A generalized fractional KN equation hierarchy and its fractional Hamiltonian structure

AbstractA generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders. We construct the generalized fractional trace identity through the Riemann–Liouville fractional derivative. An example of the fractional KN soliton equation hierarchy and Hamiltonian structure is presented, which is a new integrable hierarchy and possesses Hamiltonian structure

Classification of machinery vibration signals based on group sparse representation

The working condition of mechanical equipment can be reflected by vibration signals collected from it. Accurate classification of these vibration signals is helpful for the machinery fault diagnosis. In recent years, the L1-norm regularization based sparse representation for classification (SRC) has obtained huge success in image recognition, especially in face recognition. However, the investigation of SRC for machinery vibration signals shows that the accuracy and sparsity concentration index are not high enough. In this paper, a new classification method for machinery vibration signals is proposed, in which the L1L2-norm regularization based sparse representation, i.e. group sparse representation, is recommended as a coding strategy. The method achieves its idea classification performance by three steps. Firstly, time-domain vibration signals, including training and test samples, are transformed to frequency-domain to reduce the influence of corrupting noise. Then, the transform coefficient vectors of the test samples are coded with a combination of L1-norm and L2-norm constrain on a dictionary, which is constructed by merging the transform coefficient vectors of the training samples. At last, the fault types of the test samples are labeled by identifying their minimal reconstruction errors. The classification results of simulated and experimental vibration signals demonstrate the superiority of proposed method in comparison with the state-of-the-art classifiers

A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy

We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system; then we consider the Hamiltonian structure of the integrable coupling system. We select the U¯, V¯ and generate the nonlinear composite parts, which generate new extended WKI integrable couplings. It is also indicated that the method of block matrix is an efficient and straightforward way to construct the integrable coupling system

Transform-domain sparse representation based classification for machinery vibration signals

The working state of machinery can be reflected by vibration signals. Accurate classification of these vibration signals is helpful for the machinery fault diagnosis. A novel classification method for vibration signals, named Transform Domain Sparse Representation-based Classification (TDSRC), is proposed. The method achieves high classification accuracy by three steps. Firstly, time-domain vibration signals, including training samples and test samples, are transformed to another domain, e.g. frequency-domain, wavelet-domain etc. Then, the transform coefficients of the training samples are combined as a dictionary and the transform coefficients of the test samples are sparsely coded on the dictionary. Finally, the class label of the test samples is identified by their minimal reconstruction errors. Although the proposed method is very similar to the Sparse Representation-based Classification (SRC), experimental results illustrates its performance is far superior to SRC in the classification of vibration signals. These experiments include: frequency-domain classification of bearing vibration data from the Case Western Reserve University (CWRU) Bearing Data Center and wavelet-domain classification of six fault-types gearbox vibration data from our rotating machinery experimental platform

Transform-domain sparse representation based classification for machinery vibration signals

The working state of machinery can be reflected by vibration signals. Accurate classification of these vibration signals is helpful for the machinery fault diagnosis. A novel classification method for vibration signals, named Transform Domain Sparse Representation-based Classification (TDSRC), is proposed. The method achieves high classification accuracy by three steps. Firstly, time-domain vibration signals, including training samples and test samples, are transformed to another domain, e.g. frequency-domain, wavelet-domain etc. Then, the transform coefficients of the training samples are combined as a dictionary and the transform coefficients of the test samples are sparsely coded on the dictionary. Finally, the class label of the test samples is identified by their minimal reconstruction errors. Although the proposed method is very similar to the Sparse Representation-based Classification (SRC), experimental results illustrates its performance is far superior to SRC in the classification of vibration signals. These experiments include: frequency-domain classification of bearing vibration data from the Case Western Reserve University (CWRU) Bearing Data Center and wavelet-domain classification of six fault-types gearbox vibration data from our rotating machinery experimental platform

Viscosity and Diffusion: Crowding and Salt Effects in Protein Solutions

We report on a joint experimental-theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. The validity range of a generalized Stokes-Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [PRE 51, 1081 (1995)] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in semi-dilute systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation

Abstract In this paper, the exact solutions of generalized nonlinear Schrödinger (GNLS) equation are obtained by using Darboux transformation(DT). We derive some expressions of the 1-solitons, 2-solitons and n-soliton solutions of the GNLS equation via constructing special Lax pairs. And we choose different seed solutions and solve the GNLS equation to obtain the soliton solutions, breather solutions and rational wave solutions. Based on these obtained solutions, we consider the elastic interactions and dynamics between two solitons

Fault diagnosis method of mineral transmission equipment based on sparse classification algorithm

In view of the problem that the existing fault diagnosis methods based on feature frequency identification for mineral transmission equipments are susceptible to strong noise, a new fault diagnosis method based on sparse classification algorithm for mineral transmission equipment was proposed. Firstly, vibration signals for the known fault types of equipment are collected by computer and transformed by Fourier transformation. Then, the Fourier transformation coefficient vectors of test vibration signal are sparsely coded on a dictionary, which is constructed by merging the Fourier transformation coefficient vectors of the known vibration signals, so as to get sparse coefficient. At last, the fault types of the test samples are labeled by identifying their minimal reconstruction errors. The simulation and test results demonstrate that the method can effectively diagnose the fault type of bearing of mineral transmission equipment, which provides a novel method for fault monitoring of transmission equipment in coal mine