## 1 Introduction  
As a basic part of mechanical equipment, rolling bearing is often one of the fuses of equipment failure [1, 2, 3]. As most of the mechanical equipment in industrial production is in a very noisy environment, it is difficult to find the early weak failure, and, even when the mechanical equipment has a more serious failure caused by the early weak failure, it is still impossible to judge the problem manually [4, 5, 6]. Therefore, the main purpose of the study is to extract the weak signal characteristics of mechanical equipment under strong noise so as to implement weak fault diagnosis. Empirical mode decomposition (EMD) is a widely used time-frequency analysis method, which is extremely suitable for analyzing nonlinear and nonstationary signals because it stabilizes the signal by decomposing [7]. [PERSON] et al. [8] used variational mode decomposition for fault diagnosis of the rolling bearings. [PERSON] et al. [9] used wavelet packet to modulate bearing signals, and then EMD was used to extract fault features. [PERSON] et al. [10] combined EMD with fast Fourier transform (FFT). In this method, the useless high-frequency noise components and useful high signal-to-noise ratio (SNR) components were decomposed by using EMD, and fast Fourier transform was performed on useful components. At present, most of the weak signal features are extracted through noise suppression, which is effective but also has problems: it inhibits both noise and target features at the same time. When the noise intensity is low, it may have little effect; however, when the noise intensity is high, the weak fault features may become more difficult to extract. The theoretical basis of stochastic resonance is quite different from traditional noise suppression methods. It transfers the noise energy to the low-frequency region with weak features and strengthens the weak signal features by weakening and transferring noise. Therefore, it is of great significance for weak signal feature extraction under strong noise. Variational mode decomposition (VMD) and analytical mode decomposition are used to extract features of multi-steady stochastic resonance. [PERSON] [11] studied the structure of multi-steady signal-noise ratio(SNR) and influence of parameters, and the average output SNR was taken as the objective function of the multi-steady stochastic resonance output. The composite fault signals were used for simulation verification. [PERSON] [12] made use of the advantages of multi-steady state and wavelet transform to realize the bearing fault detection. [PERSON] et al. [13] developed a new fault feature extraction method for bearing prognostics. Two real bearing run-to-failure test datasets are used to demonstrate the effectiveness. [PERSON] et al. [14] proposed a fault feature extraction method for bearings to realize bearing fault diagnosis. [PERSON] et al. [15] proposed a multi-scale alternating direction multiplier method in order to extract a fault impact signal. In addition, some signal feature extraction methods have been proposed in recent years [8; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. EMD has been recognized by scholars and further studies since it was proposed [27]. It has been widely used in the field of fault diagnosis of rolling bearings and has shown many advantages and conveniences, but it also has some disadvantages. In order to overcome its disadvantages, a chaotic ant colony optimization algorithm with global optimization capability is introduced to adaptively adjust the parameters of the second-order trustable stochastic resonance system to obtain optimal stochastic resonance, and a fault diagnosis method based on CASTSR and EMD is proposed in this paper. In the proposed method, the interference components of low frequency are filtered by high-pass filtering, the limitation of stochastic resonance theory is solved by using an ordinary variable-scale method, and a high-frequency signal is transformed into a low-frequency signal far lower than 1 Hz.