A Super Fast Algorithm for Estimating Sample Entropy

A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling

The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of O(N2) for the series with N length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on N. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm's speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a 40% reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only 30% of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency.

Fault Diagnosis for Rolling Bearing of Combine Harvester Based on Composite-Scale-Variable Dispersion Entropy and Self-Optimization Variational Mode Decomposition Algorithm

Because of the influence of harsh and variable working environments, the vibration signals of rolling bearings for combine harvesters usually show obvious characteristics of strong non-stationarity and nonlinearity. Accomplishing accurate fault diagnosis using these signals for rolling bearings is a challenging subject. In this paper, a novel fault diagnosis method based on composite-scale-variable dispersion entropy (CSvDE) and self-optimization variational mode decomposition (SoVMD) is proposed, systematically combining the nonstationary signal analysis approach and machine learning technology. Firstly, an improved SoVMD algorithm is developed to realize adaptive parameter optimization and to further extract multiscale frequency components from original signals. Subsequently, a CSvDE-based feature learning model is established to generate the multiscale fault feature space (MsFFS) of frequency components for the improvement of fault feature learning ability. Finally, the generated MsFFS can serve as the inputs of the Softmax classifier for fault category identification. Extensive experiments on the vibration datasets collected from rolling bearings of combine harvesters are conducted, and the experimental results demonstrate the more superior and robust fault diagnosis performance of the proposed method compared to other existing approaches.

Analysis of Wide-Frequency Dense Signals Based on Fast Minimization Algorithm

To improve the detection speed for wide-frequency dense signals (WFDSs), a fast minimization algorithm (FMA) was proposed in this study. Firstly, this study modeled the WFDSs and performed a Taylor-series expansion of the sampled model. Secondly, we simplified the sampling model based on the augmented Lagrange multiplier (ALM) method and then calculated the augmented Lagrange function of the sampling model. Finally, according to the alternating minimization strategy, the Lagrange multiplier vector and the sparse block phasor in the function were iterated individually to realize the measurement of the original signal components. The results show that the algorithm improved the analysis accuracy of the WFDS by 35% to 46% on the IEEE C37.118.1a-2014 standard for the wide-frequency noise test, harmonic modulation test, and step-change test, providing a theoretical basis for the development of the P-class phasor measurement unit (PMU).