Design of auxetic sandwich panel faceplates comprising cellular networks with high stiffness and negative Poisson’s ratio

In the present work, a novel design is presented for producing auxetic laminated faceplates for structures that contain auxetic cores in order to produce fully auxetic sandwich structures. The design is based on the use of periodic cellular networks that are embedded in a fibre-reinforced polymer matrix. These networks have a high in-plane negative Poisson’s ratio and a high in-plane stiffness. Two auxetic networks were chosen for this purpose: a classical re-entrant hexagonal network and an anti-tetra chiral auxetic network. The finite elements method was used to model the auxetic network and the faceplate. For the auxetic network, the relative modulus (E_s/E_m) was investigated to determine its effect on the behaviour of the faceplate. The auxetic behaviour of the faceplate occurs when the auxetic network has a high relative modulus. For example, for a classical re-entrant hexagonal network faceplate, the auxetic behaviour starts to appear when E_s/E_m > 33, while for an anti-tetra chiral auxetic network faceplate, the auxetic behaviour starts to appear when E_s/E_m > 24. Analytical expressions for the elastic constants of the faceplates were developed using the representative volume element model (RVE) and a semi-empirical formula of the rule of mixtures (ROMs). The results of the analytical expressions were compared with the finite elements results for various values of the relative density parameter ρ^*. The relative density had a significant effect on the elastic constants of the faceplate. The model produced with the representative volume element method had higher values for the elastic constants than did that created with the finite elements model, but the semi-empirical rule of mixtures gave more accurate results for both types of faceplates. A modified design for the classical re-entrant hexagonal network that increases the in-plane stiffness of the auxetic network is presented since it has been found that it plays a major role in producing a high negative Poisson’s ratio. The modified networks are an oval re-entered and a stiffened re-entered network. Experiments were carried out on the oval re-entered faceplates to obtain the in-plane moduli and the Poisson’s ratios. The tested faceplate samples clearly showed auxetic behaviour. A good agreement between the finite elements results and the experimental data was obtained.     

面向结构健康监测的神经网络性能分析与设计

面向结构健康监测,对神经网络的工作性能从概率角度给予细致分析,区分了网络工作的两类典型错误。发现了影响网络工作性能的3个参数,并且指出随着时间的推移,3个参数对网络工作性能有着不同的影响。基于上述分析提出了面向长期结构健康监测的神经网络"错误抑制策略",可以根据结构健康监测的要求来灵活抑制两类错误。最后将该策略应用于BP网络设计,重新定义了网络误差能量函数,给出了错误抑制系数的建议公式,推导了网络学习的权值修正公式。     

An analysis of the equilibria of neural networks with linear interconnections

In this paper, we analyse the equilibria of neural networks which consist of a set of sigmoid nonlinearities with linear interconnections,without assuming that the interconnections are symmetric or that there are no self-interactions. By eliminating these assumptions, we are able to study the effects of imperfect implementation on the behaviour of Hopfield networks. If one views the neural network as evolving on the openn-dimensional hypercubeH = (0, 1) ⁿ , we have the following conclusions as the neural characteristics become steeper and steeper: (i) There is at most one equilibrium in any compact subset ofH, and under mild assumptions this equilibrium is unstable. In fact, the dimension of the stable manifold of this equilibrium is the same as the number of eigenvalues of the interconnection matrix with negative real parts. (ii) There might be some equilibria in the faces ofH, and under mild conditions these are always unstable. Moreover, it is easy to compute the dimension of the stable manifold of each such equilibrium. (iii) A systematic procedure is given for determining which corners of the hypercubeH contain equilibria, and it is shown that all equilibria in the corners ofH are asymptotically stable.     

Stability properties of the Hopfield-type neural networks

In this paper, stability properties such as eventual practical stability and uniform practical stability of Hopfield-type neural networks are discussed employing vector Lyapunov functions (Hopfield and Tank, 1986; Lakshmikantham, Leela and Martynyuk, 1990; Lakshmikantham, Matrosov and Sivasundaram. 1991). Also, invariance principle together with vector Lyapunov functions is used to study the global asymptotic stability of the same network     

A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problems

Adopting an updated Lagrange approach, the general framework for the fully non-linear analysis of curved shells is developed using a simple quadrilateral C⁰ model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate-type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so-called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton–Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.     

On reaction network implementations of neural networks

This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differential equations (ODEs) associated with certain reaction network implementations of neural networks have desirable properties including (i) existence of unique positive fixed points that are smooth in the parameters of the model (necessary for gradient descent) and (ii) fast convergence to the fixed point regardless of initial condition (necessary for efficient implementation). We do so by first making a connection between neural networks and fixed points for systems of ODEs, and then by constructing reaction networks with the correct associated set of ODEs. We demonstrate the theory by constructing a reaction network that implements a neural network with a smoothed ReLU activation function, though we also demonstrate how to generalize the construction to allow for other activation functions (each with the desirable properties listed previously). As there are multiple types of ‘networks’ used in this paper, we also give a careful introduction to both reaction networks and neural networks, in order to disambiguate the overlapping vocabulary in the two settings and to clearly highlight the role of each network’s properties.     

基于神经网络的电机转矩软测量研究

径向基函数神经网络（RBFNN）具有最优逼近和全局逼近的特性，在函数拟合方面优于传统的BP网络，将在化工领域广泛使用的软测量技术应用于电机系统的转矩测量，该方法的可行性进行了论证，并运用RBF神经网络建立转矩的软测量模型。同时建立了基于BP神经网络的软测量模型，用改进的kvenberg—Marquardt算法对BP神经网络进行学习和训练，并对两种网络进行了对比。该方法只需要电流信息，辨识方法简单。研究表明，RBF神经网络辨识效果优于BP神经网络。     

Linear elasticity of planar Delaunay networks. III: Self-consistent approximations

Summary Two-phase Delaunay and regular triangular networks, with randomness per vertex, provide generic models of granular media consisting of two types of grains — soft and stiff. We investigate effective macroscopic moduli of such networks for the whole range of area fractions of both phases and for a very wide range of stiffnesses of both phases. Results of computer simulations of such networks under periodic boundary conditions are used to determine which of several different self-consistent models can provide the best possible approximation to effective Hooke's law. The main objective is to find the effective moduli of a Delaunay network as if it was a field of inclusions, rather than vertices connected by elastic edges, without conducting the computer-intensive calculations of large windows. First, we report on the dependence of effective Poisson's ratio onp for a single-phase Delaunay network with all the spring constantsk assigned according tok=l ^p. In case of two-phase media, it is found that the Delaunay network is best approximated by a system of ellipses perfectly bonded to a matrix in a symmetric self-consistent formulation, while the regular network is best approximated by a circular inclusion-matrix model. These two models continue to be adequate up to the point of percolation of holes, but the reverse situation of percolation of rigid inclusions is better approximated by the ellipses model in an asymmetric formulation. Additionally, we give results of calculation of Voigt and Reuss bounds of two-dimensional matrix-inclusion composites with springy interfaces.     

Cellular logic array processing techniques for high-throughput image processing systems

This paper describes certain image processing techniques within the framework ofcellular automata andnormal algorithms for high-throughput data processing. The central idea on which these techniques have been developed is that a digital image can be treated as acellular automaton configuration, and an image processing operation, as anevolution of the automaton due to an updating rule that describes a relational attribute among the pixel values in a specific neighbourhood. Filtering operations on digital images, like that of thinning, edge detection segmentation, erosion and dilation are modelled and realized using cellular automata.     

Rule Extraction from Trained Artifical Neural Networks

The neural network rule extraction problem is aimed at obtaining rules from an arbitrarily trained artificial neural network. Recently there have been several approaches to rule extraction. Approaches to rule extraction implement a priori knowledge of data or rule requirements into neural networks before the rules are extracted. Although this may lead to a simplified final phase of acquitting the rules from particular type of neural networks, it limits the methodologies for general-purpose use. This article approaches the neural network rule extraction problem in its essential and general form. Preference is given to multilayer perceptron networks (MLP networks) due to their universal approximation capabilities. The article establishes general theoretical grounds for rule extraction from trained artificial neural networks and further focuses on the problem of crisp rule extraction. The problem of crisp rule extraction from trained MLP networks is first approached on theoretical level. Present ed theoretical results state conditions guaranteeing equivalence between classification by an MLP network and crisp logical formalism. Based on the theoretical results an algorithm for crisp rule extraction, independent of training strategy, is proposed. The rule extraction algorithm can be used even in cases where the theoretical conditions are not strictly satisfied; by offering an approximate classification. An introduced rule extraction algorithm is experimentally demonstrated.

     

关于随机时滞神经网络稳定性的注记(英文)

利用非负鞅收敛定理、Lyapunov泛函方法和网络自身的特性讨论了变时滞随机递归神经网络的随机指数稳定性,给出了这类神经网络随机指数稳定性的新的代数准则,所给代数准则简单易用。两个应用实例说明即使针对随机Hopfield神经网络所给的代数准则也优于相关的判别准则。     

径向网络裹包机凸轮定位差动器交流控制的非线性观察器

根据裹包机的交流控制系统控制精度较差的问题,提出采用直接转矩控制方法,但速度控制受到系统固有不确定的影响,采用RBFN不确定观察器的鲁棒机定速度控制器,建立控制输入更新权值和约束常数的自适应规律,仿真和实验结果表明该算法是可行的和有意义的.     

移动GIS网络分析的研究

近几年来,随着智能手机在生活中的普及,移动地理信息系统(GIS)应用得到快速发展,且仍有广泛需求.为适应网络分析的多样性,提出一种基于启发式A*思想的通用路径规划算法,支持目标规则、权值更新规则、结果规则的定制,能方便地实现多数移动GIS网络分析的情况.     

Some potential antenna applications of high-temperature superconductors

A review of possible applications of high-temperature superconductors (HTS) to antennas and antenna feed networks is presented. The frequency range of consideration is 1 MHz to 100 GHz. Three antenna application areas seem appropriate for HTS material. (1)Electrically small antennas and their matching networks: An increase in efficiency is possible for electrically short antennas, but at the expense of bandwidth. Substantial radiated power levels (on the order of kilowatts) can be handled by the best HTS material. Substantial improvement may be realized by making only the matching network of HTS material. (2)Feed and matching networks for compact arrays with enhanced directive gain (superdirective arrays): HTS material should permit such arrays to be fabricated that have high efficiency. (3)Feed networks for millimeter-wave arrays: Low-loss feed networks using HTS microstrip transmission lines give many decibels improvement in gain.     

Reliability and fault-tolerance in multistage interconnection networks

Reliability and fault-tolerance issues are important in the study of interconnection networks used in large multiprocessor systems because of the large number of components involved. In this paper we study these issues with respect to multistage networks which are typically built forN inputs andN outputs using 2 × 2 switching elements and log₂ N stages. In such networks, the failure of a switching element or connecting link destroys the communication capability between one or more pair(s) of source and destination terminals. Many techniques exist for designing multistage networks that tolerate switch and/or link failures without losing connectivity. Several approaches for achieving fault-tolerance in multistage interconnection networks are described in this paper. The techniques vary from providing redundant components in the network to making multiple passes through the faulty network. Quantitative measures are introduced for analysis of the reliability of these networks in terms of the component reliabilities. Several examples are given to illustrate the techniques. This research is supported by thensf Presidential Young Investigator Award No.dci-8452003, a grant from AT&T Information Systems, and a grant fromtrw.     

On the connection between Palmgren‐Miner rule and crack propagation laws

The classical Palmgren‐Miner (PM) rule, despite clearly approximation, is commonly applied for the case of variable amplitude loading, and to date, there is no simple alternative. In the literature, previous authors have commented that the PM hypothesis is based on an exponential fatigue crack growth law, ie, when da/dN is proportional to the crack size a, the case that includes also Paris law for m=2, in particular. This is because they applied it by updating the damage estimate during the crack growth. It is here shown that applying PM to the “initial” and nominal (Stress vs Number of cycles) curve of a cracked structure results exactly in the integration of the simple Paris power law equation and more in general to any crack law in the form da/dN=HΔσ^haⁿ. This leads to an interesting new interpretation of PM rule. Indeed, the fact that PM rule is often considered to be quite inaccurate pertains more to the general case when propagation cannot be simplified to this form (like when there are distinct initiation and propagation phases), rather than in long crack propagation. Indeed, results from well‐known round‐robin experiments under spectrum loading confirm that even using modified Paris laws for crack propagation, the results of the “noninteraction” models, neglecting retardation and other crack closure or plasticity effects due to overloads, are quite satisfactory, and these correspond indeed very closely to applying PM, at least when geometrical factors can be neglected. The use of generalized exponential crack growth, even in the context of spectrum loading, seems to imply the PM rule applies. Therefore, this seems closely related to the so‐called lead crack fatigue lifing framework. The connection means however that the same sort of accuracy is expected from PM rule and from assuming exponential crack growth for the entire lifetime.     

Adjoint-based optimal variable stiffness mesh deformation strategy based on bi-elliptic equations

There are many recent advances in mesh deformation methods for computational fluid dynamics simulation in deforming geometries. We present a method of constructing dynamic mesh around deforming objects by solving the bi-elliptic equation, an extension of the biharmonic equation. We show that introducing a stiffness coefficient field a(x) in the bi-elliptic equation can enable mesh deformation for very large boundary movements. An indicator of the mesh quality is constructed as an objective function of a numerical optimization procedure to find the best stiffness coefficient field a(x). The optimization is efficiently solved using steepest descent along adjoint-based, integrated Sobolev gradients. A multiscenario optimization procedure is performed to calculate the optimal stiffness coefficient field a^蜧(x) for a priori unpredictable boundary movements. Copyright © 2011 John Wiley & Sons, Ltd.     

A network-wide exact optimization approach for multiobjective routing with path protection in multiservice multiprotocol label switching networks

A multiobjective routing model for multiprotocol label switching networks with multiple service types and path protection is presented in this article. The routing problem is formulated as a biobjective integer program, where the considered objectives are formulated according to a network-wide optimization approach, i.e. the objective functions of the route optimization problem depend explicitly on all traffic flows in the network. A disjoint path pair is considered for each traffic trunk, which guarantees protection to the associated connection. A link-path formulation is proposed for the problem, in which a set of possible pairs of paths is devised in advance for each traffic trunk. An exact method (based on the classical constraint method for solving multiobjective problems) is developed for solving the formulated problem. An extensive experimental study, with results on network performance measures in various randomly generated networks, is also presented and discussed.     

Quantized hopfield networks for reliability optimization

The use of neural networks in the reliability optimization field is rare. This paper presents an application of a recent kind of neural networks in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. Our design of neural network to solve efficiently this problem is based on a quantized Hopfield network. This network allows us to obtain optimal design solutions very frequently and much more quickly than others Hopfield networks.