Nonlinear black-box modeling in system identification: a unified overview

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of ‘used’ parameters considerably less than the number of ‘offered’ parameters, by regularization, shrinking, pruning or regressor selection.     

桩土物理模型及结构—桩—土相互作用

本文将工程中常用的密集打桩土体模拟为正交各向异性弹性体。建立了刚性基础-桩-土这一空间相互作用系统的模型。根据圆柱体柱坐标的极点条件。分别选取了两组位移函数来表征桩基和土的位移,并用子区间法分析了结构-桩-土系统的相互作用地震反应。     

A real-time planning algorithm for obstacle avoidance of redundant robots

A computationally efficient, obstacle avoidance algorithm for redundant robots is presented in this paper. This algorithm incorporates the neural networks and pseudodistance function D _p in the framework of resolved motion rate control. Thus, it is well suited for real-time implementation. Robot arm kinematic control is carried out by the Hopfield network. The connection weights of the network can be determined from the current value of Jacobian matrix at each sampling time, and joint velocity commands can be generated from the outputs of the network. The obstacle avoidance task is achieved by formulating the performance criterion as D _p>d _min (d _min represents the minimal distance between the redundant robot and obstacles). Its calculation is only related to some vertices which are used to model the robot and obstacles, and the computational times are nearly linear in the total number of vertices. Several simulation cases for a four-link planar manipulator are given to prove that the proposed collision-free trajectory planning scheme is efficient and practical.     

基于自组织神经网络的实时统计特征抽取方法

应用人工神经网络讨论统计了特征抽取的原理，提出了相应的抽取方法。该方法具有实时性，容错性，高数据压缩率和良好的特征分辨率。通过计算机仿真和桥梁索力状态的实例计算分析证实了该技术具有广泛的应用价值。     

A design and analysis of objective function-based unsupervised neural networks for fuzzy clustering

Fuzzy clustering has played an important role in solving many problems. In this paper, we design an unsupervised neural network model based on a fuzzy objective function, called OFUNN. The learning rule for the OFUNN model is a result of the formal derivation by the gradient descent method of a fuzzy objective function. The performance of the cluster analysis algorithm is often evaluated by counting the number of crisp clustering errors. However, the number of clustering errors alone is not a reliable and consistent measure for the performance of clustering, especially in the case of input data with fuzzy boundaries. We introduce two measures to evaluate the performance of the fuzzy clustering algorithm. The clustering results on three data sets, Iris data and two artificial data sets, are analyzed using the proposed measures. They show that OFUNN is very competitive in terms of speed and accuracy compared to the fuzzy c-means algorithm.     

Prediction of the elastic behaviour of hybrid and non-hybrid woven composites

A micromechanical model called MESOTEX is presented for prediction of the elastic behaviour of composites reinforced with non-hybrid weave (plain weave, satin weave and twill weave) and hybrid weave (hybrid plain weave and hybrid twill weave) fabrics. By using the classical thin laminate theory applied to each woven structure, this analytical model takes into account the strand undulations in the two directions and also integrates the geometrical and mechanical parameters of each constituent (resin, fill and warp strands). A representative volume is chosen for each woven composite and the fibre architecture is described by several functions. To determine the effectiveness of this analysis, the elastic properties predicted for each woven composite are compared with experimental results and results extracted from the literature. This correlation shows excellent agreement between measured and predicted values, with a very low calculation cost (CPU time of less than 0·01 s).     

Deterministic learning of completely resonant nonlinear wave systems with Dirichlet boundary conditions

In this paper, we investigate the approximation of completely resonant nonlinear wave systems via deterministic learning. The plants are distributed parameter systems (DPS) describing homogeneous and isotropic elastic vibrating strings with fixed endpoints. The purpose of the paper is to approximate the infinite-dimensional dynamics, rather than the parameters of the wave systems. To solve the problem, the wave systems are first transformed into finite-dimensional dynamical systems described by ordinary differential equation (ODE). The properties of the finite-dimensional systems, including the convergence of the solution, as well as the dominance of partial system dynamics according to point-wise measurements, are analyzed. Based on the properties, second, by using the deterministic learning algorithm, an approximately accurate neural network (NN) approximation of the the finite-dimensional system dynamics is achieved in a local region along the recurrent trajectories. Simulation studies are included to demonstrate the effectiveness of the proposed approach.     

Negative effects of sufficiently small initial weights on back-propagation neural networks

In the training of feedforward neural networks,it is usually suggested that the initial weights should be small in magnitude in order to prevent premature saturation.The aim of this paper is to point out the other side of the story:In some cases,the gradient of the error functions is zero not only for infinitely large weights but also for zero weights.Slow convergence in the beginning of the training procedure is often the result of sufficiently small initial weights.Therefore,we suggest that,in these cases,the initial values of the weights should be neither too large,nor too small.For instance,a typical range of choices of the initial weights might be something like(0.4,0.1) ∪(0.1,0.4),rather than(0.1,0.1) as suggested by the usual strategy.Our theory that medium size weights should be used has also been extended to a few commonly used transfer functions and error functions.Numerical experiments are carried out to support our theoretical findings.     

工业计量点无线监测系统

工业企业是我国能源消耗大户。为了加强工业企业的能源计量管理,保障工业企业节能降耗的基础工作,文章在分析了现有工业计量体系所存在的技术难点的基础上,提出将无线传感器网络技术应用于能源计量管理的实现方法,同时介绍了工业计量点无线监测系统的构成和优点。