Search results for: statistical analysis model.

Authors: B. Chemali, B. Tiliouine

Abstract:

This article presents the main results of a numerical investigation on the uncertainty of dynamic response of structures with statistically correlated random damping Gamma distributed. A computational method based on a Linear Statistical Model (LSM) is implemented to predict second order statistics for the response of a typical industrial building structure. The significance of random damping with correlated parameters and its implications on the sensitivity of structural peak response in the neighborhood of a resonant frequency are discussed in light of considerable ranges of damping uncertainties and correlation coefficients. The results are compared to those generated using Monte Carlo simulation techniques. The numerical results obtained show the importance of damping uncertainty and statistical correlation of damping coefficients when obtaining accurate probabilistic estimates of dynamic response of structures. Furthermore, the effectiveness of the LSM model to efficiently predict uncertainty propagation for structural dynamic problems with correlated damping parameters is demonstrated.

Keywords: Correlated random damping, linear statistical model, Monte Carlo simulation, uncertainty of dynamic response.

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Authors: Rafik Djemili, Mouldi Bedda, Hocine Bourouba

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This paper proposes a novel approach that combines statistical models and support vector machines. A hybrid scheme which appropriately incorporates the advantages of both the generative and discriminant model paradigms is described and evaluated. Support vector machines (SVMs) are trained to divide the whole speakers' space into small subsets of speakers within a hierarchical tree structure. During testing a speech token is assigned to its corresponding group and evaluation using gaussian mixture models (GMMs) is then processed. Experimental results show that the proposed method can significantly improve the performance of text independent speaker identification task. We report improvements of up to 50% reduction in identification error rate compared to the baseline statistical model.

Keywords: Speaker identification, Gaussian mixture model (GMM), support vector machine (SVM), hybrid GMM/SVM.

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Authors: Cristina G. Dascâlu, Corina Dima Cozma, Elena Carmen Cotrutz

Abstract:

The medical data statistical analysis often requires the using of some special techniques, because of the particularities of these data. The principal components analysis and the data clustering are two statistical methods for data mining very useful in the medical field, the first one as a method to decrease the number of studied parameters, and the second one as a method to analyze the connections between diagnosis and the data about the patient-s condition. In this paper we investigate the implications obtained from a specific data analysis technique: the data clustering preceded by a selection of the most relevant parameters, made using the principal components analysis. Our assumption was that, using the principal components analysis before data clustering - in order to select and to classify only the most relevant parameters – the accuracy of clustering is improved, but the practical results showed the opposite fact: the clustering accuracy decreases, with a percentage approximately equal with the percentage of information loss reported by the principal components analysis.

Keywords: Data clustering, medical data, principal components analysis.

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Authors: J. P. Dubois, O. M. Abdul-Latif

Abstract:

Support Vector Machine (SVM) is a statistical learning tool that was initially developed by Vapnik in 1979 and later developed to a more complex concept of structural risk minimization (SRM). SVM is playing an increasing role in applications to detection problems in various engineering problems, notably in statistical signal processing, pattern recognition, image analysis, and communication systems. In this paper, SVM was applied to the detection of SAR (synthetic aperture radar) images in the presence of partially developed speckle noise. The simulation was done for single look and multi-look speckle models to give a complete overlook and insight to the new proposed model of the SVM-based detector. The structure of the SVM was derived and applied to real SAR images and its performance in terms of the mean square error (MSE) metric was calculated. We showed that the SVM-detected SAR images have a very low MSE and are of good quality. The quality of the processed speckled images improved for the multi-look model. Furthermore, the contrast of the SVM detected images was higher than that of the original non-noisy images, indicating that the SVM approach increased the distance between the pixel reflectivity levels (the detection hypotheses) in the original images.

Keywords: Least Square-Support Vector Machine, SyntheticAperture Radar. Partially Developed Speckle, Multi-Look Model.

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Authors: Alireza Ansariyar, Safieh Laaly

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Over the last decades, the vehicle industry has shown increased interest in integrating autonomous, connected, and electrical technologies in vehicle design with the primary hope of improving mobility and road safety while reducing transportation’s environmental impact. Using the State of Maryland (M.D.) in the United States as a pilot study, this research investigates Connected and Autonomous Vehicles (CAVs) fuel consumption and air pollutants including Carbon Monoxide (CO), Particulate Matter (PM), and Nitrogen Oxides (NOx) and utilizes meaningful linear regression models to predict CAV’s environmental effects. Maryland transportation network was simulated in VISUM software, and data on a set of variables were collected through a comprehensive survey. The number of pollutants and fuel consumption were obtained for the time interval 2010 to 2021 from the macro simulation. Eventually, four linear regression models were proposed to predict the amount of C.O., NOx, PM pollutants, and fuel consumption in the future. The results highlighted that CAVs’ pollutants and fuel consumption have a significant correlation with the income, age, and race of the CAV customers. Furthermore, the reliability of four statistical models was compared with the reliability of macro simulation model outputs in the year 2030. The error of three pollutants and fuel consumption was obtained at less than 9% by statistical models in SPSS. This study is expected to assist researchers and policymakers with planning decisions to reduce CAV environmental impacts in M.D.

Keywords: Connected and autonomous vehicles, statistical model, environmental effects, pollutants and fuel consumption, VISUM, linear regression models.

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Authors: Teerawach Khamkorn, Laongtip Mathurasa, Savittree Rochanasmita Arnold, Witthaya Mekhum

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The objective of this research seeks to transmit a distance training model to the community in the upper northeastern region. The group sampling consists of 60 community leaders in the municipality of sub-district Kumphawapi, Kumphawapi Disrict, Udonthani Province. The research tools rely on the following instruments, they are : 1) the achievement test of community leaders- training and 2) the satisfaction questionnaires of community leaders. The statistics used in data analysis takes the statistical mean, percentage, standard deviation, and statistical T-test. The resulted findings reveal : 1) the efficiency of the distance training developed by the researcher for the community leaders joining in the training received the average score between in-training and post-training period higher than the setup criterion, 2) the two groups of participants in the training achieved higher knowledge than their pre-training state, 3) the comparison of the achievements between the two group presented no different results, 4) the community leaders obtained the high-to-highest satisfaction.

Keywords: Distance Training, Management, Technology, Transmitting.

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Authors: S.Shokri, S.Zahedi, M.Ahmadi Marvast, B. Baloochi, H.Ganji

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In this research, a systematic investigation was carried out to determine the optimum conditions of HDS reactor. Moreover, a suitable model was developed for a rigorous RTO (real time optimization) loop of HDS (Hydro desulfurization) process. A systematic experimental series was designed based on CCD (Central Composite design) and carried out in the related pilot plant to tune the develop model. The designed variables in the experiments were Temperature, LHSV and pressure. However, the hydrogen over fresh feed ratio was remained constant. The ranges of these variables were respectively equal to 320-380ºC, 1- 21/hr and 50-55 bar. a power law kinetic model was also developed for our further research in the future .The rate order and activation energy , power of reactant concentration and frequency factor of this model was respectively equal to 1.4, 92.66 kJ/mol and k0=2.7*109 .

Keywords: Statistical model, Multiphase Reactors, Gas oil, Hydrodesulfurization, Optimization, Kinetics

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

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Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: Kenneth M. Oba

Abstract:

Adequate management, control, and optimization of cost is an essential element for a successful construction project. A multiple linear regression optimization model was formulated to address the problem of costs associated with pile construction operations. A total of 32 PVC-reinforced concrete piles with diameter of 300 mm, 5.4 m long, were studied during the construction. The soil upon which the piles were installed was mostly silty sand, and completely submerged in water at Bonny, Nigeria. The piles are friction piles installed by boring method, using a piling auger. The volumes of soil removed, the weight of reinforcement cage installed, and volumes of fresh concrete poured into the PVC void were determined. The cost of constructing each pile based on the calculated quantities was determined. A model was derived and subjected to statistical tests using Statistical Package for the Social Sciences (SPSS) software. The model turned out to be adequate, fit, and have a high predictive accuracy with an R2 value of 0.833.

Keywords: Cost optimization modelling, multiple linear models, pile construction, regression models.

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Authors: Gebriel M. Shamia

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The Improved Generalized Diversity Index (IGDI) has been proposed as a tool that can be used to identify areas that have high conservation value and measure the ecological condition of an area. IGDI is based on the species relative abundances. This paper is concerned with particular attention is given to comparisons involving the MacArthur model of species abundances. The properties and performance of various species indices were assessed. Both IGDI and species richness increased with sampling area according to a power function. IGDI were also found to be acceptable ecological indicators of conditions and consistently outperformed coefficient of conservatism indices.

Keywords: Statistical ecology, MacArthur model, Functional Diversity.

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Authors: Zdenek Kolka, Otakar Wilfert, Viera Biolkova

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The paper deals with an analysis of visibility records collected from 210 European airports to obtain a realistic estimation of the availability of Free Space Optical (FSO) data links. Commercially available optical links usually operate in the 850nm waveband. Thus the influence of the atmosphere on the optical beam and on the visible light is similar. Long-term visibility records represent an invaluable source of data for the estimation of the quality of service of FSO links. The model used characterizes both the statistical properties of fade depths and the statistical properties of individual fade durations. Results are presented for Italy, France, and Germany.

Keywords: Computer networks, free-space optical links, meteorology, quality of service.

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Authors: Jaroslav Polec, Viliam Hirner, Michal Martinovič, Kvetoslava Kotuliaková

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In this paper we present a novel error model for packet loss and subsequent error description. The proposed model simulates the error performance of wireless communication link. The model is designed as two independent Markov chains, where the first one is used for packet generation and the second one generates correctly and incorrectly transmitted bits for received packets from the first chain. The statistical analyses of real communication on the wireless link are used for determination of model-s parameters. Using the obtained parameters and the implementation of the generator, we collected generated traffic. The obtained results generated by proposed model are compared with the real data collection.

Keywords: Wireless channel, error model, Markov chain, Elliot model, Gilbert model, generator, IEEE 802.11.

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Authors: Vilma Deltuvaitė

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Comparisons of financial development across countries are central to answering many of the questions on factors leading to economic development. For this reason this study analyzes the implications of financial system’s development on country’s economic development. The aim of the article: to analyze the impact of financial system’s development on economic development. The following research methods were used: systemic, logical and comparative analysis of scientific literature, analysis of statistical data, time series model (Autoregressive Distributed Lag (ARDL) Model). The empirical results suggest about positive short and long term effect of stock market development on GDP per capita.

Keywords: Banking sector, economic development, financial system’s development, stock market, private bond market.

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Authors: Po-Wen Chen, Jin-Yu Wu, Md. Manirul Ali, Yang Peng, Chen-Te Chang, Der-Jun Jan

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Dynamics of cathode spot has become a major part of vacuum arc discharge with its high academic interest and wide application potential. In this article, using a three-dimensional statistical model, we simulate the distribution of the ignition probability of a new cathode spot occurring in different magnetic pressure on old cathode spot surface and at different arcing time. This model for the ignition probability of a new cathode spot was proposed in two typical situations, one by the pure isotropic random walk in the absence of an external magnetic field, other by the retrograde motion in external magnetic field, in parallel with the cathode surface. We mainly focus on developed relationship between the ignition probability density distribution of a new cathode spot and the external magnetic field.

Keywords: Cathode spot, vacuum arc discharge, transverse magnetic field, random walk.

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Authors: Nino Abesadze, Marine Mindorashvili, Nino Paresashvili

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The main purpose of the article is to make complex statistical analysis of tourist expenses of foreign visitors. We used mixed technique of selection that implies rules of random and proportional selection. Computer software SPSS was used to compute statistical data for corresponding analysis. Corresponding methodology of tourism statistics was implemented according to international standards. Important information was collected and grouped from the major Georgian airports. Techniques of statistical observation were prepared. A representative population of foreign visitors and a rule of selection of respondents were determined. We have a trend of growth of tourist numbers and share of tourists from post-soviet countries constantly increases. Level of satisfaction with tourist facilities and quality of service has grown, but still we have a problem of disparity between quality of service and prices. The design of tourist expenses of foreign visitors is diverse; competitiveness of tourist products of Georgian tourist companies is higher.

Keywords: Tourist, expenses, methods, statistics, analysis.

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Authors: Zeeshan Furqan, Shahabuddin Muhammad, Ratan Guha

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IEEE has designed 802.11i protocol to address the security issues in wireless local area networks. Formal analysis is important to ensure that the protocols work properly without having to resort to tedious testing and debugging which can only show the presence of errors, never their absence. In this paper, we present the formal verification of an abstract protocol model of 802.11i. We translate the 802.11i protocol into the Strand Space Model and then prove the authentication property of the resulting model using the Strand Space formalism. The intruder in our model is imbued with powerful capabilities and repercussions to possible attacks are evaluated. Our analysis proves that the authentication of 802.11i is not compromised in the presented model. We further demonstrate how changes in our model will yield a successful man-in-the-middle attack.

Keywords: authentication, formal analysis, formal verification, security.

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Authors: Naushad Mamode Khan, Cheika Jahangeer, Maleika Heenaye-Mamode Khan

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Exclusive breastfeeding is the feeding of a baby on no other milk apart from breast milk. Exclusive breastfeeding during the first 6 months of life is very important as it supports optimal growth and development during infancy and reduces the risk of obliterating diseases and problems. Moreover, it helps to reduce the incidence and/or severity of diarrhea, lower respiratory infection and urinary tract infection. In this paper, we make a survey of the factors that influence exclusive breastfeeding and use two dispersed statistical models to analyze data. The models are the Generalized Poisson regression model and the Com-Poisson regression models.

Keywords: Exclusive breastfeeding, regression model, generalized poisson, com-poisson.

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Authors: Andrés Carrión García, Aura López de Murillo, José Jabaloyes Vivas, Angela Grisales del Río

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Some quality control tools use non metric subjective information coming from experts, who qualify the intensity of relations existing inside processes, but without quantifying them. In this paper we have developed a quality control analytic tool, measuring the impact or strength of the relationship between process operations and product characteristics. The tool includes two models: a qualitative model, allowing relationships description and analysis; and a formal quantitative model, by means of which relationship quantification is achieved. In the first one, concepts from the Graphs Theory were applied to identify those process elements which can be sources of variation, that is, those quality characteristics or operations that have some sort of prelacy over the others and that should become control items. Also the most dependent elements can be identified, that is those elements receiving the effects of elements identified as variation sources. If controls are focused in those dependent elements, efficiency of control is compromised by the fact that we are controlling effects, not causes. The second model applied adapts the multivariate statistical technique of Covariance Structural Analysis. This approach allowed us to quantify the relationships. The computer package LISREL was used to obtain statistics and to validate the model.

Keywords: Characteristics matrix, covariance structure analysis, LISREL.

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Authors: Swetha Priya Darshini Thammadi, Sateesh Kumar Pisini, Sanjay Kumar Shukla

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Source apportionment using Dispersion model depends primarily on the quality of Emission Inventory. In the present study, a CMB receptor model has been used to identify the sources of PM_2.5, while the AERMOD dispersion model has been used to account for missing sources of PM_2.5 in the Emission Inventory. A statistical approach has been developed to quantify the missing sources not considered in the Emission Inventory. The inventory of each grid was improved by adjusting emissions based on road lengths and deficit in measured and modelled concentrations. The results showed that in CMB analyses, fugitive sources - soil and road dust - contribute significantly to ambient PM_2.5 pollution. As a result, AERMOD significantly underestimated the ambient air concentration at most locations. The revised Emission Inventory showed a significant improvement in AERMOD performance which is evident through statistical tests.

Keywords: CMB, GIS, AERMOD, PM2.5, fugitive, emission inventory.

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Authors: S. Golmohammadi, M. Noorian Bidgoli

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Tunneling progress is a key parameter in the blasting method of tunneling. Taking measures to enhance tunneling advance can limit the progress distance without a supporting system, subsequently reducing or eliminating the risk of damage. This paper focuses on modeling tunneling progress using three main groups of parameters (tunneling geometry, blasting pattern, and rock mass specifications) based on the Rock Engineering Systems (RES) methodology. In the proposed models, four main effective parameters on tunneling progress are considered as inputs (RMR, Q-system, Specific charge of blasting, Area), with progress as the output. Data from 86 blasts conducted at the tailrace tunnel in the Azad Dam, western Iran, were used to evaluate the progress value for each blast. The results indicated that, for the 86 blasts, the progress of the estimated model aligns mostly with the measured progress. This paper presents a method for building the interaction matrix (statistical base) of the RES model. Additionally, a comparison was made between the results of the new RES-based model and a Multi-Linear Regression (MLR) analysis model. In the RES-based model, the effective parameters are RMR (35.62%), Q (28.6%), q (specific charge of blasting) (20.35%), and A (15.42%), respectively, whereas for MLR analysis, the main parameters are RMR, Q (system), q, and A. These findings confirm the superior performance of the RES-based model over the other proposed models.

Keywords: Rock Engineering Systems, tunneling progress, Multi Linear Regression, Specific charge of blasting.

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Authors: Y. Boutiche, N. Ramou, M. Ben Gharsallah

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This paper is devoted to present and discuss a model that allows a local segmentation by using statistical information of a given image. It is based on Chan-Vese model, curve evolution, partial differential equations and binary level sets method. The proposed model uses the piecewise constant approximation of Chan-Vese model to compute Signed Pressure Force (SPF) function, this one attracts the curve to the true object(s)-s boundaries. The implemented model is used to extract weld defects from weld radiographic images in the aim to calculate the perimeter and surfaces of those weld defects; encouraged resultants are obtained on synthetic and real radiographic images.

Keywords: Active contour, Chan-Vese Model, local segmentation, weld radiographic images.

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Authors: Mohammad Ali Tabarzad, Caro Lucas, Ali Hamzeh

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Adaptive Genetic Algorithms extend the Standard Gas to use dynamic procedures to apply evolutionary operators such as crossover, mutation and selection. In this paper, we try to propose a new adaptive genetic algorithm, which is based on the statistical information of the population as a guideline to tune its crossover, selection and mutation operators. This algorithms is called Statistical Genetic Algorithm and is compared with traditional GA in some benchmark problems.

Keywords: Genetic Algorithms, Statistical Information ofthe Population, PAUX, SSO.

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Authors: Mohd Zamri Osman, Mohd Aizaini Maarof, Mohd Foad Rohani

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Human skin detection recognized as the primary step in most of the applications such as face detection, illicit image filtering, hand recognition and video surveillance. The performance of any skin detection applications greatly relies on the two components: feature extraction and classification method. Skin color is the most vital information used for skin detection purpose. However, color feature alone sometimes could not handle images with having same color distribution with skin color. A color feature of pixel-based does not eliminate the skin-like color due to the intensity of skin and skin-like color fall under the same distribution. Hence, the statistical color analysis will be exploited such mean and standard deviation as an additional feature to increase the reliability of skin detector. In this paper, we studied the effectiveness of statistical color feature for human skin detection. Furthermore, the paper analyzed the integrated color and texture using eight classifiers with three color spaces of RGB, YCbCr, and HSV. The experimental results show that the integrating statistical feature using Random Forest classifier achieved a significant performance with an F1-score 0.969.

Keywords: Color space, neural network, random forest, skin detection, statistical feature.

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Authors: Hyun-Kyu Kang

Abstract:

The Korean Government has applied the preliminary feasibility study to new government R&D program plans as a part of an evaluation system for R&D programs. The preliminary feasibility study for the R&D program is composed of 3 major criteria such as technological, policy and economic analysis. The program logic model approach is used as a part of the technological analysis in the preliminary feasibility study. We has developed and improved the R&D program logic model. The logic model is a very useful tool for evaluating R&D program plans. Using a logic model, we can generally identify important factors of the R&D program plan, analyze its logic flow and find the disconnection or jump in the logic flow among components of the logic model.

Keywords: Preliminary feasibility study, R&D program logic model, technological analysis.

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Authors: Abhijit Mitra, Bhargav Kumar Mitra, Biswajoy Chatterjee

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We present a novel scheme to recognize isolated speech signals using certain statistical parameters derived from those signals. The determination of the statistical estimates is based on extracted signal information rather than the original signal information in order to reduce the computational complexity. Subtle details of these estimates, after extracting the speech signal from ambience noise, are first exploited to segregate the polysyllabic words from the monosyllabic ones. Precise recognition of each distinct word is then carried out by analyzing the histogram, obtained from these information.

Keywords: Isolated speech signals, Block overlapping technique, Positive peaks, Histogram analysis.

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Authors: Fathi M. O. Hamed, Salma F. Elkofhaifee

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The aim of this work is to detect geometrical shape objects in an image. In this paper, the object is considered to be as a circle shape. The identification requires find three characteristics, which are number, size, and location of the object. To achieve the goal of this work, this paper presents an algorithm that combines from some of statistical approaches and image analysis techniques. This algorithm has been implemented to arrive at the major objectives in this paper. The algorithm has been evaluated by using simulated data, and yields good results, and then it has been applied to real data.

Keywords: Image processing, median filter, projection, scalespace, segmentation, threshold.

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Authors: Bharathi P. T, P. Subashini

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Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.

Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.

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Authors: Josip Vasilj, Petar Sarajcev, Damir Jakus

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One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

Keywords: Wind power, Uncertainty, Stochastic process, Monte Carlo simulation.

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Authors: S. Boria

Abstract:

In the last years, the crashworthiness of an automotive body structure can be improved, since the beginning of the design stage, thanks to the development of specific optimization tools. It is well known how the finite element codes can help the designer to investigate the crashing performance of structures under dynamic impact. Therefore, by coupling nonlinear mathematical programming procedure and statistical techniques with FE simulations, it is possible to optimize the design with reduced number of analytical evaluations. In engineering applications, many optimization methods which are based on statistical techniques and utilize estimated models, called meta-models, are quickly spreading. A meta-model is an approximation of a detailed simulation model based on a dataset of input, identified by the design of experiments (DOE); the number of simulations needed to build it depends on the number of variables. Among the various types of meta-modeling techniques, Kriging method seems to be excellent in accuracy, robustness and efficiency compared to other ones when applied to crashworthiness optimization. Therefore the application of such meta-model was used in this work, in order to improve the structural optimization of a bumper for a racing car in composite material subjected to frontal impact. The specific energy absorption represents the objective function to maximize and the geometrical parameters subjected to some design constraints are the design variables. LS-DYNA codes were interfaced with LS-OPT tool in order to find the optimized solution, through the use of a domain reduction strategy. With the use of the Kriging meta-model the crashworthiness characteristic of the composite bumper was improved.

Keywords: Composite material, crashworthiness, finite element analysis, optimization.

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Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

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