Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4519

Search results for: Gaussian processes

4519 Closed-Form Sharma-Mittal Entropy Rate for Gaussian Processes

Authors: Septimia Sarbu


The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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4518 Using Gaussian Process in Wind Power Forecasting

Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui


The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: wind power, Gaussien process, modelling, forecasting

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4517 Base Change for Fisher Metrics: Case of the q-Gaussian Inverse Distribution

Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra


It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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4516 Propagation of Cos-Gaussian Beam in Photorefractive Crystal

Authors: A. Keshavarz


A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: beam propagation, cos-Gaussian beam, numerical simulation, photorefractive crystal

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4515 Frequency Offset Estimation Schemes Based on ML for OFDM Systems in Non-Gaussian Noise Environments

Authors: Keunhong Chae, Seokho Yoon


In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol

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4514 Gaussian Operations with a Single Trapped Ion

Authors: Bruna G. M. Araújo, Pedro M. M. Q. Cruz


In this letter, we review the literature of the major concepts that govern Gaussian quantum information. As we work with quantum information and computation with continuous variables, Gaussian states are needed to better describe these systems. Analyzing a single ion locked in a Paul trap we use the interaction picture to obtain a toolbox of Gaussian operations with the ion-laser interaction Hamiltionian. This is achieved exciting the ion through the combination of two lasers of distinct frequencies corresponding to different sidebands of the external degrees of freedom. First we study the case of a trap with 1 mode and then the case with 2 modes. In this way, we achieve different continuous variables gates just by changing the external degrees of freedom of the trap and combining the Hamiltonians of blue and red sidebands.

Keywords: Paul trap, ion-laser interaction, Gaussian operations

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4513 Simulation of Propagation of Cos-Gaussian Beam in Strongly Nonlocal Nonlinear Media Using Paraxial Group Transformation

Authors: A. Keshavarz, Z. Roosta


In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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4512 Use of Gaussian-Euclidean Hybrid Function Based Artificial Immune System for Breast Cancer Diagnosis

Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel


Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: artificial immune system, breast cancer diagnosis, Euclidean function, Gaussian function

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4511 System of Linear Equations, Gaussian Elimination

Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali


In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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4510 Marker-Controlled Level-Set for Segmenting Breast Tumor from Thermal Images

Authors: Swathi Gopakumar, Sruthi Krishna, Shivasubramani Krishnamoorthy


Contactless, painless and radiation-free thermal imaging technology is one of the preferred screening modalities for detection of breast cancer. However, poor signal to noise ratio and the inexorable need to preserve edges defining cancer cells and normal cells, make the segmentation process difficult and hence unsuitable for computer-aided diagnosis of breast cancer. This paper presents key findings from a research conducted on the appraisal of two promising techniques, for the detection of breast cancer: (I) marker-controlled, Level-set segmentation of anisotropic diffusion filtered preprocessed image versus (II) Segmentation using marker-controlled level-set on a Gaussian-filtered image. Gaussian-filtering processes the image uniformly, whereas anisotropic filtering processes only in specific areas of a thermographic image. The pre-processed (Gaussian-filtered and anisotropic-filtered) images of breast samples were then applied for segmentation. The segmentation of breast starts with initial level-set function. In this study, marker refers to the position of the image to which initial level-set function is applied. The markers are generally placed on the left and right side of the breast, which may vary with the breast size. The proposed method was carried out on images from an online database with samples collected from women of varying breast characteristics. It was observed that the breast was able to be segmented out from the background by adjustment of the markers. From the results, it was observed that as a pre-processing technique, anisotropic filtering with level-set segmentation, preserved the edges more effectively than Gaussian filtering. Segmented image, by application of anisotropic filtering was found to be more suitable for feature extraction, enabling automated computer-aided diagnosis of breast cancer.

Keywords: anisotropic diffusion, breast, Gaussian, level-set, thermograms

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4509 Self-Action Effects of a Non-Gaussian Laser Beam Through Plasma

Authors: Sandeep Kumar, Naveen Gupta


The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.

Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing

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4508 Learning the Dynamics of Articulated Tracked Vehicles

Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri


In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, gaussian mixture models, learning motion patterns, tracked robots for urban search and rescue

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4507 Adaptive Target Detection of High-Range-Resolution Radar in Non-Gaussian Clutter

Authors: Lina Pan


In non-Gaussian clutter of a spherically invariant random vector, in the cases that a certain estimated covariance matrix could become singular, the adaptive target detection of high-range-resolution radar is addressed. Firstly, the restricted maximum likelihood (RML) estimates of unknown covariance matrix and scatterer amplitudes are derived for non-Gaussian clutter. And then the RML estimate of texture is obtained. Finally, a novel detector is devised. It is showed that, without secondary data, the proposed detector outperforms the existing Kelly binary integrator.

Keywords: non-Gaussian clutter, covariance matrix estimation, target detection, maximum likelihood

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4506 Least Squares Solution for Linear Quadratic Gaussian Problem with Stochastic Approximation Approach

Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo


Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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4505 The Extended Skew Gaussian Process for Regression

Authors: M. T. Alodat


In this paper, we propose a generalization to the Gaussian process regression(GPR) model called the extended skew Gaussian process for regression(ESGPr) model. The ESGPR model works better than the GPR model when the errors are skewed. We derive the predictive distribution for the ESGPR model at a new input. Also we apply the ESGPR model to FOREX data and we find that it fits the Forex data better than the GPR model.

Keywords: extended skew normal distribution, Gaussian process for regression, predictive distribution, ESGPr model

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4504 Interaction of Tungsten Tips with Laguerre-Gaussian Beams

Authors: Abhisek Sinha, Debobrata Rajak, Shilpa Rani, Ram Gopal, Vandana Sharma


The interaction of femtosecond laser pulses with metallic tips has been studied extensively, and they have proved to be a very good source of ultrashort electron pulses. A study of the interaction of femtosecond Laguerre-Gaussian (LG) laser modes with Tungsten tips is presented here. Laser pulses of 35 fs pulse durations were incident on Tungsten tips, and their electron emission rates were studied for LG (l=1, p=0) and Gaussian modes. A change in the order of the interaction for LG beams is reported, and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near-field intensity supported by numerical simulations.

Keywords: femtosecond, Laguerre-Gaussian, OAM, tip

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4503 ML-Based Blind Frequency Offset Estimation Schemes for OFDM Systems in Non-Gaussian Noise Environments

Authors: Keunhong Chae, Seokho Yoon


This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM

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4502 Physically Informed Kernels for Wave Loading Prediction

Authors: Daniel James Pitchforth, Timothy James Rogers, Ulf Tyge Tygesen, Elizabeth Jane Cross


Wave loading is a primary cause of fatigue within offshore structures and its quantification presents a challenging and important subtask within the SHM framework. The accurate representation of physics in such environments is difficult, however, driving the development of data-driven techniques in recent years. Within many industrial applications, empirical laws remain the preferred method of wave loading prediction due to their low computational cost and ease of implementation. This paper aims to develop an approach that combines data-driven Gaussian process models with physical empirical solutions for wave loading, including Morison’s Equation. The aim here is to incorporate physics directly into the covariance function (kernel) of the Gaussian process, enforcing derived behaviors whilst still allowing enough flexibility to account for phenomena such as vortex shedding, which may not be represented within the empirical laws. The combined approach has a number of advantages, including improved performance over either component used independently and interpretable hyperparameters.

Keywords: offshore structures, Gaussian processes, Physics informed machine learning, Kernel design

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4501 Unsupervised Reciter Recognition Using Gaussian Mixture Models

Authors: Ahmad Alwosheel, Ahmed Alqaraawi


This work proposes an unsupervised text-independent probabilistic approach to recognize Quran reciter voice. It is an accurate approach that works on real time applications. This approach does not require a prior information about reciter models. It has two phases, where in the training phase the reciters' acoustical features are modeled using Gaussian Mixture Models, while in the testing phase, unlabeled reciter's acoustical features are examined among GMM models. Using this approach, a high accuracy results are achieved with efficient computation time process.

Keywords: Quran, speaker recognition, reciter recognition, Gaussian Mixture Model

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4500 Second Harmonic Generation of Higher-Order Gaussian Laser Beam in Density Rippled Plasma

Authors: Jyoti Wadhwa, Arvinder Singh


This work presents the theoretical investigation of an enhanced second-harmonic generation of higher-order Gaussian laser beam in plasma having a density ramp. The mechanism responsible for the self-focusing of a laser beam in plasma is considered to be the relativistic mass variation of plasma electrons under the effect of a highly intense laser beam. Using the moment theory approach and considering the Wentzel-Kramers-Brillouin approximation for the non-linear Schrodinger wave equation, the differential equation is derived, which governs the spot size of the higher-order Gaussian laser beam in plasma. The nonlinearity induced by the laser beam creates the density gradient in the background plasma electrons, which is responsible for the excitation of the electron plasma wave. The large amplitude electron plasma wave interacts with the fundamental beam, which further produces the coherent radiations with double the frequency of the incident beam. The analysis shows the important role of the different modes of higher-order Gaussian laser beam and density ramp on the efficiency of generated harmonics.

Keywords: density rippled plasma, higher order Gaussian laser beam, moment theory approach, second harmonic generation.

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4499 Stimulated Raman Scattering of Ultra Intense Hollow Gaussian Beam

Authors: Prerana Sharma


Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.

Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering

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4498 Solving Single Machine Total Weighted Tardiness Problem Using Gaussian Process Regression

Authors: Wanatchapong Kongkaew


This paper proposes an application of probabilistic technique, namely Gaussian process regression, for estimating an optimal sequence of the single machine with total weighted tardiness (SMTWT) scheduling problem. In this work, the Gaussian process regression (GPR) model is utilized to predict an optimal sequence of the SMTWT problem, and its solution is improved by using an iterated local search based on simulated annealing scheme, called GPRISA algorithm. The results show that the proposed GPRISA method achieves a very good performance and a reasonable trade-off between solution quality and time consumption. Moreover, in the comparison of deviation from the best-known solution, the proposed mechanism noticeably outperforms the recently existing approaches.

Keywords: Gaussian process regression, iterated local search, simulated annealing, single machine total weighted tardiness

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4497 Facial Expression Recognition Using Sparse Gaussian Conditional Random Field

Authors: Mohammadamin Abbasnejad


The analysis of expression and facial Action Units (AUs) detection are very important tasks in fields of computer vision and Human Computer Interaction (HCI) due to the wide range of applications in human life. Many works have been done during the past few years which has their own advantages and disadvantages. In this work, we present a new model based on Gaussian Conditional Random Field. We solve our objective problem using ADMM and we show how well the proposed model works. We train and test our work on two facial expression datasets, CK+, and RU-FACS. Experimental evaluation shows that our proposed approach outperform state of the art expression recognition.

Keywords: Gaussian Conditional Random Field, ADMM, convergence, gradient descent

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4496 Novel Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park


In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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4495 A Comparative Asessment of Some Algorithms for Modeling and Forecasting Horizontal Displacement of Ialy Dam, Vietnam

Authors: Kien-Trinh Thi Bui, Cuong Manh Nguyen


In order to simulate and reproduce the operational characteristics of a dam visually, it is necessary to capture the displacement at different measurement points and analyze the observed movement data promptly to forecast the dam safety. The accuracy of forecasts is further improved by applying machine learning methods to data analysis progress. In this study, the horizontal displacement monitoring data of the Ialy hydroelectric dam was applied to machine learning algorithms: Gaussian processes, multi-layer perceptron neural networks, and the M5-rules algorithm for modelling and forecasting of horizontal displacement of the Ialy hydropower dam (Vietnam), respectively, for analysing. The database which used in this research was built by collecting time series of data from 2006 to 2021 and divided into two parts: training dataset and validating dataset. The final results show all three algorithms have high performance for both training and model validation, but the MLPs is the best model. The usability of them are further investigated by comparison with a benchmark models created by multi-linear regression. The result show the performance which obtained from all the GP model, the MLPs model and the M5-Rules model are much better, therefore these three models should be used to analyze and predict the horizontal displacement of the dam.

Keywords: Gaussian processes, horizontal displacement, hydropower dam, Ialy dam, M5-Rules, multi-layer perception neural networks

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4494 Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data

Authors: Wanhyun Cho, Soonja Kang, Sanggoon Kim, Soonyoung Park


We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered an efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, importance sampling, approximate posterior distribution, marginal likelihood evidence

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4493 Confidence Intervals for Process Capability Indices for Autocorrelated Data

Authors: Jane A. Luke


Persistent pressure passed on to manufacturers from escalating consumer expectations and the ever growing global competitiveness have produced a rapidly increasing interest in the development of various manufacturing strategy models. Academic and industrial circles are taking keen interest in the field of manufacturing strategy. Many manufacturing strategies are currently centered on the traditional concepts of focused manufacturing capabilities such as quality, cost, dependability and innovation. Process capability indices was conducted assuming that the process under study is in statistical control and independent observations are generated over time. However, in practice, it is very common to come across processes which, due to their inherent natures, generate autocorrelated observations. The degree of autocorrelation affects the behavior of patterns on control charts. Even, small levels of autocorrelation between successive observations can have considerable effects on the statistical properties of conventional control charts. When observations are autocorrelated the classical control charts exhibit nonrandom patterns and lack of control. Many authors have considered the effect of autocorrelation on the performance of statistical process control charts. In this paper, the effect of autocorrelation on confidence intervals for different PCIs was included. Stationary Gaussian processes is explained. Effect of autocorrelation on PCIs is described in detail. Confidence intervals for Cp and Cpk are constructed for PCIs when data are both independent and autocorrelated. Confidence intervals for Cp and Cpk are computed. Approximate lower confidence limits for various Cpk are computed assuming AR(1) model for the data. Simulation studies and industrial examples are considered to demonstrate the results.

Keywords: autocorrelation, AR(1) model, Bissell’s approximation, confidence intervals, statistical process control, specification limits, stationary Gaussian processes

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4492 Lee-Carter Mortality Forecasting Method with Dynamic Normal Inverse Gaussian Mortality Index

Authors: Funda Kul, İsmail Gür


Pension scheme providers have to price mortality risk by accurate mortality forecasting method. There are many mortality-forecasting methods constructed and used in literature. The Lee-Carter model is the first model to consider stochastic improvement trends in life expectancy. It is still precisely used. Mortality forecasting is done by mortality index in the Lee-Carter model. It is assumed that mortality index fits ARIMA time series model. In this paper, we propose and use dynamic normal inverse gaussian distribution to modeling mortality indes in the Lee-Carter model. Using population mortality data for Italy, France, and Turkey, the model is forecasting capability is investigated, and a comparative analysis with other models is ensured by some well-known benchmarking criterions.

Keywords: mortality, forecasting, lee-carter model, normal inverse gaussian distribution

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4491 Facility Anomaly Detection with Gaussian Mixture Model

Authors: Sunghoon Park, Hank Kim, Jinwon An, Sungzoon Cho


Internet of Things allows one to collect data from facilities which are then used to monitor them and even predict malfunctions in advance. Conventional quality control methods focus on setting a normal range on a sensor value defined between a lower control limit and an upper control limit, and declaring as an anomaly anything falling outside it. However, interactions among sensor values are ignored, thus leading to suboptimal performance. We propose a multivariate approach which takes into account many sensor values at the same time. In particular Gaussian Mixture Model is used which is trained to maximize likelihood value using Expectation-Maximization algorithm. The number of Gaussian component distributions is determined by Bayesian Information Criterion. The negative Log likelihood value is used as an anomaly score. The actual usage scenario goes like a following. For each instance of sensor values from a facility, an anomaly score is computed. If it is larger than a threshold, an alarm will go off and a human expert intervenes and checks the system. A real world data from Building energy system was used to test the model.

Keywords: facility anomaly detection, gaussian mixture model, anomaly score, expectation maximization algorithm

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4490 Gaussian Probability Density for Forest Fire Detection Using Satellite Imagery

Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi


we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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