Mujahed Al-Dhaifallah

An efficient regularized K-nearest neighbor based weighted twin support vector regression

Our RKNNWTSVR implements structural risk minimization principle by introducing extra regularization terms in each objective function.Our RKNNWTSVR cannot only help to alleviate overfitting issue and improve the generalization performance but also introduce invertibility in the dual formulation.The square of the 2-norm of the vector of slack variables is used in RKNNWTSVR to make the objective functions strongly convex.Four algorithms are designed to solve the proposed RKNNWTSVR.The solution reduces to solving just two systems of linear equations which makes our RKNNWTSVR extremely simple and efficient.No external optimizer is necessary for solving the RKNNWTSVR formulation. In general, pattern classification and regression tasks do not take into consideration the variation in the importance of the training samples. For twin support vector regression (TSVR), this implies that all the training samples play the same role on the bound functions. However, the number of close neighboring samples near to each training sample has an effect on the bound functions. In this paper, we formulate a regularized version of the KNN-based weighted twin support vector regression (KNNWTSVR) called RKNNWTSVR which is both efficient and effective. By introducing the regularization term and replacing 2-norm of slack variables instead of 1-norm, our RKNNWTSVR only needs to solve a simple system of linear equations with low computational cost, and at the same time, it improves the generalization performance. Particularly, we compare four implementations of RKNNWTSVR with existing approaches. Experimental results on several synthetic and benchmark datasets indicate that, comparing to SVR, WSVR, TSVR and KNNWTSVR, our proposed RKNNWTSVR has better generalization ability and requires less computational time.

An efficient implicit regularized Lagrangian twin support vector regression

Twin support vector regression (TSVR) and Lagrangian TSVR (LTSVR) satisfy only empirical risk minimization principle. Moreover, the matrices in their formulations are always positive semi-definite. To overcome these problems, we propose an efficient implicit Lagrangian formulation for the dual regularized twin support vector regression, called IRLTSVR for short. By introducing a regularization term to each objective function, the optimization problems in our IRLTSVR are positive definite and implement the structural risk minimization principle. Moreover, the 1-norm of the vector of slack variable is replaced with 2-norm to make the objective functions strongly convex. Our IRLTSVR solves two systems of linear equations instead of solving two quadratic programming problems (QPPs) in TSVR and one large QPP in SVR, which makes the learning speed of IRLTSVR faster than TSVR and SVR. Particularly, we compare three implementations of IRLTSVR with existing approaches. Computational results on several synthetic and real-world benchmark datasets clearly indicate the effectiveness and applicability of the IRLTSVR in comparison to SVR, TSVR and LTSVR.

The Umbral operator and the integration involving generalized Bessel-type functions

Abstract The main purpose of this paper is to introduce a class of new integrals involving generalized Bessel functions and generalized Struve functions by using operational method and umbral formalization of Ramanujan master theorem. Their connections with trigonometric functions with several distinct complex arguments are also presented.

Design of multiregional supervisory fuzzy PID control of ph reactors

This work concerns designing multiregional supervisory fuzzy PID (Proportional-Integral-Derivative) control for pH reactors. The proposed work focuses, mainly, on two themes. The first one is to propose a multiregional supervisory fuzzy-based cascade control structure. It would enable modifying dynamics and enhance systems stability. The fuzzy system (master loop) has been chosen as a tuner for PID controller (slave loop). It takes into consideration parameters uncertainties and reference tracking. The second theme concerns designing a hybrid neural network-based pH estimator. The proposed estimator would overcome the industrial drawbacks, that is, cost and size, found with conventional methods for pH measurement. The final end-user-interface (EUI) front panel and the results that evaluate the performance of the supervisory fuzzy PID-based control system and hybrid NN-based estimator have been presented using the compatibility found between LabView and MatLab. They lead to conclude that the proposed algorithms are appropriate to systems nonlinearities encountered with pH reactors.

Fuzzy Fractional-Order PID Controller for Fractional Model of Pneumatic Pressure System

This article presents a fuzzy fractional-order PID (FFOPID) controller scheme for a pneumatic pressure regulating system. The industrial pneumatic pressure systems are having strong dynamic and nonlinearity characteristics; further, these systems come across frequent load variations and external disturbances. Hence, for the smooth and trouble-free operation of the industrial pressure system, an effective control mechanism could be adopted. The objective of this work is to design an intelligent fuzzy-based fractional-order PID control scheme to ensure a robust performance with respect to load variation and external disturbances. A novel model of a pilot pressure regulating system is developed to validate the effectiveness of the proposed control scheme. Simulation studies are carried out in a delayed nonlinear pressure regulating system under different operating conditions using fractional-order PID (FOPID) controller with fuzzy online gain tuning mechanism. The results demonstrate the usefulness of the proposed strategy and confirm the performance improvement for the pneumatic pressure system. To highlight the advantages of the proposed scheme a comparative study with conventional PID and FOPID control schemes is made.

Modeling and identification of heat exchanger process using least squares support vector machines

In this paper, Hammerstein model and non-linear autoregressive with eXogeneous inputs (NARX) model are used to represent tubular heat exchanger. Both models have been identified using least squares support vector machines based algorithms. Both algorithms were able to model the heat exchanger system with-out requiring any a priori assumptions regarding its structure. The results indicate that the blackbox NARX model outperforms the NARX Hammerstein model in terms of accuracy and precision.

Twin Support Vector Machine Method for Identification of Wiener Models

Twin support vector regression is applied to identify nonlinear Wiener system, consisting of a linear dynamic block in series with static nonlinearity. The linear block is expanded in terms of basis functions, such as Laguerre or Kautz filters, and the static nonlinear block is determined using twin support vector machine regression. Simulation of a control valve model and pH neutralization process have been presented to show the features of the proposed algorithm over support vector machine based algorithm.

Fractional calculus operators and their applications to thermal systems

This special collection is based on interdisciplinary theoretical studies, computational algorithm development, and applications of thermal systems. Related areas such as nonlinear modeling, simulation, identification, and control are also included. Moreover, this special collection aims to provide a discussion on diverse branches of mathematics, especially in fractional calculus operator and its applications in mechanical engineering, science, and statistics. The paper of Baleanu et al. is devoted to the application of the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo–Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica. The paper by Bie et al. contains an interesting application of modeling and controlling self-reconfiguration of modular robots. They extend L-systems to the self-reconfiguration process of modules robots. On the other hand, Kilicman and Ahmood study the matrix fractional differential equations and the exact solution for the system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices in their paper. The paper by Pourbashash et al. is based on a numerical efficient method for fractional mobile/immobile equation. At the same time, Su et al.’s study is based on the fractal derivative, and a robust viscoelastic element—fractal dashpot—is proposed to characterize the rheological behaviors of non-Newtonian fluid. In the paper by Ye et al., based on the thermomechanical coupling effect that commonly exists in the loading zone of angular-contact ball bearings while the bearings are operated, several process parameters are analyzed, including coordination condition of thermal expansion–deformation load, interaction relationship of contact stress, friction heat, and temperature raised in the loading zone of bearings. All the published papers are high in quality, contain original research results, and contribute to the theory of fractional calculus and thermal systems.

Identification of ARX Hammerstein Models based on Twin Support Vector Machine Regression

In this paper we develop a new algorithm to identify Auto-Regressive Exogenous (ARX) input Hammerstein Models based on Twin Support Vector Machine Regression (TSVR). The model is determined by minimizing two ε-insensitive loss functions. One of them determines the ε1-insensitive down bound regressor while the other determines the ε1-insensitive up bound regressor. The algorithm is compared to Support Vector Machine (SVM) and Least Square Support Vector Machine (LSSVM) based algorithms using simulation.

A Predictive Neural Network-Based Cascade Control for pH Reactors

This paper is concerned with the development of predictive neural network-based cascade control for pH reactors. The cascade structure consists of a master control loop (fuzzy proportional-integral) and a slave one (predictive neural network). The master loop is chosen to be more accurate but slower than the slave one. The strong features found in cascade structure have been added to the inherent features in model predictive neural network. The neural network is used to alleviate modeling difficulties found with pH reactor and to predict its behavior. The parameters of predictive algorithm are determined using an optimization algorithm. The effectiveness and feasibility of the proposed design have been demonstrated using MatLab.