, which is used when measuring using the three-voltmeter method. There was considered the mode of checking the the insulation control system, when several test procedures performed containing simulation of the fault and operating condition of the insulation by connecting and measuring the test resistance. The results of physical simulation of the IRM system and measurement of insulation resistance, voltage between each of the high voltage supply wires and the high voltage battery case, voltage between the wires, battery voltage were obtained. The actual insulation resistance was calculated. The conclusions explain the effectiveness of physical and simulation modeling, obtaining a reliable mathematical model and low error in modeling the insulation characteristics.

Research on Reliability Prediction method of Complex Mechanical Product Based on Meta-action Unit

Reliability prediction of complex mechanical product is helpful to determine the reliability state of products and that how to optimize products. Traditional reliability prediction methods of complex mechanical products come from electronic products, which need a certain amount of reliability data as support. In addition, the reliability of system complex mechanical product is generally predicted by the parts or component that make up it. However, failure of one part may not cause failure of the whole product, that will affect the accuracy of reliability prediction. To solve these problems and in order to accurately predict the reliability of complex mechanical product, a methodology based on meta-action unit (MAU) which is the basic units affecting reliability is proposed in this paper. The mechanical product is decomposed into many MAUs, and the conception of “unit quality entropy” is introduced to predict the reliability index of MAU. Subsequently, according to the reliability mathematical model of complex mechanical product and MAU, the reliability is predicted by combining interval analytical hierarchy method and eigenvector method. This paper also verifies that the method is applicable and is more accurate with a case study of the reliability of spindle box.