Abstract: For the synchronous generator simulation and analysis and for the power system stabilizer design and synthesis a mathematical model of synchronous generator is needed. The model has to accurately describe dynamics of oscillations, while at the same time has to be transparent enough for an analysis and sufficiently simplified for design of control system. To study the oscillations of the synchronous generator against to the rest of the power system, the model of the synchronous machine connected to an infinite bus through a transmission line having resistance and inductance is needed. In this paper, the linearized reduced order dynamic model of the synchronous generator connected to the infinite bus is presented and analysed in details. This model accurately describes dynamics of the synchronous generator only in a small vicinity of an equilibrium state. With the digression from the selected equilibrium point the accuracy of this model is decreasing considerably. In this paper, the equations’ descriptions and the parameters’ determinations for the linearized reduced order mathematical model of the synchronous generator are explained and summarized and represent the useful origin for works in the areas of synchronous generators’ dynamic behaviour analysis and synchronous generator’s control systems design and synthesis. The main contribution of this paper represents the detailed analysis of the accuracy of the linearized reduced order dynamic model in the entire synchronous generator’s operating range. Borders of the areas where the linearized reduced order mathematical model represents accurate description of the synchronous generator’s dynamics are determined with the systemic numerical analysis. The thorough eigenvalue analysis of the linearized models in the entire operating range is performed. In the paper, the parameters of the linearized reduced order dynamic model of the laboratory salient poles synchronous generator were determined and used for the analysis. The theoretical conclusions were confirmed with the agreement of experimental and simulation results.
Abstract: In this paper, we will present a mathematical model to design a system able to generate electricity from ocean-sea waves. We will use the basic principles of the transfer of the energy potential of waves in a chamber to force the air inside a vertical or inclined cylindrical column, which is topped by a wind turbine to rotate the electric generator. The present mathematical model included a high number of variables such as the wave, height, width, length, velocity, and frequency, as well as others for the energy cylindrical column, like varying diameters and heights, and the wave chamber shape diameter and height. While for the wells wind turbine the variables included the number of blades, length, width, and clearance, as well as the rotor and tip radius. Additionally, the turbine rotor and blades must be made from the light and strong material for a smooth blade surface. The variables were too vast and high in number. Then the program was run successfully within the MATLAB and presented very good modeling results.
Abstract: The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.
Abstract: In this paper, type-2 fuzzy logic control (T2FLC) and neuro-fuzzy control (NFC) for a doubly fed induction generator (DFIG) based on direct power control (DPC) with a fixed switching frequency is proposed for wind generation application. First, a mathematical model of the doubly-fed induction generator implemented in d-q reference frame is achieved. Then, a DPC algorithm approach for controlling active and reactive power of DFIG via fixed switching frequency is incorporated using PID. The performance of T2FLC and NFC, which is based on the DPC algorithm, are investigated and compared to those obtained from the PID controller. Finally, simulation results demonstrate that the NFC is more robust, superior dynamic performance for wind power generation system applications.
Abstract: Osteoarthritis affects a lot of people worldwide. Local injection of glucosamine is one of the alternative treatment methods to replenish the natural lubrication of cartilage. However, multiple injections can potentially lead to possible bacterial infection. Therefore, a drug delivery system is desired to reduce the frequencies of injections. A hydrogel is one of the delivery systems that can control the release of drugs. Thermo-reversible hydrogels can be beneficial to the drug delivery system especially in the local injection route because this formulation can change from liquid to gel after getting into human body. Once the gel is in the body, it will slowly release the drug in a controlled manner. In this study, various formulations of Pluronic-based hydrogels were synthesized for the controlled release of glucosamine. One of the challenges of the Pluronic controlled release system is its fast dissolution rate. To overcome this problem, alginate and calcium sulfate (CaSO4) were added to the polymer solution. The characteristics of the hydrogels were investigated including the gelation temperature, gelation time, hydrogel dissolution and glucosamine release mechanism. Finally, a mathematical model of glucosamine release from Pluronic-alginate-hyaluronic acid hydrogel was developed. Our results have shown that crosslinking Pluronic gel with alginate did not significantly extend the dissolution rate of the gel. Moreover, the gel dissolution profiles and the glucosamine release mechanisms were best described using the zeroth-order kinetic model, indicating that the release of glucosamine was primarily governed by the gel dissolution.
Abstract: In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
included.
Abstract: Pollutants from aquacultural practices constitute environmental problems and phytoremediation could offer cheaper environmentally sustainable alternative since equipment using advanced treatment for fish tank effluent is expensive to import, install, operate and maintain, especially in developing countries. The main objective of this research was, therefore, to develop a mathematical model for phytoremediation by aquatic plants in aquaculture wastewater. Other objectives were to evaluate the retention times on phytoremediation rates using the model and to measure the nutrient level of the aquaculture effluent and phytoremediation rates of three aquatic macrophytes, namely; water hyacinth (Eichornia crassippes), water lettuce (Pistial stratoites) and morning glory (Ipomea asarifolia). A completely randomized experimental design was used in the study. Approximately 100 g of each macrophyte were introduced into the hydroponic units and phytoremediation indices monitored at 8 different intervals from the first to the 28th day. The water quality parameters measured were pH and electrical conductivity (EC). Others were concentration of ammonium–nitrogen (NH4+ -N), nitrite- nitrogen (NO2- -N), nitrate- nitrogen (NO3- -N), phosphate –phosphorus (PO43- -P), and biomass value. The biomass produced by water hyacinth was 438.2 g, 600.7 g, 688.2 g and 725.7 g at four 7–day intervals. The corresponding values for water lettuce were 361.2 g, 498.7 g, 561.2 g and 623.7 g and for morning glory were 417.0 g, 567.0 g, 642.0 g and 679.5g. Coefficient of determination was greater than 80% for EC, TDS, NO2- -N, NO3- -N and 70% for NH4+ -N using any of the macrophytes and the predicted values were within the 95% confidence interval of measured values. Therefore, the model is valuable in the design and operation of phytoremediation systems for aquaculture effluent.
Abstract: Risk management in banking sector is a key issue
linked to financial system stability and its importance has been
elevated by technological developments and emergence of new
financial instruments. In this paper, we improve the model previously
defined for quantifying internal control impact on banking risks by
automatizing the residual criticality estimation step of FMECA. For
this, we defined three equations and a maturity coefficient to obtain
a mathematical model which is tested on all banking processes and
type of risks. The new model allows an optimal assessment of residual
criticality and improves the correlation rate that has become 98%.
Abstract: The paper deals with possibilities of increase train
capacity by using a new type of railway wagon. In the first part is
created a mathematical model to calculate the capacity of the train.
The model is based on the main limiting parameters of the train -
maximum number of axles per train, maximum gross weight of train,
maximum length of train and number of TEUs per one wagon. In the
second part is the model applied to four different model trains with
different composition of the train set and three different average
weights of TEU and a train consisting of a new type of wagons. The
result is to identify where the carrying capacity of the original trains
is higher, respectively less than a capacity of train consisting of a new
type of wagons.
Abstract: This paper studies a mathematical model based on the
integral equations for dynamic analyzes numerical investigations of a
non-uniform or multi-material composite beam. The beam is
subjected to a sub-tangential follower force and elastic foundation.
The boundary conditions are represented by generalized
parameterized fixations by the linear and rotary springs. A
mathematical formula based on Euler-Bernoulli beam theory is
presented for beams with variable cross-sections. The non-uniform
section introduces non-uniformity in the rigidity and inertia of beams
and consequently, more complicated equilibrium who governs the
equation. Using the boundary element method and radial basis
functions, the equation of motion is reduced to an algebro-differential
system related to internal and boundary unknowns. A generalized
formula for the deflection, the slope, the moment and the shear force
are presented. The free vibration of non-uniform loaded beams is
formulated in a compact matrix form and all needed matrices are
explicitly given. The dynamic stability analysis of slender beam is
illustrated numerically based on the coalescence criterion. A realistic
case related to an industrial chimney is investigated.
Abstract: In this paper, we present a four-step ortho-rectification
procedure for real-time geo-referencing of video data from a low-cost
UAV equipped with a multi-sensor system. The basic procedures for
the real-time ortho-rectification are: (1) decompilation of the video
stream into individual frames; (2) establishing the interior camera
orientation parameters; (3) determining the relative orientation
parameters for each video frame with respect to each other; (4)
finding the absolute orientation parameters, using a self-calibration
bundle and adjustment with the aid of a mathematical model. Each
ortho-rectified video frame is then mosaicked together to produce a
mosaic image of the test area, which is then merged with a well
referenced existing digital map for the purpose of geo-referencing
and aerial surveillance. A test field located in Abuja, Nigeria was
used to evaluate our method. Video and telemetry data were collected
for about fifteen minutes, and they were processed using the four-step
ortho-rectification procedure. The results demonstrated that the
geometric measurement of the control field from ortho-images is
more accurate when compared with those from original perspective
images when used to pin point the exact location of targets on the
video imagery acquired by the UAV. The 2-D planimetric accuracy
when compared with the 6 control points measured by a GPS receiver
is between 3 to 5 metres.
Abstract: In dynamic system theory a mathematical model is
often used to describe their properties. In order to find a transfer
matrix of a dynamic system we need to calculate an inverse matrix.
The paper contains the fusion of the classical theory and the
procedures used in the theory of automated control for calculating the
inverse matrix. The final part of the paper models the given problem
by the Matlab.
Abstract: A mathematical model of the additional effects of the
liquid in the hydrodynamic gap is presented in the paper. An
incompressible viscous fluid is considered. Based on computational
modeling are determined the matrices of mass, stiffness and damping.
The mathematical model is experimentally verified.
Abstract: The paper deals with possibilities of interpretation of
iron ore reducibility tests. It presents a mathematical model
developed at Centre ENET, VŠB – Technical University of Ostrava,
Czech Republic for an evaluation of metallurgical material of blast
furnace feedstock such as iron ore, sinter or pellets. According to the
data from the test, the model predicts its usage in blast furnace
technology and its effects on production parameters of shaft
aggregate. At the beginning, the paper sums up the general concept
and experience in mathematical modelling of iron ore reduction. It
presents basic equation for the calculation and the main parts of the
developed model. In the experimental part, there is an example of
usage of the mathematical model. The paper describes the usage of
data for some predictive calculation. There are presented material,
method of carried test of iron ore reducibility. Then there are
graphically interpreted effects of used material on carbon
consumption, rate of direct reduction and the whole reduction
process.
Abstract: An artificial neural network is a mathematical model
inspired by biological neural networks. There are several kinds of
neural networks and they are widely used in many areas, such as:
prediction, detection, and classification. Meanwhile, in day to day life,
people always have to make many difficult decisions. For example,
the coach of a soccer club has to decide which offensive player
to be selected to play in a certain game. This work describes a
novel Neural Network using a combination of the General Regression
Neural Network and the Probabilistic Neural Networks to help a
soccer coach make an informed decision.
Abstract: Cemented carbide balls are usually implemented in
industry under the environment of high speed, high temperature,
corrosiveness and strong collisions. However, its application is limited
due to high fabrication cost, processing efficiency and quality. A novel
eccentric lapping method with two rotatable lapping plates was
proposed in this paper. A mathematical model was constructed to
analyze the influence of each design parameter on this lapping method.
To validate this new lapping method, an orthogonal experiment was
conducted with cemented carbide balls (YG6). The simulation model
was verified and the optimal lapping parameters were derived. The
results show that the surface roundness of the balls reaches to 0.65um
from 2um in 1 hour using this lapping method. So, using this novel
lapping method, it can effectively improve the machining precision
and efficiency of cemented carbide balls.
Abstract: Analysis of the properties of coconut (Cocos nucifera)
and its oil was evaluated in this work using standard analytical
techniques. The analyses carried out include proximate composition
of the fruit, extraction of oil from the fruit using different process
parameters and physicochemical analysis of the extracted oil. The
results showed the percentage (%) moisture, crude lipid, crude
protein, ash and carbohydrate content of the coconut as 7.59, 55.15,
5.65, 7.35 and 19.51 respectively. The oil from the coconut fruit was
odourless and yellowish liquid at room temperature (30oC). The
treatment combinations used (leaching time, leaching temperature
and solute: solvent ratio) showed significant differences (P
Abstract: This paper proposes a mathematical model and
examines the performance of an exact algorithm for a location–
transportation problems in humanitarian relief. The model determines
the number and location of distribution centers in a relief network,
the amount of relief supplies to be stocked at each distribution center
and the vehicles to take the supplies to meet the needs of disaster
victims under capacity restriction, transportation and budgetary
constraints. The computational experiments are conducted on the
various sizes of problems that are generated. Branch and bound
algorithm is applied for these problems. The results show that this
algorithm can solve problem sizes of up to three candidate locations
with five demand points and one candidate location with up to twenty
demand points without premature termination.
Abstract: A Motzkin shift is a mathematical model for constraints
on genetic sequences. In terms of the theory of symbolic dynamics,
the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-
Frobenius theory to calculate its topological entropy. The Motzkin
shift M(M,N) which comes from language theory, is defined to be the
shift system over an alphabet A that consists of N negative symbols,
N positive symbols and M neutral symbols. For an x in the full shift,
x will be in the Motzkin subshift M(M,N) if and only if every finite
block appearing in x has a non-zero reduced form. Therefore, the
constraint for x cannot be bounded in length. K. Inoue has shown that
the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this
paper, a new direct method of calculating the topological entropy of
the Motzkin shift is given without any measure theoretical discussion.
Abstract: In an urban area the location allocation of emergency
services mobile units, such as ambulances, police patrol cars must be
designed so as to achieve a prompt response to demand locations.
In this paper the partition of a given urban network into distinct
sub-networks is performed such that the vertices in each component
are close and simultaneously the sums of the corresponding
population in the sub-networks are almost uniform. The objective
here is to position appropriately in each sub-network a mobile
emergency unit in order to reduce the response time to the demands.
A mathematical model in framework of graph theory is developed.
In order to clarify the corresponding method a relevant numerical
example is presented on a small network.