## 1 Introduction
addressed the situation of insufficient data samples by incorporating the convolutional auto-encoder (CAE) and enhanced convolutional neural network (ECNN) to extract deep features [16]. [PERSON] et al. constructed an extended model of faulty samples by migration learning and deep convolutional generative adversarial network (DCGAN) to solve the small sample infrared image fault diagnosis [17]. Thus, it can be seen that the criteria for feature selection are either difficult to develop or difficult to understand. Even if the identified best features are selected, it is difficult to ensure the optimal and minimum number of features. So, the way of feature selection needs to be improved. Whether the data features are extracted from the infrared images as a way to characterize the images or the deep features of the images are constructed directly using deep learning, the later articulated methods are basically like those used for vibration and acoustic emission signals. [PERSON] et al. used decision tree (DT), linear discriminant analysis (LDA) and SVM for fault diagnosis of electric motors, respectively, and eventually SVM proved to be superior for diagnosis [18]. [PERSON] used a nearest neighbor classifier and back propagation neural network for fault diagnosis of infrared images of electric drills [19]. [PERSON] et al. acquired infrared images to extract pixel points in the x- and y-axis directions of the pixel histogram, light moments and Gini coefficients as data features and finally classified them using a random forest (RF) model [20]. [PERSON] et al. used SoftMax for classification after 2 DCNN [21]. In conclusion, machine learning and deep learning are heavily cited for infrared image troubleshooting of machinery or electricity. However, machine learning often possesses data dependency and poor generalization of the models. Deep models, on the other hand, are time-consuming, resemble a \"black box\" and do not have good explanatory power. In 2018, [PERSON], [PERSON] proposed the Broad Learning System (BLS), which is a random vector function linked neural network. It contains only a single layer of hidden layers and is expanded incrementally in a transversal manner anytime when faced with a learning inaccuracy. It greatly solves the problem of long training time for deep learning [22]. [PERSON] et al. extracted features describing temporal and spatial distribution from infrared images of power equipment and finally diagnosed them using BLS [23]. [PERSON] et al. used double-tree complex wavelets to decompose vibration signals of bearing faults, extracted sub-bands as feature vectors and finally completed fast fault classification using BLS [24]. [PERSON] et al. proposed TSK-BLS, which can be calculated quickly and accurately by pseudo-inverse and symmetric methods and has good fault diagnosis advantages [25]. Therefore, the introduction of width learning into the field of fault diagnosis has some practical significance. However, the parameters of the network model can have an impact on the accuracy. The parameters provided by the original authors are used in the above application of BLS for fault diagnosis. Some BLS-based fault diagnoses are aimed at the internal algorithms, which all use manually set parameters, generally for test verification or manual experience, and do not guarantee the best accuracy. [PERSON] et al. defined connection weight matrices for inter-class and intra-class graphs to improve the fault diagnosis accuracy considering the sameness between similar samples and the difference between different classes of samples [26]. However, their parameters are set to fixed values based on manual experience, which may miss the optimal accuracy. Therefore, it is very necessary work to perform an optimization search for the parameters. Infrared thermal images often contain more complex and stronger noise than ordinary optical images due to factors such as spatial and temporal environment and detection equipment.