Pattern recognition of manufacturing process signals using Gaussian mixture models-based recognition systems

Unnatural patterns exhibited in manufacturing processes can be associated with certain assignable causes for process variation. Hence, accurate identification of various process patterns (PPs) can significantly narrow down the scope of possible causes that must be investigated, and speed up the troubleshooting process. This paper proposes a Gaussian mixture models (GMM)-based PP recognition (PPR) model, which employs a collection of several GMMs trained for PPR. By using statistical features and wavelet energy features as the input features, the proposed PPR model provides more simple training procedure and better generalization performance than using single recognizer, and hence is easier to be used by quality engineers and operators. Furthermore, the proposed model is capable of adapting novel PPs through using a dynamic modeling scheme. The simulation results indicate that the GMM-based PPR model shows good detection and recognition of current PPs and adapts further novel PPs effectively. Analysis from this study provides guidelines in developing GMM – based SPC recognition systems.     

A discrete-time on–off source queueing system with negative customers

This paper studies a discrete-time single-server infinite-capacity queueing system with correlated arrivals, geometrically distributed service times and negative customers. Positive customers are generated by a Bernoulli bursty source, with geometrically distributed lengths of the on-periods and off-periods. Negative customers arrive to the system according to a geometrical arrival process which is independent of the positive arrival process. A negative customer removes a positive customer in service if any, but has no effect on the system if it finds the system empty. We analyze the Markov chain underlying the queueing system and evaluate the performance of the system based on generating functions technique. Closed-form expressions of some performance measures of the system are obtained, such as stationary probability generating functions of queue length, unfinished work, sojourn time distribution and so on. Finally, the effect of several parameters on the system is shown numerically.     

Single-allocation ordered median hub location problems

The discrete ordered median location model is a powerful tool in modeling classic and alternative location problems that have been applied with success to a large variety of discrete location problems. Nevertheless, although hub location models have been analyzed from the sum, maximum and coverage point of views, as far as we know, they have never been considered under an alternative unifying point of view. In this paper we consider new formulations, based on the ordered median objective function, for hub location problems with new distribution patterns induced by the different users’ roles within the supply chain network. This approach introduces some penalty factors associated with the position of an allocation cost with respect to the sorted sequence of these costs. First we present basic formulations for this problem, and then develop stronger formulations by exploiting properties of the model. The performance of all these formulations is compared by means of a computational analysis.     

The Dirichlet problem for a 3D elliptic equation with two singular coefficients

In the present work, we investigate the Dirichlet problem for a three-dimensional (3D) elliptic equation with two singular coefficients. We find four fundamental solutions of the equation, containing hypergeometric functions of Appell. Then using an “a-b-c” method, the uniqueness for the solution of the Dirichlet problem is proved. Applying a method of Green’s function, we are able to find the solution of the problem in an explicit form. Moreover, decomposition formulas, formulas of differentiation and some adjacent relations for Appell’s hypergeometric functions were used in order to find the explicit solution for the formulated problem.     

A novel HMM-based learning framework for improving dynamic wireless push system performance

A new machine learning framework is introduced in this paper, based on the hidden Markov model (HMM), designed to provide scheduling in dynamic wireless push systems. In realistic wireless systems, the clients’ intentions change dynamically; hence a cognitive scheduling scheme is needed to estimate the desirability of the connected clients. The proposed scheduling scheme is enhanced with self-organized HMMs, supporting the network with an estimated expectation of the clients’ intentions, since the system’s environment characteristics alter dynamically and the base station (server side) has no a priori knowledge of such changes. Compared to the original pure scheme, the proposed machine learning framework succeeds in predicting the clients’ information desires and overcomes the limitation of the original static scheme, in terms of mean delay and system efficiency.     

Applying multiquadric quasi-interpolation for boundary detection

In this paper, we propose a novel scheme for simulating geometric active contours (geometric flow) of one kind, applying multiquadric (MQ) quasi-interpolation. We first represent the geometric flow in its parametric form. Then we obtain the numerical scheme by using the derivatives of the quasi-interpolation to approximate the spatial derivative of each dependent variable and a forward difference to approximate the temporal derivative of each dependent variable. The resulting scheme is simple, efficient and easy to implement. Also images with complex boundaries can be more easily proposed on the basis of the good properties of the MQ quasi-interpolation. Several biomedical and astronomical examples of applications are shown in the paper. Comparisons with other methods are included to illustrate the validity of the method.     

Some preserving subordination and superordination of analytic functions involving the Liu-Owa integral operator

In this paper, we obtain some subordination and superordination-preserving results of analytic functions involving the Liu-Owa integral operator. Sandwich-type result is also obtained.     

Numerical method using cubic B-spline for the heat and wave equation

In the present paper, the cubic B-splines method is considered for solving one-dimensional heat and wave equations. A typical finite difference approach had been used to discretize the time derivative while the cubic B-spline is applied as an interpolation function in the space dimension. The accuracy of the method for both equations is discussed. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.     

An algorithm for solving multi-term diffusion-wave equations of fractional order

In this paper an algorithm, based on a new modified homotopy perturbation method (MHPM), is presented to obtain approximate solutions of multi-term diffusion-wave equations of fractional order. To illustrate the method some examples are provided. The results show the simplicity and the efficiency of the algorithm.     

Disaggregation & aggregation of time series components: A hybrid forecasting approach using generalized regression neural networks and the theta method

A hybrid forecasting method is proposed which leverages from statistical and neural network techniques to perform multi-step ahead forecasting. The proposed method is based on the disaggregation of time series components, the prediction of each component individually and the reassembling of the extrapolations to obtain an estimation for the global data. The STL decomposition procedure from the literature [5] is implemented to obtain the seasonal, trend and irregular components of the time series, whilst Generalized Regression Neural Networks (GRNN) [12] are used to perform out-of sample extrapolations of the seasonal and residual components. The univariate Theta model is employed for the estimation of the directional component. The application of the GRNN is based on the dynamic calibration of the training process for each of the seasonal and irregular components individually. The proposed hybrid forecasting method is applied to 60 time series from the NN3 competition and 227 time series from the M1 Competition dataset, to obtain 18 out-of sample predictions. The results from the application demonstrate that the proposed method can outperform standard statistical techniques in the literature. One of the main contributions of the current research lies in the investigation of the strengths and weaknesses of the GRNN in extrapolating structural components of time series.