A three-dimensional clustering study of gearbox system failures based on frequency-domain feature structure analysis

In actual operation, vibration signals from gearbox systems are susceptible to load fluctuations, speed variations, and environmental noise. The spectral differences between various fault states are often subtle, resulting in blurred sample boundaries and posing challenges for structural separation and state analysis. To address the aforementioned issues, this paper establishes a three-dimensional (3D) feature structure analysis framework based on frequency-domain statistical characteristics to investigate the structural distribution properties of gearbox vibration data. First, extract frequency-domain statistical features such as dominant frequency, energy, and bandwidth to construct a feature matrix. We then analyze the distribution patterns of different features in the sample space through two-dimensional projection analysis, identify key features that contribute significantly to the structure, and, by considering the correlations among features, perform structural consolidation and weighted fusion of features with similar trends to reduce the impact of redundant information on structural representation. Based on this, a 3D feature space is constructed to visualize the distribution patterns of samples under different operating conditions, and the structural separability is verified using the contour coefficient and various clustering methods. Experimental results demonstrate that, using field data and publicly available datasets that include various rotational speeds and multiple types of component failures, samples of different failure states all form distribution structures in 3D space characterized by clear boundaries and intra-class compactness, with contour coefficients all exceeding 0.92. Furthermore, the extracted feature sets exhibit a certain correspondence with fault vibration characteristics, indicating that this method is capable of effectively capturing the structural differences between various fault states under complex operating conditions. This provides a reliable feature foundation for gearbox system condition assessment, fault diagnosis, and subsequent intelligent recognition.