###### Abstract  
To address the issue of rolling bearing fault diagnosis, this paper proposes a novel model combining the Improved Gorilla Troop Optimization (IGTO) algorithm, Variational Mode Decomposition (VMD), Permutation Entropy (PE), and Long Short-Term Memory (LSTM) networks. The IGTO algorithm is used to optimize the parameters of VMD and LSTM, enhancing signal decomposition and feature extraction. The proposed model achieves fault classification accuracies of 96.67% and 98.96% in the testing and training phases, respectively, on the Case Western Reserve University dataset, with minimal accuracy fluctuations. Furthermore, on the Jiangnan University dataset, the model reaches an average testing accuracy of 98.85%, with the highest accuracy reaching 99.48%. The results also demonstrate high stability, as indicated by low standard deviations (1.2148 and 1.3217) and narrow 95% confidence intervals ([95.75%, 97.58%] and [96.73%, 97.49%]). Despite a longer average runtime of 13.88 s per sample, the model's superior accuracy justifies the computational cost. These results demonstrate the model's excellent diagnostic performance, adaptability to different datasets, and practical applicability for rolling bearing fault diagnosis. This approach provides a valuable reference for predictive maintenance and fault detection systems in industrial applications. rolling bearing; fault diagnosis; improved gorilla troops optimization; variational mode decomposition; long-term memory network +
Footnote †: journal: Applied sciences  
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vibration signals generated by the bearingss during operation. These signals are typically non-stationary and contain a mixture of different fault features, influenced by factors such as load, speed, and temperature. Advanced signal processing methods are therefore needed to isolate meaningful patterns, enabling effective fault detection and diagnosis [6]. Significant advancements have been achieved in signal processing methodologies. [PERSON] et al. [7] proposed the RIME-VMD method for rolling bearing fault diagnosis, optimizing VMD using the RIME algorithm. This method improves feature extraction and achieves efficient fault detection by utilizing Support Vector Machine (SVM), resulting in faster search times and higher efficiency. [PERSON] et al. [8] introduced the Whale Gray Wolf Optimization Algorithm (WGWOA)-VMD-SVM method, which combines Whale Optimization and Gray Wolf Optimization to optimize both VMD and SVM, achieving 100% fault detection accuracy. [PERSON] et al. [9] also proposed the Sparrow Search Algorithm (SSA)-VMD method for rolling bearing fault diagnosis, optimizing VMD parameters using the SSA and integrating it with SVM for classification. [PERSON] et al. [10] developed the Optimized Grass-hopper Optimization Algorithm (OEGOA)-VMD algorithm for early fault detection in cryogenic rolling bearings, combining OEGOA with VMD to optimize parameter extraction and avoid local optima in fault feature extraction. [PERSON] et al. [11] presented a fault diagnosis method using (bat algorithm)BAS-optimized VMD and Composite impact index (CS)-SVM, which was verified with both simulation and real bearing data, demonstrating its effectiveness. [PERSON] et al. [12] proposed a fault diagnosis method using Marine Predator Algorithm (MPA)-optimized VMD, employing the Squared Envelope Gini Index (SEGI) to identify the best IMF for fault feature extraction, with experimental results showing superior accuracy and robustness compared to kurtosis and correlation coefficient indicators. However, the methods mentioned above often rely on optimization algorithms, which result in high computational complexity [13], sensitivity to noise [14], dependence on parameter selection [15], limited generalizability [16], and increased model complexity [17], thereby posing challenges to real-time implementation and practical applications. [PERSON] et al.