Bimodal distribution detection and transformation for Gaussian merging for bearing fault classification of independent cart systems under nonstationary conditions

Independent cart systems (ICS) have emerged as transformative solutions in contemporary industrial automation, offering high-speed, precise, and flexible motion-control capabilities. Unlike conventional rotating machinery, ICS involve both rotational and translational motions as carts traverse predefined tracks, resulting in nonstationary and transient vibration signatures. These dynamics, combined with bidirectional operation and modularity, increase data complexity and challenge traditional bearing-fault diagnosis methods. This study presents a fully unsupervised, training-free diagnostic framework for bearing fault diagnosis in ICS, specifically addressing the high dimensionality, overlapping feature distributions, and false alarm susceptibility. A high-dimensional feature set was extracted from the system variables and multichannel vibration data, followed by ranking using five statistical techniques: one-way analysis of variance (ANOVA), Kruskal–Wallis, Laplacian score, variance, and monotonicity. Principal Component Analysis (PCA) is employed for dimensionality reduction; however, the resulting feature distributions often exhibit bimodal or overlapping characteristics that impair class separability. To address this, we introduce a lightweight transformation methodology that detects bimodal distributions using Kernel Density Estimation, applies clustering-based separation, and adaptively shifts and scales features to improve inter-class distinction. The proposed approach was validated using a publicly available dataset for various fault types and sizes, focusing on both inner and outer race bearing defects. The results demonstrate significant improvements in classification performance using One-Class SVM and Isolation Forest, particularly for small faults such as FIR025 and FOR025, with post-transformation metrics exhibiting substantial improvements. Owing to its domain-agnostic design, computational efficiency, and independence from training or labeling, this method is well-suited for condition monitoring in industrial systems. • A lightweight, unsupervised method to detect and transform bimodal feature distributions into compact, Gaussian-like clusters. • Enhanced bearing fault detection in independent cart systems operating under non-stationary conditions. • Validated using a publicly available dataset collected from a laboratory-scale experimental setup. • Improved class separability through feature transformation; diagnostic performance is validated using One-class SVM and Isolation Forest. • Well-suited for online condition monitoring with practical applicability in embedded and real-time industrial systems.