Search results for: Gaussian distribution
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2109

Search results for: Gaussian distribution

2049 Reliability Evaluation of Distribution System Considering Distributed Generation

Authors: Raju Kaduru, Narsaiah Srinivas Gondlala

Abstract:

This paper presents an analytical approach for evaluating distribution system reliability indices in the presence of distributed generation. Modeling distributed generation and evaluation of distribution system reliability indices using the frequency duration technique. Using model implements and case studies are discussed. Results showed that location of DG and its effect in distribution reliability indices. In this respect, impact of DG on distribution system is investigated using the IEEE Roy Billinton test system (RBTS2) included feeder 1. Therefore, it will help to the distribution system planners in the DG resource placement.

Keywords: Distributed Generation, DG Location, Distribution System, Reliability Indices.

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2048 Signal Reconstruction Using Cepstrum of Higher Order Statistics

Authors: Adnan Al-Smadi, Mahmoud Smadi

Abstract:

This paper presents an algorithm for reconstructing phase and magnitude responses of the impulse response when only the output data are available. The system is driven by a zero-mean independent identically distributed (i.i.d) non-Gaussian sequence that is not observed. The additive noise is assumed to be Gaussian. This is an important and essential problem in many practical applications of various science and engineering areas such as biomedical, seismic, and speech processing signals. The method is based on evaluating the bicepstrum of the third-order statistics of the observed output data. Simulations results are presented that demonstrate the performance of this method.

Keywords: Cepstrum, bicepstrum, third order statistics

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2047 Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution

Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.

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2046 Sparse Frequencies Extracting from Partial Phase-Only Measurements

Authors: R. Fan, Q. Wan, H. Chen, Y.L. Liu, Y.P. Liu

Abstract:

This paper considers a robust recovery of sparse frequencies from partial phase-only measurements. With the proposed method, sparse frequencies can be reconstructed, which makes full use of the sparse distribution in the Fourier representation of the complex-valued time signal. Simulation experiments illustrate the proposed method-s advantages over conventional methods in both noiseless and additive white Gaussian noise cases.

Keywords: Sparse signal recovery, phase-only measurements, Compressive sensing, convex relaxation.

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2045 A Compact Pi Network for Reducing Bit Error Rate in Dispersive FIR Channel Noise Model

Authors: Kavita Burse, R.N. Yadav, S.C. Shrivastava, Vishnu Pratap Singh Kirar

Abstract:

During signal transmission, the combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel which distort and add noise to the signal. This causes the well defined signal constellation to spread causing errors in bit detection. A compact pi neural network with minimum number of nodes is proposed. The replacement of summation at each node by multiplication results in more powerful mapping. The resultant pi network is tested on six different channels.

Keywords: Additive white Gaussian noise, digitalcommunication system, multiplicative neuron, Pi neural network.

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2044 Efficient Design of Distribution Logistics by Using a Model-Based Decision Support System

Authors: J. Becker, R. Arnold

Abstract:

The design of distribution logistics has a decisive impact on a company's logistics costs and performance. Hence, such solutions make an essential contribution to corporate success. This article describes a decision support system for analyzing the potential of distribution logistics in terms of logistics costs and performance. In contrast to previous procedures of business process re-engineering (BPR), this method maps distribution logistics holistically under variable distribution structures. Combined with qualitative measures the decision support system will contribute to a more efficient design of distribution logistics.

Keywords: Decision support system distribution logistics, potential analyses, supply chain management.

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2043 Active Linear Quadratic Gaussian Secondary Suspension Control of Flexible Bodied Railway Vehicle

Authors: Kaushalendra K. Khadanga, Lee Hee Hyol

Abstract:

Passenger comfort has been paramount in the design of suspension systems of high speed cars. To analyze the effect of vibration on vehicle ride quality, a vertical model of a six degree of freedom railway passenger vehicle, with front and rear suspension, is built. It includes car body flexible effects and vertical rigid modes. A second order linear shaping filter is constructed to model Gaussian white noise into random rail excitation. The temporal correlation between the front and rear wheels is given by a second order Pade approximation. The complete track and the vehicle model are then designed. An active secondary suspension system based on a Linear Quadratic Gaussian (LQG) optimal control method is designed. The results show that the LQG control method reduces the vertical acceleration, pitching acceleration and vertical bending vibration of the car body as compared to the passive system.

Keywords: Active suspension, bending vibration, railway vehicle, vibration control.

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2042 Edge Detection in Low Contrast Images

Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

Abstract:

The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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2041 Local Spectrum Feature Extraction for Face Recognition

Authors: Muhammad Imran Ahmad, Ruzelita Ngadiran, Mohd Nazrin Md Isa, Nor Ashidi Mat Isa, Mohd Zaizu Ilyas, Raja Abdullah Raja Ahmad, Said Amirul Anwar Ab Hamid, Muzammil Jusoh

Abstract:

This paper presents two techniques, local feature extraction using image spectrum and low frequency spectrum modelling using GMM to capture the underlying statistical information to improve the performance of face recognition system. Local spectrum features are extracted using overlap sub block window that are mapped on the face image. For each of this block, spatial domain is transformed to frequency domain using DFT. A low frequency coefficient is preserved by discarding high frequency coefficients by applying rectangular mask on the spectrum of the facial image. Low frequency information is non- Gaussian in the feature space and by using combination of several Gaussian functions that has different statistical properties, the best feature representation can be modelled using probability density function. The recognition process is performed using maximum likelihood value computed using pre-calculated GMM components. The method is tested using FERET datasets and is able to achieved 92% recognition rates.

Keywords: Local features modelling, face recognition system, Gaussian mixture models.

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2040 Design of Distribution Network for Gas Cylinders in Jordan

Authors: Hazem J. Smadi

Abstract:

Performance of a supply chain is directly related to a distribution network that entails the location of storing materials or products and how products are delivered to the end customer through different stages in the supply chain. This study analyses the current distribution network used for delivering gas cylinders to end customer in Jordan. Evaluation of current distribution has been conducted across customer service components. A modification on the current distribution network in terms of central warehousing in each city in the country improves the response time and customer experience. 

Keywords: Distribution network, gas cylinder, Jordan, supply chain.

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2039 A New Distribution and Application on the Lifetime Data

Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

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2038 Minimization of Power Loss in Distribution Networks by Different Techniques

Authors: L.Ramesh, S.P.Chowdhury, S.Chowdhury, A.A.Natarajan, C.T.Gaunt

Abstract:

Accurate loss minimization is the critical component for efficient electrical distribution power flow .The contribution of this work presents loss minimization in power distribution system through feeder restructuring, incorporating DG and placement of capacitor. The study of this work was conducted on IEEE distribution network and India Electricity Board benchmark distribution system. The executed experimental result of Indian system is recommended to board and implement practically for regulated stable output.

Keywords: Distribution system, Distributed Generation LossMinimization, Network Restructuring

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2037 A Note on Negative Hypergeometric Distribution and Its Approximation

Authors: S. B. Mansuri

Abstract:

In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.

Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.

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2036 Improved Text-Independent Speaker Identification using Fused MFCC and IMFCC Feature Sets based on Gaussian Filter

Authors: Sandipan Chakroborty, Goutam Saha

Abstract:

A state of the art Speaker Identification (SI) system requires a robust feature extraction unit followed by a speaker modeling scheme for generalized representation of these features. Over the years, Mel-Frequency Cepstral Coefficients (MFCC) modeled on the human auditory system has been used as a standard acoustic feature set for speech related applications. On a recent contribution by authors, it has been shown that the Inverted Mel- Frequency Cepstral Coefficients (IMFCC) is useful feature set for SI, which contains complementary information present in high frequency region. This paper introduces the Gaussian shaped filter (GF) while calculating MFCC and IMFCC in place of typical triangular shaped bins. The objective is to introduce a higher amount of correlation between subband outputs. The performances of both MFCC & IMFCC improve with GF over conventional triangular filter (TF) based implementation, individually as well as in combination. With GMM as speaker modeling paradigm, the performances of proposed GF based MFCC and IMFCC in individual and fused mode have been verified in two standard databases YOHO, (Microphone Speech) and POLYCOST (Telephone Speech) each of which has more than 130 speakers.

Keywords: Gaussian Filter, Triangular Filter, Subbands, Correlation, MFCC, IMFCC, GMM.

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2035 The Current Situation of Ang Thong Province’s Court Doll Distribution

Authors: P. Waiyawuththanapoom

Abstract:

This research is objected to study the pattern and channel of distribution of Ang Thong’s court doll OTOP product and try to develop the quality of distribution of the court doll product. The population of this research is 50 court doll manufacturers of Ang Thong’s court doll. The data and information was collected by using the questionnaire and use percentage, mean and standard deviation as an analysis tools. The distribution channel of Ang Thong’s court doll can be separated into 3 channels which are direct distribution from the manufacturer, via the middleman and via the co-operated manufacturing group. In the direct distribution from the manufacturer channel, it was found that the manufacturer is given the highest rate of importance to how they keep the inventory. In the distribution via the middleman channel, it was found that the manufacturer is given the highest rate of importance to the distribution efficiency. But in the distribution via the co-operated manufacturing group, it was found that the manufacturer is given the highest rate of importance to the public relationship.

Keywords: Distribution, Court Doll, Ang Thong Province.

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2034 A Robust Reception of IEEE 802.15.4a IR-TH UWB in Dense Multipath and Gaussian Noise

Authors: Farah Haroon, Haroon Rasheed, Kazi M Ahmed

Abstract:

IEEE 802.15.4a impulse radio-time hopping ultra wide band (IR-TH UWB) physical layer, due to small duty cycle and very short pulse widths is robust against multipath propagation. However, scattering and reflections with the large number of obstacles in indoor channel environments, give rise to dense multipath fading. It imposes serious problem to optimum Rake receiver architectures, for which very large number of fingers are needed. Presence of strong noise also affects the reception of fine pulses having extremely low power spectral density. A robust SRake receiver for IEEE 802.15.4a IRTH UWB in dense multipath and additive white Gaussian noise (AWGN) is proposed to efficiently recover the weak signals with much reduced complexity. It adaptively increases the signal to noise (SNR) by decreasing noise through a recursive least square (RLS) algorithm. For simulation, dense multipath environment of IEEE 802.15.4a industrial non line of sight (NLOS) is employed. The power delay profile (PDF) and the cumulative distribution function (CDF) for the respective channel environment are found. Moreover, the error performance of the proposed architecture is evaluated in comparison with conventional SRake and AWGN correlation receivers. The simulation results indicate a substantial performance improvement with very less number of Rake fingers.

Keywords: Adaptive noise cancellation, dense multipath propoagation, IEEE 802.15.4a, IR-TH UWB, industrial NLOS environment, SRake receiver

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2033 Study of Proton-9,11Li Elastic Scattering at 60~75 MeV/Nucleon

Authors: Arafa A. Alholaisi, Jamal H. Madani, M. A. Alvi

Abstract:

The radial form of nuclear matter distribution, charge and the shape of nuclei are essential properties of nuclei, and hence, are of great attention for several areas of research in nuclear physics. More than last three decades have witnessed a range of experimental means employing leptonic probes (such as muons, electrons etc.) for exploring nuclear charge distributions, whereas the hadronic probes (for example alpha particles, protons, etc.) have been used to investigate the nuclear matter distributions. In this paper, p-9,11Li elastic scattering differential cross sections in the energy range  to  MeV have been studied by means of Coulomb modified Glauber scattering formalism. By applying the semi-phenomenological Bhagwat-Gambhir-Patil [BGP] nuclear density for loosely bound neutron rich 11Li nucleus, the estimated matter radius is found to be 3.446 fm which is quite large as compared to so known experimental value 3.12 fm. The results of microscopic optical model based calculation by applying Bethe-Brueckner–Hartree–Fock formalism (BHF) have also been compared. It should be noted that in most of phenomenological density model used to reproduce the p-11Li differential elastic scattering cross sections data, the calculated matter radius lies between 2.964 and 3.55 fm. The calculated results with phenomenological BGP model density and with nucleon density calculated in the relativistic mean-field (RMF) reproduces p-9Li and p-11Li experimental data quite nicely as compared to Gaussian- Gaussian or Gaussian-Oscillator densities at all energies under consideration. In the approach described here, no free/adjustable parameter has been employed to reproduce the elastic scattering data as against the well-known optical model based studies that involve at least four to six adjustable parameters to match the experimental data. Calculated reaction cross sections σR for p-11Li at these energies are quite large as compared to estimated values reported by earlier works though so far no experimental studies have been performed to measure it.

Keywords: Bhagwat-Gambhir-Patil density, coulomb modified Glauber model, halo nucleus, optical limit approximation.

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2032 Puff Noise Detection and Cancellation for Robust Speech Recognition

Authors: Sangjun Park, Jungpyo Hong, Byung-Ok Kang, Yun-keun Lee, Minsoo Hahn

Abstract:

In this paper, an algorithm for detecting and attenuating puff noises frequently generated under the mobile environment is proposed. As a baseline system, puff detection system is designed based on Gaussian Mixture Model (GMM), and 39th Mel Frequency Cepstral Coefficient (MFCC) is extracted as feature parameters. To improve the detection performance, effective acoustic features for puff detection are proposed. In addition, detected puff intervals are attenuated by high-pass filtering. The speech recognition rate was measured for evaluation and confusion matrix and ROC curve are used to confirm the validity of the proposed system.

Keywords: Gaussian mixture model, puff detection and cancellation, speech enhancement.

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2031 An Efficient Hamiltonian for Discrete Fractional Fourier Transform

Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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2030 The Evaluation of the Performance of Different Filtering Approaches in Tracking Problem and the Effect of Noise Variance

Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

Abstract:

Performance of different filtering approaches depends on modeling of dynamical system and algorithm structure. For modeling and smoothing the data the evaluation of posterior distribution in different filtering approach should be chosen carefully. In this paper different filtering approaches like filter KALMAN, EKF, UKF, EKS and smoother RTS is simulated in some trajectory tracking of path and accuracy and limitation of these approaches are explained. Then probability of model with different filters is compered and finally the effect of the noise variance to estimation is described with simulations results.

Keywords: Gaussian approximation, KALMAN smoother, Parameter estimation.

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2029 LQG Flight Control of VTAV for Enhanced Situational Awareness

Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a linear-quadratic-Gaussian (LQG) flight control procedure for an unmanned helicopter model with vectored thrust configuration. This LQG control for chosen model of VTAV has been verified by simulation of take-off and landing maneuvers using software package Simulink and demonstrated good performance for fast flight stabilization of model, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Linear-Quadratic-Gaussian (LQG) controller, situational awareness, vectored thrust aerial vehicle.

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2028 Technique for Voltage Control in Distribution System

Authors: S. Thongkeaw, M. Boonthienthong

Abstract:

This paper presents the techniques for voltage control in distribution system. It is integrated in the distribution management system. Voltage is an important parameter for the control of electrical power systems. The distribution network operators have the responsibility to regulate the voltage supplied to consumer within statutory limits. Traditionally, the On-Load Tap Changer (OLTC) transformer equipped with automatic voltage control (AVC) relays is the most popular and effective voltage control device. A static synchronous compensator (STATCOM) may be equipped with several controllers to perform multiple control functions. Static Var Compensation (SVC) is regulation slopes and available margins for var dispatch. The voltage control in distribution networks is established as a centralized analytical function in this paper. 

Keywords: Voltage Control, Reactive Power, Distribution System.

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2027 Landslide and Debris Flow Characteristics during Extreme Rainfall in Taiwan

Authors: C. Y. Chen

Abstract:

As the global climate changes, the threat from landslides and debris flows increases. Learning how a watershed initiates landslides under abnormal rainfall conditions and predicting landslide magnitude and frequency distribution is thus important. Landslides show a power-law distribution in the frequency-area distribution. The distribution curve shows an exponent gradient 1.0 in the Sandpile model test. Will the landslide frequency-area statistics show a distribution similar to the Sandpile model under extreme rainfall conditions? The purpose of the study is to identify the extreme rainfall-induced landslide frequency-area distribution in the Laonong River Basin in southern Taiwan. Results of the analysis show that a lower gradient of landslide frequency-area distribution could be attributed to the transportation and deposition of debris flow areas that are included in the landslide area.

Keywords: Landslide, power-law distribution, GIS.

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2026 Orthogonal Functions Approach to LQG Control

Authors: B. M. Mohan, Sanjeeb Kumar Kar

Abstract:

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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2025 Techniques for Reliability Evaluation in Distribution System Planning

Authors: T. Lantharthong, N. Phanthuna

Abstract:

This paper presents reliability evaluation techniques which are applied in distribution system planning studies and operation. Reliability of distribution systems is an important issue in power engineering for both utilities and customers. Reliability is a key issue in the design and operation of electric power distribution systems and load. Reliability evaluation of distribution systems has been the subject of many recent papers and the modeling and evaluation techniques have improved considerably.

Keywords: Reliability Evaluation, Optimization Technique, Reliability Indices

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2024 Reliability Improvement with Optimal Placement of Distributed Generation in Distribution System

Authors: N. Rugthaicharoencheep, T. Langtharthong

Abstract:

This paper presents the optimal placement and sizing of distributed generation (DG) in a distribution system. The problem is to reliability improvement of distribution system with distributed generations. The technique employed to solve the minimization problem is based on a developed Tabu search algorithm and reliability worth analysis. The developed methodology is tested with a distribution system of Roy Billinton Test System (RBTS) bus 2. It can be seen from the case study that distributed generation can reduce the customer interruption cost and therefore improve the reliability of the system. It is expected that our proposed method will be utilized effectively for distribution system operator.

Keywords: Distributed generation Optimization technique Reliability improvement, Distribution system.

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2023 VoIP Source Model based on the Hyperexponential Distribution

Authors: Arkadiusz Biernacki

Abstract:

In this paper we present a statistical analysis of Voice over IP (VoIP) packet streams produced by the G.711 voice coder with voice activity detection (VAD). During telephone conversation, depending whether the interlocutor speaks (ON) or remains silent (OFF), packets are produced or not by a voice coder. As index of dispersion for both ON and OFF times distribution was greater than one, we used hyperexponential distribution for approximation of streams duration. For each stage of the hyperexponential distribution, we tested goodness of our fits using graphical methods, we calculated estimation errors, and performed Kolmogorov-Smirnov test. Obtained results showed that the precise VoIP source model can be based on the five-state Markov process.

Keywords: VoIP source modelling, distribution approximation, hyperexponential distribution.

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2022 Derivation of Monotone Likelihood Ratio Using Two Sided Uniformly Normal Distribution Techniques

Authors: D. A. Farinde

Abstract:

In this paper, two-sided uniformly normal distribution techniques were used in the derivation of monotone likelihood ratio. The approach mainly employed the parameters of the distribution for a class of all size a. The derivation technique is fast, direct and less burdensome when compared to some existing methods.

Keywords: Neyman-Pearson Lemma, Normal distribution

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2021 Support Vector Machine based Intelligent Watermark Decoding for Anticipated Attack

Authors: Syed Fahad Tahir, Asifullah Khan, Abdul Majid, Anwar M. Mirza

Abstract:

In this paper, we present an innovative scheme of blindly extracting message bits from an image distorted by an attack. Support Vector Machine (SVM) is used to nonlinearly classify the bits of the embedded message. Traditionally, a hard decoder is used with the assumption that the underlying modeling of the Discrete Cosine Transform (DCT) coefficients does not appreciably change. In case of an attack, the distribution of the image coefficients is heavily altered. The distribution of the sufficient statistics at the receiving end corresponding to the antipodal signals overlap and a simple hard decoder fails to classify them properly. We are considering message retrieval of antipodal signal as a binary classification problem. Machine learning techniques like SVM is used to retrieve the message, when certain specific class of attacks is most probable. In order to validate SVM based decoding scheme, we have taken Gaussian noise as a test case. We generate a data set using 125 images and 25 different keys. Polynomial kernel of SVM has achieved 100 percent accuracy on test data.

Keywords: Bit Correct Ratio (BCR), Grid Search, Intelligent Decoding, Jackknife Technique, Support Vector Machine (SVM), Watermarking.

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2020 Power Flow Analysis for Radial Distribution System Using Backward/Forward Sweep Method

Authors: J. A. Michline Rupa, S. Ganesh

Abstract:

This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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