## 2 Related Works  
Researchers have worked a lot on MFL detection for defects, such as the influence of speed on MFL signal [12], magnetization time of high-speed MFL detection [13], and excitation and vibration interference on the signal. In view of the interference, several methods are proposed to suppress the interference.  
[PERSON] optimized the MFL technique by finite element model to detect outer surface defects in ferromagnetic steam generator tubes. In this method, the iron core, coil, coil current, and position of the sensor are optimized, and the MFL signal is predicted. The influence of length, width, and depth of defects on the MFL signal is analyzed. The reliability of detection is improved [14].  
A probe consisting of a quantum well Hall-effect sensor, an illuminating electromagnet and sensor circuitry, is designed. This probe is used to apply magnetic fields of various frequencies and field strengths to ascertain a frequency and field range best suited to detecting longitudinal surface-breaking toe cracks in ground mild steel welds [15].  
As for the denoising process of the MFL signals, a multilevel filtering approach based on wavelet denoising combined with median filtering is proposed. By analyzing and comparing the denoising properties of three wavelet families, two wavelet bases with the best denoising performance are recognized and selected. Then, the median filtering method is cascaded [16].  
To cover the entire workpiece or obtain sufficient data, sensor arrays are used [17]. The researchers carefully set up the position of the sensors in the probe and the relative position of the sensors [18; 19]. Because the distance between the sensors is close and their vibration is similar, the lift-off interference can be suppressed through the relationship between the signals.  
Figure 1: MFL detection.  
[PERSON] proposes a noise reconstruction algorithm of transverse sensor array and constructed an adaptive interference canceller to filter the multichannel MFL signal of rail tracks [20].  
[PERSON] proposed a way of building a virtual channel signal which does not contain any defect. Multiple sensors are arranged, the sensor with the minimum absolute value of signal is considered as having not detected any defect, and this signal is used as a reference signal for filtering [21]. This method suppresses interference to a certain extent, but the lift-off interference and the leakage magnetic field of a defect may be in the reversed phase. It is unreasonable to take the minimum as the reference signal, which will cause certain misjudgment.  
A defect detection method of longitudinal array sensors is proposed according to the characteristics of the signals detected by the magnetic sensor in x and z directions [22]. The method reduces the misjudgment caused by lift-off interference but is only suitable for judging whether there is a defect and cannot be used for filtering.  
The sensor signal changes caused by vibration are found to suppress the lift-off interference, but their methods to find the signal changes are unreasonable [22]. Inspired by these references, this paper presents a method to determine the signal change caused by vibration through the difference between the signals in x and z directions of two sensors, to suppress the lift-off noise.