Transient response of Bouc–Wen hysteretic system under random excitation via RBFNN method

Hysteresis normally exhibited by mechanical systems and materials is so prevalent that its response prediction under random excitation has been extensively investigated for decades. Nevertheless, the transient solution of the response, which is crucial for assessing the system’s reliability, is still a challenging topic that requires additional development. To this regard, this work proposes a semi-analytical method using the radial basis function neural network (RBFNN) to attain the transient probability density distribution of the randomly excited Bouc–Wen system. Specifically, the trial solution of the corresponding FPK equation is configured as the RBFNN with undetermined time-varying weight coefficients. By discretizing the time derivative with the Euler difference method, a loss function with time recurrence is derived and minimized to yield the time-varying optimal weight coefficients through the optimization method. Additionally, an optimized sampling strategy is adopted to reduce the burden of calculation. Finally, the Bouc–Wen hysteretic systems with softening and hardening nonlinearity are considered to investigate the performance of the adopted technique. The numerical results have shown that the evaluation process of the probability density functions(PDFs) can be captured well with sufficient accuracy and efficiency. The proposed efficient sampling technique can provide considerable efficiency improvement for the medium dimension system. The work of the paper will contribute to the reliability design of hysteretic structures in engineering.     

Exponentially Accurate Approximations to Periodic Lipschitz Functions Based on Fourier Series Partial Sums

The problem of accurately reconstructing a piecewise smooth. 2-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. The locations of the singularities are approximated to within O(N ^–M–2), and the associated jump of the kth derivative of f is approximated to within O(N ^–M–1+k ), as N , and the method is robust. These estimates are then used with a class of singular basis functions, which have certain built-in singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M . The technique is illustrated with several examples.     

公安现役院校大学计算机基础实践指导教材研究

在公安现役院校计算机基础教学改革中,大学计算机基础实践教学的课堂教学与实践教学分离,实践教学以学员自主学习为主。作为学员学习的主要参考资料和教学的有益补充,教材在新教学模式下的重要性越发突出。本文对公安现役院校大学计算机基础实践指导教材的建设思路和教材特色进行了详细阐述。     

Some notes on Zadeh’s extensions

This paper shows that the Zadeh’s extensions of sendograph-metric-continuous fuzzy-valued functions are sendograph-metric-continuous fuzzy functions.     

Fast k most similar neighbor classifier for mixed data (tree k-MSN)

The k nearest neighbor (k-NN) classifier has been a widely used nonparametric technique in Pattern Recognition, because of its simplicity and good performance. In order to decide the class of a new prototype, the k-NN classifier performs an exhaustive comparison between the prototype to classify and the prototypes in the training set T. However, when T is large, the exhaustive comparison is expensive. For this reason, many fast k-NN classifiers have been developed, some of them are based on a tree structure, which is created during a preprocessing phase using the prototypes in T. Then, in a search phase, the tree is traversed to find the nearest neighbor. The speed up is obtained, while the exploration of some parts of the tree is avoided using pruning rules which are usually based on the triangle inequality. However, in soft sciences as Medicine, Geology, Sociology, etc., the prototypes are usually described by numerical and categorical attributes (mixed data), and sometimes the comparison function for computing the similarity between prototypes does not satisfy metric properties. Therefore, in this work an approximate fast k most similar neighbor classifier, for mixed data and similarity functions that do not satisfy metric properties, based on a tree structure (Tree k-MSN) is proposed. Some experiments with synthetic and real data are presented.     

On the lower bounds of the second order nonlinearities of some Boolean functions

The rth order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code R(r,n). In this paper we deduce the lower bounds of the second order nonlinearities of the following two types of Boolean functions:

1.

with d=2^2r+2^r+1 and , where n=6r.

2.

, where x,y∈F_2^t,n=2t,n?6 and i is an integer such that 1?i<t,gcd(2^t-1,2ⁱ+1)=1.

For some λ, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds.     

On the versatility of radial basis function neural networks: A case study in the field of intrusion detection

Classifiers based on radial basis function neural networks have a number of useful properties that can be exploited in many practical applications. Using sample data, it is possible to adjust their parameters (weights), to optimize their structure, and to select appropriate input features (attributes). Moreover, interpretable rules can be extracted from a trained classifier and input samples can be identified that cannot be classified with a sufficient degree of “certainty”. These properties support an analysis of radial basis function classifiers and allow for an adaption to “novel” kinds of input samples in a real-world application. In this article, we outline these properties and show how they can be exploited in the field of intrusion detection (detection of network-based misuse). Intrusion detection plays an increasingly important role in securing computer networks. In this case study, we first compare the classification abilities of radial basis function classifiers, multilayer perceptrons, the neuro-fuzzy system NEFCLASS, decision trees, classifying fuzzy-k-means, support vector machines, Bayesian networks, and nearest neighbor classifiers. Then, we investigate the interpretability and understandability of the best paradigms found in the previous step. We show how structure optimization and feature selection for radial basis function classifiers can be done by means of evolutionary algorithms and compare this approach to decision trees optimized using certain pruning techniques. Finally, we demonstrate that radial basis function classifiers are basically able to detect novel attack types. The many advantageous properties of radial basis function classifiers could certainly be exploited in other application fields in a similar way.     

Excel中公式和函数教学的研究与探讨

公式和函数是Excel教学中的重点与难点,电子表格中的数据运算正是通过公式和函数完成的,只有掌握了它们的使用,才能在日常的Excel使用中提高工作效率。该文介绍了Excel中公式和函数教学中的一些方法与体会。     

Analysis and evaluation of a general camera model

A versatile General Camera Model, GCM, has been developed, and is described in detail. The model is general in the sense that it can capture both fisheye and conventional as well as catadioptric cameras in a unified framework. The camera model includes efficient handling of non-central cameras as well as compensations for decentring distortion. A novel way of analysing radial distortion functions of camera models leads to a straightforward improvement of conventional models with respect to generality, accuracy and simplicity. Different camera models are experimentally compared for two cameras with conventional and fisheye lenses, and the results show that the overall performance is favourable for the GCM.     

多小波基多尺度多传感器数据融合

多传感器数据融合技术已经被广泛应用在多个领域,小波多尺度分解对数据的分析具有独特的优点,小波基的选择对数据融合结果也起着关键的作用.提出一种新的基于多个小波基的数据融合算法,先对含有噪声的传感器信号进行多个不同小波基的多尺度分解,然后对相同小波基分解的信号在多尺度上实施加权数据融合算法,之后进行不同小波基的逆变换得到的重构信号,最后将基于不同小波基的重构信号做最终的融合.实验结果表明:数据融合技术可以从多个方面多个层面以及多种融合原则来考虑,从而融合众多的因素得到最优的结果.