## 1 Introduction
ELM uses random weights between the hidden layer and the input layer in the forward neural network. A method of destructive or adding regular terms is used to solve the output weights in the final output layer to achieve regression or classification [36; 37; 38]. In Reference [39], ELM was used for identification of bearing faults. Although ELM is fast and has strong generalization ability, it is limited by a hidden danger of fitting. Random forest (RF) is an advanced classifier. Training of RF is fast and easy to parallelize and it can handle data with high dimensions [40]. Therefore, RF is an effective and frequently used classifier for classifying bearing faults. In Reference [41], Relieff ranking was used to rank the fault features obtained by calculating the statistical characteristics of the signal in the time domain and random forest was further used to identify bearing faults. In Reference [42], [PERSON] extracted the fault features of bearings by using the wavelet packet decomposition and the classification was completed by RF. In Reference [43], an intelligent fault diagnosis approach was presented with the combination of ensemble empirical mode decomposition and RF. In Reference [44], variational mode decomposition was combined with autoregressive model parameters to extract the fault features and RF was used for pattern recognition. The analysis results show that RF has a higher accuracy compared to SVM, genetic algorithm-SVM (GA-SVM) and particle swarm optimization-SVM (PSO-SVM). However, RF is a parameterized classifier and the selection of the parameters of random forest will affect the accuracy of classification. Considering that the fast spectral correlation is an advanced fault feature extraction technique and the RF is an excellent classifier. The main work of this paper was conducted on the basis of the fast spectral correlation and RF. To complete the accurate fault diagnosis of rolling bearings, an improved fast spectral correlation approach was proposed in this paper by introducing the kurtosis weighting to effectively decrease the effect of noise and highlight the fault characteristics. Moreover, a particle swarm optimization-random forest (PSO-RF) classification algorithm was proposed, which can adaptively optimize the parameters and improve the classification accuracy of RF. On the basis of the advantages of the improved fast spectral correlation and PSO-RF, a fault diagnosis method for rolling bearings was proposed with the combination of improved fast spectral correlation and PSO-RF in this work. The improved fast spectral correlation was firstly employed to extract the fault feature vectors of the faulty bearings. Then, the state classification of rolling bearings can be accomplished by training and testing the obtained fault feature vectors using the PSO-RF classifier. This paper is structured as follows. In Section 2, an approach of fault feature extraction based on the improved fast spectral correlation method is given briefly. Section 3 describes the details of random forest based on particle swarm optimization. Section 4 introduces the framework of the proposed method. In Section 5, the experiments are presented to investigate and validate the proposed method for state recognition of rolling bearing. Finally, conclusions are drawn in Section 6.