# Nonlinear Blind Source Separation and Fault Feature Extraction Method for Mining Machine Diagnosis
## 1 Introduction  
A mining machine is the most important piece of equipment for coal mining [1]. A simple failure of the machine will cause severe safety accidents and serious economic losses. Therefore, monitoring the health condition of mining machines is crucial to ensuring mining safety [2; 3; 4; 5]. The vibration, noise, temperature and pressure of mining machines can be used to detect machine faults. According to the variation characteristics of these parameters, the fault location, type and severity can be identified. Vibration analysis is among the most widely used methods in the fault detection of mining machines, owing to its costless usage and easy installation [6]. Because distinct information for early fault signature can be captured by machine vibration, vibration analysis is suitable for fault detection in the early stages. If useful fault features can be identified from the vibration signals, the potential/undergoing failures in the mining machines will be effectively detected to ensure safe, stable and reliable operation of the machines [7]. However, it is always a challenging task to extract features that are useful for indicating the state change of a machine, due to strong background noise and disturbances. In practice, the vibration signals acquired from mining machines are inevitably contaminated by heavy noise. In addition, the vibration source of a faulty part may mix with the vibration of normal machine parts, such as the vibration of a rotating shaft and meshing gears, which makes it difficult to identify useful fault vibration characteristics [8]. Consequently, it is crucial to separate the faulty vibration source from the sensory measurement of a mixture of various vibration sources before performing fault diagnosis. Different approaches for separating vibration sources have been discussed in the literature. Traditional methods attempt to arrange multiple sensors at different locations to collect the vibration signals of a machine, and then select a relatively optimal sensor for vibration analysis. However, such methods are limited by the subjective consciousness of experts. In order to solve this problem, information fusion and optimization algorithms have been developed to process multi-sensor signals. [PERSON] et al. [9] proposed a blind separation technology to realize the fault feature extraction of aero-engine from multi-sensor vibration signals. [PERSON] et al. [10] used a linear blind signal separation method to fuse the multi-sensor vibration signals of a rotating machine and extracted a useful feature for fault detection. [PERSON] et al. [11] also used a linear blind source separation technology to filter out the Gaussian noise and modulation sources from multi-sensor observations to accurately recover a fault vibration component. Linear blind separation technology has been applied to the vibration source identification of engines and rotating machinery in countless papers [12]. Previous studies show that linear blind signal separation based on the independent component analysis (ICA) can produce good fault source separation performance. However, due to linear assumption of the sources, ICA based separation algorithms, such as FastICA [13], are limited to linear systems. When the nonlinearity of the mixed observation signals increases, ICA is not effective and, in some cases, even fails to identify the fault vibration source [14]. Consequently, the linear methods are not appropriate for complex nonlinear separation problems, such as in steam turbines, generators and mining machines [15]. Therefore, nonlinear blind separation has become a hot issue in fault vibration source separation. [PERSON] et al. [16] proposed a bounded component analysis for nonlinear source separation for a wind turbine. [PERSON] et al. [17] developed a second-order statistics separator for nonlinear mixtures. [PERSON] et al. [18] presented a complex matrix joint diagonalization method for noncircular sources in typical nonlinear functions. [PERSON] et al.