Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks

This paper is concerned with pth moment exponential stability of stochastic Cohen–Grossberg neural networks (SCGNN) with time-varying connection matrix and delays. With the help of Lyapunov function, stochastic analysis technique and the generalized Halanay inequality, a set of novel sufficient conditions on pth moment exponential stability for SCGNN is given. These results are helpful to design exponentially stable non-autonomous Cohen–Grossberg neural networks when stochastic effects are taken into consideration in practice. This work was supported in part by the High-Tech Research and Development Program of China under Grant No. 2006AA04A104, the National Natural Science Foundation of China under Grant No. 50677014, China Postdoctoral Science Foundation under Grant No. 20070410300, the Hunan Provincial Natural Science Foundation of China under Grant No. 07JJ4001.     

基于自适应BP神经网络的结构损伤检测

描述基于人工神经网络的结构损伤检测的基本步骤以及该方法在实际5层钢框架结构损伤检测上的应用．提出了一种改进的BP神经网络方法，它能够解决传统BP神经网络在实际应用中存在的两个问题：收敛速度慢并存在局部极小．其基本思想是引入动态自适应算子加速传统BP算法的梯度下降速度，从而提高运算速度，通过自调节保证学习过程中每一时刻具有较大的sigmoid函数值，从而可以避免局部极小．数值仿真结果表明基于该自适应神经网络的结构损伤检测方法具有强的鲁棒性，而且与传统的BP神经网络相比，不仅提高了计算速度，并且具有很高的精度．最后，实例的应用也证明了该方法的有效性．     

Neurocomputing theory and numerical simulation on elasticity

A new finite element analysis principle based on neural networks is propsed. It can realize the finite element analysis in real time. The neural computation of a simple structure was simulated on digital computer, the effect of input parameters on convergent speed and precision was analyzed. Before solving a certain FE problem, the linking weight matrix of the neural net, i.e., the global stiffness matrix of the structure analyzed, must be defined. In this paper, a method which uses the BP net to compute the element stiffness matrix in real time is proposed. The subject is supported by the Natural Science Foundation of China     

A STUDY OF THE INFLUENCE OF INTERFACIAL DAMAGE ON STRESS CONCENTRATIONS IN INTRAPLY HYBRID COMPOSITES

In the axial tensile failure process of intraply hybrid composites, the breakage of some fibers may lead to interfacial damage, thus directly influencing the local stress concentrations near the sites of breakage. A modified shear-lag model, in which the interfacial damage is considered, is proposed. Based on the model, the influence of interfacial shear strength on the stress concentrations and the lengths of interfacial damage zone is first studied. The present results also provide an important theoretical basis for investigating the failure mechanism and hybrid effects for such kind of composites. Project supported by the National Natural Science Foundation of China (No. 199902004) and Guangdong Provincial Natural Science Foundation (No. 000391).     

基于神经网络技术的管道机电阻抗健康状况定量评估研究

将机电阻抗法用于管道法兰和主干结构健康监测,并利用BP神经网络对结构损伤进行定量评估.首先实验研究了管道法兰与主干结构健康状况对阻抗谱的影响,不同的结构损伤可通过阻抗分析仪测量的阻抗实部谱变化反映出来;然后利用BP神经网络技术对管道不同工况下得到的阻抗实部谱进行定量分析.采用阻抗值实部作为输入样本对神经网络进行训练,并使用受训的神经网络实现了对管道中不同结构损伤状况的定量评估.研究结果表明,将机电阻抗法与神经网络数据处理技术结合起来用于复杂管道的结构健康监测,不仅可实现对不同类型损伤的定量评估,同时还具有较高的稳定性.     

Computer simulation of creep damage at crack tip in short fibre composites

Creep damage at crack tip in short fibre composites has been simulated by using the finite element method (FEM). The well-known Schapery non-linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material. A modified recurrence equation was adopted to accelerate the iteration. Kachanov-Rabotnov's damage evolution law was employed. The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called “digit photo”, which was produced by the printer. The project supported by the National Natural Science Foundation of China and the LNM of Institute of Mechanics, CAS     

Combined neural network and reduced FRF techniques for slight damage detection using measured response data

Summary  This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors. Received 9 March 2000; accepted for publication 12 December 2000     

Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces

In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.     

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.     

Existence and Attractivity of Almost Periodic Solution for Recurrent Neural Networks with Unbounded Delays and Variable Coefficients

This paper presents several sufficient conditions for the existence and attractivity of almost periodic solution for a new class of recurrent neural networks with unbounded delays and variable coefficients. Different from the normal approach, that's to say, without resorting to any Lyapunov function, these results are obtained by utilizing generalized Halanay inequality technique and combining the theory of exponential dichotomy with fixed point method. Some existing results are found to be special case of this paper. In addition, the exponential stability of the almost periodic solution, which is not studied in the earlier references, is also considered for the system. An example is given to illustrate the feasibility of our results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60373067, the Hong Kong Special Administrative Region, China with Project No. 7001146, the Natural Science Foundation of Jiangsu Province, China under Grant BK2003053, Qing-Lan Engineering Project of Jiangsu Province, China.     

Investigation of the dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces by a new method

The dynamic behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces subjected to the harmonic waves is investigated by a new method. The cracks are parallel to the interfaces in the mid-plane of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved by using Schmidt’s method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of cracks, the frequency of the incident wave, the thickness of the piezoelectric layer and the constants of the materials upon the dynamic stress intensity factor of cracks.     

Mineral bridges of nacre and its effects

Nacre, or mother-of-pearl, is a kind of composites of aragonite platelets sandwiched between organic materials. Its excellent mechanical properties are thought to stem from the microarchitecture that is traditionally described as a “brick and mortar” arrangement. In this paper, a new microstructure, referred to as mineral bridge in the biomineralization, is directly observed in the organic matrix layers (mortar) of nacre. This is an indication that the organic matrix layer of nacre should be treated as a three-dimensional interface and the microarchitecture of nacre ought to be considered as a “brick-bridge-mortar” structure rather than the traditional one. Experiments and analyses show that the mineral bridges not only improve the mechanical properties of the organic matrix layers but also play an important role in the pattern of the crack extension in nacre. The project supported by the Natural Science Foundation of Chinese Academy of Sciences (KJ951-1-201) and the National Natural Science Foundation of China (19891180 and 10072067)     

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found. The project supported by the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Natural Science Foundation of China (joint RFBR-NSFC grant No. 96-01-00017c)     

Analyses on structural damage identification based on combined parameters

IntroductionServiceloads,environmentalandaccidentalactionsmaycausedamagetostructures .Whenthestructuraldamageissmalloritisintheinteriorofthestructure,itsdetectioncannotbedonevisually.Inspectionofexistingbuildingsandbridgesaftercatastrophicevents,suchasearthquakesandhurricanes,aswellasundernormaloperatingconditions ,isoftentimeconsumingandcostlybecausecriticalmembersandconnectionsareconcealedundercladdingandotherarchitecturaldecorations.Formanyimportantstructures,suchashospitals,firestations,mi…     

Evolution of a 2-D disturbance in a supersonic boundary layer and the generation of shocklets

Through direct numerical simulation, the evolution of a 2-D disturbance in a supersonic boundary layer has been investigated. At a chosen location, a small amplitude T-S wave was fed into the boundary layer to investigate its evolution. Characteristics of nonlinear evolution have been found. Two methods were applied for the detection of shocklets, and it was found that when the amplitude of the disturbance reached a certain value, shocklets would be generated, which should be taken into consideration when nonlinear theory of hydrodynamic stability for compressible flows is to be established.     

TheC k instability of navier-Stokes equation appending polynomials of unknown functions

Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined. It is proved that such kind of equation has no C^k (k≥2) stable solution by the fact that the strate transversale is a null set. Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034) Biography: HE You-hua (1960-)     

A FINITE DIFFERENCE METHOD FOR SIMULATING TRANSVERSE VIBRATIONS OF AN AXIALLY MOVING VISCOELASTIC STRING

A finite difference method is presented to simulate transverse vibrations of an axially moving string.By discretizing the governing equation and the equation of stress- strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two explicit difference schemes can be calculated alternatively, which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors,O(Δt~2 Δx~2).It also shows quite good stability for small initial values.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results.     

ANALYSES ON STRUCTURAL DAMAGE IDENTIFICATION BASED ON CIMBINED PARAMETERS

The relative sensitivities of structural dynamical parameters were analyzed using a directive derivation method. The neural network is able to approximate arbitrary nonlinear mapping relationship, so it is a powerful damage identification tool for unknown systems. A neural network-based approach was presented for the structural damage detection. The combined parameters were presented as the input vector of the neural network, which computed with the change rates of the several former natural frequencies (C), the change ratios of the frequencies (R), and the assurance criterions of flexibilities ( A ). Some numerical simulation examples, such as, cantilever and truss with different damage extends and different damage locations were analyzed. The results indicate that the combined parameters are more suitable for the input patterns of neural networks than the other parameters alone.     

A new analytical solution to axisymmetric Biot＇s consolidation of a finite soil layer

A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.     

Snap-buckling of dished shallow shells under uniform loads

I.Intr0ducti0nDishedshallowshellsareakindofthinshellswhichconsistofashallowconicalshellwithacircuiarplateatthecenterregi0n.Thesnap-bucklingphenomenonofdishedshallowshellsisusedasacontrolinformationofthepress-temperatureselfcontroIsysteminprecisioninstrume…