Lattice Element Models and Their Peculiarities

This paper presents the lattice element models, as a class of discrete models, in which the structural solid is represented as an assembly of one-dimensional elements. This idea allows one to provide robust models for propagation of discontinuities, multiple cracks interaction or cracks coalescence. Many procedures for computation of lattice element parameters for representing linear elastic continuum have been developed, with the most often used ones discussed herein. Special attention is dedicated to presenting the ability of this kind of models to consider material disorder, heterogeneities and multi-phase materials, which makes lattice models attractive for meso- or micro-scale simulations of failure phenomena in quasi-brittle materials, such as concrete or rocks. Common difficulties encountered in material failure and a way of dealing with them in the lattice models framework are explained in detail. Namely, the size of the localized fracture process zone around the propagating crack plays a key role in failure mechanism, which is observed in various models of linear elastic fracture mechanics, multi-scale theories, homogenization techniques, finite element models, molecular dynamics. An efficient way of dealing with this kind of phenomena is by introducing the embedded strong discontinuity into lattice elements, resulting with mesh-independent computations of failure response. Moreover, mechanical lattice can be coupled with mass transfer problems, such as moisture, heat or chloride ions transfer which affect the material durability. Any close interaction with a fluid can lead to additional time dependent degradation. For illustration, the lattice approach to porous media coupling is given here as well. Thus, the lattice element models can serve for efficient simulations of material failure mechanisms, even when considering multi-physics coupling. The main peculiarities of such an approach have been presented and discussed in this work.     

Morphological perceptrons with competitive learning: Lattice-theoretical framework and constructive learning algorithm

A morphological neural network is generally defined as a type of artificial neural network that performs an elementary operation of mathematical morphology at every node, possibly followed by the application of an activation function. The underlying framework of mathematical morphology can be found in lattice theory.With the advent of granular computing, lattice-based neurocomputing models such as morphological neural networks and fuzzy lattice neurocomputing models are becoming increasingly important since many information granules such as fuzzy sets and their extensions, intervals, and rough sets are lattice ordered. In this paper, we present the lattice-theoretical background and the learning algorithms for morphological perceptrons with competitive learning which arise by incorporating a winner-take-all output layer into the original morphological perceptron model. Several well-known classification problems that are available on the internet are used to compare our new model with a range of classifiers such as conventional multi-layer perceptrons, fuzzy lattice neurocomputing models, k-nearest neighbors, and decision trees.     

Analysis of spatial beamlike lattices with rigid joints

Micropolar beam models are developed for the static, free vibration and buckling analysis of repetitive spatial beamlike lattices with rigid joints. The micropolar beam models have independent microrotation and displacement fields and are characterized by their strain energy, potential energy due to initial stresses and kinetic energy from which the governing differential equations and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section, and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples for vierendeel and double-laced lattice girders with triangular cross-sections.     

Crack band model of fracture in irregular lattices

An irregular lattice model is used to simulate mode I fracture in softening materials, such as concrete. Lattice geometry is based on a three-dimensional Voronoi discretization of the material domain. The Voronoi diagram provides scaling rules for the elemental stiffness relations, leading to an elastically uniform representation of the material for simple modes of straining. Fracture is represented using a crack band approach, in which the dimensions of the crack band are also scaled according to the Voronoi diagram. The material is viewed as homogeneous and the energy dissipation mechanisms active at finer scales are lumped into a cohesive crack relation. This energy conserving crack band approach is objective with respect to the irregular geometry of the lattice. Model accuracy and performance are demonstrated through simulated fracture testing of concrete specimens under uniaxial tension and flexural loadings. Basic qualities of the simulation approach, demonstrated here for homogeneous models of concrete, are applicable toward simulating fracture in multi-phase systems where material features are explicitly modeled.     

Micropolar beam models for lattice grids with rigid joints

A simple, rational approach is presented for developing micropolar beam models for large repetitive beam-like planar lattices with rigid joints. The micropolar beam models have independent microrotation, and displacement fields and are characterized by their strain and kinetic energies, from which the equations of motion and boundary conditions can be derived. The procedure for developing the expression for the strain energy of the micropolar beam involves introducing basic assumptions regarding the variation of the displacement and microrotation components in the plane of the cross-section and obtaining effective elastic coefficients of the continuum in terms of the material properties and geometry of the original lattice structure. The high accuracy of the solutions obtained by the micropolar beam models is demonstrated by means of numerical examples.     

Reality of virtual damage identification based on neural networks and vibration analysis of a damaged bridge under a moving vehicle

Presented here is a reality of virtual damage detection and vibration behaviour study of a discrete beam-like bridge with one or several non-propagating edge cracks subjected to a moving vehicle. In this model, the simply supported beam elements are replaced by a range of rigid bars, which are connected by transverse and rotational springs, while the mass and rotational moment of inertia may be lumped at various points along the beam. The adopted vehicle model here is a four degrees-of-freedom, two axes half-vehicle model with tires flexibility and linear suspensions. Damage can be modelled by altering the spring stiffness equation at the crack position according to predictions, which allows the inclusion of simple or complex damage. To simplify, damage is represented here by an open crack, and stiffness of a given element with damage is calculated by fracture mechanics. Both the discrete element and finite element methods are used to investigate vibration analysis of a discrete beam model subjected to a moving vehicle to confirm model feasibility in vibration analysis under a moving vehicle. Besides, some dynamic response laws are obtained. Considering an irregular road profile, the effects of the moving vehicle velocity, the moving vehicle mass, the crack location and the crack depth on dynamic response of a beam-like bridge are analysed by a numerical example, combining a vehicle–bridge coupled vibration MATLAB program with ANSYS. In addition, the neural network is used to identify the damage of the structure. Numerical results of the numerical model predictions, compared with those obtained from the continuous elements beam, support the accuracy of the discrete elements beam model in both cases of undamaged beam and damaged one. The evidence for condition assessment and damage identification of bridge is obtained from this simulation as obtaining the vibrational characteristics of the damaged beam structure subjected to a moving vehicle. And the inversion results show that the neural network method can identify the injury location and injury size of the structure accurately.

     

Damage detection in Timoshenko beam structures by multilayer perceptron and radial basis function networks

This study investigates the efficiency of artificial neural networks (ANNs) in health monitoring of pristine and damaged beam-like structures. Beam modeling is based on Timoshenko theory. Two commonly used network models, multilayer perceptron (MLP) and radial basis neural network (RBNN), are used. Beam material and geometrical properties, beam end conditions and dynamically obtained data are used as input to the neural networks. The combinations of these parameters yield umpteenth input data. Therefore, to examine the effectiveness of ANNs, the frequency of intact beams is first tried to be determined by the network models, given the material and geometrical characteristics of beam elements and support conditions. The methodology to compute the vibrational data utilized in training the networks is provided. Showing the robustness of network models, the second stage of the study is carried out. At this stage, the crack parameters (e.g. the location and severity of crack) are estimated by the ANNs using the beam properties, beam end conditions and vibrational data, which consist of natural frequencies and mode shape rotation values. Despite the multiplexed input data, no data reduction schemes or multistage computations are executed in training and validation of neural network models. As a result of analysis runs, the optimal MLP and RBNN models are determined. Comparison of these models shows that the optimal RBNN algorithm performs better. The effectiveness of optimal ANN models in the presence of noise is also presented. As a conclusion, the trained network can be used as a diagnosis method in structural health monitoring of beam-like structures.     

Augmenting the Discrimination Power of HMM by NN for On-Line Cursive Script Recognition

For on-line handwriting recognition, a hybrid approach that combines the discrimination power of neural networks with the temporal structure of hidden Markov models is presented. Initially, all plausible letter components of an input pattern are detected by using a letter spotting technique based on hidden Markov models. A word hypothesis lattice is generated as a result of the letter spotting. All letter hypotheses in the lattice are evaluated by a neural network character recognizer in order to reinforce letter discrimination power. Then, as a new technique, an island-driven lattice search algorithm is performed to find the optimal path on the word hypothesis lattice which corresponds to the most probable word among the dictionary words. The results of this experiment suggest that the proposed framework works effectively in recognizing English cursive words. In a word recognition test, on average 88.5% word accuracy was obtained.     

Synchronization of ball and beam systems with neural compensation

Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory analysis is based on linear models, 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results.     

3D crystal structure identification using fuzzy neural networks

The problem of recognizing nano-scale images of lattice projections comes down to identification of crystal lattice structure. The paper considers two types of fuzzy neural networks that can be used for tackling the problem at hand: the Takagi-Sugeno-Kang model and Mamdani-Zadeh model (the latter being a modification of the Wang-Mendel fuzzy neural network). We offer a threestage neural network learning process. In the first two stages crystal lattices are grouped in non-overlapping classes, and lattices belonging to overlapping classes are recognized at the third stage. In the research, we thoroughly investigate the applicability of the neural net models to structure identification of 3D crystal lattices.     

External fixator configurations in tibia fractures: 1D optimization and 3D analysis comparison

The use of external fixation devices in orthopedic surgery is very common in open tibial fractures. A properly applied fixator may improve the healing process while one improperly applied might delay the healing process. The several external fixator systems used in clinical today, can be categorized into uniplanar–unilateral, uniplanar–bilateral, biplanar and multiplanar. The stability on the fracture focus and, therefore, the fracture healing process, is related with the type of external fixator configuration that is selected. The aim of this study is to discuss the principles for the successful application of unilateral–uniplanar external fixation, the assembly of its components, for the case of a transverse fractures using computational models. In this context, the fixation stiffness characteristics are evaluated using a simplified 1D finite element model for the tibia and external fixator. The beams are modeled with realistic cross-sectional geometry and material properties instead of a simplified model. The VABS (the Variational Asymptotic Beam Section analysis) methodology is used to compute the cross-sectional model for the generalized Timoshenko model, which was embedded in the finite element solver FEAP. The use of Timoshenko beam theory allows accounting for several kinds of loads, including torsion moments. Optimal design is performed with respect to the assembly of fixator components using a genetic algorithm. The optimization procedure is based on the evaluation of an objective function, which is dependent on the displacement at the fracture focus. The initial and optimal results are compared by performing a 3D analysis, for which different three-dimensional finite element models are created. The geometrical model of a tibia is created on the basis of data acquired by CAT scan, made for a healthy tibia of a 22 year old male. The 3D comparison of the 1D optimal results show a clear improvement on the objective function for the several load cases and, therefore, it is shown that appropriate selection of the external fixator geometrical features can lead to an improvement on the stability of the external fixator. The results obtained show that the optimal position of the side beam and the first pin should be as close as possible to the bone interface and as close as possible to the fracture focus, respectively. Concerning the second pin, it should be placed away from the first pin in case of flexion loads, to axial and torsion loads the second pin should be placed near the first pin.     

Confinement-shear lattice CSL model for fracture propagation in concrete

A previously developed lattice model is improved and then applied to simulations of mixed-mode crack propagation in concrete. The concrete meso-structure is simulated by a three-dimensional lattice system connecting nodes which represent the centers of aggregate particles. These nodes are generated randomly according to the given grain size distribution. Only coarse aggregates are taken into account. Three-dimensional Delaunay triangulation is used to determine the lattice connections. The effective cross-section areas of connecting struts are defined by performing a three-dimensional domain tessellation partly similar to Voronoi tessellation. The deformations of each link connecting two adjacent aggregate pieces are defined in the classical manner of Zubelewicz and Ba?ant in which rigid body kinematics is assumed to characterize the displacement and rotation vectors at the lattice nodes. Each strut connecting adjacent particles can transmit both axial and shear forces. The adopted constitutive law simulates fracture, friction and cohesion at the meso-level. The behavior in tension and shear is made dependent on the transversal confining strain, which is computed assuming a linear displacement field within each tetrahedron of Delaunay triangulation, and neglecting the effect of the particle rotations. A mid-point explicit scheme is used to integrate the governing equations of the problems. General procedures to handle the boundary conditions and to couple the lattice mesh to the usual elastic finite element mesh are also formulated. Numerical simulations of mixed-mode fracture test data are used to demonstrate that the model is capable of accurately predicting complex crack paths and the corresponding load-deflection responses observed in experiments.     

基于RF-Net的CT图像肋骨骨折识别

肋骨骨折是临床医学中一种常见的疾病,人工判别骨折的方法具有工作量大、识别难度大等问题.为了高效实现肋骨骨折的计算机辅助诊断,本文提出了一种基于RF-Net(rib fracture network)的肋骨骨折识别算法.该算法首先利用生成对抗网络对原始数据进行数据增强扩建数据集,以缓解过拟合现象且使模型进行有效训练.其次...     

内部结构自支撑的三维打印浮体平衡优化算法

为了使浮体能够在熔融挤压式三维打印机中一次成型,提出一种内部结构自支撑的浮体平衡优化算法.首先在给定漂浮姿势的输入模型内部,利用递归细分方法生成自支撑的格子结构,并把输入模型与格子结构组合为初始浮体模型.然后以初始浮体模型中格子单元体积为变量构建平衡优化方程,根据方程解算结果调整初始浮体模型中每个格子单元的体积,从而生成最终的浮体模型.实验结果表明,文中算法生成的浮体模型可以使用熔融挤压式三维打印机直接打印,打印的实体不但能够按照预设的姿势漂浮在液体中,而且具有较好的抗压能力;算法中的递归细分策略能够在模型内部产生较多的格子单元,具有节省打印材料的优势.     

Structural reinforcement in a spring-block model of stress-induced fracture propagation

We present a mechanism-based model of fracture propagation in a two-dimensional elastic sheet subjected to biaxial stretching. The time evolution of lattice stretching is formulated using a set of coupled nonlinear differential equations describing the network dynamics of masses connected by springs. We show that reinforcement based on a Gaussian spatial distribution of failure thresholds is effective in hindering tear propagation, that is, it delays the onset of breakage and reduces the total fractured sites at equilibrium time. The method presented here is general—it can incorporate any type of load distribution and test any reinforcement procedures.     

Integrated conditional global optimisation for discrete fracture network modelling

This paper presents a methodology to simulate discrete fracture networks for naturally fractured reservoirs by combining statistical and spatial analyses, object-based modelling and conditional global optimisation. The methodology examines and utilises both continuum and discrete fracture information, such as spatial distribution of fracture density, statistical and geostatistical distributions of fracture size and orientation. The output is a network of discrete fractures, with their corresponding details of location, size and orientation. The methodology is illustrated by a case study on the surface fault system in New York region. The results show that it is able to produce discrete fracture network that match closely to the target fault map, even in the case where data are limited. The results show that it is also able to improve results of several recent fracture models, such as integrated stochastic simulations as well as grid-based simulations.     

Fuzzy lattice neural network (FLNN): a hybrid model for learning

This paper proposes two hierarchical schemes for learning, one for clustering and the other for classification problems. Both schemes can be implemented on a fuzzy lattice neural network (FLNN) architecture, to be introduced herein. The corresponding two learning models draw on adaptive resonance theory (ART) and min-max neurocomputing principles but their application domain is a mathematical lattice. Therefore they can handle more general types of data in addition to N-dimensional vectors. The FLNN neural model stems from a cross-fertilization of lattice theory and fuzzy set theory. Hence a novel theoretical foundation is introduced in this paper, that is the framework of fuzzy lattices or FL-framework, based on the concepts fuzzy lattice and inclusion measure. Sufficient conditions for the existence of an inclusion measure in a mathematical lattice are shown. The performance of the two FLNN schemes, that is for clustering and for classification, compares quite well with other methods and it is demonstrated by examples on various data sets including several benchmark data sets.     

高冲击环境下MEMS大量程加速度传感器结构的失效分析

对设计的大量程加速度传感器进行冲击测试,分析该种传感器结构在高冲击环境下的输出信号及可靠性。加速度传感器结构采用四端全固支结构,通过在梁的端部和根部设计倒角结构以分散应力。测试结果表明该传感器在232,119.4 gn下可以测试到有效输出信号。同时,对测试中失效传感器进行了分析,总结出大量程加速度传感器的在高冲击环境下的失效模式主要为键合引线的脱落、微梁的断裂和封装失效。     

Hybrid-modelling of compact tension energy in high strength pipeline steel using a Gaussian Mixture Model based error compensation

In material science studies, it is often desired to know in advance the fracture toughness of a material, which is related to the released energy during its compact tension (CT) test to prevent catastrophic failure. In this paper, two frameworks are proposed for automatic model elicitation from experimental data to predict the fracture energy released during the CT test of X100 pipeline steel. The two models including an adaptive rule-based fuzzy modelling approach and a double-loop based neural network model, relate the load, crack mouth opening displacement (CMOD) and crack length to the released energies during this test. The relationship between how fracture is propagated and the fracture energy is further investigated in greater detail. To improve the performances of the models, a Gaussian Mixture Model (GMM)-based error compensation strategy which enables one monitor the error distributions of the predicted result is integrated in the model validation stage. This can help isolate the error distribution pattern and to establish the correlations with the predictions from the deterministic models. This is the first time a data-driven approach has been used in this fashion on an application that has conventionally been handled using finite element methods or physical models.     

Static Frequency Assignment in Cellular Networks

A cellular network is generally modeled as a subgraph of the triangular lattice. In the static frequency assignment problem, each vertex of the graph is a base station in the network, and has associated with it an integer weight that represents the number of calls that must be served at the vertex by assigning distinct frequencies per call. The edges of the graph model interference constraints for frequencies assigned to neighboring stations. The static frequency assignment problem can be abstracted as a graph multicoloring problem. We describe an efficient algorithm to multicolor optimally any weighted even or odd length cycle representing a cellular network. This result is further extended to any outerplanar graph. For the problem of multicoloring an arbitrary connected subgraph of the triangular lattice, we demonstrate an approximation algorithm which guarantees that no more than 4/3 times the minimum number of required colors are used. Further, we show that this algorithm can be implemented in a distributed manner, where each station needs to have knowledge only of the weights at a small neighborhood. Received May 13, 1997; revised August 24, 1998.