# Weak Signal Processing Methods Based on Improved HHT and Filtering Techniques for Steel Wire Rope
## 2 Experiments
### Time and Frequency Analysis  
According to the aforementioned experiments conducted, six main original weak signals were acquired and are presented in Figure 2. Explanatorily, signal 1 and signal 2 from Figure 2a,b were obtained from the testing sample of wire rope 1 indicated in Figure 1a with different wire broken numbers of 1 and 3 through inductive transducer, and the sensor liftoff distance was set as 13 mm. Signal 3 and signal 6 shown in Figure 2c,f were acquired through the magnetic sensitive element of copper coils with different liftoff distances of 13 mm and 20 mm for wire rope sample 2. While signal 4 and signal 5 expressed in Figure 2d,e represent the weak original signals obtained from the inner defect of wire rope 3 with the surface liftoff distances of 13 mm and 20 mm by the sensor of inductive transducer. From the perspective of geometric structures, a broken wire defect features sudden loss of the metal cross-section, which leads to the change of wire rope permeability and the magnetized field leak from the body of the tested wire rope, while almost no abnormal magnetic flux leaks from the wire rope except for the strand signal. Therefore, the defect  
Figure 1: Experimental samples and apparatus. (**a**) Different steel wire ropes; (**b**) MFL detector. signals are usually characterized with an obvious peak or valley, while the non-damaged wire rope is detected with strand and random noise signals, as marked in Figure 2a. Apparently, under the inspection condition of big liftoff distance and other severe environment, wire rope inspection signals are featured with the weak and low signal-to noise-ratio (SNR). Concretely, the testing signals are shapely attenuated due to the liftoff effect and micro defect, and the defect signals are almost overwhelmed by the wire rope strand and other noise signals, which makes the inspection for wire rope difficult and full of challenges. Furthermore, comparing signal 1 and 3, it can be deduced that the coil sensor has a wider detection range than an inductive transducer for defect signals, and a higher signal amplitude under the same liftoff distance, while the inductive transducer is more sensitive to the magnetic leakage of defect than a coil sensor when considering the defect features of signal 1 and 4. Consequently, judging from the time domain signals, the testing results are susceptible to various factors such as the sensor types and precision, liftoff distance, which also manifests that a suitable weak signal processing technique is of great significance to high precision defect inspection. Furthermore, the corresponding time and frequency analysis by short-time Fourier transform (STFT) is preliminarily conducted. By moving the hamming window through the non-stationary wire rope testing signals, the instantaneous frequency information could be obtained, and the STFT is described as follows,  
\[\mathrm{X}(\omega,\tau)=\int_{-\infty}^{+\infty}\!\!\!\mathrm{x}(\mathrm{t}) \mathrm{g}(\mathrm{t}-\tau)\mathrm{e}^{-\mathrm{j}\omega\mathrm{t}}\mathrm{d}t \tag{1}\]  
where, \(\mathrm{t}\) is the time, \(\mathrm{j}\) is the imaginary unit, \(\tau\) is the moving center time of the window function, \(\omega\) is the angular frequency, \(\mathrm{x}(\mathrm{t})\) is the system input of wire rope testing signals, \(\mathrm{g}(\mathrm{t})\) represents the hamming window function, and \(\mathrm{X}(\omega,\tau)\) are the STFT results in Equation (1). Specifically, the corresponding STFT spectrum of signal 1 to signal 6 shown in Figure 2 are presented in Figure 3, which indicates that these weak signals of wire rope are nearly under the frequency of 250 Hz, and most of the signal components are mixed distributed under the frequency of 50 Hz, while it is difficult to differentiate the specific frequency component of  
Figure 2: Weak signals of steel wire rope with different defects and liftoff distances.