The unknown fault diagnosis technology in industrial systems implies significant engineering application value and opportunities. The difficulty stems from the fact that the unknown fault samples frequently originate from the diagnostic model’s unknow distribution, leading to an out-of-distribution (OOD) problem. An incorrect diagnosis in the diagnostic model might readily arise from this. To deal with this problem, this article proposes a novel trustworthy fault diagnosis with OOD detection which can be applied on industrial systems and equipment. First, deep base learners (DBLs) with different activation functions are designed to construct the deep ensemble model. After that, use in-distribution (ID) inputs to train the initial deep ensemble model. Then, with the proposed max consistency and min similarity guided criterion, the DBLs of the initial ensemble model are chosen to reconstruct the ensemble model. Finally, the diagnostic results’ uncertainty of the reconstruct ensemble model is estimated to accurately determine the type of the sample to be diagnosed. To verify the effectiveness of the proposed method, two gearbox data sets were used to test the proposed method and the max consistency and min similarity guided criterion. The experimental results demonstrate that the proposed approach can accurately identify unknown fault samples in the gearbox.

Fault diagnosis under distribution shifts induced by previously unseen operating conditions is of significant practical value. The main challenge lies in the lack of data from unseen conditions, which prevents diagnostic models from capturing the corresponding distribution patterns, resulting in degraded prediction accuracy. To address this issue, we propose a fault diagnosis framework aimed at enhancing generalization against distribution shifts arising from unseen operating conditions, with its effectiveness validated specifically on gearbox diagnostics. Our approach first employs a modified 1-D stable diffusion model to generate samples under unseen operating conditions. Concurrently, adversarial samples are supplied from monitoring data under known operating conditions using the fast gradient sign method to further enhance model robustness. Then, the monitoring samples, the synthetic samples, and the adversarial samples are jointly used to train an uncertainty-aware deep learning (UDL) model until convergence. Finally, both the classification accuracy and prediction uncertainty of the UDL model are assessed. To validate the effectiveness of the proposed approach, two planetary gearbox datasets were employed for testing. Experimental results demonstrate that the proposed method is capable of accurately performing fault diagnosis under unseen operating conditions, thereby verifying its robustness and generalization capability.

To diagnose rotating machinery fault for imbalanced data, a method based on fast clustering algorithm (FCA) and support vector machine (SVM) was proposed. Combined with variational mode decomposition (VMD) and principal component analysis (PCA), sensitive features of the rotating machinery fault were obtained and constituted the imbalanced fault sample set. Next, a fast clustering algorithm was adopted to reduce the number of the majority data from the imbalanced fault sample set. Consequently, the balanced fault sample set consisted of the clustered data and the minority data from the imbalanced fault sample set. After that, SVM was trained with the balanced fault sample set and tested with the imbalanced fault sample set so the fault diagnosis model of the rotating machinery could be obtained. Finally, the gearbox fault data set and the rolling bearing fault data set were adopted to test the fault diagnosis model. The experimental results showed that the fault diagnosis model could effectively diagnose the rotating machinery fault for imbalanced data.

To diagnose rotating machinery fault for imbalanced data, a kind of method based on fast clustering algorithm and decision tree is proposed. Combined with wavelet packet decomposition and isometric mapping (Isomap), sensitive features of different faults can be obtained so the imbalanced fault sample set is constituted. Then the fast clustering algorithm is applied to search core samples from the majority data of the imbalanced fault sample set. Consequently, the balanced fault sample set consisted of the clustered data and the minority data is built. After that, decision tree is trained with the balanced fault sample set to get the fault diagnosis model. Finally, gearbox fault data set and rolling bearing fault data set are used to test the fault diagnosis model. The experiment results show that proposed fault diagnosis model could accurately diagnose the rotating machinery fault for imbalanced data.

The state of health (SOH) reflects the health status of the lithium-ion battery and is expected to accurately predicted, so as the corresponding maintenance measures can be taken to ensure the safe operation of the battery. This paper proposed a SOH prediction method based on multi-kernel relevance vector machine (RVM) and whale optimization algorithm (WOA). Firstly, the original features were obtained from the battery voltage and temperature data in charging and discharging phases. Secondly, the minimal-redundancy-maximal-relevance (mRMR) algorithm was introduced to select the optimal feature set. Then, the online model and offline model based on multi-kernel RVM and WOA were constructed. Finally, a hybrid model which combines the online model and offline model was proposed to prediction the SOH of the lithium-ion battery. The performance of the proposed method was evaluated with two kinds of data sets. The experimental results showed that the proposed method obtained higher prediction accuracy in both long-term and short-term periods than other methods.