Diagnosis of unbalanced rolling bearing fault sample based on adaptive sparse contrative Auto-encoder and IGWO-USELM

•We incorporate a sparse group objective function to consider the sparsity and generalization. Subsequently, the sparse and penalty coefficients are adaptively optimized using homotopy regularization.•Subsequently, the IGWO is used to dynamically optimize the USELM's penalty coefficient and neighbor number.•Three fault datasets are used to validate the proposed method. Additionally, the proposed method exhibits a high degree of contractive accuracy when dealing with unbalanced fault samples. Importantly, the proposed method maintains a high level of robustness even in the presence of noise interference. At present, numerous deep learning techniques are being used in fault diagnosis with good effects. However, obtaining a sample of a fault may be difficult in certain circumstances. Moreover, the distribution of the sample is highly unbalanced. Typically, when the sample size is unbalanced, deep learning methods exhibit the phenomenon of overfitting, which results in a lack of generalizability and precision. In this paper, we proposed an adaptive sparse contractive auto-encoder (ASCAE) and an improved gray wolf optimization unsupervised extreme learning machine (IGWO-USELM) model for diagnosing unbalanced rolling bearing faults. First, CAE was improved by employing sparse graph embedding. Additionally, homotopy regularization was utilized to optimize sparse coefficients. Consequently, the effect of fault feature extraction was improved. The IGWO model was improved using Tent chaotic mapping to compensate for the fault sample’s sparse information. Subsequently, we used the IGWO to dynamically optimize USELM's performance. Accordingly, the IGWO-USELM model was developed. The ASCAE was used to extract multi-layer features from the vibration signal. Additionally, the extracted features were fed into the IGWO-USELM fault diagnosis model. Lastly, we performed experimental analysis on the fault dataset from Case Western Reserve University and the two real datasets. The results demonstrate that our method is capable of extracting time–frequency features of high faults. The proposed method is the most accurate when the fault samples are unbalanced. It has demonstrated excellent performance, particularly on the real-world fault dataset. When noise is present, the proposed method exhibits excellent noise immunity and a short run time. A further advantage is that it can be used to perform real-time bearing fault diagnosis.