Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244
Sensors & Transducers © 2014 by IFSA Publishing, S. L. http://www.sensorsportal.com
A Fault Diagnosis Approach for the Hydraulic System by Artificial Neural Networks 1 1
Xiangyu He, 2 Shanghong He
College of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410004, China 2 State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China E-mail:
[email protected]
Received: 10 May 2014 /Accepted: 29 April 2014 /Published: 31 May 2014 Abstract: Based on artificial neural networks, a fault diagnosis approach for the hydraulic system was proposed in this paper. Normal state samples were used as the training data to develop a dynamic general regression neural network (DGRNN) model. The trained DGRNN model then served as the fault determinant to diagnose test faults and the work condition of the hydraulic system was identified. Several typical faults of the hydraulic system were used to verify the fault diagnosis approach. Experiment results showed that the fault diagnosis approach is feasible and effective for improving the reliability of hydraulic systems. Copyright © 2014 IFSA Publishing, S. L. Keywords: Hydraulic system, Fault diagnosis, Artificial neural networks (ANNs), Nonlinear system, General regression neural network (GRNN).
1. Introduction Faults in a hydraulic system can take many forms, such as pump faults, valve faults, and cylinder faults. Hydraulic faults are generally sorted in several grades according to severity. Complete failures and abrupt faults are comparatively easy to detect. Thus, fault diagnosis techniques related to the complete failures of the control and equipment components of hydraulic systems have been proposed in previous studies. Gradually generating faults are difficult to detect early by limit-checking methods with simple residuals because fault effects are often masked by control actions. However, hydraulic systems are nonlinear with dynamic properties. Hence, diagnosing fault information on hydraulic systems by conventional techniques is difficult.
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The main challenges of fault diagnosis are given by knowledge representation, prior knowledge introduction, typical symptom distributions, and data size. Classification methods are important in diagnosis, particularly if structural knowledge is unavailable for the relationship between symptoms and faults. Techniques based on artificial neural networks (ANNs) have an advantage over conventional techniques in significantly improving the accuracy of fault diagnosis because ANNs are capable of nonlinear mapping, parallel processing, and learning. These attributes make ANNs ideally suited for providing high accuracy in fault detection under a wide variety of systems and conditions. Moreover, mathematical process models to describe the relationship between measured input and output values of the system are fundamental
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Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244 for model-based fault diagnosis. In many cases the process models are unknown at all or some parameters are hard to obtain. Extensive studies have been devoted to developing identification methods for linear system. Comparatively, identification for nonlinear system is more difficult. Recently, Donald F. Specht presented general regression neural network (GRNN) for identification and control of nonlinear system. As a new kind of radial basis networks, GRNN is a powerful regression model [2, 3]. The principal advantages of GRNN are fast learning and convergence to the optimal regression surface. GRNN can train in one step through sample data and can generalize from samples as soon as they stored [4, 5]. Moreover, GRNN is particularly useful with sparse data in a real-time environment. GRNN has been widely used in forecasting, fault diagnosis and so on [6-8]. In this study, a fault diagnosis approach based on RBF networks was proposed. First, Normal state samples were used as the training data to develop a dynamic general regression neural network (DGRNN) model. Second, the trained DGRNN model served as the fault determinant to diagnose test faults and the work condition of the hydraulic system was identified. This approach was effectively applied on an excavator hydraulic system and could accurately diagnose faults.
continuous probability density function of a random vector x , and a scalar random variable y . The condition mean of y (or the regression of y on x ) is given by: +∞
E ( y / x ) = yˆ ( x ) =
−∞ +∞ −∞
yf ( x , y ) dy f ( x , y ) dy
,
(1)
where the density function f ( x, y ) usually can be estimated by use of from a sample of observation of x and y . The probability estimate can be written as follows:
fˆ ( x, y ) =
1
1 n −d ( x,xi ) −d ( y, yi ) e e , (2) m+1 m+1 n i =1 ( 2π ) 2 σ
where
d (x , x i ) =
240
(x − x i ) (x − x i ) , T
2σ
2
2σ
x i and yi are the i th sample data points, n is the number of samples, m is the dimension of the vector variable x , and σ is the width. A physical interpretation of the probability
estimate
fˆ ( x, y ) is that it assign sample
probability of width
σ
for each sample x i and yi ,
and the probability estimate is the sum of those sample probabilities. Substitute
the
f ( x, y )
fˆ ( x, y ) in Eq. (2) and
in Eq. (1) with the
summation yields the desired conditional mean, designated yˆ ( x ) :
(e n
yˆ ( x) =
i =1 n
− d ( x,xi )
+∞
−∞
(e
− d ( x,xi )
) dy )
ye−d ( y, yi )dy
+∞ − d y , y ( i)
−∞
i =1
e
(3)
Let +∞
−∞
f ( x, y ) represents the joint
Assume that
2
2. DGRNN Model
( y − yi ) , 2
d ( y, yi ) =
2
ze − z dz = 0
Thus, Eq. (3) can be rewritten as follows: n
yˆ ( x ) =
ye
− d ( x ,xi )
i
i =1 n
e
− d ( x ,x i )
(4)
i =1
The estimate yˆ ( x ) is the weighted mean of all sample observations yi , where each observation is weighted exponentially according to the Euclidean
x . The estimate yˆ ( x ) changes between the random variable y and the sample observations yi . A GRNN consists of four layers distance from x i to
including input layer, pattern layer, summation layer and output layer (Fig. 1). As a novel neural network, GRNN is able to train and convergence in a short time. However, GRNN is just a local recurrent and static neural network, which is well suited for applications where both the input and output that are independent of time. To capture dynamic behaviour of the process, the GRNN has to contain dynamic elements. For this reason, external dynamics were considered to the GRNN, which can greatly improve dynamic identification ability of nonlinear system.
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244
Fig. 1. Diagram of GRNN.
As a novel neural network, GRNN is able to train and convergence in a short time. However, GRNN is just a local recurrent and static neural network, which is well suited for applications where both the input and output that are independent of time. To capture dynamic behaviour of the process, the GRNN has to contain dynamic elements. For this reason, external dynamics were considered to the GRNN, which can greatly improve dynamic identification ability of nonlinear system. A dynamic GRNN model can be constructed as Fig. 2. The input of dynamic GRNN model can be written as follows: x ( t ) = u ( t − n u ) , , u ( t − 1 ) , y ( t − n y ) , , y ( t )
multiple step prediction is selected as it has better performance for the dynamic GRNN model.
(5)
The corresponding output of the dynamic GRNN model is:
(
y (t + 1) = Γ y (t ) , , y (t − n y ) , u (t − 1) , , u (t − nu ))
,
(6)
Γ(•) represent the nonlinear mapping of the GRNN. A dynamic GRNN model of mapping can be used for two objectives: single step prediction and multiple step prediction. In the case of single step prediction, the n previous values of the series are assumed to be available. In the case of multiple step prediction, the predicted output is fed back as an input to the following prediction. In this paper,
where
Fig. 2. Structure of DGRNN.
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Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244 Assume that the initial input of the dynamic GRNN model at time t = k is:
Assume that the threshold value is
then the
fault can be determined by:
x ( k ) = u ( k − nu ) ,, u ( k − 1) ,
J ≤ ε 0 , Normal J > ε 0 , Fault
y ( k − n y ) ,, y ( k ) and
Then the predicted output at time t = k + 1 is
ε0 ,
ε 0 = 2J 0
, where
(10)
J 0 is the sum of square
residual under normal condition.
(
yˆ ( k + 1) = Γ y ( k ) , , y ( t − n y ) , u ( t − 1) , , u ( t − nu ) )
4. Experiment
and the predicted output at time t = k + 2 can be written as follows:
(
yˆ ( k + 2 ) = Γ yˆ ( k + 1) , , y ( t − n y + 1) ,
In this section, a 1.7 ton excavator hydraulic system was developed as the experimental platform for testing the proposed fault diagnosis approach. This excavator was produced by Sunward Equipment Group (Fig. 3).
u ( t + 1 ) , , u ( t − n u + 1) )
Hence we can obtain the predicted output at time
t = k + p as follows:
yˆ ( k + p ) = Γ ( yˆ ( k + p − 1) ,,
yˆ ( t − n y + p − 1) , u ( t + p − 1) ,
(7)
, u ( t − nu + p − 1) ) where
p > nu , n y .
3. Fault Diagnosis Approach A DGRNN model under the normal condition is established in the first step. Faults in a broad sense result in symptoms that involve the deviation of measured values. Therefore, a fault can be detected by observing residual values, which are defined as the difference between the actual measured values under a fault condition and the expected values under the normal condition. The output residual of a dynamic model can be calculated by:
e = yˆ − y ,
(8)
where yˆ is the predicted output of the DGRNN model and y is the actual input. The sum of square residual can be calculated as:
J ( k + 1) = where
242
k +1 1 e2 (i ) , N + 1 i =k +1− N
N is the length of the sample.
(9)
Fig. 3. Experimental platform of the 1.7 ton excavator.
This experimental excavator consists of a boom, stick, and bucket and moves via tracks or wheels. The motion of the boom, stick, and bucket are driven by corresponding hydraulic cylinders. A basic operating cycle involves a digging pass through the bank, a loaded swing to dump position, a dump into a haul truck, empty swing back to digging, and repositioning or spotting of the bucket at the face. To fulfill these complex operations, an excavator is usually equipped with various hydraulic components, including a variable pump, proportional valves and
Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244 cylinders. The variable pump converts mechanical energy to hydraulic energy and proportional valves distribute hydraulic energy to cylinders to drive the boom, stick, and bucket. Hence, we can simplify the hydraulic system of an excavator to several similar basic hydraulic loops despite of the functional difference (Fig. 4).
procedure, the training data should be normalized. The normalization consisted of two steps: the first step was to subtract the mean from each variable in the data; the second step was to divide each mean-centered variable by its standard deviation. This scaled each variable in the sample data to zero mean and unit variance. Since the sample data of F0 represented the normal condition, other sample data should be scaled with mean and variance vector of the sample data of F0. We define the DGRNN model under normal condition as follows: QP1 ( t ) = Γ F 0 (QP1 ( t − 1) , PP1 ( t − 1) , PA1 ( t − 1) , PB1 ( t − 1) ,
(11)
QP1 ( t − 2 ) , PP1 ( t − 2 ) , PA1 ( t − 2 ) , PB1 ( t − 2 ) )
Then the threshold of fault diagnosis can be obtained as follows:
ε 0 = 2 × J 0 = 0.221
Fig. 4. Basic hydraulic loop of the excavator.
By using the experimental excavator, the sample data was generated from three single fault cases including piston wear, spool stroke, and spool wear. The observation vector at time t, which was composed of variables from the simulation model, could be written as follows:
x ( t ) = PP ( t ) , PA ( t ) , PB ( t ) , QP ( t ) , T
where
PP and QP are the pressure and the flow rate at pump outlet respectively. PA and PB are the pressure at port A and port B of valve respectively. By using the experimental excavator, sample data was generated from three target fault cases: Fault 0: No faults; Fault 1: Piston wear; Fault 2: Spool stroke; Fault 3: Spool wear. A case where more than one fault occurs simultaneously was not considered in this study. To obtain an adequate resolution for the hydraulic system, a 100 Hz sample frequency could be used. The computation and analysis of the sample data were implemented in Matlab environment to verify the fault diagnosis approach [9]. In order to avoid particular variables inappropriately dominating the
Ten test fault samples were used to verify fault diagnosis approach. They were computed with Eq. (11) and Table 1 showed that fault diagnosis results of the ten first test samples. The fault diagnosis approach could achieve an accuracy of 90 % after analyzing 10 test samples. Table 1. Result of fault diagnosis. Sample 1 2 3 4 5 6 7 8 9 10
The sum of square residuals 0.116 0.302 0.300 0.447 0.388 0.434 0.311 0.272 0.324 0.319
Result √ √ √ √ √ √ √ √ √ √
6. Conclusions Aiming at the hydraulic system, a fault diagnosis approach using DGRNN model was proposed in this paper. As a novel artificial neural network, the D GRNN model can greatly improve dynamic identification ability of nonlinear system. With this approach, a DGRNN model was developed using sample data under normal condition, which could effectively detect the test fault under different fault conditions. The hydraulic system of a 1.7 ton excavator was used to verify the fault diagnosis approach. The proposed fault diagnosis approach was verified via
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Sensors & Transducers, Vol. 171, Issue 5, May 2014, pp. 239-244 this experimental excavator. Experiment results show that the proposed approach could be effectively applied to the fault detection of the excavator’s hydraulic system.
Acknowledgement
[3].
[4].
This work is a project funded by the open foundation of the State Key Laboratory of Fluid Power Transmission and Control under Grant No. GZKF-201211 and the Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Education Department of Hunan Province (Changsha University of Science & Technology) under Grant No. 2013KFJJ07. The authors are would also like to express their sincerest gratitude to Shanghong He, Ying Jiang and Ping Jiang for helpful discussions on this topic, and valuable comments on earlier drafts of this paper.
[5].
[6]. [7].
[8].
References [1]. Qinghua He, Daqing Zhang, Peng Hao and Jianxin Zhu, Model and experimental research on control of hydraulic excavator's manipulator, Journal of Central South University (Science and Technology), 37, 7, 2006, pp. 542-546. [2]. T. Marcu, B. Köppen-Seliger, R. Stücher, Design
[9].
of fault detection for a hydraulic looper using dynamic neural networks, Control Engineering Practice, 16, 2, 2008, pp. 192-213. A. E. Ben-Nakhi, M. A. Mahmoud, Cooling load prediction for buildings using general regression neural networks, Energy Conversion and Management, 45, 2004, pp. 2127-2141. W. Y. Lee, J. M. House, N. H. Kyong, Subsystem level fault diagnosis of a building's air-handling unit using general regression neural networks, Applied Energy, 77, 12, 2004, pp. 153-170. H. K. Cigizoglua, M. Alpb, Generalized regression neural network in modeling river sediment yield, Advances in Engineering Software, 37, 2006, pp. 63-68. R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer Berlin Heidelberg, Berlin, Germany, 2006. Achmad Widodo, Bo-Suk Yang, Application of nonlinear feature extraction and support vector machines for fault diagnosis of induction motors, Expert Systems with Applications, 33, 1, 2007, pp. 241-250. D. Zogg, E. Shafai, H.P. Geering, Fault diagnosis for heat pumps with parameter identification and clustering, Control Engineering Practice, 14, 12, 2006, pp. 1435-1444. The MathWorks Inc., Matlab, (http://www. mathworks.com).
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