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.
Highlights
When the operating speed of a high-speed train reaches 300 to 380 km/h, the vibration environment experienced by its on-board equipment becomes harsher, and increasingly more fatigue failures, such as cracks in the components, the deformation and dropping of parts, and the loosening of fasteners, are triggered by the vibrations
The results show that the PSD obtained by using the proposed method for Gaussian vibration data is very close to that obtained by using the statistical tolerance method, demonstrating that the induction accuracy of the proposed method is high for Gaussian vibration data
The power spectral density data belonging to the same population are merged into the same feature sample, and the probability density function of all power spectral density data at the first frequency point is calculated through the kernel density estimation method
Summary
When the operating speed of a high-speed train reaches 300 to 380 km/h, the vibration environment experienced by its on-board equipment becomes harsher, and increasingly more fatigue failures, such as cracks in the components, the deformation and dropping of parts, and the loosening of fasteners, are triggered by the vibrations. To solve the problem of the induction of measured non-Gaussian vibration data, the Johnson or Bootstrap method is often used These two methods can convert non-Gaussian data into data that approximately obey a normal distribution, but their transformation process is not always effective; at the same time, more intermediary conversions will increase the estimation error [15]–[18]. With the kernel estimation method [19]–[22], there is no need to assume in advance that the data obey a certain specific standard parameter distribution, and this method can directly fit the Probability Density Function (PDF) of the data sample Due to this unique advantage, this method has attained wide application for Gaussian or non-Gaussian data processing in many fields, such as engineering, medicine, finance, and the Internet [23]–[27]. The induction method is verified to have very good universality and estimation accuracy
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