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Daubechies 8 wavelet has been chosen as thewavelet basis function in this paper.4.2. Leakage characteristic parameters selection4.2.1. Piston rod reciprocating speedIn this study, the inlet pressure signals of 7 different sizes ofleakage are decomposed by 4-layers wavelet packet. The inverteris adjusted at 20 Hz, and the calculated rotating speed of the pumpis 1200 rpm. The load pressure is 5 MPa. Because the main pulsat-ing pressure signals of the fluids in the testbed are within 500 Hz,so the sampling frequency is set at 1000 Hz based on the Nyquistlaw. As shown in Table 2, the collected signals are further subdi-vided into 16 bands.The displacement signal of the piston rod is decomposed by4-layers wavelet packet and the low-frequency signal is recon-structed. Compared with the original displacement signals, thelow frequency S4,0 removes the effect of fluid pulsation and noise,as shown in Fig. 4.Then calculate the velocity of piston rod as a feature by least-squares fitting method, which is shown in Table 3.In Table 3, the direction of the piston rod stretching correspondto the direction of the piston from rodless chamber to the rodIt indicate that the actual useful system flow reduces with theincrease of internal leakage in the hydraulic cylinder, and the resultis the reduction of the piston rod speed. More accurate speed curvecan be got through wavelet packet denoising.4.2.2. Pressure rising speedPressure signal is decomposed by 4-layers wavelet packet, andthen reconstruct low-frequency signal S4,0, which is shown inFig. 5.Use the least square linear fitting to calculate pressure risingspeed v with S. The result is listed in Table 4.It can be found from Table 4, the pressure rising speed falls withthe increase of leakage, so it is set as fault feature P1. It indicate thatthe building up of the pressure difference between two chambersof hydraulic cylinder will be slow down when the internal leakageoccurs in the hydraulic cylinder.Because pressure signal contains the system’s frequency-modu-lated signal, the pressure fluctuation signal and the noise signal, soits fluctuation usually is considerable. As we known, the usefulpressure rising signal mainly exists in the low frequency band, sothe original pressure signal is decomposed into multiple frequencythrough the multi-level decomposition of wavelet packet, then thewavelet reconstruction can be proceeded with the low frequencysignal bands. In this way, the noise signals in the high frequencybands can be removed and the pressure rising speed become moreprecisely.4.2.3. Wavelet packet energy of pressure signalAs mentioned before, Daubechies 8 wavelet package was cho-sen to decompose the 16 brands pressure signals in Table 2, andthe result is shown in Fig. 6.The pressure signal energy is mainly concentrated in the S4,0/E4,0, its energy value is too big contrasted to other frequency bands that it’s not suitable to be compared with other band’s sig-nals.
Thus S4,0/E4,0 is not considered when analyzing energy fea-tures by wavelet packet. Reconstructing and composing the left 15sub-signals, the result is shown in Fig. 7.Extract effective frequency features from pressure signal.Firstly, normalize the frequency energy of S4,1 to S4,15; then com-pare the value with the wavelet packet energy value of variousleakage. The result is shown in Fig. 8 by using the bar chart.From Fig. 8, it can be found that energy values of S4,1 declinewith the increase of leakage. Meanwhile, the power generated bythe hydraulic oil on the piston rod decrease, and the stretchingspeed of piston rod falls due to the increase of the leakage. There-fore, the energy value of S4,1 signal can be set as fault feature P2.This feature can be used to reveal the influence of internal leakageon the oil within system from the perspective of energy. With theincrease of the internal leakage of the hydraulic cylinder, the disor-der degree of the oil’s internal movement increased, the pressurerising speed dropped, and the system energy loss increased. Fromthe perspective of signal frequency, the most affected signal is thelow frequency band signal.