The Rational Spline Interpolation Based-LOD Method and Its Application to Rotating Machinery Fault Diagnosis

Local oscillatory-characteristic decomposition (LOD) is a relatively new self-adaptive time-frequency analysis methodology. The method, based on local oscillatory characteristics of the signal itself uses three mathematical operations such as differential, coordinate domain transform, and piecewise linear transform to decompose the multi-component signal into a series of mono-oscillation components (MOCs), which is very suitable for processing multi-component signals. However, in the LOD method, the computational efficiency and real-time processing performance of the algorithm can be significantly improved by the use of piecewise linear transformation, but the MOC component lacks smoothness, resulting in distortion. In order to overcome the disadvantages mentioned above, the rational spline function that spline shape can be adjusted and controlled is introduced into the LOD method instead of the piecewise linear transformation, and the rational spline-local oscillatory-characteristic decomposition (RS-LOD) method is proposed in this paper. Based on the detailed illustration of the principle of RS-LOD method, the RS-LOD, LOD, and empirical mode decomposition (EMD) are compared and analyzed by simulation signals. The results show that the RS-LOD method can significantly improve the problem of poor smoothness of the MOC component in the original LOD method. Moreover, the RS-LOD method is applied to the fault feature extraction of rotating machinery for the multi-component modulation characteristics of rotating machinery fault vibration signals. The analysis results of the rolling bearing and fan gearbox fault vibration signals show that the RS-LOD method can effectively extract the fault feature of the rotating mechanical vibration signals.

Pig Ear Extraction Based on an Improved Active Contour Model

With the integration and scale of pig breeding, the frequency of some diseases is also increasing. To automatically detect porcine reproductive and respiratory syndrome (PRRS) during the pig cultivation process, this article proposes an improved method for pig ear extraction that is based on the active contour model. Firstly, we use the Gaussian scale space filtering and piecewise linear transformation algorithm to highlight the target zones of interest. Secondly, we use a randomly picked ear image point to reconstruct the image region and combine the active contour model to coarse segment the ear image. Finally, by taking advantage of the modified active contour model, the method precisely extracts the pig ear image. The experimental result shows that the proposed method can achieve better segmentation results. The segmentation accuracy of the image of pig contains only one ear can exceed 90%, and the accuracy of the image of pig contains two ears is greater than 85%. Keywords: Active contour model, Ear extraction, Image enhancement, Spline interpolation.

Generic point equivalence and Pisot numbers

Let $\unicode[STIX]{x1D6FD}>1$ be an integer or, generally, a Pisot number. Put $T(x)=\{\unicode[STIX]{x1D6FD}x\}$ on $[0,1]$ and let $S:[0,1]\rightarrow [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm \unicode[STIX]{x1D6FD}^{m}$ with positive integers $m$. We give a sufficient condition for $T$ and $S$ to have the same generic points. We also give an uncountable family of maps which share the same set of generic points.

SIMULATED-DATA ADAPTATION BASED PIECEWISE LINEAR TRANSFORMATION FOR ROBUST SPEECH RECOGNITION

This paper proposes an efficient method of simulated-data adaptation for robust speech recognition. The method is applied to tree-structured piecewise linear transformation (PLT). The original PLT selects an acoustic model using tree-structured HMMs and the acoustic model is adapted by input speech in an unsupervised scheme. This adaptation can degrade the acoustic model if the input speech is incorrectly transcribed during the adaptation process. Moreover, adaptation may not be effective if only the input speech is used. Our proposed method increases the size of adaptation data by adding noise portions from the input speech to a set of prerecorded clean speech, of which correct transcriptions are known. We investigate various configurations of the proposed method. Evaluations are performed with both additive and real noisy speech. The experimental results show that the proposed system reaches higher recognition rate than MLLR, HMM-based model selection and PLT.

Toric degenerations of integrable systems on Grassmannians and polygon spaces

We introduce a completely integrable system on the Grassmannian of 2-planes in ann-space associated with any triangulation of a polygon withnsides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.

Toric degenerations of integrable systems on Grassmannians and polygon spaces

We introduce a completely integrable system on the Grassmannian of 2-planes in an n-space associated with any triangulation of a polygon with n sides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.