Search results for: Domain Modelling

Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Dimitri Perrin, Heather J. Ruskin, Martin Crane

Abstract:

This study focuses on examining why the range of experience with respect to HIV infection is so diverse, especially in regard to the latency period. An agent-based approach in modelling the infection is used to extract high-level behaviour which cannot be obtained analytically from the set of interaction rules at the cellular level. A prototype model encompasses local variation in baseline properties, contributing to the individual disease experience, and is included in a network which mimics the chain of lymph nodes. The model also accounts for stochastic events such as viral mutations. The size and complexity of the model require major computational effort and parallelisation methods are used.

Keywords: HIV, Immune modelling, Agent-based system, individual response.

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Authors: Tahmine. V. Moghaddam, N. Bigdeli, K. Afshar

Abstract:

To achieve the desired specifications of gain and phase margins for plants with time-delay that stabilized with FO-PID controller a lead compensator is designed. At first the range of controlled system stability based on stability boundary criteria is determined. Using stability boundary locus method in frequency domain the fractional order controller parameters are tuned and then with drawing bode diagram in frequency domain accessing to desired gain and phase margin are shown. Numerical examples are given to illustrate the shapes of the stabilizing region and to show the design procedure.

Keywords: Fractional controller, Lead compensator, Stabilityregions, Stability boundary locus

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Authors: Sumit Tiwari, Rohit Tripathi, G. N. Tiwari

Abstract:

Present study focused on the utilization of solar energy by the help of photovoltaic greenhouse solar dryer under forced mode. A single slope photovoltaic greenhouse solar dryer has been proposed and thermal modelling has been developed. Various parameters have been calculated by thermal modelling such as greenhouse room temperature, cell temperature, crop temperature and air temperature at exit of greenhouse. Further cell efficiency, thermal efficiency, and overall thermal efficiency have been calculated for a typical day of May and November. It was found that system can generate equivalent thermal energy up to 7.65 kW and 6.66 kW per day for clear day of May and November respectively.

Keywords: Characteristics curve, Photovoltaic, Thermal modelling, Thermal efficiency.

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Authors: Ju Peng Poh, Jun Yu Charles Lee, Jonathan Chew Hoe Khoo

Abstract:

The emergence of digital twin technology, a digital replica of physical world, has improved the real-time access to data from sensors about the performance of buildings. This digital transformation has opened up many opportunities to improve the management of the building by using the data collected to help monitor consumption patterns and energy leakages. One example is the integration of predictive models for anomaly detection. In this paper, we use the GAM (Generalised Additive Model) for the anomaly detection of Air Handling Units (AHU) power consumption pattern. There is ample research work on the use of GAM for the prediction of power consumption at the office building and nation-wide level. However, there is limited illustration of its anomaly detection capabilities, prescriptive analytics case study, and its integration with the latest development of digital twin technology. In this paper, we applied the general GAM modelling framework on the historical data of the AHU power consumption and cooling load of the building between Jan 2018 to Aug 2019 from an education campus in Singapore to train prediction models that, in turn, yield predicted values and ranges. The historical data are seamlessly extracted from the digital twin for modelling purposes. We enhanced the utility of the GAM model by using it to power a real-time anomaly detection system based on the forward predicted ranges. The magnitude of deviation from the upper and lower bounds of the uncertainty intervals is used to inform and identify anomalous data points, all based on historical data, without explicit intervention from domain experts. Notwithstanding, the domain expert fits in through an optional feedback loop through which iterative data cleansing is performed. After an anomalously high or low level of power consumption detected, a set of rule-based conditions are evaluated in real-time to help determine the next course of action for the facilities manager. The performance of GAM is then compared with other approaches to evaluate its effectiveness. Lastly, we discuss the successfully deployment of this approach for the detection of anomalous power consumption pattern and illustrated with real-world use cases.

Keywords: Anomaly detection, digital twin, Generalised Additive Model, Power Consumption Model.

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Authors: C. Perez, O. Reinoso, N. Garcia, J. M. Sabater, L. Gracia

Abstract:

For high-speed control of robots, a good knowledge of system modelling is necessary to obtain the desired bandwidth. In this paper, we present a cartesian robot with a pan/tilt unit in end-effector (5 dof). This robot is implemented with powerful direct drive AC induction machines. The dynamic model, parameter identification and model validation of the robot are studied (including actuators). This work considers the cartesian robot coupled and non linear (contrary to normal considerations for this type of robots). The mechanical and control architecture proposed in this paper is efficient for industrial and research application in which high speed, well known model and very high accuracy are required.

Keywords: Robot modelling, parameter identification and validation, AC servo-motors.

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Authors: Gilbert Ndjatou

Abstract:

We propose a formal framework for the specification of the behavior of a system of agents, as well as those of the constituting agents. This framework allows us to model each agent-s effectoric capability including its interactions with the other agents. We also provide an algorithm based on Milner-s "observation equivalence" to derive an agent-s perception of its task domain situations from its effectoric capability, and use "system computations" to model the coordinated efforts of the agents in the system . Formal definitions of the concept of "behavior equivalence" of two agents and that of system computations equivalence for an agent are also provided.

Keywords: Multiagent system, object system, observation equivalence, reactive systems.

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Authors: Zahra Ghadampour, Gholamreza Rakhshandehroo

Abstract:

A concern that researchers usually face in different applications of Artificial Neural Network (ANN) is determination of the size of effective domain in time series. In this paper, trial and error method was used on groundwater depth time series to determine the size of effective domain in the series in an observation well in Union County, New Jersey, U.S. different domains of 20, 40, 60, 80, 100, and 120 preceding day were examined and the 80 days was considered as effective length of the domain. Data sets in different domains were fed to a Feed Forward Back Propagation ANN with one hidden layer and the groundwater depths were forecasted. Root Mean Square Error (RMSE) and the correlation factor (R2) of estimated and observed groundwater depths for all domains were determined. In general, groundwater depth forecast improved, as evidenced by lower RMSEs and higher R2s, when the domain length increased from 20 to 120. However, 80 days was selected as the effective domain because the improvement was less than 1% beyond that. Forecasted ground water depths utilizing measured daily data (set #1) and data averaged over the effective domain (set #2) were compared. It was postulated that more accurate nature of measured daily data was the reason for a better forecast with lower RMSE (0.1027 m compared to 0.255 m) in set #1. However, the size of input data in this set was 80 times the size of input data in set #2; a factor that may increase the computational effort unpredictably. It was concluded that 80 daily data may be successfully utilized to lower the size of input data sets considerably, while maintaining the effective information in the data set.

Keywords: Neural networks, groundwater depth, forecast.

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Authors: Jong-Whoi Shin, Soon-Tai Park, Chong-Sun Hwang

Abstract:

Active network was developed to solve the problem of the current sharing-based network–difficulty in applying new technology, service or standard, and duplicated operation at several protocol layers. Active network can transport the packet loaded with the executable codes, which enables to change the state of the network node. However, if the network node is placed in the sharing-based network, security and safety issues should be resolved. To satisfy this requirement, various security aspects are required such as authentication, authorization, confidentiality and integrity. Among these security components, the core factor is the encryption key. As a result, this study is designed to propose the scheme that manages the encryption key, which is used to provide security of the comprehensive active directory, based on the domain.

Keywords: Active Network, Domain-based Key Management, Security Components.

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Authors: Jawad Makki, Anne-Marie Alquier, Violaine Prince

Abstract:

In this paper we propose an NLP-based method for Ontology Population from texts and apply it to semi automatic instantiate a Generic Knowledge Base (Generic Domain Ontology) in the risk management domain. The approach is semi-automatic and uses a domain expert intervention for validation. The proposed approach relies on a set of Instances Recognition Rules based on syntactic structures, and on the predicative power of verbs in the instantiation process. It is not domain dependent since it heavily relies on linguistic knowledge. A description of an experiment performed on a part of the ontology of the PRIMA1 project (supported by the European community) is given. A first validation of the method is done by populating this ontology with Chemical Fact Sheets from Environmental Protection Agency2. The results of this experiment complete the paper and support the hypothesis that relying on the predicative power of verbs in the instantiation process improves the performance.

Keywords: Information Extraction, Instance Recognition Rules, Ontology Population, Risk Management, Semantic analysis.

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Authors: Changjin Xu

Abstract:

In this paper, applying frequency domain approach, a delayed predator-prey fishery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.

Keywords: Predator-prey model, stability, Hopf bifurcation, frequency domain, Nyquist criterion.

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Authors: E. Ramprasath, P. Manojkumar, P. Veena

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Proposed paper dealt with the modelling and analysis of induction motor based on the mathematical expression using the graphical programming environment of Laboratory Virtual Instrument Engineering Workbench (LabVIEW). Induction motor modelling with the mathematical expression enables the motor to be simulated with the various required parameters. Owing to the invention of variable speed drives study about the induction motor characteristics became complex. In this simulation motor internal parameter such as stator resistance and reactance, rotor resistance and reactance, phase voltage, frequency and losses will be given as input. By varying the speed of motor corresponding parameters can be obtained they are input power, output power, efficiency, torque induced, slip and current.

Keywords: Induction motor, LabVIEW software, modelling and analysis, electrical and mechanical characteristics of motor.

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Authors: Bhim Kumar Dahal

Abstract:

Transportation network development in the developing country is in rapid pace. The majority of the network belongs to railway and expressway which passes through diverse topography, landform and geological conditions despite the avoidance principle during route selection. Construction of such networks demand many low to high embankment which required improvement in the foundation soil. This paper is mainly focused on the various advanced ground improvement techniques used to improve the soft soil, modelling approach and its predictability for embankments construction. The ground improvement techniques can be broadly classified in to three groups i.e. densification group, drainage and consolidation group and reinforcement group which are discussed with some case studies.  Various methods were used in modelling of the embankments from simple 1-dimensional to complex 3-dimensional model using variety of constitutive models. However, the reliability of the predictions is not found systematically improved with the level of sophistication.  And sometimes the predictions are deviated more than 60% to the monitored value besides using same level of erudition. This deviation is found mainly due to the selection of constitutive model, assumptions made during different stages, deviation in the selection of model parameters and simplification during physical modelling of the ground condition. This deviation can be reduced by using optimization process, optimization tools and sensitivity analysis of the model parameters which will guide to select the appropriate model parameters.

Keywords: Embankment, ground improvement, modelling, model prediction.

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Authors: Mingyu Zhong, Yi Xie

Abstract:

Results in one field necessarily give insight into the others, and all have much potential for scientific and technological application. The Hadamard-transform technique once been applied to the spectrometry also has its use in the SNR Enhancement of OTDR. In this report, a new set of code (Simplex-codes) is discussed and where the addition gain of SNR come from is implied.

Keywords: Hadamard-transform, matrixes, averaging, opticaltime-domain reflectometry (OTDR).

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Authors: Wei Jun-xia, Yuan Guang-wei, Yang Shu-lin, Shen Wei-dong

Abstract:

In order to make conventional implicit algorithm to be applicable in large scale parallel computers , an interface prediction and correction of discontinuous finite element method is presented to solve time-dependent neutron transport equations under 2-D cylindrical geometry. Domain decomposition is adopted in the computational domain.The numerical experiments show that our parallel algorithm with explicit prediction and implicit correction has good precision, parallelism and simplicity. Especially, it can reach perfect speedup even on hundreds of processors for large-scale problems.

Keywords: Transport Equation, Discontinuous Finite Element, Domain Decomposition, Interface Prediction And Correction

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Authors: Ali M. Al-Shaery

Abstract:

The purpose of this paper is to address the functions of sustainability dimensions in city information modelling and to present the required sustainability criteria that support establishing a sustainable planning framework for enhancing existing cities and developing future smart cities. The paper is divided into two sections. The first section is based on the examination of a wide and extensive array of cross-disciplinary literature in the last decade and a half to conceptualize the terms ‘sustainable’ and ‘smart city’, and map their associated criteria to city information modelling. The second section is based on analyzing two approaches relating to city information modelling, namely statistical and dynamic approaches, and their suitability in the development of cities’ action plans. The paper argues that the use of statistical approaches to embed sustainability dimensions in city information modelling have limited value. Despite the popularity of such approaches in addressing other dimensions like utility and service management in development and action plans of the world cities, these approaches are unable to address the dynamics across various city sectors with regards to economic, environmental and social criteria. The paper suggests an integrative dynamic and cross-disciplinary planning approach to embedding sustainability dimensions in city information modelling frameworks. Such an approach will pave the way towards optimal planning and implementation of priority actions of projects and investments. The approach can be used to achieve three main goals: (1) better development and action plans for world cities (2) serve the development of an integrative dynamic and cross-disciplinary framework that incorporates economic, environmental and social sustainability criteria and (3) address areas that require further attention in the development of future sustainable and smart cities. The paper presents an innovative approach for city information modelling and a well-argued, balanced hierarchy of sustainability criteria that can contribute to an area of research which is still in its infancy in terms of development and management.

Keywords: Information modelling, smart city, sustainable city, sustainability dimensions, sustainability criteria, city development planning.

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Authors: A. M. Maqableh

Abstract:

Modelling techniques for a fluid coupling taken from published literature have been extended to include the effects of the filling and emptying of the coupling with oil and the variation in losses when the coupling is partially full. In the model, the fluid flow inside the coupling is considered to have two principal velocity components; one circumferentially about the coupling axis (centrifugal head) and the other representing the secondary vortex within the coupling itself (vortex head). The calculation of liquid mass flow rate circulating between the two halves of the coupling is based on: the assumption of a linear velocity variation in the circulating vortex flow; the head differential in the fluid due to the speed difference between the two shafts; and the losses in the circulating vortex flow as a result of the impingement of the flow with the blades in the coupling and friction within the passages between the blades.

Keywords: Fluid Coupling, Mathematical Modelling, partially filled.

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Authors: Mohamed Tarek Khadir, Damien Fay, Ahmed Boughrira

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Short term electricity demand forecasts are required by power utilities for efficient operation of the power grid. In a competitive market environment, suppliers and large consumers also require short term forecasts in order to estimate their energy requirements in advance. Electricity demand is influenced (among other things) by the day of the week, the time of year and special periods and/or days such as Ramadhan, all of which must be identified prior to modelling. This identification, known as day-type identification, must be included in the modelling stage either by segmenting the data and modelling each day-type separately or by including the day-type as an input. Day-type identification is the main focus of this paper. A Kohonen map is employed to identify the separate day-types in Algerian data.

Keywords: Day type identification, electricity Load, Kohonenmaps, load forecasting.

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Authors: Nabilah Filzah Mohd Radzuan, Andi Putra, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

Abstract:

Precipitation forecast is important in avoid incident of natural disaster which can cause loss in involved area. This review paper involves three techniques from artificial intelligence namely logistic regression, decisions tree, and random forest which used in making precipitation forecast. These combination techniques through VAR model in finding advantages and strength for every technique in forecast process. Data contains variables from rain domain. Adaptation of artificial intelligence techniques involved on rain domain enables the process to be easier and systematic for precipitation forecast.

Keywords: Logistic regression, decisions tree, random forest, VAR model.

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Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali

Abstract:

In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.

Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.

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Authors: A. Shebani, C. Pislaru

Abstract:

The wear measuring and wear modelling are fundamental issues in the industrial field, mainly correlated to the economy and safety. Therefore, there is a need to study the wear measurements and wear estimation. Pin-on-disc test is the most common test which is used to study the wear behaviour. In this paper, the pin-on-disc (AEROTECH UNIDEX 11) is used for the investigation of the effects of normal load and hardness of material on the wear under dry and sliding conditions. In the pin-on-disc rig, two specimens were used; one, a pin is made of steel with a tip, positioned perpendicular to the disc, where the disc is made of aluminium. The pin wear and disc wear were measured by using the following instruments: The Talysurf instrument, a digital microscope, and the alicona instrument. The Talysurf profilometer was used to measure the pin/disc wear scar depth, digital microscope was used to measure the diameter and width of wear scar, and the alicona was used to measure the pin wear and disc wear. After that, the Archard model, American Society for Testing and Materials model (ASTM), and neural network model were used for pin/disc wear modelling. Simulation results were implemented by using the Matlab program. This paper focuses on how the alicona can be used for wear measurements and how the neural network can be used for wear estimation.

Keywords: Wear measuring, Wear modelling, Neural Network, Alicona.

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Authors: Kahraman Ayyildiz, Stefan Conrad

Abstract:

In this paper we illuminate a frequency domain based classification method for video scenes. Videos from certain topical areas often contain activities with repeating movements. Sports videos, home improvement videos, or videos showing mechanical motion are some example areas. Assessing main and side frequencies of each repeating movement gives rise to the motion type. We obtain the frequency domain by transforming spatio-temporal motion trajectories. Further on we explain how to compute frequency features for video clips and how to use them for classifying. The focus of the experimental phase is on transforms utilized for our system. By comparing various transforms, experiments show the optimal transform for a motion frequency based approach.

Keywords: action recognition, frequency, transform, motion recognition, repeating movement, video classification

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Authors: Meltem Serhatli, Ferda N. Alpaslan

Abstract:

Processing the data by computers and performing reasoning tasks is an important aim in Computer Science. Semantic Web is one step towards it. The use of ontologies to enhance the information by semantically is the current trend. Huge amount of domain specific, unstructured on-line data needs to be expressed in machine understandable and semantically searchable format. Currently users are often forced to search manually in the results returned by the keyword-based search services. They also want to use their native languages to express what they search. In this paper, an ontology-based automated question answering system on software test documents domain is presented. The system allows users to enter a question about the domain by means of natural language and returns exact answer of the questions. Conversion of the natural language question into the ontology based query is the challenging part of the system. To be able to achieve this, a new algorithm regarding free text to ontology based search engine query conversion is proposed. The algorithm is based on investigation of suitable question type and parsing the words of the question sentence.

Keywords: Description Logics, ontology, question answering, reasoning.

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Authors: Mohamed EL Boujnouni, Mohamed Jedra, Noureddine Zahid

Abstract:

Support Vector Domain Description (SVDD) is one of the best-known one-class support vector learning methods, in which one tries the strategy of using balls defined on the feature space in order to distinguish a set of normal data from all other possible abnormal objects. As all kernel-based learning algorithms its performance depends heavily on the proper choice of the kernel parameter. This paper proposes a new approach to select kernel's parameter based on maximizing the distance between both gravity centers of normal and abnormal classes, and at the same time minimizing the variance within each class. The performance of the proposed algorithm is evaluated on several benchmarks. The experimental results demonstrate the feasibility and the effectiveness of the presented method.

Keywords: Gravity centers, Kernel’s parameter, Support Vector Domain Description, Variance.

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Authors: I. Severin, M. Caramihai, R. El Abdi, M. Poulain, A. Avadanii

Abstract:

In order to assess optical fiber reliability in different environmental and stress conditions series of testing are performed simulating overlapping of chemical and mechanical controlled varying factors. Each series of testing may be compared using statistical processing: i.e. Weibull plots. Due to the numerous data to treat, a software application has appeared useful to interpret selected series of experiments in function of envisaged factors. The current paper presents a software application used in the storage, modelling and interpretation of experimental data gathered from optical fibre testing. The present paper strictly deals with the software part of the project (regarding the modelling, storage and processing of user supplied data).

Keywords: Optical fibres, computer aided analysis, data models, data processing, graphical user interfaces.

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Authors: Shen Jian, Hu Jie, Ma Jin, Peng Ying Hong, Fang Yi, Liu Wen Hai

Abstract:

Biologically inspired design inspires inventions and new technologies in the field of engineering by mimicking functions, principles, and structures in the biological domain. To deal with the obstacles of cross-domain knowledge acquisition in the existing biologically inspired design process, functional semantic clustering based on functional feature semantic correlation and environmental constraint clustering composition based on environmental characteristic constraining adaptability are proposed. A knowledge cell clustering algorithm and the corresponding prototype system is developed. Finally, the effectiveness of the method is verified by the visual prosthetic device design.

Keywords: Knowledge based engineering, biologically inspired design, knowledge cell, knowledge clustering, knowledge acquisition.

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Authors: Liu Dan, Wang Xue, Wang Guiqin, Qian Zhihong

Abstract:

The burst noise is a kind of noises that are destructive and frequently found in semiconductor devices and ICs, yet detecting and removing the noise has proved challenging for IC designers or users. According to the properties of burst noise, a methodological approach is presented (proposed) in the paper, by which the burst noise can be analysed and detected in time domain. In this paper, principles and properties of burst noise are expounded first, Afterwards, feasibility (viable) of burst noise detection by means of wavelet transform in the time domain is corroborated in the paper, and the multi-resolution characters of Gaussian noise, burst noise and blurred burst noise are discussed in details by computer emulation. Furthermore, the practical method to decide parameters of wavelet transform is acquired through a great deal of experiment and data statistics. The methodology may yield an expectation in a wide variety of applications.

Keywords: Burst noise, detection, wavelet transform

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Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: L. Tani, N. El Ouzzani

Abstract:

Crosstalk among interconnects and printed-circuit board (PCB) traces is a major limiting factor of signal quality in highspeed digital and communication equipments especially when fast data buses are involved. Such a bus is considered as a planar multiconductor transmission line. This paper will demonstrate how the finite difference time domain (FDTD) method provides an exact solution of the transmission-line equations to analyze the near end and the far end crosstalk. In addition, this study makes it possible to analyze the rise time effect on the near and far end voltages of the victim conductor. The paper also discusses a statistical analysis, based upon a set of several simulations. Such analysis leads to a better understanding of the phenomenon and yields useful information.

Keywords: Multiconductor transmission line, Crosstalk, Finite difference time domain (FDTD), printed-circuit board (PCB), Rise time, Statistical analysis.

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