## 1 Introduction
[25] proposed variational mode extraction (VME), an approach derived from VMD. By accurately determining the center frequency \(\omega\) and penalty factor \(\alpha\), VME efficiently isolates the desired mode components, significantly reducing the computation time. This method has been effectively applied to fault diagnosis of rolling bearings. [PERSON] et al. [26] combined VME with an improved one-dimensional convolutional neural network for the intelligent diagnosis of rolling bearings. However, the selection of the VME parameters was based on empirical judgment, raising concerns about its reliability. [PERSON] et al. [27] employed the whale optimization algorithm to refine the parameters of VME, integrating this improved algorithm with the k-nearest neighbor algorithm (KNN). [PERSON] et al. [28] proposed a window fusion strategy that adaptively determines the center frequency \(\omega\) and penalty factor \(\alpha\). Despite this innovation, their method still necessitates manual intervention for fault identification, highlighting a gap in the development of fully automated, intelligent diagnostic systems. In recent years, intelligent fault diagnosis has emerged as a novel and increasingly popular approach. Common methodologies in this domain include the back-propagation neural network (BPNN), support vector machine (SVM), and random forest (RF). These techniques are adept at determining the health status of bearings through effective feature selection and extraction. However, the manual process of feature extraction remains time consuming. Identifying features that are highly sensitive to vibration signals and filtering out noise remain significant challenges. Deep learning, a subset of machine learning, has attracted research interest in recent years, especially with the advancements in computational capabilities and sensor technology [29]. [PERSON] et al. [30] used stacked autoencoder structures for feature extraction and fusion to achieve an enhanced condition assessment, demonstrating its effectiveness for fault diagnosis across various bearing technologies. The convolutional neural network (CNN) [31; 32], primarily recognized for its applications in image processing, leverages a local receptive field, shared weights, and subsampling within a spatial domain. This approach significantly reduces the computational demands on the network, minimizes the risk of overfitting, and facilitates the automatic extraction of crucial signal features [33]. CNNs are typically employed for pattern recognition using two approaches: directly using the vibration signal as the input and preprocessing the vibration signal into a two-dimensional image for model input. The latter often involves transforming the vibration signal into a grayscale image [34; 35], or converting it into a time-domain image through continuous wavelet transform or short-time Fourier transform [36; 37; 38; 39]. Despite the success of two-dimensional CNNs in intelligent fault diagnosis [40; 41], vibration signals are inherently one-dimensional sequences. Converting them into two-dimensional images necessitates extra preprocessing, potentially exaggerating the impact of periodic shock signals and reducing diagnostic efficacy in noisy conditions. Consequently, some scholars have explored directly using one-dimensional vibration signals as inputs for diagnosis via a 1D-CNN. For example, [PERSON] et al. [42] employed vibration and acoustic signals as inputs for a 1D-CNN in their diagnostic models; [PERSON] et al. [43] utilized VMD-preprocessed vibration signals with a 1D-CNN for diagnosis; and [PERSON] et al. [44] applied a 1D-CNN for fault feature extraction and trained an SVM on rolling bearing fault diagnosis. However, traditional 1D-CNNs face the challenges of computational demand and limited noise immunity. To overcome these issues, this study proposes a one-dimensional multi-scale residual convolutional neural network (1D-MRCNN), designed to lower the computational costs and enhance noise resistance.