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Abstract

Internal leakage in the hydraulic actuators is concerned in this article, which is caused by seal damage, resulting in the limited performance of the system. To study the issue, this article proposes a method based on time–frequency analysis for the detection in hydraulic actuators. First, the pressure signal after filtering of the actuator in one side is collected when the control valve is affected by sinusoidal-like inputs. Second, the time–frequency image of pressure signal in a period at different leakage levels is obtained after continuous wavelet transform. Third is the sum of pixels in the time–frequency image. It is shown that the feature pattern is established by the sum of pixels in the time–frequency image that internal leakage and its severity could be detected effectively. The proposed method required two baselines and premeasured the pressure signal at 11 leakage levels. Once the sum of pixels in the time–frequency image values, obtained from the time–frequency image by continuous wavelet transform based on wavelet Cmor1-1 in subsequent offline tests, are greater than the first baseline, a leakage alarm is triggered. Furthermore, a severe leakage alarm is triggered when the value is greater than the second baseline. Experimental tests show the accuracy of the proposed scheme at different mother wavelets, and it is done without knowing the model of actuator or leakage.

Keywords

Internal leakage continuous wavelet transform time–frequency analysis hydraulic actuators fault diagnosis feature extraction

Introduction

Hydraulic systems have been widely used in industries due to the advantages of small size-to-power ratios and large force/torques output.^1,2 As the function becomes more powerful, the structure and the information become more complicated, the connection between every part becomes more close, resulting in the high failure rate in the hydraulic systems. Hence, fault detection is very useful to avoid fails of the working parts and the security bring down in the hydraulic systems. Consequently, it is very essential to study on fault diagnosis for hydraulic systems.³

The fault of hydraulic systems ranges from the failure of component, the pollution of the fluid, and the leakage of pipeline to the wear of the material.^4,5 Hydraulic actuators are the critical working part of the hydraulic systems, and its working state has a relation to the lifetime and performance of the systems. For the hydraulic actuators, the most common concern is the fluid leakage, which will result in the slower work pace, and with the leakage degree increased, the systems cannot work anymore, a severe consequence result from sudden leakage when the systems have a load.⁶ According to the location of the leakage, it can be classified into internal leakage and external leakage. Fluid leaks to another part of the circulation within the hydraulic system called internal leakage and external leakage is where the fluid leaks out of the hydraulic circulation. External leakage results in the pollution of environment, but is easy to discover due to its visibility. For the internal leakage, it causes the hydraulic fluid to be displaced between the two chambers of the actuator and the dynamic performance of the systems was influenced for the reason that the piston with a load cannot be moved availably by the flow in the actuator. Generally speaking, internal leakage is hard to detect before seal in the actuator is completely damaged and the actuator cannot follow a control signal.

Even though internal leakage detection for hydraulic actuator is very important, study for it is still limited. At present, methods to detect internal leakage are mostly based on modeling and signal processing. A linear model was constructed by Skormin for a flight actuation system where leakage in the hydraulic pump was researched via simulations.^7,8 Afterward, Volterra nonlinear modeling concept was applied by Tan and Sepehri to carry out an online fault diagnosis scheme in hydraulic systems. Actuator leakage faults were detected through constructing a parametric space.⁹ For the reason that hydraulic system is a nonlinear system and leakage is a kind of non-ideality state that cannot be modeled precisely,^10,11 it is an issue that the uncertainty is associated with modeling leakage in the framework of fault detection based on model.¹² A method based on back propagation (BP) neural network and wavelet analysis was used by Tang et al.¹³ Afterward, the feasibility of using extended Kalman filter was studied by Goharrizi and Sepehri for the faults detection of actuator internal and external leakage.¹⁴ They removed the requirement of using a model for leakage or actuator, but it is still a challenge for the need to know the model of hydraulic actuator. To overcome the challenge to model the nonlinear hydraulic systems, Shi et al.¹⁵ used a linearized model with an adaptive threshold to offset the error result from linearization. However, for the purpose to be dependent less on a model of the system or fault by developing techniques, Goharrizi and Sepehri study directed at using methods based on signal processing for internal leakage detection in valve-controlled hydraulic actuators and do a great deal of work. Discrete wavelet transform (WT) was applied by them for offline and online internal leakage detection;^16,17 it was shown that the transient response of the pressure signal at each chamber of the hydraulic actuator is altered by internal leakage. This characteristic distinctly reveals in finer scales represented by detail coefficients, particularly the level-2 detail coefficient. Explicit model to the actuator or leakage was not needed for the method and a promising result was obtained. Furthermore, external leakage detection and its isolation from internal leakage was also attempted by the method.¹⁸ In addition, they adopted Fourier transform¹⁹ and Hilbert-Huang transform (HHT) to deal with the issue.²⁰ The least degree of internal leakage (2.6%) to this day was detected by discrete wavelet transform (DWT) and HHT.^16,20

To model the hydraulic systems exactly is being more difficult since they are being more complicated. However, the signal of the systems contains abundant information about what reflect the performance of systems; the method-based signal processing do a better work than modeling-based signal processing. With the development of wavelet theory, it has recently got widespread attention as a tool with great promise to handle fault detection through extracting feature patterns spectral signal.^21,22 Zhang and Yan developed a method based on wavelet to detect the sensor faults of different kinds. WT was applied by Gao et al.²³ for online hydraulic pump health detection. They used the pulsation pressure signal and isolated the faults rely on the detail wavelet coefficients. Goharrizi and Sepehri employed WT to detect internal leakage. They demonstrated that internal leakage alters the transient response of pressure signal at each chamber of the hydraulic actuator. This characteristic reveals distinctly in finer scales represented by level-2 detail coefficient which was used for internal leakage detection.^16–18

As mentioned above, the signal of the systems contains abundant information about what reflect the performance of systems and wavelet theory do better in signal processing. After signal processing by continuous wavelet transform (CWT), different signals will present different time–frequency features which are obtained by the time–frequency image. Through the analysis, the difference in different signals could be distinguished.

In the article, internal leakage in hydraulic actuators is detected by the method based on time–frequency analysis. First, the pressure signals at one side of the actuator at different levels were obtained in response to sinusoidal-like inputs to the control valve; the time–frequency image which contains the feature of signal at time–frequency domain was obtained by CWT. Then, the author calculated the sum of pixels in the time–frequency image (SPI) of the image at different leakage levels and the variation of the SPI was found out. Finally, the different leakage degrees were detected by test samples and proved the feasibility of the method.

The rest of this article is organized as follows. The hydraulic actuator on which all experiments are executed is shown in section “Experimental system and the analysis of internal leakage.” Section “Wavelet transformation and time–frequency analysis” provides a brief description of CWT and time–frequency image processing which is used in this article. Section “Experimental results” details about how the method is used to detect the internal leakage fault, and a comparison with different mother wavelets is also conducted. Section “Conclusion” concludes with the conclusion.

Experimental system and the analysis of internal leakage

The experimental test equipment is shown in Figure 1 and a throttle valve underneath Figure 1 is used to actively exert internal leakage to simulate different internal leakage faults. In total, 11 different internal leakage levels are realized by adjusting the opening area of the throttle valve, that is, turning the knob with different graduation. Every graduation represents different leakage conditions, which is shown in Figure 2. A high-performance MOOG D761 servo valve with a flow capacity of 19 L/min at 70 bar drop with 21 MPa supply pressure is employed to control the double rod actuator, whose effective area is 904.32 mm² and the stroke is 44 mm. Traditional proportional–integral–derivative (PID) controller is employed to complete the closed-loop control. Two pressure sensors located at the surface of the cylinder at each side are used to measure the pressure signal of chambers, denoted by P₁ and P₂, respectively. The schematic of the valve-controlled hydraulic actuator is shown in Figure 3. The sampling period of the control system is 0.5 ms. The periodic sinusoidal-like desired position with 2 mm amplitude and 20 Hz frequency is utilized as the exciting signal in all experiments with a total of 50 s (i.e. 1000 periods).

Figure 1.

Experimental platform of the hydraulic system with simulated internal leakage fault.

Figure 2.

The flow curve of the throttle valve for internal leakage simulation.

Figure 3.

The schematic of the valve-controlled hydraulic actuator.

Internal leakage alters the quantity of flow in actuators. Otherwise, the pressure of the chambers and shifting of the rod were affected. In general, the rod-shifting signal is difficult to get the feature patterns of internal leakage. Flow signal is a better option for internal leakage detection; however, the flow sensor is expensive and it influences the flow since it insets in the circulation of systems. Consequently, the pressure signal is employed in earlier studies,^16–20 and it is affected easily by other working parts, resulting in the particularly close connection with the systems, as mentioned above. In this article, as it is necessary, a filter is applied to the pressure signal as the noise was removed, and the cutoff frequency is 50 Hz.

Wavelet transformation and time–frequency analysis

Wavelet analysis is a promising tool deal with signal developed from Fourier analysis, it analyzes a non-stationary signal at time–frequency domain in the same time and decomposes the signal into scales with different frequencies and time resolutions. Different shifted and scaled versions of the basic are decomposed by wavelet analysis that breaks up a signal into shifted and scaled versions of the mother wavelet when compared with Fourier transform (FT) which only breaks up a signal into sine waves of different frequencies. For dealing with non-stationary signal, the Fourier analysis, which cannot reserve the time information when the signal is transformed into the frequency domain, is not effective. In order to deal with non-stationary signal well, the short-time Fourier transform (STFT) is suggested because it analyzes a small section of the signal at a time—a technique called windowing; however, it has the deficiency where the size of the time window cannot be changed at other frequencies. Wavelet analysis, which overcomes the drawback, has a window with variable-sized regions; it obtains high-frequency information and high-frequency information about the non-stationary signal using short time regions and long time intervals, respectively. Moreover, past researches have proved that wavelet analysis produces result from which faults are distinct to distinguish and easy to explain as compared to FT and STFT.²⁴

As mentioned in section “Experimental system and the analysis of internal leakage,” pressure signal of the chamber is collected and it is certain that the time–frequency feature is different at different internal leakage levels. In this article, a time–frequency image is obtained after CWT, as shown in Figures 4 and 5. In Figure 5, the color presents the valve in that time and frequency, the X-axis is time and the Y-axis is frequency. Image processing is a tool used to get the feature patterns from image in this article, and a detailed description of the technique was provided in Donald.²⁵ As mentioned above, the time–frequency image is obtained from signal, by CWT, whose pixels contain the time–frequency information of signal. Image is a three-dimensional matrix where the elements of the matrix (28 × 28 × 28) represent pixels in MATLAB. Then, the elements were added one by one and the SPI was produced. The above SPI can be calculated by the following equation

$y = \sum_{i = 1}^{28} \sum_{j = 1}^{28} \sum_{k = 1}^{28} x_{ijk}$ (1)

where i, j, and k denote the site in an image; x denotes the pixel-value; and y is the sum of all the pixels.

Figure 4.

Original signal.

Figure 5.

A time–frequency image for original signal by CWT.

Experimental results

In order to detect offline internal leakage, our approach is based on the analysis of time–frequency image transformed from the pressure signal of actuator chamber one by CWT (the mother wavelet is Cmor1-1). As was mentioned in Goharrizi and colleagues,^16–18 internal leakage alters the response of pressure signal since the flow is shifty and the dynamics of the electrohydraulic actuation system is damped. In this section, a sinusoidal-like input is applied to the servo valve, which caused the actuator to move similar to the input voltage. Our offline application adopts the structured input signal in which low- and high-frequency components concluded. The frequency of the input signal is 20 Hz and the amplitude of this signal is 2 mm. The values of the pixels in time–frequency image of pressure signal are applied to detect internal leakage and relate it to the severity. The transform is done on a program developed using MATLAB wavelet toolbox and is used for the transformation of CWT,²⁶ and then the values of SPI were calculated by adding the pixels of the image.

The method proposed by this article

As we can see in Figure 6, it is obvious that the magnitude of the pressure signal (after filtering) at different levels is changed no matter chamber 1 or 2. In order to get the feature pattern, the time–frequency image, as shown in Figure 7, of the pressure signal in a period at different levels is obtained by CWT. The difference between two images at different leakage levels is hard to distinguish and is existing. Then two images were subtracted to find out the difference between them. From the results shown in Figure 8 (the image is processed by enlarging the pixels to enable the difference in display apparently), we can find out that the distribution of pixels in images altered with the leakage level changed.

Figure 6.

Pressure signal at 11 different leakage levels.

Figure 7.

The time–frequency image of pressure signal in a period at different leakage levels.

Figure 8.

The difference between two images of pressure signal in a period at different leakage levels.

For the sake of distinguishing the leakage level by the image, the SPI values were calculated. As shown in Table 1, it is obvious that the value increased with the decrease in leakage. A total of 800 periods of the pressure signal of chamber 1 at leakage graduation 0, 2, 5 8, 10, respectively, were measured to verify the tendency proposed before, and the results shown in Table 2 proved the tendency discussed above. At the same time, 800 periods of the pressure signal of chamber 2 at leakage graduation 0, 2, 5 8, 10, respectively, were measured too. Then, two baselines shown in Table 3 were set to distinguish different leakage degrees after the value of SPI was obtained. The leakage at graduation 0, 1, 2 is called small leakage, which means that it has no influence on the state of the systems; medium leakage includes graduation 3, 4, 5, 6, which means that the state of the systems has been affected; the leakage at graduation 7, 8, 9, 10 is called severe leakage and it expresses that the actuators cannot work normally anymore. In order to confirm the veracity proposed above, another 200 periods of the pressure signal at leakage graduation 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, respectively, were used to test the accuracy. As we can see, Table 4 reveals the results that the accuracy is high enough to confirm the veracity of the method for detecting internal leakage by CWT and the analysis of SPI.

Table 1.

The SPI transformed from pressure signal of chamber 1 in a period at different leakage levels.

Different leakage levels	The SPI transformed from pressure signal of chamber 1 in a period
Graduation 0	19,636,549
Graduation 1	19,642,837
Graduation 2	19,647,892
Graduation 3	19,651,655
Graduation 4	19,651,886
Graduation 5	19,654,362
Graduation 6	19,651,509
Graduation 7	19,656,661
Graduation 8	19,657,806
Graduation 9	19,661,502
Graduation 10	19,665,454

SPI: sum of pixels in the time–frequency image.

Table 2.

The SPI transformed from pressure signal in chamber 1 of 800 periods at leakage levels 0, 2, 5 8, 10, respectively.

	Minimum values of SPI	Maximum values of SPI
Different conditions of chamber 1
Graduation 0	19,629,138	19,643,473
Graduation 2	19,642,472	19,652,289
Graduation 5	19,652,107	19,658,942
Graduation 8	19,655,213	19,662,682
Graduation 10	19,659,246	19,666,686
Different conditions of chamber 2
Graduation 0	19,931,674	19,953,713
Graduation 2	19,925,857	19,935,886
Graduation 5	19,926,009	19,932,595
Graduation 8	19,922,042	19,930,503
Graduation 10	19,916,590	19,923,998

SPI: sum of pixels in the time–frequency image.

Table 3.

The baseline between different leakage degrees.

The degree of the leakage	Different levels	Baseline
Small leakage	Graduation 0	<19,650,000
	Graduation 1
	Graduation 2
Medium leakage	Graduation 3	19,650,000∼19,657,000
	Graduation 4
	Graduation 5
	Graduation 6
Severe leakage	Graduation 7	>19,657,000
	Graduation 8
	Graduation 9
	Graduation 10

Table 4.

Test result of another 200 periods of the pressure signal at different levels.

Condition	Number of the coincident samples	Number of the test samples	Accuracy (%)	Baseline
Graduation 0	200	200	96.2	<19,650,000
Graduation 1	200	200
Graduation 2	177	200
Graduation 3	121	200	87.5	1,965,000∼19,657,000
Graduation 4	184	200
Graduation 5	200	200
Graduation 6	195	200
Graduation 7	197	200	99.6	>19,657,000
Graduation 8	200	200
Graduation 9	200	200
Graduation 10	200	200

The CWT of the experiment above was based on Cmor1-1. In order to demonstrate the conclusion obtained above deeply, other mother wavelet was attempted. Table 5 shows the results based on Haar wavelet, we discovered that the SPI decreased with the increase in the leakage and even proved that the feature of internal leakage is obtained by the SPI, using pressure signal, no matter whether the SPI increases or decreases.

Table 5.

The SPI transformed from pressure signal in chamber 1 of 800 periods at leakage levels 0, 2, 5 8, 10, respectively, based on Haar wavelet.

Different levels	Minimum values of SPI	Maximum values of SPI
Graduation 0	19,311,778	19,322,230
Graduation 2	19,309,064	19,311,753
Graduation 5	19,305,840	19,308,780
Graduation 8	19,306,224	19,308,408
Graduation 10	19,302,753	19,307,652

SPI: sum of pixels in the time–frequency image.

The other signal-based method

For the method based on WT,^7–9 we first randomly take a basic signal unit at every operation condition (from graduation 0 to graduation 10). Then, the level-2 wavelet decomposition is applied on the selected signals to achieve the level-1 detail coefficient value (marked as D1) and level-2 detail coefficient value (marked as D₂). As suggested by Goharrizi and Sepehri,^7–9 the usage of D₂ will achieve better detection performance. After wavelet decomposition, the root mean square (RMS) of D₂ is calculated. Above procedure is repeated three times. And all the RMS results are collected in Table 6.

Table 6.

The method based on WT.

Condition	RMS of D₂ by WT
	1	2	3
Graduation 0	89.6360	89.8132	113.6782
Graduation 1	124.3839	144.5577	176.2681
Graduation 2	151.2686	159.5379	146.2233
Graduation 3	139.8340	152.3464	141.9391
Graduation 4	185.8945	143.6472	141.6366
Graduation 5	193.7245	144.3977	131.8177
Graduation 6	88.1883	92.1784	105.2028
Graduation 7	167.6934	149.1089	157.6823
Graduation 8	202.0830	186.1835	177.8806
Graduation 9	215.8955	210.4844	225.8941
Graduation 10	258.5396	267.7276	242.4687

RMS: root mean square; WT: wavelet transform.

From Table 6, this method is feasible to estimate the internal leakage; however, as we can see, it cannot predict the leakage degree precisely as the method this article proposed.

Conclusion

In this article, we presented the application of time–frequency image analysis and CWT, for the first time, to detect the internal leakage in hydraulic actuators. Pressure signal at chamber 1 of the cylinder was found to be a valuable source, which carries adequate information to sustain dependable diagnosis. CWT was used to obtain the time–frequency image of signal in a period, in response to sinusoidal-like input signal. It was then demonstrated that the SPI of the signal in a period is subtle to internal leakage. The use of Cmor1-1 wavelet showed good recognition to display this feature signature of the primordial pressure signal.

Two baselines were required by the proposed method to distinguish between small leakage, medium leakage, and severe leakage. The values of the baseline were determined by choosing the SPI, obtained from the pressure signal of actuator running under different operating situations and for a great deal times. Then, it was shown that, for small leakages, medium leakage, and severe leakage, the SPI values of the signal in a period correspond to the baseline values 96.2%, 87.5%, and 99.6% of the test times, respectively. Furthermore, the SPI value increases with the severity of leakage. And that small leakage and severe leakage can be detected more easily.

In conclusion, this article has demonstrated that the approach based on time–frequency image analysis and CWT, as described in this article, is a tool with great promise to detect internal leakage for hydraulic actuators caused by seal damage or wear. The advantages of this approach are as follows: its ability to detect different leakage degrees, it overcomes the drawback of using model for the actuator or leakage, and its ease to come true since the measurement of pressure signal at one side of the actuator is only required; moreover, it is precise compared with other signal-based method.

Footnotes

Academic Editor: Nasim Ullah

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

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A time–frequency analysis based internal leakage detection method for hydraulic actuators

Abstract

Keywords

Introduction

Experimental system and the analysis of internal leakage

Wavelet transformation and time–frequency analysis

Experimental results

The method proposed by this article

The other signal-based method

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References