An analytical solution for static stability of multi-scale hybrid nanocomposite plates

An analytical answer to the buckling problem of a composite plate consisted of multi-scale hybrid nanocomposites is presented here for the first time. In other words, the constituent material of the structure is made of an epoxy matrix which is reinforced by both macro- and nanosize reinforcements, namely, carbon fiber (CF) and carbon nanotube (CNT). The effective material properties such as Young’s modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin–Tsai model. To present a more realistic problem, the plate is placed on a two-parameter elastic substrate. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived using the classical theory of plates. Finally, the governing equations are solved analytically to obtain the critical buckling load of the system. Afterward, the normalized form of the results is presented to emphasize the impact of each parameter on the dimensionless buckling load of composite plates. It is worth mentioning that the effects of various boundary conditions are covered, too. To show the efficiency of presented modeling, the results of this article are compared to those of former attempts.

     

On the performances of a nonlinear hybrid piezoelectric and electromagnetic energy harvester

Microsystem Technologies - A nonlinear energy harvester combined piezoelectric (PE) and electromagnetic (EM) is studied for the low vibration frequency excitation, and its resonant frequency can be...     

Simulation of the head-disk interface gap using a hybrid multi-scale method

We present a hybrid multi-scale method that provides a capability to capture the disparate scales associated with modelling flow in micro- and nano-devices. Our model extends the applicability of an internal-flow multi-scale method by providing a framework to couple the internal (small scale) flow regions to the external (large scale) flow regions. We demonstrate the application of both the original methodology and the new hybrid approach to model the flow field in the vicinity of the head-disk interface gap of a hard disk drive enclosure. The internal flow regions within the gap are modelled by an extended internal-flow multi-scale method that utilises a finite-difference scheme for non-uniform grids. Our proposed hybrid multi-scale method is then employed to couple the internal micro-flow region to the flow external to the gap, to capture entrance/exit effects. We also demonstrate the successful application of the method in capturing other localised phenomena (e.g. those due to localised wall heating).     

Static stability analysis of agglomerated multi-scale hybrid nanocomposites via a refined theory

Present paper is proposed to capture the influences of carbon nanotubes’ agglomeration on the stability behaviors of multi-scale hybrid nanocomposite beams within the frameworks of refined higher order beam theories for the first time. In this research, a mixture of macroscale and nanoscale fillers will be utilized to be dispersed in an initial matrix to possess a multi-scale hybrid nanocomposite. The equivalent material properties are seemed to be calculated coupling the Eshelby–Mori–Tanaka model with the rule of the mixture to consider the effects of carbon nanotubes inside the probably generated clusters while finding the mechanical properties of such novel hybrid nanocomposites. Furthermore, an energy-based approach is implemented to obtain the governing equations of the problem utilizing a refined higher order beam theorem. Next, the derived equations will be solved in the framework of Galerkin’s well-known analytical method to reach the critical buckling load. It is worth mentioning that influence of various boundary conditions is included, too. Once the validity of presented results is proven, a set of numerical examples are presented to explain how each variant can affect the structure’s stability endurance.

     

On the complemented disk algebra

The importance of relational methods in temporal and spatial reasoning has been widely recognised in the last two decades. A quite large part of contemporary spatial reasoning is concerned with the research of relation algebras generated by the “part of” and “connection” relations in various domains. This paper is devoted to the study of one particular relation algebra appeared in the literature, viz. the complemented disk algebra. This algebra was first described by Düntsch [I. Düntsch, A tutorial on relation algebras and their application in spatial reasoning, Given at COSIT, August 1999, Available from: <http://www.cosc.brocku.ca/~duentsch/papers/relspat.html>] and then, Li et al. [Y. Li, S. Li, M. Ying, Relational reasoning in the Region Connection Calculus, Preprint, 2003, Available from: http://arxiv.org/abs/cs/0505041] showed that closed disks and their complements provides a representation. This set of regions is rather restrictive and, thus, of limited practical values. This paper will provide a general method for generating representations of this algebra in the framework of Region Connection Calculus. In particular, connected regions bounded by Jordan curves and their complements is also such a representation.     

Robust stability of a class of hybrid nonlinear systems

In this paper, we analyze the discrete behavior to identify all kinds of cycles of hybrid nonlinear systems and then study the continuous behavior along each kind of cycle. Based on these analysis, we construct some continuous functions to bound Lyapunov functions along all subsystems and identify a subsequence of time points where the Lyapunov functions are non-increasing. We use these results to derive some new sufficient conditions for the robust stability of a class of hybrid nonlinear systems with polytopic uncertainties. These conditions do not require the Lyapunov functions to be non-increasing along each subsystem nor the whole sequence of the switching. Furthermore, they do not require the knowledge of continuous trajectory     

On the estimation of the domain of attraction for discrete-time switched and hybrid nonlinear systems

This paper addresses the estimation of the domain of attraction for discrete-time nonlinear systems where the vector field is subject to changes. First, the paper considers the case of switched systems, where the vector field is allowed to arbitrarily switch among the elements of a finite family. Second, the paper considers the case of hybrid systems, where the state space is partitioned into several regions described by polynomial inequalities, and the vector field is defined on each region independently from the other ones. In both cases, the problem consists of computing the largest sublevel set of a Lyapunov function included in the domain of attraction. An approach is proposed for solving this problem based on convex programming, which provides a guaranteed inner estimate of the sought sublevel set. The conservatism of the provided estimate can be decreased by increasing the size of the optimisation problem. Some numerical examples illustrate the proposed approach.     

On hybrid impulsive and switching systems and application to nonlinear control

In this note, a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established. In addition, a new hybrid impulsive and switching control strategy for nonlinear systems is developed. A typical example, the unified chaotic system, is given to illustrate the theoretical results.     

Intriguing nonlinear dynamics of a controller with a sluggish actuator

We apply a bifurcation-theoretic approach to the standard Moore–Greitzer compressor model in effort to understand a curious phenomenon. When one forces the actuator to respond sluggishly to commanded inputs, performance of the controller improves dramatically. We show that the behavior can be explained via Hopf–Hopf interactions of surge and rotating stall. Also, we argue that there is a broad class of controllers which possess the general dynamic features responsible for the surprising effectiveness of sluggish actuators.     

On the smallest enclosing information disk

We present a generalization of Welzl's smallest enclosing disk algorithm [E. Welzl, Smallest enclosing disks (balls and ellipsoids), in: New Results and New Trends in Computer Science, in: Lecture Notes in Computer Science, vol. 555, Springer, 1991, pp. 359-370] for point sets lying in information-geometric spaces. Given a set of points equipped with a Bregman divergence as a (dis)similarity measure, we investigate the problem of finding its unique (circum)center defined as the point minimizing the maximum divergence to the point set. As an application, we show how to solve a statistical model estimation problem by computing the center of a finite set of univariate normal distributions.     

基于多尺寸特征融合的快速转码算法

为了降低H.264转码器的运算复杂度,满足视频转码实时应用的要求,提出一种结合多尺寸视频特征的快速视频转码帧内预测算法。首先利用二维直方图提取小尺寸视频中宏块的空间特性,结合双阈值的方法,选择Intra 16×16或Intra 4×4模式。然后从输入的视频码流中提取编码信息组成多维特征向量训练支持向量机(SVM)分类器模型,通过SVM建立大尺寸视频编码信息与小尺寸视频宏块编码模式之间的联系,进而对Intra 4×4中的9种模式进行细分。此算法减少了预测模式数量,实现率失真优化算法的提前终止,在高效转码的同时保证了转码后视频的高质量。     

Multi-model decomposition of nonlinear dynamics using a fuzzy-CART approach

In this work, we propose an extension of the CART (Classification and Regression Tree) based methodology proposed earlier [Ind. Eng. Chem. Res. 31(8) (1992) 1989; Comp. Chem. Eng. 16(4) (1992) 413], for modelling and identification of complex nonlinear systems. The suggested scheme employs the ‘divide and rule’ based strategy which decomposes the overall complex nonlinear dynamics into a set of linear or simple nonlinear models. The CART analysis picks up only the most representative model at any time. This model strategy involves discontinuous boundaries in the overall model structure. Therefore this structure is further refined here using a fuzzification procedure. The traditional backpropagation algorithm is used to incorporate the fuzzification. The fuzzification imposed over the CART skeleton replaces the crisp boundaries of the CART models by smooth boundaries thus enabling better prediction during transitions. This approach can deal with both steady state and dynamic data. The models built using the proposed fuzzy-CART methodology has been shown to give significant improvement in performance over that built using the CART alone. Validation results involving simulations of a nonlinear fermenter of Henson and Seborg [Chem. Eng. Sci. 47 (1992) 821] have demonstrated the practicality of the approach.     

On the controllability of a nonlinear control system

This paper considers the problem of controllability of a class of nonlinear systems. Sufficient conditions are given for a nonlinear system to be locally controllable and globally completely controllable. In the case of a linear time-invariant system, these conditions are also necessary. Furthermore, our result reveals that, for a nonlinear control system, there is a relationship among controllability, stability and optimality.     

Algorithmic analysis of nonlinear hybrid systems

We present two methods for translating nonlinear hybrid systems into linear hybrid automata. Properties of the nonlinear systems can then be inferred from the automatic analysis of the translated linear hybrid automata. The first method, called clock translation, replaces constraints on nonlinear variables by constraints on clock variables. The second method, called linear phase-portrait approximation, conservatively overapproximates the phase portrait of a hybrid automaton using piecewise-constant polyhedral differential inclusions. Both methods are sound for safety properties. We illustrate both methods by using HYTECH, a symbolic model checker for linear hybrid automata, to automatically check properties of a nonlinear temperature controller and of a predator-prey ecology     

On the observability codistributions of a nonlinear system

The purpose of this is to introduce the notion of observability codistribution for a nonlinear system, which extends the (dual of the) notion of “unobservability subspace”. Then, we study its properties, which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems.     

On the self-organization of a hybrid peer-to-peer system

Decentralized peer-to-peer (P2P) systems can be classified into unstructured and structured. The former is easy to implement, and often simply uses flooding for search, which can be effective only when target objects are popular or nearby. The latter requires peers to cooperate closely to maintain an overlay topology so as to ensure an efficient routing path between any two nodes. Recently, a hybrid use of both paradigms has gained its popularity in several popular file sharing tools to take advantage of each. What is lacking, and thus the purpose of the paper, is a fully decentralized algorithm to build such hybrid systems, as existing methods often require human intervention and some centralized gateway to select peers and guide them to build the structured overlay. The challenges include how to ensure that only one connected overlay is constructed in the lack of any global knowledge, and that only stable peers are selected for the structured overlay so as to reduce its maintenance cost. In addition, the construction must be efficient, scalable, robust, and easy to implement in a highly dynamic environment.     

一种混合优化算法及其收敛性证明

针对改进的混沌优化方法和Alopex算法的特性，将改进的Alopex算法嵌入到改进的混沌优化算法中，提出一种混合优化算法，此算法充分发挥了改进的Alopex算法的快速搜索能力和改进的混沌优化方法细致寻优的特性，提高了算法的收敛速度，避免了优化算法陷入局部最优；同时对改进的混沌优化算法和混合优化算法的收敛性进行了证明，仿真结果表明了算法的有效性。     

On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics

This paper deals with applications of sliding‐mode‐based fractional control techniques to address tracking and stabilization control tasks for some classes of nonlinear uncertain fractional‐order systems. Both single‐input and multi‐input systems are considered. A second‐order sliding‐mode approach is taken, in suitable combination with PI‐based design, in the single‐input case, while the unit‐vector approach is the main tool of reference in the multi‐input case. Sliding manifolds containing fractional derivatives of the state variables are used in the present work. Constructive tuning conditions for the control parameters are derived by Lyapunov analysis, and the convergence properties of the proposed schemes are supported by simulation results. Copyright © 2015 John Wiley & Sons, Ltd.     

Solving nonlinear optimal control problems using a hybrid IPSO-SQP algorithm

A hybrid algorithm by integrating an improved particle swarm optimization (IPSO) with successive quadratic programming (SQP), namely IPSO-SQP, is proposed for solving nonlinear optimal control problems. The particle swarm optimization (PSO) is showed to converge rapidly to a near optimum solution, but the search process will become very slow around global optimum. On the contrary, the ability of SQP is weak to escape local optimum but can achieve faster convergent speed around global optimum and the convergent accuracy can be higher. Hence, in the proposed method, at the beginning stage of search process, a PSO algorithm is employed to find a near optimum solution. In this case, an improved PSO (IPSO) algorithm is used to enhance global search ability and convergence speed of algorithm. When the change in fitness value is smaller than a predefined value, the searching process is switched to SQP to accelerate the search process and find an accurate solution. In this way, this hybrid algorithm may find an optimum solution more accurately. To validate the performance of the proposed IPSO-SQP approach, it is evaluated on two optimal control problems. Results show that the performance of the proposed algorithm is satisfactory.