Reliable Mathematical Model Research Articles

Comprehensive and Integrated Mine Ventilation Consultation Model – CIMVCM

Since the beginning of mining, the problems induced by ventilation in underground coal mining practices have prompted great needs of reliable consulting tools to assist mining engineers, government agencies or researchers’ investigating and analyzing the mine ventilation system, or making any ventilation managements. Due to the development of mining method and modern mining (e.g. longwall mining) employed in recent years, the mentioned needs become more and more critical for mine operators. In this paper, a PC based computer mine ventilation consultation software model developed by the authors is introduced. This model is called CIMVCM (Comprehensive and Integrated Mine Ventilation Consultation Model). The computer model is a comprehensive, reliable and user-friendly one. The nature of “comprehensive” means the model can be used to consult the system’s rational reliability allocation, can assist engineers to select the best ventilation plan from multiple candidate ones, can quantitatively rate a system’s potential risk and safety degree and also can check the system’s reliability based on field observations. All of those works are very important to mine operators understanding the system and then taking proper measures to control the potential risk. In addition to that, usages of developed computer program are also very easy. Users can operate the program without possessing an in-depth knowledge on computer and mathematical theory. Until today, CIMVCM has been successfully employed in numerous cases of designing and assessing various mine ventilation systems during the past decades. The reliability of mathematical models used in CIMVCM has also been proven by such applications.

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

Functionally graded material (FGM) bars in axial motion (hereafter called “FGM axial bars”) have great potential for applications in many engineering fields. Therefore, it is important to develop a reliable mathematical model that can provide very accurate dynamic and wave propagation characteristics in FGM axial bars, especially at high frequencies. As an extension of our previous work, we present a spectral element model for a modified FGM axial bar model wherein nonuniform lateral contraction in the thickness direction is taken into account. We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the power law. The performance of the proposed spectral element model is validated through comparison with solutions from a conventional finite element model, and with the results from the previous FGM axial bar model. In addition, the effects of lateral contraction on the dynamic and wave propagation characteristics in example FGM axial bars are numerically investigated.

Modeling ecosystem processes with variable freshwater inflow to the Caloosahatchee River Estuary, southwest Florida. I. Model development

Variations in freshwater inflow have ecological consequences for estuaries ranging among eutrophication, flushing and transport, and high and low salinity impacts on biota. Predicting the potential effects of the magnitude and composition of inflow on estuaries over a range of spatial and temporal scales requires reliable mathematical models. The goal of this study was to develop and test a model of ecosystem processes with variable freshwater inflow to the sub-tropical Caloosahatchee River Estuary (CRE) in southwest Florida from 2002 to 2009. The modeling framework combined empirically derived inputs of freshwater and materials from the watershed, daily predictions of salinity, a box model for physical transport, and simulation models of biogeochemical and seagrass dynamics. The CRE was split into 3 segments to estimate advective and dispersive transport of water column constituents. Each segment contained a sub-model to simulate changes in the concentrations of organic nitrogen and phosphorus (ON and OP), ammonium (NH4+), nitrate-nitrite (NOx−), ortho-phosphate (PO4−3), phytoplankton chlorophyll a (CHL), and sediment microalgae (SM). The seaward segment also had sub-models for seagrasses (Halodule wrightii and Thalassia testudinum). The model provided realistic predictions of ON in the upper estuary during wet conditions since organic nitrogen is associated with freshwater inflow and low salinity. Although simulated CHL concentrations were variable, the model proved to be a reliable predictor in time and space. While predicted NOx− concentrations were proportional to freshwater inflow, NH4+ was less predictable due to the complexity of internal cycling during times of reduced freshwater inflow. Overall, the model provided a representation of seagrass biomass changes despite the absence of epiphytes, nutrient effects, or sophisticated translocation in the formulation. The model is being used to investigate the relative importance of colored dissolved organic matter (CDOM) vs. CHL in submarine light availability throughout the CRE, assess if reductions in nutrient loads are more feasible by controlling freshwater quantity or N and P concentrations, and explore the role of inflow and flushing on the fates of externally and internally derived dissolved and particulate constituents.

Performance analysis results of a battery fuel gauge algorithm at multiple temperatures

Evaluating a battery fuel gauge (BFG) algorithm is a challenging problem due to the fact that there are no reliable mathematical models to represent the complex features of a Li-ion battery, such as hysteresis and relaxation effects, temperature effects on parameters, aging, power fade (PF), and capacity fade (CF) with respect to the chemical composition of the battery. The existing literature is largely focused on developing different BFG strategies and BFG validation has received little attention. In this paper, using hardware in the loop (HIL) data collected form three Li-ion batteries at nine different temperatures ranging from −20 °C to 40 °C, we demonstrate detailed validation results of a battery fuel gauge (BFG) algorithm. The BFG validation is based on three different BFG validation metrics; we provide implementation details of these three BFG evaluation metrics by proposing three different BFG validation load profiles that satisfy varying levels of user requirements.

LiDAR data reduction assisted by optical image for 3D building reconstruction

The focus of LiDAR data compression and reduction has been raised in recent years due to the dramatically huge amount of points cloud. To improve the disposal efficiency of LiDAR data, a data reduction method assisted by optical image for 3D reconstruction of building facade is proposed in this article. The method involves a series of procedures of “2D feature line extraction – 3D feature line converting – buffer area of LiDAR points”. The main issue here is finding out a LiDAR point dataset around the 3D feature segment converted from 2D feature lines, which benefits to improving the efficiency of post-processing based on LiDAR data. The reduced LiDAR data can be obtained with reliable structures and accurate geometric position. Furthermore, the experiment of the LiDAR data reduction was conducted over the Xingyuan Building in Nanjing Normal University. The reduction method in this paper proved to be suit for the regular objects modeling, on the basis of the reliable and rigorous mathematical models and computer algorithms, and was a fundamental and useful approach to improve the efficiency of 3D reconstruction of building with the higher modeling accuracy.

Towards the real-life implementation of MPC for an office building: Identification issues

Modern control methods such as Model Predictive Control (MPC) are getting popular in recent years in many fields of industry. One of the branches that have witnessed great increase of interest in use of the MPC over the last few years is the building climate control area. According to the studies, the energy used in the building sector counts for 20–40% of the overall energy consumption. Almost half of this amount consists of heating, ventilation and air-conditioning (HVAC) costs which implies that energy consumption decrease in this area is one of the most interesting challenges today.Besides enormous potential in reduction of energy consumed by heating, ventilation and air conditioning (HVAC) systems brought by such controller, it suffers from a bottleneck being the necessity of having a reliable mathematical model of the building at disposal. By finding a mathematical model appropriate for the MPC, it is meant to obtain such a model that is able to predict the behavior of the building sufficiently accurately for several hours ahead, which is an especially delicate task. This task is getting even more complicated in case of a real-life application.In this paper, we are looking for a reliable model of a huge three-storey office building in Hasselt, Belgium. For parameter estimation, an advanced identification approach is used – its advantage is that it attacks the problem of minimization of multi-step prediction error and in this way, it corresponds to MPC requirements for a good multi-step predictor. Moreover, we discuss not only the identification approach itself but we also focus on accompanying problems with real-operation data acquisition, processing and special treatment which is an indispensable step for achieving satisfactory identification results. The chosen model is now used in real operation with MPC at Hollandsch Huys.

Life Cycle Costing Decision Analysis for Electric Multiple Units Based on Reliability

According to the relationship between reliability and Life Cycle Costing (LCC), we studied the best optimized solution of system reliability and LCC when researching and manufacturing EMU subsystem, choosing the overall system scheme and the purchase scheme. Classified by the different stages of life cycle, the composition of LCC on EMU was introduced, and the decomposition process of LCC structure, the method for estimating purchasing cost and acquisition and maintenance cost were put forward. By the analysis of the effect of reliability indexes on LCC of EMU, the mathematical model of reliability and LCC was established. Based on the model of the relationship between reliability and LCC, we providing a new way of researching and manufacturing EMU and making the purchase scheme by an optimization method to achieve a goal of increasing reliability while reducing LCC.

Practical Optimization of EMI Reduction in Spread Spectrum Clock Generators With Application to Switching DC/DC Converters

We here consider the most common technique used in spread spectrum clock generators that is the frequency modulation of a timing signal by means of a triangularly shaped waveform. As a first step, we develop a reliable mathematical model of a spectrum analyzer, which allows us to compute the power spectrum as measured by this instrument for any signal put at its input. This is particularly important when considering spread spectrum clocking methods for electromagnetic interference reduction, since international regulations impose constraints on the peak of the spectrum of interfering signals as measured by this instrument. Thanks to the developed mathematical tool, we are able to theoretically prove that the maximum peak reduction of the measured spectrum is achieved for a well-defined frequency of the triangular driving signal. This is in contrast with what one can obtain by optimizing the theoretical power density spectrum, where the minimum interference is ideally obtained when the triangular signal has a vanishing frequency. The results are confirmed by measurements on two commercial dc/dc switching converters.

Kinetics of hydrolysis of poly(ethylene terephthalate) wastes catalyzed by dual functional phase transfer catalyst: A mechanism of chain-end scission

The dual functional phase transfer catalyst [(CH3)3N(C16H33)]3[PW12O40] was used in the hydrolysis of poly(ethylene terephthalate) (PET) wastes and exhibited outstanding catalytic activity. In this work, the kinetic study about this reaction was carried out. The quantification of ethylene glycol (EG) formed in the hydrolysis was used to describe the reaction rate, which could result in more feasible and accurate kinetic analysis than terephthalic acid (TPA) formation or PET consumption used in traditional method. The results of kinetic analysis showed that the depolymerization reaction rate was first order to PET and catalyst concentration. This indicated that the ester linkages on the surface of the PET sequentially reacted with water to produce products. A mechanism for the reaction occurring on the polymer chain end section was proposed. Also the activation energy value was derived. Kinetic correlations provided a reliable mathematical reaction model for this recycling process, which is in agreement with the principles of sustainable development.

An application of fractional factorial design in wire electrochemical turning process

Design of experiment (DOE) is a structured, organized method for determining the significant and insignificant factors as well as the relationship between the different input factors affecting the outputs of a process. DOE involves designing a set of experiments, in which all relevant factors are varied systematically. One of the most important methods of DOE is fractional factorial design. Fractional factorial design sacrifices interaction effects so that main effects may still be computed correctly. This paper proposes an application of fractional factorial design to execute the experimental procedures, to determine the significant and insignificant factors, and finally, to investigate a reliable mathematical model for maximizing the metal removal rate in the one of the nontraditional machining processes. Nontraditional machining processes have the ability to machine the highly alloyed materials with a fine surface finish and high-dimensional accuracy. To provide a realistic environment for applying the fractional factorial design, wire electrochemical turning (WECT) process is adopted as a test bed.

PROTECTION OF INFORMATION IN CRITICAL APPLICATION DATA PROCESSING SYSTEMS

The results of researches, allowing raising the level of protection of the automated data processing systems of critical applications and intellectual information systems of enterprises are presented in the article. The mathematical models and results of vulnerability estimation of information systems which have Internet connection through various communication channels are resulted in this work. The system approach to solving problems of information security, proposed in this work provides for the integration of mathematical models of the processing and protection of information. The method of modeling the security policy to provide a highly reliable information processing has been developed. The mathematical models of synthesis of policy safe interaction of information processes, allowing security policy to consider separately the various structural components of network with the ability to its further interlinkages have been developed. Using the new mathematical models of flexible reliability, availability, confidentiality and integrity of information processed, allowing mathematically describe the mechanisms to ensure the availability and confidentiality of the information and take into account the quantitative requirements for data integrity.

Chemical warfare and survival strategies in bacterial range expansions.

Dispersal of species is a fundamental ecological process in the evolution and maintenance of biodiversity. Limited control over ecological parameters has hindered progress in understanding of what enables species to colonize new areas, as well as the importance of interspecies interactions. Such control is necessary to construct reliable mathematical models of ecosystems. In our work, we studied dispersal in the context of bacterial range expansions and identified the major determinants of species coexistence for a bacterial model system of three Escherichia coli strains (toxin-producing, sensitive and resistant). Genetic engineering allowed us to tune strain growth rates and to design different ecological scenarios (cyclic and hierarchical). We found that coexistence of all strains depended on three strongly interdependent factors: composition of inoculum, relative strain growth rates and effective toxin range. Robust agreement between our experiments and a thoroughly calibrated computational model enabled us to extrapolate these intricate interdependencies in terms of phenomenological biodiversity laws. Our mathematical analysis also suggested that cyclic dominance between strains is not a prerequisite for coexistence in competitive range expansions. Instead, robust three-strain coexistence required a balance between growth rates and either a reduced initial ratio of the toxin-producing strain, or a sufficiently short toxin range.

A Study of the Contact Interface of a T-slot Milling Cutter Using an Ultrasonic Method

As there is no reliable mathematical model to analyze a simultaneous multi-point contact, ultrasound offers an effective way to study the contact between two objects. In this study, a measurement of the contact area between a T-slot milling cutter and a steel plate was investigated by using ultrasonic regional detection. A single transducer was equipped to inspect the contact surface. The transducer movement was 0.15 mm, which resulted in 25,600 scanning data points within a 24 mm × 24 mm square area. The scanned readings were taken from the original signal and then processed to plot the contact patches, using MATLAB. The image of contact area between a T-slot milling cutter and specimen can be worked out using image analysis software. The range of contact areas varies from 3 mm2 to 49 mm2 in axial contact and from 0.3 mm2 to 9.6 mm2 in lateral contact, depending on the contact force and the definition of contrast ratio. Knowing the size of contact area is helpful for conducting a wear diagnosis. In addition, a distribution map of contact pressure against the applied loading is presented.

Reliability Analysis Based on Markov Process for Repairable Systems

The problems of reliability and maintainability for repairable systems are investigated in this paper, and Markov process is employed to build the mathematical models of availability and reliability for the repairable systems. Firstly, the formulas of availability and reliability for single repairable systems are deduced. Then, the repairable system with two parallel components and one standby are investigated, which is common in engineering application. Finally, simple approaches are summarized for availability of complicated repairable systems. Since the two approaches has the same result, which provides theoretical proof for the study of repairable systems’reliability and availability.

Reliability Study of Aviation Equipment

It is well-known that reliability of equipment is the most important of all performance to all equipments. In order to make the equipments which include mechanical equipments, electrical equipments and so on work normally, reliability theory FMECA is applied in an aviation equipment to study its reliability and improve operational reliability of the product. Through its reliability mathematical model, average of operational time is predicted based on calculating failure probability of all electrical components. According to the process of FMECA, all kinds of the failure mode, reasons, effects and criticality of the products can be determined completely. By comparing these criticality data as shown, the paper analyses adopted method by that the contents, accents and operating process of maintenance may be instituted finally. FMECA-based method for reliability study of the equipment and the equipment maintenance perform well. The results indicate that application of FMECA method can analyze reliability in detail and improve operational reliability of the equipment. Therefore this will supply theoretical bases and concrete measures of maintenance of the products to improve operational reliability of products. FMECA can be feasible and effective for improving operational reliability of all equipments.

ENSURING OF INFORMATION PROCESSES’ RELIABILITY AND SECURITY IN CRITICAL APPLICATION DATA PROCESSING SYSTEMS

Summary: The system approach to solving problems of information security, proposed in this work provides for the integration of mathematical models of the processing and protection of information. This model connects invulnerability and flexibility for each of three aspects of security (confidentiality, availability and integrity) of information based on structural unification of these contradictions. The method of modeling the security policy (SP) to provide a highly reliable information processing (HRIP) has been developed. This method differs by using a new problem-based graph-theoretic unit of standard model of the protected automated system for connection flexibility the discretionary model with the principled security of models of the final states of the SP. The mathematical models of synthesis of policy safe interaction of information processes, allowing SP to consider separately the various structural components of network with the ability to its further interlinkages have been developed. Using the new mathematical models of flexible reliability, availability, confidentiality and integrity of information processed, allowing mathematically describe the mechanisms to ensure the availability and confidentiality of the information and take into account the quantitative requirements for data integrity.

Configuration Analysis of a High-Altitude Airship’s Regenerative Power System

In the design of the power system of a high-altitude airship (HAA), the principal target is to satisfy the needs of the power demand and achieve the best balance of minimum weight and maximum reliability. To handle this problem, configuration analysis of the power system is performed. Mathematical models of output power, reliability, and weight are presented. Relationships between weight, reliability, and configurations are discussed in detail. Several design rules related to the design of the HAA’s power system are deduced. For obtaining the optimal configuration, the self-adaptive genetic algorithm (GA) is applied. Results show that the optimal configuration, compared to the configuration without redundancy, has a 258% increase in reliability and a 55.9% increase in weight. The weight increase is necessary to achieve more reliability improvement.

Modelling and Computer Simulation of Nanostructured Devices

Theory, modeling, and simulation provide investigative tools that support nanotechnology. Multi scale modeling is essential for exploring the numerous, new technology possibilities that research in nanoscience is creating. The purpose of the proposed review work is to explore models and techniques for designing and controlling nanostructured devices and establish links between physical (quantum) device modelling, experimental system identification, model verification and quantum control. Having reliable mathematical and computational models, methods and using standard tools with efficient computer simulation, it is essential to design complicated quantum devices such as semi-conductor nanostructures, superconducting devices before they are fabricated experimentally. The proposed review work will be useful to know the current status of nanostructure devices simulations and the work that is carried out in various centers to understand the physics and transport phenomena occurring in the nanoscale and better design of nanostructured devices.

Temperature control of a crude oil preheating furnace using a modified Smith predictor improved with a disturbance rejection term

This paper proposes a two degrees of freedom modified Smith predictor scheme for controlling the outlet temperature uniformity of a crude oil preheating furnace. A reliable mathematical model for describing the nominal process dynamics has been obtained from an identification procedure using realtime field data. This procedure yields a second order model with a dominant time-delay term (significantly higher than the time constant values). Moreover, disturbances have been identified as step responses of first order processes. A PI controller embedded in a modified Smith predictor scheme is therefore designed. A disturbance rejection term is designed for this scheme. This term is designed using a new methodology which reduces the effect of unknown disturbances on the process output. Simulations show that our proposal significantly outperforms the one degree of freedom Smith predictor and a well-known two degrees of freedom Smith predictor.

Analytical solutions and moment analysis of general rate model for linear liquid chromatography

The general rate model (GRM) is considered to be a comprehensive and reliable mathematical model for describing the separation and mass transfer processes of solutes in chromatographic columns. However, the numerical solution of model equations is complicated and time consuming. This paper presents analytical solutions of the GRM for linear adsorption isotherms and different sets of boundary conditions at the column inlet and outlet. The analytical solutions are obtained by means of the Laplace transformation. Numerical Laplace inversion is used to transform back the solution in the time domain because analytical inversion cannot be obtained. The first four temporal moments are derived analytically using the Laplace domain solutions. The moments of GRM are utilized to analyze the retention times, band broadenings, front asymmetries and kurtosis of the elution profiles. Relationships are derived among the kinetic parameters to match the first four moments of GRM and the simpler lumped kinetic model (LKM). For validation, the analytical solutions are compared with numerical solutions of a second order finite volume scheme. Good agreements in the results verify the correctness of analytical solutions and the accuracy of the numerical scheme.