Kernel Density Estimation Based Gaussian and Non-Gaussian Random Vibration Data Induction for High-Speed Train Equipment

Abstract

Because general statistics tolerance is not applicable to the induction of non-Gaussian vibration data and the methods for converting non-Gaussian data into Gaussian data are not always effective and can increase the estimation error, a novel kernel density estimation method in which induction is carried out on power spectral density data for the measured vibration of high-speed trains is proposed in this paper. First, data belonging to the same population of power spectral density are merged into the same feature sample. Then, the probability density function of all power spectral density values at the first frequency point is calculated through the kernel density estimation method, and the upper-limit estimate of all power spectral density values under the set quantile is obtained. This process is repeated, and the upper limit values of the power spectral density values at all frequency points can be obtained to convert the measured acceleration data to the acceleration power spectral density spectrum of the vibration test. Engineering examples are used to verify the proposed method. For the same Gaussian power spectral density data, the relative error between the root mean squares of the power spectral density spectrum obtained from induction by the kernel density estimation method and the statistics tolerance is 0.155% ∼ 1.55%; for the non-Gaussian power spectral density data, the acceleration power spectral density spectrum of the non-Gaussian vibration can be obtained with the induction by the kernel density estimation method. The proposed kernel density estimation method satisfies the induction requirements for the measured Gaussian and non-Gaussian vibration data of high-speed trains with two different distributions, and its induction results have very good universality and estimation accuracy.

Distribution line parameter estimation driven by probabilistic data fusion of D‐PMU and AMI

“…Therefore, The non‐parametric Kernel density estimation (KDE) approach is introduced to obtain the PD curve of TSE of the up‐stream smart meter. Histogram and kernel [34] concepts are deployed to estimate the non‐parametric probabilistic density model [35]. The kernels, like the Gaussian Kernel adopted by us or the Laplacian Kernel used in [3], with enhanced mathematical properties are selected to perform the nonparametric kernel density estimation of TSE.…”

4D Epanechnikov Mixture Regression in LF Image Compression

“…We determine the expression for the 4-D EK f µj ,Σj (ϕ) according to the principle that a kernel function K(x) must satisfy K(x)dx = 1 and K(x) 0 [40]. To simplify the calculation, we can firstly consider a basic form of the 4-D EK with sampleφ = (x,ŷ,ẑ,ŵ) T and Λ…”