The Chebyshev-polynomials-based unified model neural networks forfunction approximation

In this paper, we propose the approximate transformable technique, which includes the direct transformation and indirect transformation, to obtain a Chebyshev-Polynomials-Based (CPB) unified model neural networks for feedforward/recurrent neural networks via Chebyshev polynomials approximation. Based on this approximate transformable technique, we have derived the relationship between the single-layer neural networks and multilayer perceptron neural networks. It is shown that the CPB unified model neural networks can be represented as a functional link networks that are based on Chebyshev polynomials, and those networks use the recursive least square method with forgetting factor as learning algorithm. It turns out that the CPB unified model neural networks not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural networks. Furthermore, we have also derived the condition such that the unified model generating by Chebyshev polynomials is optimal in the sense of error least square approximation in the single variable ease. Computer simulations show that the proposed method does have the capability of universal approximator in some functional approximation with considerable reduction in learning time.     

基于遗传规划实现泛函网络神经元函数类型优化

泛函网络是最近提出的一种对神经网络的有效推广。与神经网络不同,它处理的是一般的泛函模型,其神经元函数不固定,而是可学习的,且在各个处理单元之间没有权值。同神经网络一样,至今还没有系统设计方法能够对给定问题设计出近似最优的结构。鉴于此,将整个泛函网络的设计分解为单个神经元的逐个设计;然后,在此框架下提出了基于遗传规划的单个神经元的设计方法,该方法可实现对神经元函数类型的优化。仿真实验表明,本方法是有效可行的,能用较小的网络规模获得更满意的泛化特性。     

强化学习在导弹制导中的应用

阐述了强化学习的基本原理和特点,讨论了强化学习中评价函数的神经网络近似问题,重点分析了采用多神经网络近似评价函数的学习问题,实现了状态空间或任务的自动分解,提高了评价函数的推广能力,网络的学习是离线进行,并作为反馈控制器在线应用,并以A－学习为例,将强化学习应用于导弹的制导问题,仿真结果表明了强化学习在导弹制导或控制问题中的应用前景和有效性。     

Extracting rules from trained neural networks

Presents an algorithm for extracting rules from trained neural networks. The algorithm is a decompositional approach which can be applied to any neural network whose output function is monotone such as a sigmoid function. Therefore, the algorithm can be applied to multilayer neural networks, recurrent neural networks and so on. It does not depend on training algorithms, and its computational complexity is polynomial. The basic idea is that the units of neural networks are approximated by Boolean functions. But the computational complexity of the approximation is exponential, and so a polynomial algorithm is presented. The author has applied the algorithm to several problems to extract understandable and accurate rules. The paper shows the results for the votes data, mushroom data, and others. The algorithm is extended to the continuous domain, where extracted rules are continuous Boolean functions. Roughly speaking, the representation by continuous Boolean functions means the representation using conjunction, disjunction, direct proportion, and reverse proportion. This paper shows the results for iris data.     

一种分式过程神经元网络及其应用研究

针对带有奇异值复杂时变信号的模式分类和系统建模问题，提出了一种分式过程神经元网络．该模型是基于有理式函数具有的对复杂过程信号的逼近性质和过程神经元网络对时变信息的非线性变换机制构建的。其基本信息处理单元由两个过程神经元成对偶组成。逻辑上构成一个分式过程神经元，是人工神经网络在结构和信息处理机制上的一种扩展．分析了分式过程神经元网络的连续性和泛函数逼近能力，给出了基于函数正交基展开的学习算法．实验结果表明，分式过程神经元网络对于带有奇异值时变函数样本的学习性质和泛化性质要优于BP网络和一般过程神经元网络。网络隐层数和节点数可较大减少，且算法的学习性质与传统BP算法相同．     

Adaptive structures with algebraic loops

The contraction theorem has many fields of application, including linear algebraic equations, differential and integral equations, control systems theory, optimization, etc. The paper aims at showing how contraction mapping can be applied to the computation and the training of adaptive structures with algebraic loops. These structures are used for the approximation of unknown functional relations (mappings) represented by training sets. The technique is extended to multilayer neural networks with algebraic loops. Application of a two-layer neural network to breast cancer diagnosis is described.     

Contingency evaluation and monitorization using artificial neural networks

In this paper, different neural network-based solutions to the contingency analysis problem are presented. Contingency analysis is examined from two perspectives: as a functional approximation problem obtaining a numerical evaluation and ranking contingencies; and as a graphical monitoring problem, obtaining an easy visualization system of the relative severity of the contingencies. For the functional evaluation problem, we analyze the use of different supervised feed-forward artificial neural networks (multilayer perceptron and radial basis function networks). The proposed systems produce a very accurate evaluation and ranking, and so present a high applicability. For the graphical monitoring problem, unsupervised artificial neural networks such as self-organizing maps by Kohonen have been used. This solution allows both a rapid, easy and simultaneous visualization of the severity level of the complete contingency set. The proposed solutions avoid the main drawbacks of previous neural network approaches to this problem, which are explicitly analyzed here.     

Improved Complex-valued Radial Basis Function (ICRBF) neural networks on multiple crack identification

This paper introduces a new class of neural networks in complex space called Complex-valued Radial Basis Function (CRBF) neural networks and also an improved version of CRBF called Improved Complex-valued Radial Basis Function (ICRBF) neural networks. They are used for multiple crack identification in a cantilever beam in the frequency domain. The novelty of the paper is that, these complex-valued neural networks are first applied on inverse problems (damage identification) which come under the category of function approximation. The conventional CRBF network was used in the first stage of ICRBF network and in the second stage a reduced search space moving technique was employed for accurate crack identification. The effectiveness of proposed ICRBF neural network was studied first on a single crack identification problem and then applied to a more challenging problem of multiple crack identification in a cantilever beam with zero noise as well as 5% noise polluted signals. The results proved that, the proposed ICRBF and real-valued Improved RBF (IRBF) neural networks have identified the single and multiple cracks with less than 1% absolute mean percentage error as compared to conventional CRBF and RBF neural networks, mainly because of their second stage reduced search space moving technique. It appears that IRBF neural network is a good compromise considering all factors like accuracy, simplicity and computational effort.     

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.     

基于再生核神经网络的断层面模型重构

为了提高勘探精度及采油效率,需要更深入地了解地质构造,因此断层面模型的重构有着重要的意义,为此提出了基于再生核神经网络的断层面重构方法。再生核源于不同学科分支,目前已成为函数逼近的重要工具。将再生核与神经网络有机地结合起来,提出一种新型的神经网络———再生核神经网络,且将网络的训练归结为求解线性方程组问题,为了建立既具有足够精度又能表现系统行为的简单模型,考虑线性方程组的稀疏解是必要的,稀疏解就是具有大量零元素的近似解。虽然稀疏解整体误差较小,但可能在一些点上的误差较大,为此提出对稀疏解的误差修正方法。将再生核神经网络应用于大庆地区的断层面模型重构,实验结果表明,本文重构的断层面与传统方法重构的断层面相比,更符合大庆地区的地质情况。     

An efficient multilayered shielded microwave circuit analysis method based on neural networks

In previous works, a neural network based technique to analyze multilayered shielded microwave circuits was developed. The method is based on the approximation of the shielded media Green's functions by radial‐basis‐function neural networks (RBFNNs). The trained neural networks, substitute the original Green's functions during the application of the integral equation approach, allowing a faster analysis than the direct solution. In this article, new and important improvements are applied to the training of the RBFNNs, which permit a reduction in the approximation error introduced by the neural networks. Furthermore, outstanding time reductions in the analysis of printed circuits are achieved, clearly outperforming the former technique. The main improvement consists on a better processing of the Green's function singularity near the source. The singularity produces rapid variations near the source that makes difficult the neural network training. In this work, the singularity is extracted in a more suitable fashion than in previous works. The functions resulting from the singularity extraction present a smooth behavior, so they can be easily approximated by neural networks. In addition, a new subdivision strategy for the input space is proposed to efficiently train the neural networks. Two practical microwave filters are analyzed using the new techniques. Comparisons with measured results are also presented for validation. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

基于径向基函数神经网络的转子系统裂纹故障诊断

结合基于模型的转子系统诊断技术和径向基函数(RBF)神经网络在辨识非线性系统动态时的优势,本文提出了一种新的转子系统裂纹故障诊断方法.该方法采用RBF神经网络对裂纹转子系统的未知动态进行辨识,实现部分神经网络权值收敛到最优值以及神经网络对系统未知动态的局部准确逼近;诊断过程中利用已辨识的信息实现转子系统裂纹故障的快速检测与分离.所提方法尤其适用于微小裂纹的在线检测与定量识别.最后,以Jeffcott转子系统裂纹故障诊断为例进行仿真,仿真结果验证了所提方法的有效性.     

Deep-SBFL:基于频谱的深度神经网络缺陷定位方法

深度神经网络已经在自动驾驶和智能医疗等领域取得了广泛的应用.与传统软件一样,深度神经网络也不可避免地包含缺陷,如果做出错误决定,可能会造成严重后果.因此,深度神经网络的质量保障受到了广泛关注.然而,深度神经网络与传统软件存在较大差异,传统软件质量保障方法无法直接应用于深度神经网络,需要设计有针对性的质量保障方法.软件缺陷定位是保障软件质量的重要方法之一,基于频谱的缺陷定位方法在传统软件的缺陷定位中取得了很好的效果,但无法直接应用于深度神经网络.在传统软件缺陷定位方法的基础上提出了一种基于频谱的深度神经网络缺陷定位方法 Deep-SBFL.该方法首先通过收集深度神经网络的神经元输出信息和预测结果作为频谱信息;然后将频谱信息进行处理作为贡献信息,以用于量化神经元对预测结果所做的贡献;最后提出了针对深度神经网络缺陷定位的怀疑度公式,基于贡献信息计算深度神经网络中神经元的怀疑度并进行排序,以找出最有可能存在缺陷的神经元.为验证该方法的有效性,以E_Inspect@n (结果排序列表前n个位置内成功定位的缺陷数)和EXAM (在找到缺陷元素之前必须检查元素的百分比)作为评测指...     

一种基于神经网络在线逼近器的非线性鲁棒故障诊断方法

针对一类不确定非线性动态系统，提出了一种基于神经网络在线逼近结构的鲁棒故障 检测方法．该方法通过构造神经网络通过在线逼近结构学习非线性故障特性来监测动态系统 的反常行为,当故障发生时，在线估计器可逼近各种可能的未知故障，然后对其进行诊断和 适应．神经网络权重的在线学习律没有持续激励的要求，并采用Lyapunov稳定性理论保证了 闭环误差系统一致最终有界稳定．     

有理式二阶前馈型神经网络

文章提出了二阶有理式多层前馈神经网络的数学模型。有理式多层神经网络的思想来源于函数逼近理论中的有理式逼近。有理式前馈神经网络模型是传统前俯神经网络模型的推广，能有效地求解函数逼近问题。文章给出了有理式多层神经网络的学习算法，即误差反传播学习算法。就计算复杂度而言，有理式神经网络的学习算法与传统的多层神经网络反传播算法是同阶的。文章还给出了函数逼近和模式识别两个应用实例，实验结果说明二阶有理式多层神经网络在解决传统的问题上是有效的。     

An Experimental Study on Nonlinear Function Computation for Neural/Fuzzy Hardware Design

An experimental study on the influence of the computation of basic nodal nonlinear functions on the performance of (NFSs) is described in this paper. Systems' architecture size, their approximation capability, and the smoothness of provided mappings are used as performance indexes for this comparative paper. Two widely used kernel functions, the sigmoid-logistic function and the Gaussian function, are analyzed by their computation through an accuracy-controllable approximation algorithm designed for hardware implementation. Two artificial neural network (ANN) paradigms are selected for the analysis: backpropagation neural networks (BPNNs) with one hidden layer and radial basis function (RBF) networks. Extensive simulation of simple benchmark approximation problems is used in order to achieve generalizable conclusions. For the performance analysis of fuzzy systems, a functional equivalence theorem is used to extend obtained results to fuzzy inference systems (FISs). Finally, the adaptive neurofuzzy inference system (ANFIS) paradigm is used to observe the behavior of neurofuzzy systems with learning capabilities     

基于粗糙集理论的RBF神经网络剪枝算法

分析了满足给定学习误差要求的最小结构神经网络的各种实现方法.把粗糙集理论引入神经网络的结构构造中;提出了一种基于粗糙集理论的RBF神经网络剪枝算法,并将这种算法与现有剪枝算法相比较.最后将该算法应用于热工过程中过热气温动态特性建模.仿真结果表明基于该算法的神经网络模型具有较高的建模精度以及泛化能力.     

A stable learning algorithm for block-diagonal recurrent neural networks: application to the analysis of lung sounds.

A novel learning algorithm, the Recurrent Neural Network Constrained Optimization Method (RENNCOM) is suggested in this paper, for training block-diagonal recurrent neural networks. The training task is formulated as a constrained optimization problem, whose objective is twofold: (1) minimization of an error measure, leading to successful approximation of the input/output mapping and (2) optimization of an additional functional, the payoff function, which aims at ensuring network stability throughout the learning process. Having assured the network and training stability conditions, the payoff function is switched to an alternative form with the scope to accelerate learning. Simulation results on a benchmark identification problem demonstrate that, compared to other learning schemes with stabilizing attributes, the RENNCOM algorithm has enhanced qualities, including, improved speed of convergence, accuracy and robustness. The proposed algorithm is also applied to the problem of the analysis of lung sounds. Particularly, a filter based on block-diagonal recurrent neural networks is developed, trained with the RENNCOM method. Extensive experimental results are given and performance comparisons with a series of other models are conducted, underlining the effectiveness of the proposed filter.     

概率神经网络在化工过程故障检测中的应用

提出将一种径向基网络的重要变形—概率神经网络(PNN)应用于化工过程的故障检测中。与其他网络相比,概率神经网络学习速度快,适合于故障检测问题。将概率神经网络用于Tennessee Eastman(TE)过程故障检测的仿真实验,将实验结果与BP网络进行比较,结果表明概率神经网络的网络设计时间明显少于BP网络,故障检测的准确率明显提高。该方法可行、有效。     

Neural networks for feedback feedforward nonlinear control systems

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.