Application of the blind source separation method to feature extraction of machine sound signals

As the result of vibration emission in air, a machine sound signal carries important information about the working condition of machinery. But in practice, the sound signal is typically received with a very low signal-to-noise ratio. To obtain features of the original sound signal, uncorrelated sound signals must be removed and the wavelet coefficients related to fault condition must be retrieved. In this paper, the blind source separation technique is used to recover the wavelet coefficients of a monitored source from complex observed signals. Since in the proposed blind source separation (BSS) algorithms it is generally assumed that the number of sources is known, the Gerschgorin disk estimator method is introduced to determine the number of sound sources before applying the BSS method. This method can estimate the number of sound sources under non-Gaussian and non-white noise conditions. Then, the partial singular value analysis method is used to select these significant observations for BSS analysis. This method ensures that signals are separated with the smallest distortion. Afterwards, the time-frequency separation algorithm, converted to a suitable BSS algorithm for the separation of a non-stationary signal, is introduced. The transfer channel between observations and sources and the wavelet coefficients of the source signals can be blindly identified via this algorithm. The reconstructed wavelet coefficients can be used for diagnosis. Finally, the separation results obtained from the observed signals recorded in a semi-anechoic chamber demonstrate the effectiveness of the presented methods .     

A new approach to the decomposition of Boolean functions by the method of <Emphasis Type="Italic">q</Emphasis>-partitions. III. Joint decomposition of a function system

The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples. Parts I and II of this article are published in No. 5 (2001) and No. 1 (2002). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–58, March–April 2007.     

Antimagic labeling and canonical decomposition of graphs

An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1,…,m} to the edges such that the sums of incident labels are distinct at distinct vertices. Hartsfield and Ringel conjectured that every connected graph other than K₂ has an antimagic labeling. We prove this for the classes of split graphs and graphs decomposable under the canonical decomposition introduced by Tyshkevich. As a consequence, we provide a sufficient condition on graph degree sequences to guarantee an antimagic labeling.     

3带紧支撑的正交小波

本文首先通过Householder矩阵扩充构造了3带紧支撑的正交小波．当尺度函数具有紧支撑对称正交性时,本文通过仿酉矩阵对称扩充构造了3带紧支撑对称的正交小波,并且研究了所构造对称小波的结构．所构造小波函数的支撑不超过尺度函数的支撑,构造方法容易推广到一般d带的情形．另外,本文还给出了容易实施的显式构造算法．最后,给出了构造算例．     

Structure damage diagnosis using neural network and feature fusion

A structure damage diagnosis method combining the wavelet packet decomposition, multi-sensor feature fusion theory and neural network pattern classification was presented. Firstly, vibration signals gathered from sensors were decomposed using orthogonal wavelet. Secondly, the relative energy of decomposed frequency band was calculated. Thirdly, the input feature vectors of neural network classifier were built by fusing wavelet packet relative energy distribution of these sensors. Finally, with the trained classifier, damage diagnosis and assessment was realized. The result indicates that, a much more precise and reliable diagnosis information is obtained and the diagnosis accuracy is improved as well.     

Large-scale linear system solver using secondary storage: Self-energy in hybrid nanostructures

We present a Fortran library which can be used to solve large-scale dense linear systems, Ax=b. The library is based on the LU decomposition included in the parallel linear algebra library PLAPACK and on its out-of-core extension POOCLAPACK. The library is complemented with a code which calculates the self-polarization charges and self-energy potential of axially symmetric nanostructures, following an induced charge computation method. Illustrative calculations are provided for hybrid semiconductor–quasi-metal zero-dimensional nanostructures. In these systems, the numerical integration of the self-polarization equations requires using a very fine mesh. This translates into very large and dense linear systems, which we solve for ranks up to 3×¹⁰⁵. It is shown that the self-energy potential on the semiconductor–metal interface has important effects on the electronic wavefunction.

Program summary

Program title: HDSS (Huge Dense System Solver)Catalogue identifier: AEHU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 98 889No. of bytes in distributed program, including test data, etc.: 1 009 622Distribution format: tar.gzProgramming language: Fortran 90, CComputer: Parallel architectures: multiprocessors, computer clustersOperating system: Linux/UnixHas the code been vectorized or parallelized?: Yes. 4 processors used in the sample tests; tested from 1 to 288 processorsRAM: 2 GB for the sample tests; tested for up to 80 GBClassification: 7.3External routines: MPI, BLAS, PLAPACK, POOCLAPACK. PLAPACK and POOCLAPACK are included in the distribution file.Nature of problem: Huge scale dense systems of linear equations, Ax=B, beyond standard LAPACK capabilities. Application to calculations of self-energy potential in dielectrically mismatched semiconductor quantum dots.Solution method: The linear systems are solved by means of parallelized routines based on the LU factorization, using efficient secondary storage algorithms when the available main memory is insufficient. The self-energy solver relies on an induced charge computation method. The differential equation is discretized to yield linear systems of equations, which we then solve by calling the HDSS library.Restrictions: Simple precision. For the self-energy solver, axially symmetric systems must be considered.Running time: About 32 minutes to solve a system with approximately 100 000 equations and more than 6000 right-hand side vectors using a four-node commodity cluster with a total of 32 Intel cores.     

Influence-based model decomposition for reasoning about spatially distributed physical systems

Many important science and engineering applications, such as regulating the temperature distribution over a semiconductor wafer and controlling the noise from a photocopy machine, require interpreting distributed data and designing decentralized controllers for spatially distributed systems. Developing effective computational techniques for representing and reasoning about these systems, which are usually modeled with partial differential equations (PDEs), is one of the major challenge problems for qualitative and spatial reasoning research.

This paper introduces a novel approach to decentralized control design, influence-based model decomposition, and applies it in the context of thermal regulation. Influence-based model decomposition uses a decentralized model, called an influence graph, as a key data abstraction representing influences of controls on distributed physical fields. It serves as the basis for novel algorithms for control placement and parameter design for distributed systems with large numbers of coupled variables. These algorithms exploit physical knowledge of locality, linear superposability, and continuity, encapsulated in influence graphs representing dependencies of field nodes on control nodes. The control placement design algorithms utilize influence graphs to decompose a problem domain so as to decouple the resulting regions. The decentralized control parameter optimization algorithms utilize influence graphs to efficiently evaluate thermal fields and to explicitly trade off computation, communication, and control quality. By leveraging the physical knowledge encapsulated in influence graphs, these control design algorithms are more efficient than standard techniques, and produce designs explainable in terms of problem structures.     

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+A T X −2 A=I

Necessary and sufficient conditions for the matrix equation X+A ^T X ^?2 A=I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.