###### Abstract
Its advancement and effectiveness have been demonstrated in previous studies [11; 12]. With signals processed by non-stationary analytical method, the non-stationarity of signals would be weakened to some extent, and fault features can be further extracted. Due to the smoothness and robustness, as well as fewer samples required, fuzzy entropy (FuzzyEn) [13] is introduced to measure the features of vibration data and construct fault samples, which has been widely applied for feature extraction and shows superior performance in the field of fault diagnosis [14; 15]. Fault diagnosis of rolling bearings is actually a problem of pattern recognition [16], and many machine learning methods have been developed for this problem [17]. Traditional machine learning methods require a large amount of labeled data to ensure the generalization of the algorithm. However, in practical problems, most of the samples are unlabeled, which results in unsatisfactory results of trained learning models in practical applications and makes a large number of unlabeled samples useless. Hence, semi-supervised methods are applied to fully exploit the information inside samples and expand the training set of machine learning algorithms. Semi-supervised fuzzy C-means clustering (SSFCM) [18] is a \"semi-supervised version\" of the fuzzy C-means clustering (FCM) algorithm. By introducing semi-supervised learning theory into FCM, training samples can be labeled under the supervision of the partly labeled samples, which makes up for the deficiency of labeled samples and improving the accuracy of pattern recognition [19; 20]. In engineering application, several machine learning methods, including k-nearest neighbor (KNN) [21], artificial neural network (ANN) [22], support vector machine (SVM) [23] and support vector data description (SVDD) [24] are widely applied to solve pattern recognition problems. KNN is easy to realize and susceptible to the distribution of samples. ANN has good performance in dealing with non-linear problems under the circumstance of a large number of samples. Based on structural risk minimization and statistical learning theory, SVM proposed by [PERSON] finds an optimal hyperplane that meets the classification requirements, thus the hyperplane maximizes the interval between two classes while ensuring classification effect. Correspondingly, SVDD is a kernel method inspired by the idea of SVM theory [25], which possesses a prominent recognition ability through establishing a minimum hypersphere that contains as many samples as possible [26]. Currently, combined with relative distance decision strategy, SVDD has been successfully employed in the field of pattern recognition [27; 28]. However, traditional relative distance decision strategy is difficult to accurately classify unknown samples locating in overlap regions of the hyperspheres and regions outside all the hyperspheres. To solve this problem, SVDD based on an improved decision strategy (ID-SVDD) with the fusion of KNN method is proposed. To be specific, support vectors (SVs) are firstly extracted by establishing SVDD models. Next, the Euclidean distances between the testing sample and SVs are calculated. Whereupon, a fault type of the testing sample can be determined according to the proposed decision strategy. Although SVDD has excellent effect in pattern recognition, its performance is affected by the parameters. In view of this, various optimization algorithms are proposed and applied to search the best parameters [29; 30], including genetic algorithm (GA) [31], particle swarm optimization (PSO) [32], bacterial foraging algorithm (BFA) [33] and artificial sheep algorithm (ASA) [34]. As a novel optimization algorithm, sine cosine algorithm (SCA) proposed by [PERSON] [35] is proved to be effective in many studies [36; 37]. To achieve better performance in convergence precision, a reformed sine cosine algorithm with adaptive strategy (ASCA) is developed in this paper.