Experimental Investigation for Fault Diagnosis Based on a Hybrid Approach Using Wavelet Packet and Support Vector Classification

To deal with the difficulty to obtain a large number of fault samples under the practical condition for mechanical fault diagnosis, a hybrid method that combined wavelet packet decomposition and support vector classification (SVC) is proposed. The wavelet packet is employed to decompose the vibration signal to obtain the energy ratio in each frequency band. Taking energy ratios as feature vectors, the pattern recognition results are obtained by the SVC. The rolling bearing and gear fault diagnostic results of the typical experimental platform show that the present approach is robust to noise and has higher classification accuracy and, thus, provides a better way to diagnose mechanical faults under the condition of small fault samples

Tight Guarantees for Multi-unit Prophet Inequalities and Online Stochastic Knapsack

Prophet inequalities are a useful tool for designing online allocation procedures and comparing their performance to the optimal offline allocation. In the basic setting of $k$-unit prophet inequalities, the magical procedure of Alaei (2011) with its celebrated performance guarantee of $1-\frac{1}{\sqrt{k+3}}$ has found widespread adoption in mechanism design and other online allocation problems in online advertising, healthcare scheduling, and revenue management. Despite being commonly used for implementing online allocation, the tightness of Alaei's procedure for a given $k$ has remained unknown. In this paper we resolve this question, characterizing the tight bound by identifying the structure of the optimal online implementation, and consequently improving the best-known guarantee for $k$-unit prophet inequalities for all $k>1$. We also consider a more general online stochastic knapsack problem where each individual allocation can consume an arbitrary fraction of the initial capacity. We introduce a new "best-fit" procedure for implementing a fractionally-feasible knapsack solution online, with a performance guarantee of $\frac{1}{3+e^{-2}}\approx0.319$, which we also show is tight. This improves the previously best-known guarantee of 0.2 for online knapsack. Our analysis differs from existing ones by eschewing the need to split items into "large" or "small" based on capacity consumption, using instead an invariant for the overall utilization on different sample paths. Finally, we refine our technique for the unit-density special case of knapsack, and improve the guarantee from 0.321 to 0.3557 in the multi-resource appointment scheduling application of Stein et al. (2020). All in all, our results imply \textit{tight} Online Contention Resolution Schemes for $k$-uniform matroids and the knapsack polytope, respectively, which has further implications in mechanism design

A THz Video SAR Imaging Algorithm Based on Chirp Scaling

In video synthetic aperture radar (SAR) imaging mode, the polar format algorithm (PFA) is more computational effective than the backprojection algorithm (BPA). However, the two-dimensional (2-D) interpolation in PFA greatly affects its computational speed, which is detrimental to the real-time imaging of video SAR. In this paper, a terahertz (THz) video SAR imaging algorithm based on chirp scaling is proposed, which utilizes the small synthetic angular feature of THz SAR and the inherent property of linear frequency modulation. Then, two-step chirp scaling is used to replace the 2-D interpolation in the PFA to obtain a similar focusing effect, but with a faster operation. Point target simulation is used to verify the effectiveness of the proposed method.Comment: 5 pages, 7 figure