## 1 Introduction  
Rapid technological development has brought automated and intelligent production processes to manufacturing. Numerical control (NC) machines are flexible, high-performance automated machines that can solve complex and sophisticated processing problems. NC machines play an important role in industries that rely on high precision, high productivity and strong adaptability. However, in practice, owing to tool damage or failure, NC machine processing performance degrades, even leading to scraping of the workpiece. According to our statistics, tool faults account for about 20% of machine failures. Therefore, monitoring and identifying NC machine tool faults in a timely and accurate manner has attracted considerable interest. However, it is a challenge to develop and adopt effective signal processing techniques that can discover the crucial damage information from responsive signals [1]. Owing to the high-speed friction between the tool and the workpiece, the tool is prone to faults such as surface damage or deformation that can lead to a decline in processing quality. The most common resolution is detection of faults by processing and analyzing signals measured by sensors. Traditional signal processing techniques in fault diagnosis include time-domain analysis [2; 3] and frequency-domain analysis [4; 5]. The main disadvantage of the above two techniques is that only single-domain information is utilized. Although this information may be enough in some simple systems, it is too little for many complex systems. The time-frequency analysis method was proposed to overcome the disadvantages of the above two methods by characterizing the signal in both time and frequency domains. Time-frequency analysis provides a solution to separate physical signals (such as vibrations, acoustic emissions, or cutting forces) in the frequency domain or in the time domain [6; 7]. The wavelet analysis method, which can be viewed as an extension of the conventional spectral technique, has been widely used in machinery fault diagnostics, including for rotators, bearings and gears [8; 9; 10; 11]. Wavelet analysis is a local transform of time and frequency. It can effectively extract the information from the signal, and multi-scale analysis can be performed on a signal using expansion and translation operators through a wavelet basis function. However, selection of the wavelet basis function does not yet have unified theoretical criteria [12]. A suitable wavelet basis function can achieve good results, but an improper wavelet basis function could get bad results. The selection of wavelet basis function is subjective and informal in many studies for machine fault diagnosis. Recently, hybrid intelligent methods have attracted considerable interest for tool fault diagnosis, e.g., Wavelet packet transform (WPT), Artificial neural networks (ANN), and support vector machine (SVM), because they can overcome deficiencies in time-domain or frequency-domain analyses and wavelet transforms. [PERSON] et al. [13] proposed a hybrid tool-wear monitoring method for determining the state of a micro-end mill using wavelet packet transforms and Fisher's linear discriminant. [PERSON] et al. [14] developed a personalized machine fault diagnosis method using finite element method, wavelet packet transform and SVM. [PERSON] et al. [15] proposed a hybrid-learning-based Gaussian ARTMAP (GAM) network to realize online monitoring of the tool condition. [PERSON] et al. [16] integrated Fisher discriminant ratio and support vector machine (SVM) techniques to classify tool wear states. [PERSON] et al. [17] used fuzzy c-means clustering and wavelet analysis to diagnosis tool faults in a high-speed milling process. These hybrid intelligent methods typically outperform conventional methods; however, they require the signal analyzed to satisfy certain conditions.