A WSN Node Fault Diagnosis Model Based on BRB with Self-Adaptive Quality Factor

Wireless sensor networks (WSNs) operate in complex and harshenvironments;thus, node faults are inevitable. Therefore, fault diagnosis ofthe WSNs node is essential. Affected by the harsh working environment ofWSNs and wireless data transmission, the data collected by WSNs containnoisy data, leading to unreliable data among the data features extracted duringfault diagnosis. To reduce the influence of unreliable data features on faultdiagnosis accuracy, this paper proposes a belief rule base (BRB) with a selfadaptivequality factor (BRB-SAQF) fault diagnosis model. First, the datafeatures required for WSN node fault diagnosis are extracted. Second, thequality factors of input attributes are introduced and calculated. Third, themodel inference process with an attribute quality factor is designed. Fourth,the projection covariance matrix adaptation evolution strategy (P-CMA-ES)algorithm is used to optimize the model’s initial parameters. Finally, the effectivenessof the proposed model is verified by comparing the commonly usedfault diagnosis methods for WSN nodes with the BRB method consideringstatic attribute reliability (BRB-Sr). The experimental results show that BRBSAQFcan reduce the influence of unreliable data features. The self-adaptivequality factor calculation method is more reasonable and accurate than thestatic attribute reliability method.

Hetero-Epitaxy and Self-Adaptive Stressor Based on Freestanding Fin for the 10 nm Node and Beyond

A promising technology named epitaxy on nano-scale freestanding fin （ENFF） is firstly proposed for hetero- epitaxy. This technology can effectively release total strain energy and then can reduce the probability of gener- ating mismatch dislocations. Based on the calculation, dislocation defects can be eliminated completely when the thickness of the Si freestanding fin is less than 10nm for the epitaxial Ge layer. In addition, this proposed ENFF process can provide sufficient uniaxial stress for the epitaxy layer, which can be the major stressor for the SiGe or Ge channel fin field-effect transistor or nanowire at the 10nm node and beyond. According to the results of technology computer-aided design simulation, nanowires integrated with ENFF show excellent electrical perfor- mance for uniaxial stress and band offset. The ENFF process is compatible with the state of the art mainstream technology, which has a good potential for future applications.

WAVELET-BASED FAIRING OF B-SPLINE SURFACES

A method of fairing B spline surfaces by wavelet decomposition is investigated. The wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces are described in detail. A method is introduced to approximate a B spline surface by a quasi uniform one. An error control approach for wavelet based fairing is suggested. Samples are given to show the feasibility of the algorithms presented in this paper. The practice showed that the wavelet based fairing is better than energy based one in case where the number of vertices of the B spline surface is greater than 1000. The quantitative variance of the approximation error in accordance with the change of decomposition levels needs to be further explored.

Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications

We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.

Characteristics and method of synthesis seismic wave based on wavelet reconstruction

A novel method of synthesizing seismic wave using wavelet reconstruction is proposed and compared with the traditional method of using theory of Fourier transform. By adjusting the frequency band energy and taking it as criterion, the formula of synthesizing seismic wave is deduced. Using the design parameters specified in Chinese Seismic Design Code for buildings, seismic waves are synthesized. Moreover, the method of selecting wavelet bases in synthesizing seismic wave and the influence of the damping ratio on synthesizing results are analyzed. The results show that the synthesis seismic waves using wavelet bases can represent the characteristics of the seismic wave as well as the ground characteristic period, and have good time-frequency non-stationary.

The Boundary Processing of Wavelet Based Image Compression

When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.

CONSTRUCTION METHODS AND ALGORITHM DESIGN OF WAVELET BASES

Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper.

Detection of Edge with the Aid of Mollification Based on Wavelets

In preceding papers, the present authors proposed the application of the mollification based on wavelets to the calculation of the fractional derivative (fD) or the derivative of a function involving noise. We study here the application of that method to the detection of edge of a function. Mathieu et al. proposed the CRONE detector for a detection of an edge of an image. For a function without noise, we note that the CRONE detector is expressed as the Riesz fractional derivative (fD) of the derivative. We study here the application of the mollification to the calculation of the Riesz fD of the derivative for a data involving noise, and compare the results with the results obtained by our method of applying simple derivative to mollified data.

A NEW ADAPTIVE FILTERING SCHEME BASED ON WAVELET TRANSFORM

Based on the scale function representation for a function in L2(R), a new wavelet transform based adaptive system identification scheme is proposed. It can reduce the amount of computation by exploiting the decimation properties and keep the advantage of quasi-orthogonal transform of the discrete wavelet, transform (DWT). The issue has been supported by computer simulations.

WAVELET-BASED ESTIMATORS OF MEAN REGRESSION FUNCTION WITH LONG MEMORY DATA

This paper provides an asymptotic expansion for the mean integrated squared error （MISE） of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel estimators.However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

Performance Analysis of an Optimal Circular 16-QAM for Wavelet Based OFDM Systems

The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.

Theory and Application of Natural-Based Wavelet Method

Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.

FAULT DIAGNOSIS APPROACH FOR ROLLER BEARINGS BASED ON EMPIRICAL MODE DECOMPOSITION METHOD AND HILBERT TRANSFORM

Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.

Wavelet-Galerkin方法在微分方程中的应用

运用小波理论,针对某一类变系数微分方程,首次将Littlewood-paley小波引入到变系数微分方程求解中,得到了Littlewood-paky小波ψ的尺度函数(?),构造了L2[0,1]中的正交小波基ψj,kfold,证明了该正交小波基满足方程的初始条件.运用Galerkin方法求出了方程在子空间中的逼近解,得出了变系数微分方程的准确解.拓宽了小波理论的适用范围,并为微分方程的求解问题提供了新的理论空间.

ORTHONORMAL POLYNOMIAL BASSES AND WAVELET-PACKETS

For any fixed ε > 0, an explicit construction of anorthonormal trigonometric polynomial basis {Tk}∞k=1 inL2 [0,1) with degTk≤ 0.5(1 +ε)k is presented. Thus weimprove the results obtained by D. Offin and K. Oskolkov in [4] and by Al. A. Privalov in [6]. and practically solve the open problemasked in [4], [8] and [9]. Moreover, as in [4], Fourier sums with respectto this polynomial basis are projectors onto subspaces of trigonometricpolynomials of high degree, which implies almost best approximation- properties.

Cement Pavement Surface Crack Detection Based on Image Processing

This article introduces the application of image recognition technology in cement pavement crack detection and put forward to method fordetermining threshold about grayscale stretching. This algorithm is designed for binarization which has a self-adaptive characteristic. After theimage is preprocessed, we apply 2D wavelet and Laplace operator to process the image. According to the characteristic of pixel of gray image, analgorithm designed on binarization for Binary image. The feasibility of this method can be verified the image processed by comparing with theresults of three algorithms: Otsu method, iteration method and fixed threshold method.

Entropy of images after wavelet transform

We studied the variation of image entropy before and after wavelet decomposition, the optimal number of wavelet decomposition layers, and the effect of wavelet bases and image frequency components on entropy. Numerous experiments were done on typical images to calculate (using Matlab) the entropy before and after wavelet transform. It was verified that, to obtain minimal entropy, a three-layer decomposition should be adopted rather than higher orders. The result achieved by using biorthogonal wavelet decomposition is better than that of the orthogonal wavelet decomposition. The results are not directly proportional to the vanishing moment, however.

Tracking of Non-Rigid Object in Complex Wavelet Domain

In this paper we have proposed an object tracking method using Dual Tree Complex Wavelet Transform (DTCxWT). The proposed method is capable of tracking the moving object in video sequences. The object is assumed to be deform-able under limit i.e. it may change its shape from one frame to another. The basic idea in the proposed method is to decompose the image into two components: a two dimensional motion and a two dimensional shape change. The motion component is factored out while the shape is explicitly represented by storing a sequence of two dimensional models. Each model corresponds to each image frame. The proposed method performs well when the change in the shape in the consecutive frames is small however the 2-D motion in consecutive frames may be large. The proposed algorithm is capable of handling the partial as well as full occlusion of the object.

Genetic Wavelet and Harmonic Waveletand Their Application to Non-stationary Machinery Equipment Diagnosis

The thesis introduces various characteristic wavelet bases used in non-stationary machinery equipment diagnosis, then discusses genetic wavelets and harmonic wavelets and their practical application respectively in fault diagnosis of an internal combustion engine and in orbits extracting (analysis) of rotating machinery.