###### Abstract
[18] proposed a fault diagnosis method based on a Multi-channel Residual Attention Network with Efficient Channel Attention (ECA-MRANet), where the original time-domain signal is processed through multi-domain transforms and features are extracted using MRANet. These features are then fused by ECA for fault identification. [PERSON] et al. [19] introduced the ISCV-ViT method for rolling bearing fault diagnosis, utilizing motor current signals (MCS) and the Vision Transformer (ViT) model. This method processes the MCS using an instantaneous square current value (ISCV)-based signal processing technique to convert the signal into time-domain images, which are then used for fault diagnosis with the ViT model. [PERSON] et al. [20] proposed a fault diagnosis method based on a deep residual network combined with transfer learning (ResNet-TL), where one-dimensional vibration signal data are preprocessed into image data and the ResNet34 network is trained using transfer learning. Experimental results with datasets from both a practical test bench and Case Western Reserve University demonstrate that the ResNet34-TL model outperforms other classification models in fault diagnosis. [PERSON] et al. [21] proposed a rolling bearing fault diagnosis method combining VMD and Artificial Neural Networks (ANN), achieving high prediction accuracy with reduced computation time. The method demonstrated an average prediction accuracy of 99.3% with a computation time of only 2.4 s, outperforming other machine learning and deep learning algorithms. [PERSON] et al. [22] introduced an intelligent fault diagnosis method for rolling bearings, using a one-dimensional multi-scale residual convolutional neural network (1D-MRCNN) for feature extraction and fault-type identification. Both simulation and experimental results show that the method accurately diagnoses various fault types, even under different noise levels. [PERSON] et al. [1] proposed a multi-scale rolling bearing fault diagnosis method based on transfer learning. Experimental results with datasets from Case Western Reserve University and Jiangnan University indicate that this method achieves high diagnostic accuracy. The methods mentioned above have several common limitations, including reliance on complex models and optimization algorithms, which result in high computational complexity. Some methods also require careful parameter tuning and data preprocessing, which can lead to long model training times [23]. Furthermore, the generalizability and adaptability of certain methods may be limited by the specific datasets and fault types considered. To address the limitations of traditional methods, such as high computational complexity, sensitivity to noise, and dependence on parameter tuning, this paper proposes an IGTO to enhance the performance of VMD and LSTM in signal processing. The method introduces Circle chaotic mapping to increase population diversity, utilizes Lens-based Opposite Learning (LOBL) to optimize local search capabilities, and incorporates an Adaptive \(\beta\) Hill Climbing (A\(\beta\)HC) mechanism to improve global search efficiency. These improvements overcome the tendency of traditional GTO to get trapped in local optima when dealing with high-dimensional and complex optimization problems. VMD, as an efficient signal processing method, is particularly suitable for the analysis of non-stationary signals. It avoids the problem of mode mixing and provides clearer modal separation, demonstrating strong signal analysis and processing capabilities [24; 25; 26]. LSTM, by introducing gating mechanisms, successfully addresses the vanishing gradient problem in traditional recurrent neural networks (RNNs) when handling long-term dependencies. It selectively remembers and forgets information, maintains essential long-term dependencies, and exhibits strong adaptive learning capabilities, a stable training process, and efficient parallel computation, making it particularly suitable for analyzing complex sequential signals [27; 28].