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The flow of non-Newtonian fluids is extremely important in a variety of industrial applications and processes, including painting, printing, and coating. The goal of this paper is to develop a mathematical model for an incompressible, non-isothermal third-grade fluid as it travels through a minor gap between two heated rolls that are revolving in the opposite direction. Using appropriate dimensionless parameters, the dimensionless version of the governing equations is constructed. To simplify the nondimensional form of the governing equations, the LAT (lubrication approximation theory) is applied. It is mentioned that the perturbation approach should be used. It is a very important tool in modern mathematical physics and practical fluid mechanics, and it is used a lot. Through perturbation techniques, exact solutions for velocity distribution, flow rate, temperature distribution, and pressure gradient are offered. To observe the flow pattern, streamlines are also drawn. Numerical outcomes of some substantial engineering quantities like flow rate, roll separation force, power input, and pressure distribution are found. Some outcomes are displayed graphically although others are presented in tabular form. We have observed that the third-grade parameters give a way to control velocity, pressure gradients, flow rate, and coating thickness. Further, increasing the velocities ratio values lowers the coating thickness on the web. Furthermore, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Both the model and the numerical calculations are in agreement with the viscous fluid model that is already present in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the thin film roll coating process of an incompressible Williamson material, passing through a closed passage between a rotating roll and a web. In light of lubrication approximation theory, the flow equations are nondimensionalized. The regular perturbation approach is used to provide solutions for the velocity profile, pressure gradient, flow rate per unit width, and shear stress at the roll surface. Important engineering quantities such as coating thickness, maximum pressure, separation point, roll/sheet separating force, and roll-transmitted power to the fluid are also obtained. The effects of several factors are graphically projected. The study shows that the material factors that are involved determine the operating variables. Coating thickness and separation point are controlled by Weissenberg's number, therefore acting as a controlling parameter for the rate of flow, thickness in coating, power contribution, pressure, roll separating force, and separation point. In comparison to the existing results in the literature, the current results are broader and zero-order results are more accurate. [ABSTRACT FROM AUTHOR]

Management of electric equipment has a direct impact on companies’ performance and profitability. Considering the critical role that electric power materials play in supporting maintenance operations and preventing equipment failure, it is essential to maintain an inventory to a reasonable level. However, a majority of these electric power materials exhibit an intermittent demand pattern characterized by random arrivals interspersed with time periods with no demand at all. These characteristics cause additional difficulty for companies in managing these electric power material inventories. In response to the above problem, this paper, based on the electric power material demand data of Shanghai Electric Power Company, develops a new method to determine the optimal order quantity Q⁎ in a cost-oriented periodic review (T,Q) system, whereby unsatisfied demands are backordered and demand follows a compound Erlang distribution. Q⁎corresponds to the value of Q that gives the minimum expected total inventory holding and backordering cost. Subsequently, an empirical investigation is conducted to compare this method with the Newsvendor model. Results verify its superiority in cost savings. Ultimately, considering the complicated calculation and low efficiency of that algorithm, this paper proposes an approximation and a heuristic algorithm which have a higher level of utility in a real industrial context. The approximation algorithm simplifies the calculation process by reducing iterative times while the heuristic algorithm achieves it by generalizing the relationship between the optimal order quantity Q⁎ and mean demand interarrival rate λ. [ABSTRACT FROM AUTHOR]

The approximations for the Q-function reported in the literature so far have mainly been developed to overcome not only the difficulties, but also the limitations, caused in different research areas, by the nonexistence of the closed form expression for the Q-function. Unlike the previous papers, we propose the novel approximation for the Q-function not for solving some particular problem. Instead, we analyze this problem in one general manner and we provide one general solution, which has wide applicability. Specifically, in this paper, we set two goals, which are somewhat contrary to each other. The one is the simplicity of the analytical form of Q-function approximation and the other is the relatively high accuracy of the approximation for a wide range of arguments. Since we propose a two-parametric approximation for the Q-function, by examining the effect of the parameters choice on the accuracy of the approximation, we manage to determine the most suitable parameters of approximation and to achieve these goals simultaneously. The simplicity of the analytical form of our approximation along with its relatively high accuracy, which is comparable to or even better than that of the previously proposed approximations of similar analytical form complexity, indicates its wide applicability. [ABSTRACT FROM AUTHOR]

This paper addresses an energy-based extension of the Multimode Resource-Constrained Project Scheduling Problem (MRCPSP) called MRCPSP-ENERGY. This extension considers the energy consumption as an additional resource that leads to different execution modes (and durations) of the activities. Consequently, different schedules can be obtained. The objective is to maximize the efficiency of the project, which takes into account the minimization of both makespan and energy consumption. This is a well-known NP-hard problem, such that the application of metaheuristic techniques is necessary to address real-size problems in a reasonable time. This paper shows that the Activity List representation, commonly used in metaheuristics, can lead to obtaining many redundant solutions, that is, solutions that have different representations but are in fact the same. This is a serious disadvantage for a search procedure. We propose a genetic algorithm (GA) for solving the MRCPSP-ENERGY, trying to avoid redundant solutions by focusing the search on the execution modes, by using the Mode List representation. The proposed GA is evaluated on different instances of the PSPLIB-ENERGY library and compared to the results obtained by both exact methods and approximate methods reported in the literature. This library is an extension of the well-known PSPLIB library, which contains MRCPSP-ENERGY test cases. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameter perturbation homotopy continuation method for solving fixed point problems on more general nonconvex sets with both inequality and equality constraints. By adopting appropriate techniques, we make the initial points not certainly in the set consisting of the equality constraints. This point can improve the computational efficiency greatly when the equality constraints are complex. In addition, we also weaken the assumptions of the previous results in the literature so that the method proposed in this paper can be applied to solve fixed point problems in more general nonconvex sets. Under suitable conditions, we obtain the global convergence of this homotopy continuation method. Moreover, we provide several numerical examples to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

Short-term load forecasting model based on quantum Elman neural networks was constructed in this paper. The quantum computation and Elman feedback mechanism were integrated into quantum Elman neural networks. Quantum computation can effectively improve the approximation capability and the information processing ability of the neural networks. Quantum Elman neural networks have not only the feedforward connection but also the feedback connection. The feedback connection between the hidden nodes and the context nodes belongs to the state feedback in the internal system, which has formed specific dynamic memory performance. Phase space reconstruction theory is the theoretical basis of constructing the forecasting model. The training samples are formed by means of K-nearest neighbor approach. Through the example simulation, the testing results show that the model based on quantum Elman neural networks is better than the model based on the quantum feedforward neural network, the model based on the conventional Elman neural network, and the model based on the conventional feedforward neural network. So the proposed model can effectively improve the prediction accuracy. The research in the paper makes a theoretical foundation for the practical engineering application of the short-term load forecasting model based on quantum Elman neural networks. [ABSTRACT FROM AUTHOR]

Nowadays, a wide class of problems can be solved by using the classical newsboy model. However, in problems where uncertainty of events and randomness are omnipresent, there is a necessity to adapt the existing solutions and/or find new extensions that will properly answer all requirements. This paper considers a multistage assembly system where interrelated assembly operations with independent stochastic operation times should be planned in an optimal way. Delivery of items in a requested time implies that either delay costs or holding costs appear. The goal is to find optimal safety times. We propose an approximate technique based on successive application of the solution of simpler one-stage problem. The generalized mathematical model suggested is built up on the relaxed hypothesis and can be used in multistage assembly networks. The existence and uniqueness of the solution are proven. The preliminary tests are performed and our approximate technique is compared to exact results. [ABSTRACT FROM AUTHOR]

The differential problem given by a parabolic equation describing the purely viscous flow generated by a constant or an oscillating motion of a boundary is the well-known Stokes’ problem. The one-dimensional equation is generally solved for unbounded or bounded domains; for the latter, either free slip (i.e., zero normal gradient) or no-slip (i.e., zero velocity) conditions are enforced on one boundary. Generally, the analytical strategy to solve these problems is based on finding the solutions of the Laplace-transformed (in time) equation and on inverting these solutions. In the present paper this problem is solved by making use of the residuals theorem; as it will be shown, this strategy allows achieving the solutions of First and Second Stokes’ problems in both infinite and finite depth. The extension to generally periodic boundaries with the presence of a periodic pressure gradient is also presented. This approach allows getting closed form solutions in the time domain in a rather fast and simple way. An ad hoc numerical algorithm, based on a finite difference approximation of the differential equation, has been developed to check the correctness of the analytical solutions. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence. [ABSTRACT FROM AUTHOR]

This paper presents a multiconstrained quality-of-service routing (QoSR) based on a differentially guided krill herd (DGKH) algorithm in mobile ad hoc networks (MANETs). QoSR is a NP-complete and significant problem with immense challenges in determining an optimum path that simultaneously satisfies various constraints in MANETs, where the topology varies constantly. Various heuristic algorithms are widely used to solve this problem with compromise on excessive computational complexities and/or low performance. This paper proposes a krill herd based algorithm called DGKH, where the krill individuals do not update the position in comparison with one-to-one (as usual), but instead it uses the information from various krill individuals and then searches to determine a feasible path. Experiment results on MANETs with different number nodes (routes) are considered with three constraints which are maximum allowed delay, maximum allowed jitter, and minimum requested bandwidth. It is demonstrated that the proposed DGKH algorithm is an effective approximation algorithm exhibiting satisfactory performance than the KHA and existing algorithms in the literature by determining an optimum path that satisfies more than one QoS constraint in MANETs. [ABSTRACT FROM AUTHOR]

Capacitive micromachined ultrasonic transducers (CMUTs) are one of the appealing MEMS devices. Most studies treat CMUTs as rigid plates vibrating in open air, ignoring the mechanical boundary conditions for simplification and resulting in cumulative errors in coupled fields. This paper presents a new analytical model for the pull-in characteristics of the flat circular CMUT cell featuring sealed cavity. Utilizing the plate theory coupled with Boyle’s law, the paper establishes a strong relation between the pressures inside the sealed cavity and the pull-in characteristics for the first time. Not only did we point out that the existence of the pressure inside the sealed cavity cannot be omitted, but we also quantified the direct effect of the pressure ratios on the pull-in phenomenon. The pull-in voltages increase while the pull-in ratios decrease with the pressure ratios of the pressure inside the sealed cavity to the ambient pressure. The proposed calculation process delivers a good approximation of the pull-in voltages and displacements, which are consistent with COMSOL simulation results. Particularly, the percentage error of our calculation process is 6.986% for the worst case. Therefore, our proposed analytical model accurately and efficiently predicts the pull-in characteristics and this paper offers new perspectives and reference value in designing and modeling the CMUTs. [ABSTRACT FROM AUTHOR]

In order to characterize the controllability of the aggregate demand response, that is, the aggregated consumer behaviors, the paper introduces the concept of controllability index which expresses the lowest occurrence probability in total electric consumption which can be changed by electric price. As the number of consumers is larger, it becomes difficult to directly analyze the controllability index. To resolve the difficulty of the large number of consumers, by using the central limit theorem, the paper approximates the controllability index and gives the solution maximizing the approximated controllability index. [ABSTRACT FROM AUTHOR]

Robust optimization is a powerful and relatively novel methodology to cope with optimization problems in the presence of uncertainty. The positive aspect of robust optimization approach is its computational tractability that attracts more and more attention. In this paper, we focus on an ambiguous P-model where probability distributions are partially known. We discuss robust counterpart (RC) of uncertain linear constraints under two refined uncertain sets by robust approach and further find the safe tractable approximations of chance constraints in the ambiguous P-model. Because of the probability constraints embedded in the ambiguous P-model, it is computationally intractable. The advantage of our approach lies in choosing an implicit way to treat stochastic uncertainty models instead of solving them directly. The process above can enable the transformation of proposed P-model to a tractable deterministic one under the refined uncertainty sets. A numerical example about portfolio selection demonstrates that the ambiguous P-model can help the decision maker to determine the optimal investment proportions of various stocks. Sensitivity analyses explore the trade-off between optimization and robustness by adjusting parameter values. Comparison study is conducted to validate the benefit of our ambiguous P-model. [ABSTRACT FROM AUTHOR]

When superheated steam flows along the horizontal wellbore, it may change to saturated steam at some point of the wellbore. In this paper, to accurately predict the heat radius of cyclic superheated steam stimulation with horizontal wellbore, the distribution of thermophysical properties of superheated steam along the horizontal wellbore is considered. The heating process is divided into 4 stages for superheated steam and 3 stages for saturated steam when the phase change undergoes in the wellbore. On this basis, the mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore was established according to energy conservation principle and Laplace transformation method. The calculation result of the new mathematical model is in good agreement with that of the numerical simulation (CMG STARS) for the same parameters from a specific heavy oil reservoir, which verified the correctness of the new mathematical model. The effect of degree of superheat and the cycle of stimulation are analyzed in detail after the new mathematical model is validated. The results show that the heat radius of superheated zone, steam zone, and hot fluid zone all decrease with horizontal well length and increase with the cycle of stimulation. The higher the degree of superheat is, the farther from the heel of the horizontal wellbore the phase change undergoes. Besides, the radius of superheated zone, steam zone, and hot fluid zone increases with the degree of superheat, but the value increases little at steam zone and hot fluid zone. [ABSTRACT FROM AUTHOR]

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example. [ABSTRACT FROM AUTHOR]

Dealing with practical control systems, it is equally important to establish the controllability of the system under study and to find corresponding control functions explicitly. The most challenging problem in this path is the rigorous analysis of the state constraints, which can be especially sophisticated in the case of nonlinear systems. However, some heuristic considerations related to physical, mechanical, or other aspects of the problem may allow coming up with specific hierarchic controls containing a set of free parameters. Such an approach allows reducing the computational complexity of the problem by reducing the nonlinear state constraints to nonlinear algebraic equations with respect to the free parameters. This paper is devoted to heuristic determination of control functions providing exact and approximate controllability of dynamic systems with nonlinear state constraints. Using the recently developed approach based on Green’s function method, the controllability analysis of nonlinear dynamic systems, in general, is reduced to nonlinear integral constraints with respect to the control function. We construct parametric families of control functions having certain physical meanings, which reduce the nonlinear integral constraints to a system of nonlinear algebraic equations. Regimes such as time-harmonic, switching, impulsive, and optimal stopping ones are considered. Two concrete examples arising from engineering help to reveal advantages and drawbacks of the technique. [ABSTRACT FROM AUTHOR]

This paper designs a kind of adaptive fuzzy controller for robotic manipulator considering external disturbances and modeling errors. First, n-link uncertain robotic manipulator dynamics based on the Lagrange equation is changed into a two-order multiple-input multiple-output (MIMO) system via feedback technique. Then, an adaptive fuzzy logic control scheme is studied by using sliding theory, which adopts the adaptive fuzzy logic systems to estimate the uncertainties and employs a filtered error to make up for the approximation errors, hence enhancing the robust performance of robotic manipulator system uncertainties. It is proved that the tracking errors converge into zero asymptotically by using Lyapunov stability theory. Last, we take a two-link rigid robotic manipulator as an example and give its simulations. Compared with the existing results in the literature, the proposed controller shows higher precision and stronger robustness. [ABSTRACT FROM AUTHOR]

Detecting and counting elliptical objects are an interesting problem in digital image processing. There are real-world applications of this problem in various disciplines. Solving this problem is harder when there is occlusion among the elliptical objects, since in general these objects are considered as part of the bigger object (conglomerate). The solution to this problem focusses on the detection and segmentation of the precise number of occluded elliptical objects, while omitting all noninteresting objects. There are a variety of computational approximations that focus on this problem; however, such approximations are not accurate when there is occlusion. This paper presents an algorithm designed to solve this problem, specifically, to detect, segment, and count elliptical objects of a specific size when these are in occlusion with other objects within the conglomerate. Our algorithm deals with a time-consuming combinatorial process. To optimize the execution time of our algorithm, we implemented a parallel GPU version with CUDA-C, which experimentally improved the detection of occluded objects, as well as lowering processing times compared to the sequential version of the method. Comparative test results with another method featured in literature showed improved detection of objects in occlusion when using the proposed parallel method. [ABSTRACT FROM AUTHOR]

The popular deep Q learning algorithm is known to be instability because of the Q-value’s shake and overestimation action values under certain conditions. These issues tend to adversely affect their performance. In this paper, we develop the ensemble network architecture for deep reinforcement learning which is based on value function approximation. The temporal ensemble stabilizes the training process by reducing the variance of target approximation error and the ensemble of target values reduces the overestimate and makes better performance by estimating more accurate Q-value. Our results show that this architecture leads to statistically significant better value evaluation and more stable and better performance on several classical control tasks at OpenAI Gym environment. [ABSTRACT FROM AUTHOR]

This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using the P1-P1 finite element pair and then solving an additional Stokes problem using the P2-P2 finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergence analysis is given. Finally, numerical results are presented to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

The information of temperature field distribution is complex but quite important for theoretical study and industrial applications, such as burning, drying, and heating, because it can reflect the internal running state of industrial equipment, assist to develop control strategy, and ensure safety in operation. Acoustic imaging is a kind of noncontact temperature measurement technique which is able to achieve temperature field distribution reconstruction. The process of temperature field distribution reconstruction using acoustic imaging is an inverse problem and its reconstruction performance depends on reconstruction algorithm. In this paper, a modified reconstruction algorithm is investigated. Compared with other reconstruction methods of least square algorithm and radial basis function approximation, the reconstruction results indicate that the modified reconstruction algorithm occupies the best information reflection of temperature field distribution and the reconstruction accuracy is improved. [ABSTRACT FROM AUTHOR]

Most real-world engineering optimization problems are inherently multi objective, for example, searching for trade-off solutions of high quality and low cost. As no single optimal solution exists for such problems, multi objective optimizers provide sets of optimal (or near-optimal) trade-off solutions to choose from. The empirical attainment function (EAF) is a powerful tool that can be used to analyze and compare the performance of these optimizers. While the visualization of EAFs is rather straightforward in two objectives, the three-objective case presents a great challenge as we need to visualize a large number of 3D cuboids. This paper addresses the visualization of exact as well as approximated 3D EAF values and differences in these values provided by two competing multi objective optimizers. We show that the exact EAFs can be visualized using slicing and maximum intensity projection (MIP), while the approximated EAFs can be visualized using slicing, MIP, and direct volume rendering. In addition, the paper demonstrates the use of the proposed visualization techniques on a steel casting optimization problem. [ABSTRACT FROM AUTHOR]

Based on the moving least-squares (MLS) approximation, an improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element-free Galerkin (IIEFG) method is presented for two-dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kronecker δ function, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element-free Galerkin (EFG) method and interpolating element-free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods. [ABSTRACT FROM AUTHOR]

As a continuous state space problem, air combat is difficult to be resolved by traditional dynamic programming (DP) with discretized state space. The approximated dynamic programming (ADP) approach is studied in this paper to build a high performance decision model for air combat in 1 versus 1 scenario, in which the iterative process for policy improvement is replaced by mass sampling from history trajectories and utility function approximating, leading to high efficiency on policy improvement eventually. A continuous reward function is also constructed to better guide the plane to find its way to "winner" state from any initial situation. According to our experiments, the plane is more offensive when following policy derived from ADP approach other than the baseline Min-Max policy, in which the "time to win" is reduced greatly but the cumulated probability of being killed by enemy is higher. The reason is analyzed in this paper. [ABSTRACT FROM AUTHOR]

Based upon the framework of the structural support vector machines, this paper proposes two approaches to the depth restoration towards different scenes, that is, margin rescaling and the slack rescaling. The results show that both approaches achieve high convergence, while the slack approach yields better performance in prediction accuracy. However, due to its nondecomposability nature, the application of the slack approach is limited. This paper therefore introduces a novel approximation slack method to solve this problem, in which we propose a modified way of defining the loss functions to ensure the decomposability of the object function. During the training process, a bundle method is used to improve the computing efficiency. The results on Middlebury datasets show that proposed depth inference method solves the nondecomposability of slack scaling method and achieves relative acceptable accuracy. Our approximation approach can be an alternative for the slack scaling method to ensure efficient computation. [ABSTRACT FROM AUTHOR]

This paper is concerned with an integral terminal slidingmode tracking control for a class of uncertain nonaffine nonlinear systems. Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique. Next, for the unmeasured disturbance of nonlinear systems, integral terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Subsequently, based on approximated nonlinear model and the designed disturbance observer, the integral terminal sliding mode tracking control is presented for nonaffine nonlinear systems with uncertainty. Different from traditional terminal slidingmode control, this paper accomplishes finite convergence time for nonaffine nonlinear systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. Finally, two numerical simulation results are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Online tracking time-varying number of targets is a challenging issue due to measurement noise, target birth or death, and association uncertainty, especially when target number is large. In this paper, we propose an efficient approximation of the Labeled Multi-Bernoulli (LMB) filter to perform online multitarget state estimation and track maintenance efficiently. On the basis of the original LMB filer, we propose a target posterior approximation technique to use a weighted single Gaussian component representing each individual target. Moreover, we present the Gaussian mixture implementation of the proposed efficient approximation of the LMB filter under linear, Gaussian assumptions on the target dynamic model and measurement model. Numerical results verify that our proposed efficient approximation of the LMB filer achieves accurate tracking performance and runs several times faster than the original LMB filer. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs). At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs. [ABSTRACT FROM AUTHOR]

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters. The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors. This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous-time linear equalizer. [ABSTRACT FROM AUTHOR]

The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the problems concerned with the trajectory tracking control with prescribed performance for marine surface vessels without velocity measurements in uncertain dynamical environments, in the presence of parametric uncertainties, unknown disturbances, and unknown dead-zone. First, only the ship position and heading measurements are available and a high-gain observer is used to estimate the unmeasurable velocities. Second, by utilizing the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed via the preprocessing. At last, based on neural network approximation in combination with backstepping and Lyapunov synthesis, a robust adaptive neural control scheme is developed to handle the uncertainties and input dead-zone characteristics. Under the designed adaptive controller for marine surface vessels, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the prescribed transient and steady tracking control performance is guaranteed. Simulation studies are performed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction. [ABSTRACT FROM AUTHOR]

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much harder problem, a heuristic algorithm is proposed to find approximate solutions. Through computational experiments, the heuristic algorithms’ performance is evaluated with problems up to 500 jobs. [ABSTRACT FROM AUTHOR]

The time-band approximation model for flight operations recovery following disruption (Bard, Yu, Arguello, IIE Transactions, 33, 931–947, 2001) is constructed by partitioning the recovery period into time bands and by approximating the delay costs associated with the possible flight connections. However, for disruptions occurring in a hub-and-spoke network, a large number of possible flight connections are constructed throughout the entire flight schedule, so as to obtain the approximate optimal. In this paper, we show the application of the simplex group cycle approach to hub-and-spoke airlines in China, along with the related weighted threshold necessary for controlling the computation time and the flight disruption scope and depth. Subsequently, we present the weighted time-band approximation model for flight operations recovery, which incorporates the simplex group cycle approach. Simple numerical experiments using actual data from Air China show that the weighted time-band approximation model is feasible, and the results of stochastic experiments using actual data from Sichuan Airlines show that the flight disruption and computation time are controlled by the airline operations control center, which aims to achieve a balance between the flight disruption scope and depth, computation time, and recovery value. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established. [ABSTRACT FROM AUTHOR]

Maximum weight independent set (MWIS) is a combinatorial optimization problem that naturally arises in many applications especially wireless networking. This paper studies distributed approximation algorithms for finding MWIS in a general graph. In the proposed algorithm, each node keeps exchanging messages with neighbors in which each message contains partial solutions of the MWIS optimization program. A parameter H is introduced to achieve different tradeoff between approximation accuracy and space complexity. Theoretical analysis shows that the proposed algorithm is guaranteed to converge to an approximate solution after finite iterations; specifically, the proposed algorithm is guaranteed to converge to the optimal solution with H=+∞. Simulation results confirm the effectiveness of the proposed distributed algorithm in terms of weight sum, message size, and convergence performance. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes a stabilized finite-volume method (FVM) for the threedimensional stationary Navier-Stokes equations approximated by the lowest order finite element pairs. The method studies the new stabilized FVM with the relationship between the stabilized FEM (FEM) and the stabilized FVM under the assumption of the uniqueness condition. The results have three prominent features in this paper. Firstly, the error analysis shows that the stabilized FVM provides an approximate solution with the optimal convergence rate of the same order as the usual stabilized FEM solution solving the stationary Navier-Stokes equations. Secondly, superconvergence results on the solutions of the stabilized FEM and stabilized FVM are derived on the H¹-norm and the L²-norm for the velocity and pressure. Thirdly, residual technique is applied to obtain the L²-norm error for the velocity without additional regular assumption on the exact solution. [ABSTRACT FROM AUTHOR]

Retrial queues can only be solved in a closed form in very few and simple cases, so researchers must resort to approximate models. However, most of the papers that propose approximate models assume the convergence of the proposed models to their exact counterparts, without providing a rigorous mathematical proof. In this paper we demonstrate the convergence of finite truncated models with two reattempt orbits. [ABSTRACT FROM AUTHOR]

This paper reviewed the research on the nonlinear free vibration of pre-stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures. [ABSTRACT FROM AUTHOR]

The Cattaneo-Vernotte equation is a generalization of the heat and particle diffusion equations; this mathematical model combines waves and diffusion with a finite velocity of propagation. In disordered systems the diffusion can be anomalous. In these kinds of systems, the mean-square displacement is proportional to a fractional power of time not equal to one. The anomalous diffusion concept is naturally obtained from diffusion equations using the fractional calculus approach. In this paper we present an alternative representation of the Cattaneo-Vernotte equation using the fractional calculus approach; the spatial-time derivatives of fractional order are approximated using the Caputo-type derivative in the range (0,2]. In this alternative representation we introduce the appropriate fractional dimensional parameters which characterize consistently the existence of the fractional space-time derivatives into the fractional Cattaneo-Vernotte equation. Finally, consider the Dirichlet conditions, the Fourier method was used to find the full solution of the fractional Cattaneo-Vernotte equation in analytic way, and Caputo and Riesz fractional derivatives are considered. The advantage of our representation appears according to the comparison between our model and models presented in the literature, which are not acceptable physically due to the dimensional incompatibility of the solutions. The classical cases are recovered when the fractional derivative exponents are equal to 1. [ABSTRACT FROM AUTHOR]

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging. [ABSTRACT FROM AUTHOR]

Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2. [ABSTRACT FROM AUTHOR]

Besides inheriting the properties of classical Bézier curves of degree n, the corresponding λ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction of λ-Bézier curves in the L2-norm. By analysing the properties of λ-Bézier curves of degree n, a method which can deal with approximating λ-Bézier curve of degree n+1 by λ-Bézier curve of degree m  (m≤n) is presented. Then, in unrestricted and C0, C1 constraint conditions, the new control points of approximating λ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement. [ABSTRACT FROM AUTHOR]

The aim of this paper is to determine the stabilizing PID parametric region for multivariable systems. Firstly, a general equivalent transfer function parameterization method is proposed to construct the multiloop equivalent process for multivariable systems. Then, based on the equivalent single loops, a model-based method is presented to derive the stabilizing PID parametric region by using the generalized Hermite-Biehler theorem. By sweeping over the entire ranges of feasible proportional gains and determining the stabilizing regions in the space of integral and derivative gains, the complete set of stabilizing PID controllers can be determined. The robustness of the design procedure against the approximation in getting the SISO plants is analyzed. Finally, simulation of a practical model is carried out to illustrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

A probabilistic method is presented to analyze the temperature and the maximum frequency for multicore processors based on consideration of workload variation, in this paper. Firstly, at the microarchitecture level, dynamic powers are modeled as the linear function of IPCs (instructions per cycle), and leakage powers are approximated as the linear function of temperature. Secondly, the microarchitecture-level hotspot temperatures of both active cores and inactive cores are derived as the linear functions of IPCs. The normal probabilistic distribution of hotspot temperatures is derived based on the assumption that IPCs of all cores follow the same normal distribution. Thirdly and lastly, the probabilistic distribution of the set of discrete frequencies is determined. It can be seen from the experimental results that hotspot temperatures of multicore processors are not deterministic and have significant variations, and the number of active cores and running frequency simultaneously determine the probabilistic distribution of hotspot temperatures. The number of active cores not only results in different probabilistic distribution of frequencies, but also leads to different probabilities for triggering DFS (dynamic frequency scaling). [ABSTRACT FROM AUTHOR]

Structural load types, on the one hand, and structural capacity to withstand these loads, on the other hand, are of a probabilistic nature as they cannot be calculated and presented in a fully deterministic way. As such, the past few decades have witnessed the development of numerous probabilistic approaches towards the analysis and design of structures. Among the conventional methods used to assess structural reliability, the Monte Carlo sampling method has proved to be very convenient and efficient. However, it does suffer from certain disadvantages, the biggest one being the requirement of a very large number of samples to handle small probabilities, leading to a high computational cost. In this paper, a simple algorithm was proposed to estimate low failure probabilities using a small number of samples in conjunction with the Monte Carlo method. This revised approach was then presented in a step-by-step flowchart, for the purpose of easy programming and implementation. [ABSTRACT FROM AUTHOR]

Autonomous vehicles need to perform social accepted behaviors in complex urban scenarios including human-driven vehicles with uncertain intentions. This leads to many difficult decision-making problems, such as deciding a lane change maneuver and generating policies to pass through intersections. In this paper, we propose an intention-aware decision-making algorithm to solve this challenging problem in an uncontrolled intersection scenario. In order to consider uncertain intentions, we first develop a continuous hidden Markov model to predict both the high-level motion intention (e.g., turn right, turn left, and go straight) and the low level interaction intentions (e.g., yield status for related vehicles). Then a partially observable Markov decision process (POMDP) is built to model the general decision-making framework. Due to the difficulty in solving POMDP, we use proper assumptions and approximations to simplify this problem. A human-like policy generation mechanism is used to generate the possible candidates. Human-driven vehicles’ future motion model is proposed to be applied in state transition process and the intention is updated during each prediction time step. The reward function, which considers the driving safety, traffic laws, time efficiency, and so forth, is designed to calculate the optimal policy. Finally, our method is evaluated in simulation with PreScan software and a driving simulator. The experiments show that our method could lead autonomous vehicle to pass through uncontrolled intersections safely and efficiently. [ABSTRACT FROM AUTHOR]

This paper proposes a two-level additive Schwarz preconditioning algorithm for the weak Galerkin approximation of the second-order elliptic equation. In the algorithm, a P1 conforming finite element space is defined on the coarse mesh, and a stable intergrid transfer operator is proposed to exchange the information between the spaces on the coarse mesh and the fine mesh. With the framework of the Schwarz method, it is proved that the condition number of the preconditioned system only depends on the rate of the coarse mesh size and the overlapping size. Some numerical experiments are carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]