Research and application of Volterra series theory in rolling bearing fault state feature extraction

Guo

Mathematical Problems in Engineering

et al. 2022

In the process of extracting the characteristic frequency of the fault signal of the rolling bearing in the mechanical system, the signal transmission paths between the fault points inside the bearing and the sensor are diversified, which will produce compound faults of different forms and combinations. These composite faults will lead to a series of serious consequences such as distortion and aliasing of the fault characteristic spectrum. In order to solve these problems, this paper proposes a composite fault feature separation method for rolling bearing based on the mixed function decoupling model. Firstly, the functional series model of the fault system is established, and some kernel functions of functional series are obtained. Secondly, the coupling frequency relationship is established and the recursive search algorithm of frequency energy is applied to decouple the compound fault coupling frequency into a single fault frequency feature set. Finally, the threshold method of fault characteristic frequency energy entropy is utilized to optimize the single fault frequency feature set and identify the true and false features, so as to identify each characteristic frequency point of the composite fault. Experimental results show that, under the condition of low SNR, the proposed method can decouple no more than three typical composite fault signals without depending on the signal filter.

Section: Introductionmentioning

confidence: 99%

Mathematical Problems in Engineering Research on Composite Fault Separation of Rolling Bearing Based on Functional Mixing Decoupling Model

Guo

Mathematical Problems in Engineering

et al. 2022

Fault Evolution Characteristic Analysis of Planetary Gear Based on Multidimensional Nonlinear Frequency Response

Tao

Journal of Computational and Nonlinear Dynamics

et al. 2019

This study presented a method for modeling the nonlinear system of a planetary gearbox and the fault diagnosis of a crack in a planetary gear based on the Volterra series theory. First, the exponential Hilbert reproducing kernel and its fast optimization algorithm was proposed and deduced in theory, and the fast solution of the fourth-order kernel of the Volterra series was successfully solved. Second, the Volterra series model estimation was compared with the least squares estimation of the actual collected signals from the planetary gearbox and the time-domain output signal was estimated using a neural network. The accuracy and the superiority of the Volterra series model of the planetary gearbox were then verified. At the same time, the convergence and the memory length of the Volterra series were discussed. In order to further mine and extract fault feature information, coupling relationship between the generalized frequency response of higher order spectrum of the Volterra series model and fault frequency was also studied. This study attempted to reflect the fault state and fault degree of a crack in a planetary gear from different observation angles and dimensions. Finally, the real condition loading test of a gearbox's comprehensive fault test platform was carried out. The validity of the method of nonlinear system modeling and fault diagnosis of the planetary gearbox, based on the Volterra series theory, was verified, and a new solution has been provided for related research in this field.

Research on Fault Evolution Feature Extraction and Identification of Sun Gear Cracks in Planetary Gearbox Based on Volterra High-Order Kernel Generalized Frequency Response Graphic Analysis

Kang

Mathematical Problems in Engineering

et al. 2018

Self Cite

In this paper, relying on the Volterra series nonlinear system model and the high-order kernel Hilbert’s reconstructed kernel fast solved algorithm, a fault feature frequency domain identification method based on Volterra high-order kernel generalized frequency response graph analysis is proposed. Firstly, the method uses the system input and output vibration signals to determine the Volterra model. Then, the Volterra high-order kernel function is solved quickly by reproducing kernel Hilbert space method, and the generalized frequency response function is used to identify the model. Finally, multidimensional high-order spectral pattern analysis is used to separate and extract the fault and degree characteristic information implied by frequency and phase coupling in the third-order kernel function. Following the theoretical approach, in the experimental part, this paper uses the planetary gearbox fault loading test rig to complete the data collection and establishes the Volterra experimental model through the measured data. The generalized frequency responses of each order kernel function are compared and analyzed and the capability of distinguishing and the adaptability of different order kernel functions for the degree of crack failure are discussed. The effects of changing the memory length of the Volterra model and the order of the kernel function on the recognition result are verified. The final experimental results show that the use of reproducing kernel Hilbert space can effectively avoid the dimension disaster problem that occurs in the high-order kernel solution process. Moreover, the third-order kernel can describe more intuitively the nonlinear system model under multifactor coupling than the second-order kernel. Finally, Volterra series model the third-order kernel’s generalized frequency response can effectively distinguish between nondefective and faulty gears, and its resolution is enough to distinguish the degree of failure of gear cracks.