• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.517-530
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• 2007

We studied a modelling process for unimodal and multimodal circular data by using von Mises and its mixture distribution. In particular we suggested EM algorithm to find ML estimates of the mixture model. Simulation results showed the suggested methods are very accurate. Applications to two kinds of real data sets are also included.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.59-66
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• 2013

In this paper, we propose a probabilistic framework for model-based clustering of direction of arrival (DOA) data to obtain stable sound source localization (SSL) estimates. Model-based clustering has been shown capable of handling highly overlapped and noisy datasets, such as those involved in DOA detection. Although the Gaussian mixture model is commonly used for model-based clustering, we propose use of the von Mises mixture model as more befitting circular DOA data than a Gaussian distribution. The EM framework for the von Mises mixture model in a unit hyper sphere is degenerated for the 2D case and used as such in the proposed method. We also use a histogram of the dataset to initialize the number of clusters and the initial values of parameters, thereby saving calculation time and improving the efficiency. Experiments using simulated and real-world datasets demonstrate the performance of the proposed method.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.651-659
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• 2012

In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied the suggested method to fit 2008 EHFRS(Epidemic Hemorrhagic Fever with Renal Syndrome) data provided by the KCDC(Korea Centers for Disease Control and Prevention).

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.241-250
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• 2010

Over the past few decades, several studies have been made on the modeling of circular data. But these studies focused mainly on the symmetrical cases including von Mises distribution. Recently, many studies with skew-normal distribution have been conducted in the linear case. In this paper, we dealt the problem of fitting of non-symmetrical circular data with wrapped skew-normal distribution which can be derived by using the principle of wrapping. Wrapped skew-normal distribution is very flexible to asymmetical data as well as to symmetrical data. Multi-modal data are also fitted by using the mixture of wrapped skew-normal distributions. To estimate the parameters of mixture, we suggested the EM algorithm. Finally we verified the accuracy of the suggested algorithm through simulation studies. Application with real data is also considered.

• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.547-557
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• 2011

In this paper we developed a statistical model for traffic volume data which collected from a spot of specific local state road. One peculiar property of daily traffic data is that it has bimodal shape which have two peaks on times of both going to office and coming back to home. So, various mixture models of circular distribution are suggested for bimodal traffic data and EM algorithms are applied to estimate the parameters of the suggested models. To compare the accuracy of the suggested models, classical regressions with dummy variables are also considered. The suggested models for traffic volumn data can be effectively used to estimate missing values due to measuring instrument disorder.

• Smart Structures and Systems
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• v.21 no.5
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• pp.591-600
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• 2018

The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

• Journal of Korean Society of Transportation
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• v.25 no.4
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• pp.109-121
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• 2007

In this study, an imputation model using circular probability distribution was developed in order to overcome problems of missing data from a traffic survey. The existing ad-hoc or heuristic, model-based and algorithm-based imputation techniques were reviewed through previous studies, and then their limitations for imputing missing traffic volume data were revealed. The statistical computing language 'R' was employed for model construction, and a mixture of von Mises probability distribution, which is classified as symmetric, and unimodal circular probability were finally fitted on the basis of traffic volume data at survey stations in urban and rural areas, respectively. The circular probability distribution model largely proved to outperform a dummy variable regression model in regards to various evaluation conditions. It turned out that circular probability distribution models depict circularity of hourly volumes well and are very cost-effective and robust to changes in missing mechanisms.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.863-871
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• 2010

Until now, many studies related circular data are carried out, but the focuses are mainly on mildly peaked symmetric or asymmetric cases. In this paper we studied a modeling process for sharply peaked asymmetric circular data. By using wrapped Laplace, which was firstly introduced by Jammalamadaka and Kozbowski (2003), and its mixture distributions, we considered the model fitting problem of multi-modal circular data as well as unimodal one. In particular we suggested EM algorithm to find ML estimates of the mixture of wrapped Laplace distributions. Simulation results showed that the suggested EM algorithm is very accurate and useful.

• Advances in materials Research
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• v.9 no.2
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• pp.115-131
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• 2020

Limit elastic speed analysis of Al/SiC-based functionally graded annular disk of uniform thickness has been carried out for two cases, namely: metal-rich and ceramic rich. In the present study, the unknown field variable for radial displacement is solved using variational method wherein the solution was obtained by Galerkin's error minimization principle. One of the objectives was to identify the variation of induced stress in a functionally graded disk of uniform thickness at limit elastic speed using modified rule of mixture by comparing the induced von-Mises stress with the yield stress along the disk radius, thereby locating the yield initiation. Furthermore, limit elastic speed has been reported for a combination of varying grading index (n) and aspect ratios (a/b).Results indicate, limit elastic speed increases with an increase in grading indices. In case of an increase in aspect ratio, limit elastic speed increases up to a critical value beyond which it recedes. Also, the objective was to look at the variation of yield stress corresponding to volume fraction variation within the disk which later helps in material tailoring. The study reveals the qualitative variation of yield stress for FG disk with volume fraction, resulting in the possibility of material tailoring from the processing standpoint, in practice.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.65-72
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• 2001

This paper demonstrates an explicit-implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for an existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory. Darcy's law is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full Newton-Raphson method is used for solving the nonlinear governing equations.