Are primitive polynomials always best in signature analysis?

It is shown that in testing technique based on linear-feedback shift registers, the use of primitive polynomials in a signature-analysis register is not always better than using nonprimitive polynomials. The results show how some primitive polynomials may actually yield maximum aliasing errors. These results are based on the simulation of single stuck-at faults, but they also hold for certain multiple stuck-at faults. The best testing technique appears to be one that uses a binary counter in test-pattern generation with a primitive polynomial in signature analysis     

Capacity and error estimates for boolean classifiers with limited complexity

This paper extends the notions of capacity and distribution-free error estimation to nonlinear Boolean classifiers on patterns with binary-valued features. We establish quantitative relationships between the dimensionality of the feature vectors (d), the combinational complexity of the decision rule (c), the number of samples in the training set (n), and the classification performance of the resulting classifier. Our results state that the discriminating capacity of Boolean classifiers is given by the product dc, and the probability of ambiguous generalization is asymptotically given by (n/dc-1)-1 0(log d)/d) for large d, and n=0(dc). In addition we show that if a fraction ? of the training samples is misclassified then the probability of error (?) in subsequent samples satisfies P(|?-?| ?) m=<2.773 exp (dc-e2n/8) for all distributions, regardless of how the classifier was discovered.     

AMU故障检测中测试响应压缩方法研究

测试响应压缩是对AMU故障检测过程中产生的大量数据进行处理的有效方法,如何选择一种有效的压缩方法是AMU测试中一个非常关键的问题;针对常用的两种压缩方法:奇偶压缩和特征分析进行了分析比较;通过建立故障检测模型,找出故障特征矩阵,进而确定测试矩阵;在得出响应矩阵之后,采用两种方法分别进行压缩处理;从硬件开销、故障覆盖率、混淆率和压缩率四个方面出发,对两种方法的性能指标进行理论分析与计算;结果表明,不彻底的奇偶压缩适用于要求测试混淆率比较低的情况,特征分析适用于要求硬件开销较少、检测率较高、压缩效率较高的情况。     

Sensitivity of feedforward neural networks to weight errors

An analysis is made of the sensitivity of feedforward layered networks of Adaline elements (threshold logic units) to weight errors. An approximation is derived which expresses the probability of error for an output neuron of a large network (a network with many neurons per layer) as a function of the percentage change in the weights. As would be expected, the probability of error increases with the number of layers in the network and with the percentage change in the weights. The probability of error is essentially independent of the number of weights per neuron and of the number of neurons per layer, as long as these numbers are large (on the order of 100 or more).     

用于程序循环控制的错误检测算法

为确保安全苛求系统中程序执行的正确性,针对程序循环控制中内存未更新、循环提前结束和循环滞后结束的问题,提出一种基于含签名和时间戳的算术(ANBD)码的循环控制错误检测算法。该算法通过ANBD码,将程序变量编码为含签名的码字。通过校验码字签名,检测循环控制错误。运用ANBD码中的时间标签,可检测内存未更新错误。另外,在ANBD码基础上,通过采用在线语句块签名分配算法、语句块签名函数和变量签名补偿函数,检测循环提前结束错误和循环滞后结束错误。该算法理论错误漏检概率为1/A,其中A为编码素数,选取97~10993的素数进行错误漏检概率测试,得到理论模型与测试结果的归一化均方误差(NMSE)约为-30 dB。测试结果表明,该算法可检测循环控制中出现的各类错误,且编码素数A接近2³²时,错误漏检概率可达10^-9,能够满足安全苛求系统的应用要求。     

On the inequality of cover and hart in nearest neighbor discrimination

When (X1, ?1),..., (Xn, ?n) are independent identically distributed random vectors from IRd X {0, 1} distributed as (X, ?), and when ? is estimated by its nearest neighbor estimate ?(1), then Cover and Hart have shown that P{?(1) ? ?}n ? ? ? 2E {? (X) (1 - ?(X))} ? 2R*(1 - R*) where R* is the Bayes probability of error and ?(x) = P{? = 1 | X = x}. They have conditions on the distribution of (X, ?). We give two proofs, one due to Stone and a short original one, of the same result for all distributions of (X, ?). If ties are carefully taken care of, we also show that P{?(1) ? ?|X1, ?1, ..., Xn, ?n} converges in probability to a constant for all distributions of (X, ?), thereby strengthening results of Wagner and Fritz.     

Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea

In the Japan/East Sea (Sea of Japan), the basin-scale barotropic high-frequency signals cause aliasing error in the gridded sea level anomaly (SLA) product of the satellite altimeters. The aliasing errors can produce false mesoscale eddies and alter the dynamical explanation of ocean circulation. In this article, we corrected non-tidal aliasing errors in gridded SLA product using bottom pressure (BP) data and tide gauge (TG) data. The root mean square (RMS) of the aliasing induced SLA is about 3 cm in the Sea of Japan, which accounts for about 20% of the total energy. We found that, after BP correction, the percentage of error variance (PEV) is reduced from 43% to 34% for satellite-derived velocity, and from 22% to14% for 70-day low-pass filtered gridded SLA product. However, the improvement for TG correction is not notable. The basin-scale barotropic high-frequency signals are likely to be found in other nearly enclosed marginal seas. We suggested that more BP measurements should be conducted in the marginal seas for aliasing correction. The work in this article offers a useful reference for suppressing non-tidal alias errors in other marginal seas.     

考虑输入错误时一个BP网络的高可靠重构

本文将BP网络的输入错误分为死区错误和反相错误,提出了对输入容错的高可靠的 BP网络的构造方法.对上述两种错误,分别讨论了在高可靠构造下的可靠性问题,指出当输 入正确的概率在一定范围内变化时,通过增加输入重复数,可以使得网络正确实现规定功能的 概率接近于1,或者说,使得网络对于输入错误不敏感.     

基于曲面形状误差的多层前向神经网络快速训练

如何显著提高多层前向神经网络训练速度一直是国内外共同关注的一个问题，而解决这个问题的关键在于充分了解导致现有网络训练算法训练效率低的根本原因．文中首先提出了网络输出函数的曲面形状误差和偏移误差的概念，并将指导网络训练的平方和误差分解为这两种误差，进而分析了这两种误差的主要特性，给出了导致现有算法网络训练效率低的主要原因，最后提出了新的网络训练误差模型和具体的网络训练算法．典型实例计算结果表明，与目前常用的网络训练算法相比，该文所提出的算法可显著减少网络训练时间。     

基于DFT的信号子带分解与准确重构新方法

根据正交分解原理和离散傅里叶变换的物理意义,提出了一种分析滤波器组具有理想特性的信号分解与重构新方法(Discrete Fourier transform subband decomposition,DFTSD).对于给定序列,通过离散傅里叶变换,将其变换到频域,通过谱线分组,在频域实现信号的分解,经反变换得到时域子带信号.频谱上无交叠的子带信号,从根本上解决了抽取过程所带来的带内混叠问题.综合滤波器组的设计仅需考虑内插后引入的镜像频率分量的滤除.实验结果表明,在无子带抽取和存在子带抽取情况下,重构信号与原信号的平均绝对误差在10~(-16)量级.     

Any discrimination rule can have an arbitrarily bad probability of error for finite sample size

Consider the basic discrimination problem based on a sample of size n drawn from the distribution of (X, Y) on the Borel sets of Rdx {0, 1}. If 0 < R*. < ? is a given number, and ?n ? 0 is an arbitrary positive sequence, then for any discrimination rule one can find a distribution for (X, Y), not depending upon n, with Bayes probability of error R* such that the probability of error (Rn) of the discrimination rule is larger than R* + ?n for infinitely many n. We give a formal proof of this result, which is a generalization of a result by Cover [1]. Furthermore, sup all distributions of (X, Y) with R* = 0 Rn > ?. Thus, any attempt to find a nontrivial distribution-free upper bound for Rn will fail, and any results on the rate of convergence of Rn to R* must use assumptions about the distribution of (X, Y).     

Output Feedback Adaptive Neural Control Without Seeking SPR Condition

For output‐feedback adaptive control of affine nonlinear systems based on feedback linearization and function approximation, the observation error dynamics usually should be augmented by a low‐pass filter to satisfy a strictly positive real (SPR) condition so that output feedback can be realized. Yet, this manipulation results in filtering basis functions of approximators, which makes the order of the controller dynamics very large. This paper presents a novel output‐feedback adaptive neural control (ANC) scheme to avoid seeking the SPR condition. A saturated output‐feedback control law is introduced based on a state‐feedback indirect ANC structure. An adaptive neural network (NN) observer is applied to estimate immeasurable system state variables. The output estimation error rather than the basis functions is filtered and the filter output is employed to update NNs. Under given initial conditions and sufficient control parameter constraints, it is proved that the closed‐loop system is uniformly ultimately bounded stable in the sense that both the state estimation errors and the tracking errors converge to small neighborhoods of zero. An illustrative example is provided to demonstrate the effectiveness of this approach.     

用泛函网络求任意高阶多项式的近似根

本文提出了一种新的基于泛函网络的多项式求根模型及学习算法，而泛函网络的参数利用解线性不等式组，可得到所求任意高阶多项式近似根的一般参数表达式。文章还讨论了基于泛函网络的多项式求根学习算法实现的一些技术问题，相对传统方法，能够有效地获得任意多项式对应根的参数表达式。     

A norm selection criterion for the generalized delta rule

The derivation of a supervised training algorithm for a neural network implies the selection of a norm criterion which gives a suitable global measure of the particular distribution of errors. The author addresses this problem and proposes a correspondence between error distribution at the output of a layered feedforward neural network and L(p) norms. The generalized delta rule is investigated in order to verify how its structure can be modified in order to perform a minimization in the generic L(p) norm. The particular case of the Chebyshev norm is developed and tested.     

基于输出层权值解析修正的神经网络有效训练

根据神经网络训练误差对权值的梯度特征分析,提出了网络输出层权值与网络隐含层权值轮换修正的思想,并基于网络输出层权值与网络隐含层权值之间的依赖关系,建立了网络输出层权值解析修正和隐含层权值修正的具体方法,所提出的方法通过提高网络权值修正的准确性而提高网络训练的有效性。根据网络输出节点的输出误差与其总输入误差的关系,提出了进一步提高所获得网络推广性的具体方法。实例计算结果表明,所提出的方法可以显著地提高网络的训练效率,并有效地增强网络推广性。     

Analysis of Fault Tolerance in Artificial Neural Networks

Wide attention was recently given to the problem of fault-tolerance in neural networks; while most authors dealt with aspects related to specific VLSI implementations, attention was also given to the intrinsic capacity of survival to faults characterizing the neural modes. The present paper tackles this second theme, considering in particular multilayered feed forward nets. One of the main goals is to identify the real influence of faults on the neural computation in order to show that neural paradigms cannot be considered intrinsically fault tolerant (i.e., able to survive to faults, even several of the most common and simple ones). A high abstraction level (corresponding to the neural graphs) is taken as the basis of the study and a corresponding error model is introduced. The effects of such errors induced by faults are analytically derived to verify the probability of intrinsic masking in the final neural outputs. Then, conditions allowing for complete compensation of the errors induced by faults through weight adjustment are evaluated to test the masking abilities of the network. The designer of a neural architecture should perform such a mathematical analysis to check the actual fault-tolerance features of his or her system. Unfortunately, this involves a very high computational overhead. As a cost-effective alternative for the designer, the use of a behavioral simulation is proposed for a quantitative evaluation of the error effect on the neural computation. Repeated learning (i.e., a new application of the learning procedure on the faulty network) is then experimented to induce error masking. Experimental results prove that even single errors affect the computation in a relevant way and that weight redistribution is not able to induce complete masking after a fault occurred, i.e., the network cannot be considered per se intrinsically fault tolerant and it is not possible to rely on learning only in order to achieve complete masking abilities. Mapping criteria of physical faults onto the abstract errors are finally examined to show the usability of the proposed analysis in evaluating the actual robustness of a neural networks' implementation and in identifying the critical areas where architectural redundancy should be introduced to achieve fault tolerance.     

Sensitivity analysis of single hidden-layer neural networks withthreshold functions

An important consideration when applying neural networks to pattern recognition is the sensitivity to weight perturbation or to input errors. In this paper, we analyze the sensitivity of single hidden-layer networks with threshold functions. In a case of weight perturbation or input errors, the probability of inversion error for an output neuron is derived as a function of the trained weights, the input pattern, and the variance of weight perturbation or the bit error probability of the input pattern. The derived results are verified with a simulation of the Madaline recognizing handwritten digits. The result shows that the sensitivity of trained networks is far different from that of networks with random weights.     

The selection of weight accuracies for Madalines

The sensitivity of the outputs of a neural network to perturbations in its weights is an important consideration in both the design of hardware realizations and in the development of training algorithms for neural networks. In designing dense, high-speed realizations of neural networks, understanding the consequences of using simple neurons with significant weight errors is important. Similarly, in developing training algorithms, it is important to understand the effects of small weight changes to determine the required precision of the weight updates at each iteration. In this paper, an analysis of the sensitivity of feedforward neural networks (Madalines) to weight errors is considered. We focus our attention on Madalines composed of sigmoidal, threshold, and linear units. Using a stochastic model for weight errors, we derive simple analytical expressions for the variance of the output error of a Madaline. These analytical expressions agree closely with simulation results. In addition, we develop a technique for selecting the appropriate accuracy of the weights in a neural network realization. Using this technique, we compare the required weight precision for threshold versus sigmoidal Madalines. We show that for a given desired variance of the output error, the weights of a threshold Madaline must be more accurate.     

Applying a dynamic testability technique to debugging certain classes of software faults

Testability, the tendency for software to reveal its faults during testing, is an important issue for verification and quality assurance. But testability can also be used to good advantage as a debugging technique. Although this concept is more general, we will illustrate it with a specific example: propagation analysis.Propagation Analysis (PA) is a technique for predicting the probability that a data state error affects program output. PA is a technique that produces information about a piece of software's testability. PA bases its prediction on empirical measurement of the probability that an artificial data state error affects program output. After obtaining propagation analysis information for a program and obtaining a failure probability estimate for the program during execution we build a model that can be used to identify possible sites of missing-assignment faults of the form x f(x). Thus we can apply the testability technique PA as a debugging tool.This work supported by a National Research Council NASA-Langley Resident Research Associateship and NASA-Langley Grant NAG-1-884.