Impulsive component extraction using shift-invariant dictionary learning and its application to gear-box bearing early fault diagnosis

The impulsive components induced by bearing faults are key features for assessing gear-box bearing faults.However,because of heavy background noise and the interferences of other vibrations,it is difficult to extract these impulsive components caused by faults,particularly early faults,from the measured vibration signals.To capture the high-level structure of impulsive components embedded in measured vibration signals,a dictionary learning method called shift-invariant K-means singular value decomposition(SI-K-SVD)dictionary learning is used to detect the early faults of gear-box bearings.Although SI-K-SVD is more flexible and adaptable than existing methods,the improper selection of two SI-K-SVD-related parameters,namely,the number of iterations and the pattern lengths,has an adverse influence on fault detection performance.Therefore,the sparsity of the envelope spectrum(SES)and the kurtosis of the envelope spectrum(KES)are used to select these two key parameters,respectively.SI-K-SVD with the two selected optimal parameter values,referred to as optimal parameter SI-K-SVD(OP-SI-K-SVD),is proposed to detect gear-box bearing faults.The proposed method is verified by both simulations and an experiment.Compared to the state-of-the-art methods,namely,empirical model decomposition,wavelet transform and K-SVD,OP-SI-K-SVD has better performance in diagnosing the early faults of a gear-box bearing.

Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform

In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.

Reconstruction of sampling in shift-invariant space using generalized inverse

A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.

CHARACTERIZATIONS OF PRINCIPAL SHIFT-INVARIANT SPACES

Shifts-invariant spaces in L 1(R) are investigated. First,based on a study of the system of linearly difference operators,the method of constructing generators with linearly independent shifts is provided. Then the characterizations of the closed shift-invariant subspaces in L 1(R) are given in terms of such generators and the local basis of shift-invariant subspaces.

Regular and Irregular Sampling Linear Transforms in Series of Shift-Invariant Spaces

In this article we show that there exists an analogue of the Fourier duality technique in the setting a series of shift-invariant spaces.Really,every a series shift-invariant spaceΣ^𝑛𝑖=1𝑉𝜙𝑖𝑖with a stable generator^𝑛𝑖=1𝜙𝑖is the range space of a bounded one-to-one linear operator𝑇𝑇between𝐿𝐿2(0,1)and𝐿𝐿2(R).We show regular and irregular sampling formulas inΣ𝑛𝑛𝑖𝑖=1𝑉𝑉𝜙𝜙𝑖𝑖are obtained by transforming.

THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM

The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich (1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz (1991).

General A-P Iterative Algorithm in Shift-invariant Spaces

A general A-P iterative algorithm in a shift-invariant space is presented. We use the algorithm to show reconstruction of signals from weighted samples and also show that the general improved algorithm has better convergence rate than the existing one. An explicit estimate for a guaranteed rate of convergence is given.

Invariance of shift-invariant spaces

In this paper, we give a characterization of shift-invariant subspaces which are also invariant under additional non-integer translations. Both principal and finitely generated shift-invariant subspaces are studied. Our results improve some known ones.

Sufficient Conditions for Shift-Invariant Systems to be Frames in L^2(R^n)

The main purpose of this paper is to establish some new sufficient conditions under which shift-invariant systems become frames in L2（Rn）. As applications, we obtain new results for Gabor frames.

A Note on Shift-Invariant Spaces Admitting a Single Generator

In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2（0, 1） and L^2（R）. In this paper, in terms of bases for L^2（0, α）, two sampling theorems for αZ-shift invariant spaces with a single generator are obtained.

如何在通用人工智能系统中实现“知识锁定标杆浮动效应”——一种基于“时间压力”的简易心智模型

所谓“知识锁定标杆浮动效应”,是指面对同样的信念内容,认知主体会在某些环境下将其判定为“知识”,而在另一些环境下将其判定为“非知识”。该效应的存在,使得人类能够根据环境信息的变化,灵活地改变自身信念,更好地适应环境。人工智能体对于该效应机制的模拟,也能够更好地适应环境。不过,这种模拟必须建立在对于该效应的正确理解上,而西方主流知识论学界对于该效应的解释,如语境主义、比对主义与不变主义提出的解释,要么缺乏足够的普遍性,要么本身建立在一些有待解释的概念上。与之相比较,基于“时间压力”的模型,则将智能体的知识指派倾向的强度视为与其感受的时间压力彼此负相关的一项因素,而“时间压力”本身被视为“主体所预估的问题解决所需要的时间”与其“所愿意付出且能够付出的时间”之间的差值。这样的模型不仅能够对所谓的“银行案例”与“斑马案例”作出简洁的解释,而且在原则上可以被算法化。

一种关于“判知结论浮动”现象的多元主义解释框架

“判知结论浮动”指的是面对同样的信念,只要产生这个信念的内外条件发生了变化,知识裁判人就会对这个信念本身的知识地位做出不同的评估。英美知识论学界用于解释判知结论浮动的主流理论,包括语境主义、比对主义、不变主义,等等。这些理论都可以被顺化为一个统一的概率学框架。根据这一框架,一个信念P的知识地位的稳固程度,取决于这个信念本身抵御其“异常使真者”之颠覆的能力,抵御力的大小,也可以得到概率学的表征。“异常使真者”能引导主体产生P的信念,却又不是直接与P对应的那个“正常事实”,而是某个非常反常的、其出现又具有极大偶然性的事实,因此,“异常使真者”的引入是会削弱信念P的知识地位的。不过,对于到底哪些具体的认知因素可以充当“异常使真者”这一点,统一框架持一种多元主义的态度,亦能够方便我们在哲学层面上以多元主义态度应对各种关于判知结论浮动的成因。西方学界针对判知结论浮动问题的主流解释方略,往往夸大某个导致判知结论浮动的因素的影响力,忽略了其他成因,难免陷入“盲人摸象”之境地。

Contrast Enhancement Based Image Detection Using Edge Preserved Key Pixel Point Filtering

In existing methods for segmented images,either edge point extraction or preservation of edges,compromising contrast images is so sensitive to noise.The Degeneration Threshold Image Detection(DTID)framework has been proposed to improve the contrast of edge filtered images.Initially,DTID uses a Rapid Bilateral Filtering process for filtering edges of contrast images.This filter decomposes input images into base layers in the DTID framework.With minimal filtering time,Rapid Bilateral Filtering handles high dynamic contrast images for smoothening edge preservation.In the DTID framework,Rapid Bilateral Filtering with Shift-Invariant Base Pass Domain Filter is insensitive to noise.This Shift-Invariant Filtering estimates value across edges for removing outliers(i.e.,noise preserving base layers of the contrast image).The intensity values are calculated in the base layer of the contrast image for accurately detecting nearby spatial locations using Shift-Invariant base Pass Domain Filter(SIDF).At last,Affine Planar Transformation is applied to detect edge filtered contrast images in the DTID framework for attaining a high quality of the image.It normalizes the translation and rotation of images.With this,Degeneration Threshold Image Detection maximizes average contrast enhancement quality and performs an experimental evaluation of factors such as detection accuracy,rate,and filtering time on contrast images.Experimental analysis shows that the DTID framework reduces the filtering time taken on contrast images by 54%and improves average contrast enhancement quality by 27%compared to GUMA,HMRF,SWT,and EHS.It provides better performance on the enhancement of average contrast enhancement quality by 28%,detection accuracy rate by 26%,and reduction in filtering time taken on contrast images by 30%compared to state-of-art methods.

A pseudo wavelet system-based vibration signature extracting method for rotating machinery fault detection

The rotating machinery,as a typical example of large and complex mechanical systems,is prone to diversified sorts of mechanical faults,especially on their rotating components.Although they can be collected via vibration measurements,the critical fault signatures are always masked by overwhelming interfering contents,therefore difficult to be identified.Moreover,owing to the distinguished time-frequency characteristics of the machinery fault signatures,classical dyadic wavelet transforms(DWTs) are not perfect for detecting them in noisy environments.In order to address the deficiencies of DWTs,a pseudo wavelet system(PWS) is proposed based on the filter constructing strategies of wavelet tight frames.The presented PWS is implemented via a specially devised shift-invariant filterbank structure,which generates non-dyadic wavelet subbands as well as dyadic ones.The PWS offers a finer partition of the vibration signal into the frequency-scale plane.In addition,in order to correctly identify the essential transient signatures produced by the faulty mechanical components,a new signal impulsiveness measure,named spatial spectral ensemble kurtosis(SSEK),is put forward.SSEK is used for selecting the optimal analyzing parameters among the decomposed wavelet subbands so that the masked critical fault signatures can be explicitly recognized.The proposed method has been applied to engineering fault diagnosis cases,in which the processing results showed its effectiveness and superiority to some existing methods.

CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).

Homogeneous wavelets and framelets with the refinable structure

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.