Adaptive distribution transformation for enhanced bearing fault detection in independent cart systems

: Unlike conventional rotary systems, where bearings remain fixed around a single axis and experience only rotational motion, bearings in independent cart systems exhibit coupled translational-rotational motion and highly nonstationary dynamics. This simultaneous translational-rotational motion of the bearings along the guide rail results in time-varying vibration signatures, complicating fault diagnosis using conventional methods. Furthermore, each cart in an independent cart system is supported by multiple rolling bearings, and industrial machines involve hundreds of carts operating simultaneously, resulting in a large number of interacting bearings whose condition monitoring is both challenging and highly desirable. This study proposes an adaptive distribution-based feature transformation method to enhance the detection of bearing faults under complex operating conditions. The proposed method effectively reshapes the skewed, bimodal, and high-variance feature distributions commonly observed in vibration signals from independent cart systems, thereby improving class separability without the need for labeled data or deep learning architectures. The approach was validated on the open-access bearing dataset based on independent cart systems comprising single- and three-cart experiments and benchmarked against established transformations including Box-Cox, Yeo-Johnson, Rotation-Based Iterative Gaussianization, hyperbolic power transformation, Cumulative Density Function - Transform-and-Shift, dip test based extraction, and Dip transformation. The results demonstrate that the proposed transformation produces compact, well-separated clusters in principal component analysis and t-distributed stochastic neighbor embeddings, achieving very high F1-scores under both One-Class Support Vector Machine and isolation forest anomaly detection methods. The proposed method exhibited robustness against broadband, narrowband, and structural noise, presenting a geometry-agnostic and computationally efficient alternative for real-time bearing diagnostics in non-stationary industrial environments.