Search results for: estimation purposes

Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

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The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in the form of the prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: nonparametric estimation, sequential confidence estimation, multichannel monitoring systems, C-OTDR-system, non-lineary regression

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Authors: James Purnama, Riri Fitri Sari

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We investigate the machine learning algorithm selection problem in the term of a depth image based eye gaze estimation, with respect to its essential difficulty in reducing the number of required training samples and duration time of training. Statistics based prediction accuracy are increasingly used to assess and evaluate prediction or estimation in gaze estimation. This article evaluates Root Mean Squared Error (RMSE) and R-Squared statistical analysis to assess machine learning methods on depth camera data for gaze estimation. There are 4 machines learning methods have been evaluated: Random Forest Regression, Regression Tree, Support Vector Machine (SVM), and Linear Regression. The experiment results show that the Random Forest Regression has the lowest RMSE and the highest R-Squared, which means that it is the best among other methods.

Keywords: gaze estimation, gaze tracking, eye tracking, kinect, regression model, orange python

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Authors: Pilar Cornejo Ulloa, Guy Willems, Steffen Fieuws, Kim Quintelier, Wim Van Neer, Patrick Thevissen

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Dental age estimation can be performed both in living and deceased individuals. In anthropology, few studies have tested the reliability of dental age estimation methods complementary to the usually applied osteological methods. Objectives: In this study, destructive and non-destructive dental age estimation methods were applied on an archeological sample in order to compare them with the previously obtained anthropological age estimates. Materials and Methods: One hundred and thirty-four teeth from 24 individuals were analyzed using Kvaal, Kvaal and Solheim, Bang and Ramm, Lamendin, Gustafson, Maples, Dalitz and Johanson’s methods. Results: A high variability and wider age ranges than the ones previously obtained by the anthropologist could be observed. Destructive methods had a slightly higher agreement than the non-destructive. Discussion: Due to the heterogeneity of the sample and the lack of the real age at death, the obtained results were not representative, and it was not possible to suggest one dental age estimation method over another.

Keywords: archeology, dental age estimation, forensic anthropology, forensic dentistry

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Rashi Jain

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The LTE systems employ Orthogonal Frequency Division Multiplexing (OFDM) as the multiple access technology for the Downlink channels. For enhanced performance, accurate channel estimation is required. Various algorithms such as Least Squares (LS), Minimum Mean Square Error (MMSE) and Recursive Least Squares (RLS) can be employed for the purpose. The paper proposes channel estimation algorithm based on Kalman Filter for LTE-Downlink system. Using the frequency domain pilots, the initial channel response is obtained using the LS criterion. Then Kalman Filter is employed to track the channel variations in time-domain. To suppress the noise within a symbol, threshold processing is employed. The paper draws comparison between the LS, MMSE, RLS and Kalman filter for channel estimation. The parameters for evaluation are Bit Error Rate (BER), Mean Square Error (MSE) and run-time.

Keywords: LTE, channel estimation, OFDM, RLS, Kalman filter, threshold

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Authors: So-Young Ju, Sung-Mi Jo, Eui-Rim Jeong

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In this paper, based on the conventional single carrier frequency domain equalization (SC-FDE) structure, we propose a new SC-FDE structure to cope with narrowband jammer. In the conventional SC-FDE structure, channel estimation is performed in the time domain. When a narrowband jammer exists, time-domain channel estimation is very difficult due to high power jamming interference, which degrades receiver performance. To relieve from this problem, a new SC-FDE frame is proposed to enable channel estimation under narrow band jamming environments. In this paper, we proposed a modified SC-FDE structure that can perform channel estimation in the frequency domain and verified the performance via computer simulation.

Keywords: channel estimation, jammer, pilot, SC-FDE

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Authors: Swarnadip Ghosh

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Sentiment Analysis is the process of detecting the contextual polarity of text. In other words, it determines whether a piece of writing is positive, negative or neutral.Sentiment analysis of documents holds great importance in today's world, when numerous information is stored in databases and in the world wide web. An efficient algorithm to illicit such information, would be beneficial for social, economic as well as medical purposes. In this project, we have developed an algorithm to classify a document into positive or negative. Using our algorithm, we obtained a feature set from the data, and classified the documents based on this feature set. It is important to note that, in the classification, we have not used the independence assumption, which is considered by many procedures like the Naive Bayes. This makes the algorithm more general in scope. Moreover, because of the sparsity and high dimensionality of such data, we did not use empirical distribution for estimation, but developed a method by finding degree of close clustering of the data points. We have applied our algorithm on a movie review data set obtained from IMDb and obtained satisfactory results.

Keywords: sentiment, Run's Test, cross validation, higher dimensional pmf estimation

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Authors: Hongkui Li, Tongli Lu , Jianwu Zhang

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This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.

Keywords: clutch drag torque, wet DCT, dynamic viscosity, recursive least squares

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Authors: Somayeh Komeylian

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The direction of arrival (DoA) estimation is the crucial aspect of the radar technologies for detecting and dividing several signal sources. In this scenario, the antenna array output modeling involves numerous parameters including noise samples, signal waveform, signal directions, signal number, and signal to noise ratio (SNR), and thereby the methods of the DoA estimation rely heavily on the generalization characteristic for establishing a large number of the training data sets. Hence, we have analogously represented the two different optimization models of the DoA estimation; (1) the implementation of the decision directed acyclic graph (DDAG) for the multiclass least-squares support vector machine (LS-SVM), and (2) the optimization method of the deep neural network (DNN) radial basis function (RBF). We have rigorously verified that the LS-SVM DDAG algorithm is capable of accurately classifying DoAs for the three classes. However, the accuracy and robustness of the DoA estimation are still highly sensitive to technological imperfections of the antenna arrays such as non-ideal array design and manufacture, array implementation, mutual coupling effect, and background radiation and thereby the method may fail in representing high precision for the DoA estimation. Therefore, this work has a further contribution on developing the DNN-RBF model for the DoA estimation for overcoming the limitations of the non-parametric and data-driven methods in terms of array imperfection and generalization. The numerical results of implementing the DNN-RBF model have confirmed the better performance of the DoA estimation compared with the LS-SVM algorithm. Consequently, we have analogously evaluated the performance of utilizing the two aforementioned optimization methods for the DoA estimation using the concept of the mean squared error (MSE).

Keywords: DoA estimation, Adaptive antenna array, Deep Neural Network, LS-SVM optimization model, Radial basis function, and MSE

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Authors: Seda Yavuz, Anıl Çelebi, Aysun Taşyapı Çelebi, Oğuzhan Urhan

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Nowadays, demand for using real-time video transmission capable devices is ever-increasing. So, high resolution videos have made efficient video compression techniques an essential component for capturing and transmitting video data. Motion estimation has a critical role in encoding raw video. Hence, various motion estimation methods are introduced to efficiently compress the video. Low bit‑depth representation based motion estimation methods facilitate computation of matching criteria and thus, provide small hardware footprint. In this paper, a hardware implementation of a two-bit transformation based low-complexity motion estimation method using local binary pattern approach is proposed. Image frames are represented in two-bit depth instead of full-depth by making use of the local binary pattern as a binarization approach and the binarization part of the hardware architecture is explained in detail. Experimental results demonstrate the difference between the proposed hardware architecture and the architectures of well-known low-complexity motion estimation methods in terms of important aspects such as resource utilization, energy and power consumption.

Keywords: binarization, hardware architecture, local binary pattern, motion estimation, two-bit transform

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Authors: Ana Staneva, Vessela Stoimenova

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A parametric estimation of the MBP with Power Series offspring distribution family is considered in this paper. The MLE for the parameters is obtained in the case when the observable data are incomplete and consist only with the generation sizes of the family tree of MBP. The parameter estimation is calculated by using the Monte Carlo EM algorithm. The estimation for the posterior distribution and for the offspring distribution parameters are calculated by using the Bayesian approach and the Gibbs sampler. The article proposes various examples with bivariate branching processes together with computational results, simulation and an implementation using R.

Keywords: Bayesian, branching processes, EM algorithm, Gibbs sampler, Monte Carlo methods, statistical estimation

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Authors: Phong Nguyen, Phap Nguyen, Thang Nguyen

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High Efficiency Video Coding (HEVC) or H.265 Standard fulfills the demand of high resolution video storage and transmission since it achieves high compression ratio. However, it requires a huge amount of calculation. Since Motion Estimation (ME) block composes about 80 % of calculation load of HEVC, there are a lot of researches to reduce the computation cost. In this paper, we propose a new algorithm to lower the number of Motion Estimation’s searching points. The number of computing points in search pattern is down from 77 for Diamond Pattern and 81 for Square Pattern to only 31. Meanwhile, the Peak Signal to Noise Ratio (PSNR) and bit rate are almost equal to those of conventional patterns. The motion estimation time of new algorithm reduces by at 68.23%, 65.83%compared to the recommended search pattern of diamond pattern, square pattern, respectively.

Keywords: motion estimation, wide diamond, search pattern, H.265, test zone search, HM software

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Authors: Chin-Yun Chen

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Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature.

Keywords: numerical quadrature, error estimation, derivative free method, interval computation

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Authors: Y. T. Lee, J. H. Na, S. H. Kim, S. U. Hong

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In this study, an experimental research for estimation of slab depth, column size and location of rebar of concrete specimen is conducted using the Impact Echo Method (IE) based on stress wave among non-destructive test methods. Estimation of slab depth had total length of 1800×300 and 6 different depths including 150 mm, 180 mm, 210 mm, 240 mm, 270 mm and 300 mm. The concrete column specimen was manufactured by differentiating the size into 300×300×300 mm, 400×400×400 mm and 500×500×500 mm. In case of the specimen for estimation of rebar, rebar of ∅22 mm was used in a specimen of 300×370×200 and arranged at 130 mm and 150 mm from the top to the rebar top. As a result of error rate of slab depth was overall mean of 3.1%. Error rate of column size was overall mean of 1.7%. Mean error rate of rebar location was 1.72% for top, 1.19% for bottom and 1.5% for overall mean showing relative accuracy.

Keywords: impact echo method, estimation, slab depth, column size, rebar location, concrete

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Authors: Hao Chen, Bo Guo, Ping Jiang

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Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model

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Authors: I. Gahlouz, A. Chellil

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The paper concerns the estimation of system components faults by using an unknown inputs observer. To reach this goal, we used the Bond Graph approach to physical modelling. We showed that this graphical tool is allowing the representation of system components faults as unknown inputs within the state representation of the considered physical system. The study of the causal and structural features of the system (controllability, observability, finite structure, and infinite structure) based on the Bond Graph approach was hence fulfilled in order to design an unknown inputs observer which is used for the system component fault estimation.

Keywords: estimation, bond graph, controllability, observability

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Authors: Navid Daryasafar, Nima Farshidfar

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In this article, we make attempt to hide error in video with an emphasis on the time-wise use of autoregressive (AR) models. To resolve this problem, we assume that all information in one or more video frames is lost. Then, lost frames are estimated using analogous Pixels time information in successive frames. Accordingly, after presenting autoregressive models and how they are applied to estimate lost frames, two general methods are presented for using these models. The first method which is the same standard method of autoregressive models estimates lost frame in unidirectional form. Usually, in such condition, previous frames information is used for estimating lost frame. Yet, in the second method, information from the previous and next frames is used for estimating the lost frame. As a result, this method is known as bidirectional estimation. Then, carrying out a series of tests, performance of each method is assessed in different modes. And, results are compared.

Keywords: error steganography, unidirectional estimation, bidirectional estimation, AR linear estimation

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Authors: P. P. S. Sifolo, P. Tladi, J. Maimela

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This article investigates technology used by Tshwane residents intended for tourism purposes. The aim is to contribute information to the Tshwane interested parties for planning and management concerning technology within the tourism sector. This study identified the types of tourist related technologies used by the Tshwane residents, be it for business purposes or personal use. The study connected the exploitation of technology for tourism purposes through unpacking the tourism sector as it utilizes technology. Quantitative research methodology was used whereby self-completed questionnaires were chosen as research instruments. The research study carried out a search for knowledge on technology for tourism and the Tshwane residents; however the study revealed that technology has certainly imprinted tourism massively because of its effectiveness and efficiency. Technology has assisted tourism businesses stay abreast of competition with ICT and because of that, SA is on the map as one the economically performing countries in Africa. Moreover, technology and tourism make a meaningful impact on job creation and Gross Domestic Product (GDP).

Keywords: tourism, information and communication technology, Tshwane residents, technology for tourism

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Authors: Nurbanu Guzey, S. Jagannathan

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Locating radio controlled (RC) devices using their unintended emissions has a great interest considering security concerns. Weak nature of these emissions requires near field localization approach since it is hard to detect these signals in far field region of array. Instead of only angle estimation, near field localization also requires range estimation of the source which makes this method more complicated than far field models. Challenges of locating such devices in a near field region and real time environment are analyzed in this paper. An ESPRIT like near field localization scheme is utilized for both angle and range estimation. 1-D search with symmetric subarrays is provided. Two 7 element uniform linear antenna arrays (ULA) are employed for locating RC source. Experiment results of location estimation for one unintended emitting walkie-talkie for different positions are given.

Keywords: localization, angle of arrival (AoA), range estimation, array signal processing, ESPRIT, Uniform Linear Array (ULA)

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Authors: Kriangkrai Maneerat, Chutima Prommak

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Indoor wireless localization systems have played an important role to enhance context-aware services. Determining the position of mobile objects in complex indoor environments, such as those in multi-floor buildings, is very challenging problems. This paper presents an effective floor estimation algorithm, which can accurately determine the floor where mobile objects located. The proposed algorithm is based on the confidence interval of the summation of online Received Signal Strength (RSS) obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSN). We compare the performance of the proposed algorithm with those of other floor estimation algorithms in literature by conducting a real implementation of WSN in our facility. The experimental results and analysis showed that the proposed floor estimation algorithm outperformed the other algorithms and provided highest percentage of floor accuracy up to 100% with 95-percent confidence interval.

Keywords: floor estimation algorithm, floor determination, multi-floor building, indoor wireless systems

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Authors: Mostafa Aminzadeh, Min Deng

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Modeling loss data is an important part of actuarial science. Actuaries use models to predict future losses and manage financial risk, which can be beneficial for marketing purposes. In the insurance industry, small claims happen frequently while large claims are rare. Traditional distributions such as Normal, Exponential, and inverse-Gaussian are not suitable for describing insurance data, which often show skewness and fat tails. Several authors have studied classical and Bayesian inference for parameters of composite distributions, such as Exponential-Pareto, Weibull-Pareto, and Inverse Gamma-Pareto. These models separate small to moderate losses from large losses using a threshold parameter. This research introduces a computational approach using a nonlinear regression model for loss data that relies on multiple predictors. Simulation studies were conducted to assess the accuracy of the proposed estimation method. The simulations confirmed that the proposed method provides precise estimates for regression parameters. It's important to note that this approach can be applied to datasets if goodness-of-fit tests confirm that the composite distribution under study fits the data well. To demonstrate the computations, a real data set from the insurance industry is analyzed. A Mathematica code uses the Fisher information algorithm as an iteration method to obtain the maximum likelihood estimation (MLE) of regression parameters.

Keywords: maximum likelihood estimation, fisher scoring method, non-linear regression models, composite distributions

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Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: N. Ben Si Ali, N. Benalia, N. Zarzouri

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Speed sensorless systems are intensively studied during recent years; this is mainly due to their economical benefit and fragility of mechanical sensors and also the difficulty of installing this type of sensor in many applications. These systems suffer from instability problems and sensitivity to parameter mismatch at low speed operation. In this paper an analysis of adaptive observer stability with stator resistance estimation is given.

Keywords: motor drive, sensorless control, adaptive observer, stator resistance estimation

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Authors: Etienne Alain Feukeu, L. W. Snyman

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Water scarcity is becoming a real issue nowadays. Most countries in the world are facing it in their own way based on their own geographical coordinate and condition. Many countries are facing a challenge of a growing water demand as a result of not only an increased population, economic growth, but also as a pressure of the population dynamic and urbanization. In view to mitigate some of this related problem, an accurate method of water estimation and future prediction, forecast is essential to guarantee not only the sufficient quantity, but also a good water distribution and management system. Beside the fact that several works have been undertaken to address this concern, there is still a considerable disparity between different methods and standard used for water prediction and estimation. Hence this work contrast and compare two well-defined and established methods from two countries (USA and South Africa) to demonstrate the inconsistency when different method and standards are used interchangeably.

Keywords: water scarcity, water estimation, water prediction, water forecast.

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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Authors: Omar Nasr, Yasser Naguib, Mohamed Hafez

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This paper aims at providing an innovative solution for blind interference threshold estimation in an underlay cognitive network to be used in adaptive beamforming by secondary user Transmitter and Receiver. For the task of threshold estimation, blind detection of modulation and SNR are used. For the sake of beamforming several localization algorithms are compared to settle on best one for cognitive environment. Beamforming algorithms as LCMV (Linear Constraint Minimum Variance) and MVDR (Minimum Variance Distortion less) are also proposed and compared. The idea of just nulling the primary user after knowledge of its location is discussed against the idea of working under interference threshold.

Keywords: cognitive radio, underlay, beamforming, MUSIC, MVDR, LCMV, threshold estimation

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Authors: ByoungJoon Yu, Junkyeong Kim, Seunghee Park

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The tensile force estimation PS tendons is in great demand on monitoring the structural health condition of PSC girder bridges. Measuring the tensile force of the PS tendons inside the PSC girder using conventional methods is hard due to its location. In this paper, an embedded EM sensor based tensile force estimation of PS tendon was carried out by measuring the permeability of the PS tendons in PSC girder. The permeability is changed due to the induced tensile force by the magneto-elastic effect and the effect then lead to the gradient change of the B-H curve. An experiment was performed to obtain the signals from the EM sensor using three down-scaled PSC girder models. The permeability of PS tendons was proportionally decreased according to the increase of the tensile forces. To verify the experiment results, a simulation of tensile force estimation will be conducted in further study. Consequently, it is expected that both the experiment results and the simulation results increase the accuracy of the tensile force estimation, and then it could be one of the solutions for evaluating the performance of PSC girder.

Keywords: tensile force estimation, embedded EM sensor, PSC girder, EM sensor simulation, cross section loss

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Authors: Behrooz Khalilloo, Hamid Shahriari, Emad Roghanian

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Process capability indices (PCIs) are important concepts of statistical quality control and measure the capability of processes and how much processes are meeting certain specifications. An important issue in statistical quality control is parameter estimation. Under the assumption of multivariate normality, the distribution parameters, mean vector and variance-covariance matrix must be estimated, when they are unknown. Classic estimation methods like method of moment estimation (MME) or maximum likelihood estimation (MLE) makes good estimation of the population parameters when data are not contaminated. But when outliers exist in the data, MME and MLE make weak estimators of the population parameters. So we need some estimators which have good estimation in the presence of outliers. In this work robust M-estimators for estimating these parameters are used and based on robust parameter estimators, robust process capability indices are introduced. The performances of these robust estimators in the presence of outliers and their effects on process capability indices are evaluated by real and simulated multivariate data. The results indicate that the proposed robust capability indices perform much better than the existing process capability indices.

Keywords: multivariate process capability indices, robust M-estimator, outlier, multivariate quality control, statistical quality control

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