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We give a counter example to the comparison principle for the multipoint BVPs (by Xuxin Yang, Zhimin He, and Jianhua Shen, in Mathematical Problems in Engineering, Volume 2009, Article ID 258090, doi:10.1155/2009/258090). Then we suggest and prove a corrected version of the comparison principle.

On the basis of basic law in AASHTO2007 model, the forecasting mathematical model of drying shrinkage of recycled aggregate concrete (RAC) is established by regression analysis and experimental study. The research results show that (1) with the replacement rate of RCA increases, the drying shrinkage value of RAC increases; this trend is even more obvious in the early drying time. (2) The addition of fly ash can inhibit the drying shrinkage of RAC, but the effect is not very obvious. Specifically, the addition of fly ash will increase the shrinkage to some extent when the mixing amount is 20%. (3) The addition of expansive agent can obviously inhibit the shrinkage of RAC; the inhibition affection is better than that of fly ash. (4) The forecasting mathematical models of drying shrinkage of RAC established in this paper have high accuracy and rationality according to experiment validation and error analysis.

This paper describes a valuable linear yaw-roll tractor-semitrailer (TST) model with five-degree-of-freedom (DOFs) for control algorithm development when steering and braking. The key parameters, roll stiffness, axle cornering stiffness, and fifth-wheel stiffness, are identified by the genetic algorithm (GA) and multistage genetic algorithm (MGA) based on TruckSim outputs to increase the accuracy of the model. Thus, the key parameters of the simplified model can be modified according to the real-time vehicle states by online lookup table and interpolation. The TruckSim vehicle model is built referring to the real tractor (JAC-HFC4251P1K7E33ZTF6×2) and semitrailer (Luyue LHX9406) used in the field test later. The validation of the linear yaw-roll model of a tractor-semitrailer using field test data is presented in this paper. The field test in the performance testing ground is detailed, and the test data of roll angle, roll rate, and yaw rate are compared with the outputs of the model with maps of the key parameters. The results indicate that the error of the tractor’s roll angle and semitrailer’s roll angle between model data and test data is 1.13% and 1.24%, respectively. The roll rate and yaw rate of the tractor and semitrailer are also in good agreement.

The traditional predictive method cannot fully reflect the complex nonlinear characteristics and regularities of automobile and parts sales data, so the prediction precision is not high. The purpose of this paper is to propose the gray GM(1,1) nonlinear periodic predictive model by introducing the seasonal variation index to improve predictive accuracy of the single GM(1,1) model. Firstly, the paper analyzes concept of GM(1,1) and then proposes the gray GM(1,1) nonlinear periodic predictive model to forecast automobile parts sales. The model algorithm used gray theory and accumulated technology to generate new data and set up unified differential equations to find the fitting curve of automobile parts sales prediction by the seasonal variation index to remove random elements. Lastly, the gray GM(1,1) nonlinear periodic predictive model is used for empirical analysis; the result of example shows that the model proposed in the paper is feasible. The superiority of the proposed predictive model compared with the single gray GM(1,1) model is demonstrated. The reliability of this model is experienced by the accuracy test, which provides a theoretical guidance for the prediction of automobile part sales. And the average relative error is reduced by 8.52% compared with the single GM(1,1) model.

The digging resistance in a normal state is the key to excavator design and automated excavation. It is difficult to accurately predict, simulate, or directly measure the digging resistance in a normal state due to uncertainties in the soil properties and excavation parameters. In this paper, a research idea is proposed that uses the working device as the entry point to indirectly calculate the digging resistance in a normal state by measuring the motion parameters and the cylinder pressure intensity. Based on the rule of combination for spatial force systems, a method for combining and projecting the system of the digging resistance is proposed in which the system is projected as six parts, and the tangential force, normal force, and bending moment in the plane of symmetry of the working device are the objects of the solution to avoid redundant equations. Based on kinematics and dynamics models of the excavator and the force and moment equilibrium conditions of the working device, equations for the active-side calculation of the incomplete digging resistance are derived. Based on these equations, the motion parameters of the working device and data on the cylinder pressure intensity obtained by measurement are used to calculate the incomplete digging resistance. The validation scheme and process proposed use the incomplete digging resistance as the external load to obtain the simulated stress of the working device through transient analysis. The simulated stress and the measured stress corresponding to the position of the measurement point are extracted and compared. The results show that there is a difference in the size of the numerical value between the simulated and measured stress, but the variation law is highly consistent, which validates the calculation method. In this paper, an active-side calculation method is provided for the incomplete digging resistance in a normal state without considering the soil-tool interaction relationships, which lays a theoretical foundation for the study of the digging resistance characteristics in a normal state, as well as excavator design and automated excavation.

This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.

The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.

The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

One of the most popular statistical models is a low-order polynomial response surface model, i.e., a polynomial of first order or second order. These polynomials can be used for global metamodels in weakly nonlinear simulation to approximate their global tendency and local metamodels in response surface methodology (RSM), which has been studied in various applications in engineering design and analysis. The order of the selected polynomial determines the number of sampling points (input combinations) and the resulting accuracy (validity, adequacy). This paper derives a novel method to obtain an accurate high-order polynomial while requiring fewer sampling points. This method uses a two-stage procedure such that the second stage modifies the low-order polynomial estimated in the first stage; this second stage does not require new points. This paper evaluates the performance of the method numerically by using several test functions. These numerical results show that the proposed method can provide more accurate predictions than the traditional method.

This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.

This paper presents a new solubility optimal system to improve the efficiency of supercritical fluid extraction (SFE). The major contribution is a nonlinear temperature-pressure decoupling model constructed with unequal-interval grey optimal models (UEIGOMs) and Peng-Robinson models (PRMs). The linear parts of temperature and pressure process can be constructed with UEIGOM, respectively. The nonlinear parts of temperature and pressure process can be described by PRMs, respectively. The whole nonlinear model cannot be input-output decoupled resulting from the singularity of decoupling matrix for PRM. This problem on input-output nondecoupling can be transformed to the problem on disturbance decoupling for a class of MIMO nonlinear systems. Therefore, the whole nonlinear coupling model can be disturbance decoupled. Furthermore, solubility optimal method is presented in the paper; it can calculate the optimal pressure according to the given temperature, namely, optimal working points, to maximize solubility for SFE process. The feasibility, effectiveness, and practicality of the proposed nonlinear temperature-pressure decoupling model constructed with UEIGOMs and PRMs are verified by SFE experiments in biphenyl. Experiments using the designed solubility optimal system are carried out to demonstrate the effectiveness in control scheme, simplicity in structure, and flexibility in implementation for the proposed solubility optimal system based on a new nonlinear temperature-pressure coupling model constructed with UEIGOMs and PRMs.

We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

This paper proposes a new scientific decision framework (SDF) under interval valued intuitionistic fuzzy (IVIF) environment for supplier selection (SS). The framework consists of two phases, where, in the first phase, criteria weights are estimated in a sensible manner using newly proposed IVIF based statistical variance (SV) method and, in the second phase, the suitable supplier is selected using ELECTRE (ELimination and Choice Expressing REality) ranking method under IVIF environment. This method involves three categories of outranking, namely, strong, moderate, and weak. Previous studies on ELECTRE ranking reveal that scholars have only used two categories of outranking, namely, strong and weak, in the formulation of IVIF based ELECTRE, which eventually aggravates fuzziness and vagueness in decision making process due to the potential loss of information. Motivated by this challenge, third outranking category, called moderate, is proposed, which considerably reduces the loss of information by improving checks to the concordance and discordance matrices. Thus, in this paper, IVIF-ELECTRE (IVIFE) method is presented and popular TOPSIS method is integrated with IVIFE for obtaining a linear ranking. Finally, the practicality of the proposed framework is demonstrated using SS example and the strength of proposed SDF is realized by comparing the framework with other similar methods.

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.

This paper aims to investigate the stationary probability density functions of the Duffing oscillator with time delay subjected to combined harmonic and white noise excitation by the method of stochastic averaging and equivalent linearization. By the transformation based on the fundamental matrix of the degenerate Duffing system, the paper shows that the displacement and the velocity with time delay in the Duffing oscillator can be computed approximately in non-time delay terms. Hence, the stochastic system with time delay is transformed into the corresponding stochastic non-time delay equation in Ito sense. The approximate stationary probability density function of the original system can be found by combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function. The response of Duffing oscillator is investigated. The analytical results are verified by numerical simulation results.

In order to detect infrared (IR) dim and small targets in a strong clutter background, a method based on local energy center of sequential image is proposed. This paper began by using improved anisotropy for background prediction (IABP), followed by target enhancement by improved high-order cumulates (HOC). Finally, on the basis of image preprocessing, the paper constructs a sequential image energy center detection algorithm that integrates the neighborhood, continuity, area, and energy and other motion characteristics of the target. Experiments showed that the improved anisotropic background predication could be loyal to the true background of the original image to the maximum extent, presenting a superior overall performance to other background prediction methods; the improved HOC significantly increased the signal-noise ratio of images; when the signal-noise ratio (SNR) is lower than 2.5 dB, the proposed method could effectively eliminate noise and detect targets.

The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

Relative position of seismic source and sensors has great influence on locating accuracy, particularly in far field conditions, and the accuracy will decrease seriously due to limited calculation precision and prior velocity error. In order to improve the locating accuracy of far field sources by isometric placed sensors in a straight line, a new locating method with nonprior velocity is proposed. After exhaustive research, this paper states that the hyperbola which is used for locating will be very close to its asymptote when seismic source locates in far field of sensors; therefore, the locating problem with prior velocity is equivalent to solving linear equations and the problem with nonprior velocity is equivalent to a nonlinear optimization problem with respect to the unknown velocity. And then, this paper proposed a new locating method based on a one-variable objective function with respect to the unknown velocity. Numerical experiments show that the proposed method has faster convergence speed, higher accuracy, and better stability.

This paper focuses on the periodic event-triggered consensus problem for multiagent systems under undirected graph. In the periodic event-triggered control, the event condition is tested only periodically to decide when to exert the control behaviors and when to broadcast the sampling data. Two sets of event-triggered strategies combining with sampled-data control are designed based on an exponential decay function and a quadratic Lyapunov function, respectively. Some useful theorems for these two periodic event-triggered strategies about the choice of period are derived to guarantee the asymptotical stability of the closed-loop multiagent systems. In addition, this paper gives a sufficient condition about the bounds of communication delay for the multiagent systems. It is rigorously proved that the overall system will achieve the consensus under the proposed strategy if the period and time delay satisfy the theorems. Finally, we extend these solutions to general linear dynamical systems. Simulation results are presented to show the effectiveness.

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

Judgment matrix aggregation, as an important part of group decision-making, has been widely and deeply studied due to the universality and importance of group decision-making in the management field. For the variety of judgment matrix in group decision-making, the matrix aggregation result can be obtained by using the mode of glowworm swarm optimization. First, this paper introduces the basic principle of the glowworm swarm optimization (GSO) algorithm and gives the improved GSO algorithm to solve the matrix aggregation problems. In this approach, the consistency ratio is introduced to the objective function of the glowworm swarm optimization, thus reducing the subjectivity and information loss in the aggregation process. Then, the improved GSO algorithm is applied to the solution of the deterministic matrix and the fuzzy matrix. The method optimization can provide an effective and relatively uniform aggregation method for matrix aggregation. Finally, through comparative analysis, it is shown that the method of this paper has certain advantages in terms of adaptability, accuracy, and stability to solving the matrix aggregation problems.

WOS: 000374093400001, Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach., Anadolu University Scientific Research Projects Commission [1403F077], This study was supported by the Anadolu University Scientific Research Projects Commission under Grant no. 1403F077.

In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy.

In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.

This paper investigates the consensus problem of high-order continuous-time linear multiagent systems (LMASs) with multitype switching topologies which include both consensusable and unconsensusable communication topologies. A linear transformation is introduced, which equivalently transforms the consensus problem into the stability problem of a corresponding switched system, along with a necessary and sufficient condition to analyze the consensus problem. This paper is aimed at studying the impact of a switching rule on communication topologies for consensus of LMASs. Based on the dynamic dwell time method, a sufficient condition is derived for consensus of LMASs. It is shown that, with switching signals that satisfy this switching rule, LMASs can achieve consensus under directed switching communication topologies. A numerical example is provided to illustrate the effectiveness of the theoretical results.

The sensor location problem (SLP) discussed in this paper is to find the minimum number and optimum locations of the flow counting points in the road network so that the traffic flows over the whole network can be inferred uniquely. Flow conservation system at intersections is formulated firstly using the turning ratios as the prior information. Then the coefficient matrix of the flow conservation system is proved to be nonsingular. Based on that, the minimal number of counting points is determined to be the total number of exclusive incoming roads and dummy roads, which are added to the network to represent the trips generated on real roads. So the task of SLP model based on turning ratios is just to determine the optimal sensor locations. The following analysis in this paper shows that placing sensors on all the exclusive incoming roads and dummy roads can always generate a unique network flow vector for any network topology. After that, a detection set composed of only real roads is proven to exist from the view of feasibility in reality. Finally, considering the roads importance and cost of the sensors, a weighted SLP model is formulated to find the optimal detection set. The greedy algorithm is proven to be able to provide the optimal solution for the proposed weighted SLP model.

First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.

Methods of utilizing independent component analysis (ICA) give little guidance about practical considerations for separating single-channel real-world data, in which most of them are nonlinear, nonstationary, and even chaotic in many fields. To solve this problem, a three-step method is provided in this paper. In the first step, the measured signal which is assumed to be piecewise higher order stationary time series is introduced and divided into a series of higher order stationary segments by applying a modified segmentation algorithm. Then the state space is reconstructed and the single-channel signal is transformed into a pseudo multiple input multiple output (MIMO) mode using a method of nonlinear analysis based on the high order statistics (HOS). In the last step, ICA is performed on the pseudo MIMO data to decompose the single channel recording into its underlying independent components (ICs) and the interested ICs are then extracted. Finally, the effectiveness and excellence of the higher order single-channel ICA (SCICA) method are validated with measured data throughout experiments. Also, the proposed method in this paper is proved to be more robust under different SNR and/or embedding dimension via explicit formulae and simulations.

This paper presents a predictive control strategy for an image-based visual servoing scheme that employs evolutionary optimization. The visual control task is approached as a nonlinear optimization problem that naturally handles relevant visual servoing constraints such as workspace limitations and visibility restrictions. As the predictive scheme requires a reliable model, this paper uses a local model that is based on the visual interaction matrix and a global model that employs 3D trajectory data extracted from a quaternion-based interpolator. The work assumes a free-flying camera with 6-DOF simulation whose results support the discussion on the constraint handling and the image prediction scheme.

This paper presents a method to perform chord classification from recorded audio. The signal harmonics are obtained by using the Fast Fourier Transform, and timbral information is suppressed by spectral whitening. A multiple fundamental frequency estimation of whitened data is achieved by adding attenuated harmonics by a weighting function. This paper proposes a method that performs feature selection by using a thresholding of the uncertainty of all frequency bins. Those measurements under the threshold are removed from the signal in the frequency domain. This allows a reduction of 95.53% of the signal characteristics, and the other 4.47% of frequency bins are used as enhanced information for the classifier. An Artificial Neural Network was utilized to classify four types of chords: major, minor, major 7th, and minor 7th. Those, played in the twelve musical notes, give a total of 48 different chords. Two reference methods (based on Hidden Markov Models) were compared with the method proposed in this paper by having the same database for the evaluation test. In most of the performed tests, the proposed method achieved a reasonably high performance, with an accuracy of 93%.

Currently superresolution from a motion blurred image still remains a challenging task. The conventional approach, which preprocesses the blurry low resolution (LR) image with a deblurring algorithm and employs a superresolution algorithm, has the following limitation. The high frequency texture of the image is unavoidably lost in the deblurring process and this loss restricts the performance of the subsequent superresolution process. This paper presents a novel technique that performs motion deblurring and superresolution jointly from one single blurry image. The basic idea is to regularize the ill-posed reconstruction problem using an edge-preserving gradient prior and a sparse kernel prior. This method derives from an inverse problem approach under an efficient optimization scheme that alternates between blur kernel estimation and superresolving until convergence. Furthermore, this paper proposes a simple and efficient refinement formulation to remove artifacts and render better deblurred high resolution (HR) images. The improvements brought by the proposed combined framework are demonstrated by the processing results of both simulated and real-life images. Quantitative and qualitative results on challenging examples show that the proposed method outperforms the existing state-of-the-art methods and effectively eliminates motion blur and artifacts in the superresolved image.

Thresholding function is an important part of the wavelet threshold denoising method, which can influence the signal denoising effect significantly. However, some defects are present in the existing methods, such as function discontinuity, fixed bias, and parameters determined by trial and error. In order to solve these problems, a new wavelet thresholding function based on hyperbolic tangent function is proposed in this paper. Firstly, the basic properties of hyperbolic tangent function are analyzed. Then, a new thresholding function with a shape parameter is presented based on hyperbolic tangent function. The continuity, monotonicity, and high-order differentiability of the new function are theoretically proven. Finally, in order to determine the final form of the new function, a shape parameter optimization strategy based on artificial fish swarm algorithm is given in this paper. Mean square error is adopted to construct the objective function, and the optimal shape parameter is achieved by iterative search. At the end of the paper, a simulation experiment is provided to verify the effectiveness of the new function. In the experiment, two benchmark signals are used as test signals. Simulation results show that the proposed function can achieve better denoising effect than the classical hard and soft thresholding functions under different signal types and noise intensities.

This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out.

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

Combining the correction technique proposed by Lin and Xie and the shifted inverse iteration, a multilevel correction scheme for the Steklov eigenvalue problem is proposed in this paper. The theoretical analysis and numerical experiments indicate that the scheme proposed in this paper is efficient for both simple and multiple eigenvalues of the Steklov eigenvalue problem.

Reliability testing is often carried out with small sample sizes and short duration because of increasing costs and the restriction of development time. Therefore, for highly reliable products, zero-failure data are often collected in such tests, which could not be used to evaluate reliability by traditional methods. To cope with this problem, the match distribution curve method was proposed by some researchers. The key step needed to exercise this method is to estimate the failure probability, which has yet to be solved in the case of the Weibull distribution. This paper presents a method to estimate the intervals of failure probability for the Weibull distribution by using the concavity or convexity and property of the distribution function. Furthermore, to use the method in practice, this paper proposes using the approximate value of the shape parameter determined by either engineering experience or by hypothesis testing through apvalue. The estimation of the failure probability is thus calculated using a Bayesian approach. A numerical example is presented to validate the effectiveness and robustness of the method.

Feature interaction has gained considerable attention recently. However, many feature selection methods considering interaction are only designed for categorical features. This paper proposes a mixed feature selection algorithm based on neighborhood rough sets that can be used to search for interacting features. In this paper, feature relevance, feature redundancy, and feature interaction are defined in the framework of neighborhood rough sets, the neighborhood interaction weight factor reflecting whether a feature is redundant or interactive is proposed, and a neighborhood interaction weight based feature selection algorithm (NIWFS) is brought forward. To evaluate the performance of the proposed algorithm, we compare NIWFS with other three feature selection algorithms, including INTERACT, NRS, and NMI, in terms of the classification accuracies and the number of selected features with C4.5 and IB1. The results from ten real world datasets indicate that NIWFS not only deals with mixed datasets directly, but also reduces the dimensionality of feature space with the highest average accuracies.

Multiplicative relations are one of most powerful techniques to express the preferences over alternatives (or criteria). In this paper, we propose a wide range of hesitant multiplicative fuzzy power aggregation geometric operators on multiattribute group decision making (MAGDM) problems for hesitant multiplicative information. In this paper, we first develop some compatibility measures for hesitant multiplicative fuzzy numbers, based on which the corresponding support measures can be obtained. Then we propose several aggregation techniques, and investigate their properties. In the end, we develop two approaches for multiple attribute group decision making with hesitant multiplicative fuzzy information and illustrate a real world example to show the behavior of the proposed operators.

Vehicles are often caught in dilemma zone when they approach signalized intersections in yellow interval. The existence of dilemma zone which is significantly influenced by driver behavior seriously affects the efficiency and safety of intersections. This paper proposes the driver behavior models in yellow interval by logistic regression and fuzzy decision tree modeling, respectively, based on camera image data. Vehicle’s speed and distance to stop line are considered in logistic regression model, which also brings in a dummy variable to describe installation of countdown timer display. Fuzzy decision tree model is generated by FID3 algorithm whose heuristic information is fuzzy information entropy based on membership functions. This paper concludes that fuzzy decision tree is more accurate to describe driver behavior at signalized intersection than logistic regression model.

The nearest neighbor is one of the most popular classifiers, and it has been successfully used in pattern recognition and machine learning. One drawback ofkNN is that it performs poorly when class distributions are overlapping. Recently, local probability center (LPC) algorithm is proposed to solve this problem; its main idea is giving weight to samples according to their posterior probability. However, LPC performs poorly when the value ofkis very small and the higher-dimensional datasets are used. To deal with this problem, this paper suggests that the gradient of the posterior probability function can be estimated under sufficient assumption. The theoretic property is beneficial to faithfully calculate the inner product of two vectors. To increase the performance in high-dimensional datasets, the multidimensional Parzen window and Euler-Richardson method are utilized, and a new classifier based on local probability centers is developed in this paper. Experimental results show that the proposed method yields stable performance with a wide range ofkfor usage, robust performance to overlapping issue, and good performance to dimensionality. The proposed theorem can be applied to mathematical problems and other applications. Furthermore, the proposed method is an attractive classifier because of its simplicity.

This paper is devoted to the average consensus problems in directed networks of agents with unknown control direction. In this paper, by using Nussbaum function techniques and Laplacian matrix, novel average consensus protocols are designed for multiagent systems with unknown control direction in the cases of directed networks with fixed and switching topology. In the case of switching topology, the disagreement vector is utilized. Finally, simulation is provided to demonstrate the effectiveness of our results.

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist ofκmodes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employingM-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results.

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.

The one-dimensional continuous genetic algorithm (CGA) previously developed by the principal author is extended and enhanced to deal with two-dimensional spaces in this paper. The enhanced CGA converts the partial differential equations into algebraic equations by replacing the derivatives appearing in the differential equation with their proper finite difference formula in 2D spaces. This optimization methodology is then applied for the solution of steady-state two-dimensional Stokes and nonlinear Navier Stokes problems. The main advantage of using CGA for the solution of partial differential equations is that the algorithm can be applied to linear and nonlinear equations without any modification in its structure. A comparison between the results obtained using the 2D CGA and the known Galerkin finite element method using COMSOL is presented in this paper. The results showed that CGA has an excellent accuracy as compared to other numerical solvers.

Multiobjective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multiobjective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods.

Spheroid disturbance of input data brings great challenges to support vector regression; thus it is essential to study the robust regression model. This paper is dedicated to establish a robust regression model which makes the regression function robust against disturbance of data and system parameter. Firstly, two theorems have been given to show that the robust linearε-support vector regression problem could be settled by solving the dual problems. Secondly, it has been focused on the development of robust support vector regression algorithm which is extended from linear domain to nonlinear domain. Finally, the numerical experiments result demonstrates the effectiveness of the models and algorithms proposed in this paper.