# Application of a New Enhanced Deconvolution Method in Gearbox Fault Diagnosis
## 1 Introduction  
When bearing gear, inner ring, outer ring, or rolling element faults occur, the transmission system will be affected and the vibration signal will appear periodically impacted [1; 2; 3; 4; 5]. When the bearing faults occur, the background noise becomes loud owing to the gearbox harsh working environment [6; 7; 8; 9; 10]. The weak fault signal is often overwhelmed by noise, and it is difficult to extract the characteristic information. Therefore, the weak fault extraction of the rotating machine is still a big challenge [11; 12; 13; 14]. The extraction of the fault information is actually to weaken the noise in the collected vibration signals through an optimal filter, which effectively preserves the integrity of the faultinformation [15; 16; 17; 18]. At present, the existing fault diagnosis methods include time-frequency analysis, mode decomposition [19], sparse theory [20], order tracking [21], fuzzy theory [22], morphology theory [23; 24; 25], stochastic resonance [26], intelligent recognition method [27], deconvolution theory, and others. As the noise and fault characteristics in the vibration signals are convolution, the deconvolution of vibration signals can separate the noise and fault information. Minimum entropy deconvolution (MED) is an adaptive system identification method. Its basic principle is to solve the deconvolution so that the results highlight a few sharp pulses, and the maximum kurtosis is used as the iterative termination condition [28]. [PERSON] [29] first applied MED to the diagnosis of rolling bearing and gear faults in 2007. However, the MED algorithm is susceptible to noise and the maximum kurtosis as the objective function cannot reasonably reflect the continuity of the impact signal [30; 31]. In order to overcome the shortcomings of MED, [PERSON] et al. [32] proposed a fault feature extraction method of rotating machinery, called multi-point optimal minimum entropy deconvolution (MOMEDA). Compared with MED, this method can obtain the optimal filter without iteration. It defines the position and weight of the deconvoluted pulse sequence with the time objective function [33; 34]. Every rotation period can be collected with the shock pulse. When the fault period is not an integer, MOMEDA can directly extract the fault without resampling. In addition, owing to the introduction of multi-point kurtosis, the periodic components of fault signals can be calculated, which provides a new idea for the fault feature extraction of rotating machinery [35]. The MOMEDA method proposed by [PERSON] et al. mainly focuses on the gear fault in the gearbox at the beginning of the fault signal extraction. The fault signal is a strong shock signal, but the fault information extraction performance of MOMEDA is significantly variable under different SNR (signal-to-noise ratio) conditions. In order to ensure the accuracy of MOMEDA algorithm for fault information extraction, it is necessary to improve the anti-noise performance of MOMEDA. [PERSON], [PERSON] et al. [36] successfully extracted the fault features in the wind turbine gearbox by combining MED and MOMEDA, however, the defects of the MED algorithm in iteratively selecting filters cannot be ignored [37; 38]. The time series autoregressive (AR) model is widely used in the noise reduction processing of vibration signals. [PERSON], [PERSON] et al. [39] applied the AR (autoregressive) model to reduce the noise in SPECT (single photon emission computed tomography) images, which compared the filtered signal of an AR filter with a Butterworth filter to verify the advantages of the AR filter in noise reduction. In recent years, AR has been successfully applied to fault diagnosis. [PERSON] [40] proposed an autoregressive minimum entropy deconvolution (AR-MED) fault extraction method. Using AR filtering technology is insensitive and can be better to distinguish the performance of noise and pulse, thus improving the fault feature extraction ability of MED; this method can also be used to achieve fault extraction for gear spline and tooth angle crack.