## 1 Introduction
The GWO algorithm [13] is a heuristic method with strong global optimization searchability, which is more advantageous than other intelligent algorithms in finding the best parameter combination. [PERSON] et al. [14] successfully applied GWO to fault detection and verified the feasibility of GWO in the field of fault detection. However, the GWO algorithm still has some weaknesses, such as premature convergence of the algorithm, poor solution accuracy, and the tendency to fall into local optimality on some complex problems [15; 16]. Therefore, many scholars have conducted relevant studies to improve the performance of GWO [17; 18; 19]. It has been demonstrated through existing research that there is significant room for performance improvement in the grey wolf algorithm. This study focuses on the following aspects to overcome these weaknesses. Firstly, a new non-linear convergence factor is designed to maintain a proper balance between exploration and exploitation. Secondly, Levy flight [20] is introduced to enhance the exploration capability of the algorithm by increasing the population diversity. Finally, an adaptively tuned position update strategy is utilized to speed up the convergence of the algorithm. This article proposes an improved grey wolf optimization algorithm (IGWO) based on the above strategies. Because the signal with a periodic pulse feature of the fault feature has strong signal sparsity, its envelope entropy is small, and conversely, its envelope entropy is larger. Therefore, the minimum envelope entropy [21] is introduced as the fitness function of the optimization algorithm, and the method of optimizing VMD parameters based on IGWO (IGVMD) is designed to extract bearing fault features. The essence of bearing fault diagnosis is actually a classification problem. Many classification algorithms such as shallow artificial neural networks (ANNs), support vector machines (SVMs), and convolutional neural networks (CNNs) have been proposed for classification problems in engineering applications. Compared with traditional machine learning algorithms, deep learning algorithms [22] have greater advantages in dealing with massive, high-dimensional, and noisy data, and can automatically and efficiently extract fault characteristics from massive data. Convolutional neural networks (CNNs) have achieved better results for mechanical faults [23]. Other commonly used methods, such as CNN-based VGG [24], ResNet [25], and other network architectures, have achieved great success in computer vision and successfully applied to fault diagnosis. [PERSON] et al. [26] proposed a fault diagnosis method by converting original vibration signals into two-dimensional feature maps and feeding them into a CNN for training. [PERSON] et al. [27] combined the continuous wavelet transform (CWT) method, the CNN model, and an extreme learning machine (ELM) classifier to extract high-level fault features. [PERSON] et al. [28] developed a novel multiscale convolutional neural network (MSCNN) to extract multiscale features of gearboxes and simultaneously recognize fault conditions. However, important features such as periodic or short-time pulse features are easily lost when they are transformed into two-dimensional feature maps. To avoid the abovementioned problems, [PERSON] et al. [29] proposed the one-dimensional CNN method, which can directly extract the best features from vibration data. Compared with the two-dimensional CNN, it has higher recognition accuracy and faster convergence speed. [PERSON] et al. [30] realized fault identification of rolling bearings through a one-dimensional CNN and had a strong generalization ability. Inspired by [PERSON] and [PERSON] et al., one-dimensional convolution is used to improve structures such as deep convolutional generative adversarial networks [31], residual neural networks [32], and long-short memory networks [33]. [PERSON] et al. [34] applied the VMD method as a depression filter to eliminate the dominant modes and then input the features into a one-dimensional CNN model for fault diagnosis.