1Shool of Automobile Engineering, Wuhan University of Technology, Wuhan 430070, China 2School of Automation, Wuhan University of Technology, Wuhan 430070, China
Abstract
Sensors are critical for the monitoring and real-time control of fuel cell system, according to the reliability requirements of multi-sensor of 60kW automotive fuel cell system designed by our group, a two-level neural networks based fault diagnosis method is put forward in this paper. The two-level neural networks include a main net and five sub nets which are corresponding to inlet hydrogen pressure sensor, inlet air pressure sensor, outlet temperature sensor, output voltage sensor and output current sensor, and they are trained with 2100 different groups of normal data of the five sensors stated above from time t-1 to t-3 with LM algorithm. In the faults detection of these sensors, we set the threshold errors of the main net and the five sub nets at 0.005 and 0.05 respectively, when the errors of both main net and a certain sub net exceed the threshold values set, the fault of sensor corresponding to the certain sub net is detected, then its output signal is replaced by the sampled value of the former time and updated into the two-level neural networks accordingly. Finally, taking output current sensor for instance, the simulation results are presented, which validates that the approach adopted can facilitate the real-time fault detection and active fault-tolerant control for multi-sensor of automotive fuel cell system.
As the important components of automotive fuel cell system, sensors play significant roles in its monitoring and real-time control [1]. The structure of fuel cell system is complicated and the Electro Magnetic Interference(EMI) environment is severe, so the faults of multi-sensor are unavoidable. Once the faults occur without any detection, if no protective measures are taken in time, there may be misoperation or even direct damage to the costly fuel cell stack. Thus, it is essential to study on the fault diagnosis and fault-tolerant control for multi-sensor of automotive fuel cell system.
Up till now, the popular approaches to the fault diagnosis for sensors include the ones based on hardware redundancy, Kalman filter, signal processing, neural networks and so on. The hardware redundancy based method demands additional sensors to measure the same parameters, it increases the development costs of fuel cell system. Kalman filter is a promising method in the real time fault diagnosis of sensors for it can describe their dynamic performance [2], but its diagnosis performance mainly depends on their precise models. In fact, the accurate models of different sensors are difficult to set up even though the accurate
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models during a certain time can be acquired, their accuracy may slowly decline or the object parameters fluctuates as time flies. Signal processing method especially wavelet analysis [3, 4] is suitable for the signal singularity identification of sensors, whereas the output load of vehicle hybrid system varies all the time and all the parameters of fuel cell system keep changing accordingly, so it is deficient to the fault diagnosis for sensors only by detecting the sudden mutation of their output signals.
Artificial neural network(ANN) has excellent ability of non-linear mapping and self learning, and it can avoid the negative influence and subjective factors of unfaithful model established [5, 6], therefore, it is applicable to the fault diagnosis of complicated non-linear systems. In this paper, we adopt a two-level neural networks based method in the fault diagnosis and active fault-tolerant control for the multi-sensor of fuel cell system which have redundancy relations among one another.
This paper is organized as follows. In section 2 we will analyse the multi-sensor faults of fuel cell system designed by our group, and analyse their influence on fuel cell system’s reliability and performance in section 3. In section 4 we will introduce our two-level neural networks based fault diagnosis framework, followed by the experimental and simulation results in section 5. The conclusions are given in section 6.
2. Multi-Sensor Faults Analysis of Fuel Cell System
The stucture of 60kW automotive fuel cell system studied is designed by State Key Laboratory of Advanced Technology for Material Synthesis and Processing of Wuhan University of Technology(China), as shown in Fig.1, its sensors network includes pressure sensors(P1~P5), flow sensors(F1~F4), temperature sensors(T1~T4), inlet relative humidity sensors(W1~W2), liquid height sensor(H), conductance rate sensor(C), voltage sensor(U), current sensors(A1~A2) and so on.
Fig.1 The Structure of Automotive 60kW Fuel Cell System Designed
Like other mechanical and electric devices, from the aspects of fault degree, the sensors faults of fuel cell system can be classified as hardware faults and soft faults. From the point of existing characteristic, they may be divided into intermittent faults and permanent ones. From the evolution course of faults, they are classified as emergent ones and gradually changed ones. The common sensors faults types and their faults reasons are presented as follows:
(1) Offset fault: output change induced by the offset voltage or current. (2) Impact fault: it is caused by the disturbance between supplied power with ground, surge, electronic
spark or the burr of D/A converter.
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(3) Open-circuit fault: it is due to the turnoff of circuit, unreliable welding spots or the pins of chips are not rightly connected to the desired position.
(4) Short circuit fault: birdge circuits erosion because of contamination or the sensor is short connected. (5) Floating fault: zero point floating,temperature floating or measurement sensitivity floating of sensors
output signals. (6) Periodic fault: caused by 50Hz disturbance of supplied power. (7) Nonperiodic fault: caused by the saturation of operational amplifier or the non-linear parts of sensors
of their own. According to our pratical testing results and maintenance experience of fuel cell system since 2004, the
typical kinds of sensors faults are offset fault, impact fault, floating fault and nonperiodic fault, and the sensors faults of fuel cell system are characterized by uncertainty and randomicity.
3. Influence of Multi-Sensor Faults on Fuel Cell System
Based on the electrochemistry reaciton mechanism [7], during the operation of fuel cell system, the needed air mass flow Qam= 3.57×10-7λnIo(kg/s), and the needed hydrogen mass flow Qhm=1.05×10-8nIo(kg/s). Where λ is excess coefficient of air, Io is the output current of fuel cell stack, n is the number of single fuel cells, for the mass density of air(1.29kg/m3 in standarded circumstance) and hydrogen(0.0899kg/m3 in standarded circumstance) is well known, the volumn flow of air and hydrogen needed in practical operation can be easily figured out when Qam and Qhm are divided by their mass density values.
From the formulas of Qam and Qhm above, the current sensor(A1) can be treated as flow adjusting basis of both air and hydrogen, once the soft fault arises that its output value is much lower than the practical current value, if the fault is not detected or its output value is not reconstructed, the air volumn will be out of control, or the fuel cell stack will be starved for the lack of supplied hydrogen, which will lead to the deficient reaction or even permanent devastation to fuel cell stack especially under large output load [8].
During middle or big vehicle load operation, lots of heat is generated inside the fuel cell stack, similarly, if the fault of temperature sensor (T4 ) is not detected and its output value is smaller than the desired one, the control of water pump and fans will be postponed for a little while. In this case, the stack may be dried or even be burned by the undispersed heat inside [9]. Contrarily, if its output value is bigger than the valid one, the control of water pump and fans will be advanced, which will make the reaction temperature cool down quickly and slowly disbenefits the overall output performance of fuel cell system [10].
The sensors A2 and F2 are applied to monitor H2 pump which is in charge of outlet hydrogen recycling and inlet hydrogen humidifying, sensors F4 and P5 mainly monitor water pump which guarantees the water flow according to temperature inside fuel cell stack. Sometimes only one of they is selected for the costs reason, if they go wrong, whether H2 pump and water pump are in order will be unknown, which brings in humidity problems(drying and flooding) to fuel cell stack [11].
High pressure of reaction fuel may not be found out and no protection measures will be taken especially if there are offset faults, floating faults and nonperiodic faults in pressure sensors P1, P2 and P4, which will lead to the rupture and perforation of Proton Exchange Membrane(PEM) [8].
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The conductance sensor C is applied to measure the ion density of water, its faults will interfer with the updating of deioned water, so once the ion density exceeds the security threshold set before, the short circuit risk of fuel cell stack arises accordingly.
In all, the remaining sensors such as F1, F3, W1, W2 and so on in Fig.1 have similar function as A2, P5, they are also crucial to the variables measurement and state monitoring of fuel cell system, however, they are not inclined to bring in harms to fuel cell stack even though they are at fault without any detection.
4. Establishment of Multi-Sensor Fault Diagnosis System
4.1. Structure of Fault Diagnosis System
From the analysis above, we can found out that the output signals of sensors are related to their own reliabilty, precision and sensitivity. To enhance their reliability, scientific detection method is badly needed other than improving their own quality. For the limitation of manufacture technics and material quality, the reliability and precision of sensor of fuel cell system can not be raised without limits, the signal of a single sensor can not always reflect the true states of the whole fuel cell system, which is decided by the uncertainty of a single sensor. Considering the redundancy relations among the sensors in Fig.1, we propose a two-level neural networks based system to their fault diagnosis research, its framewok is composed of a main net and n sub nets, the basic structure of the main net is given by Fig.2.
Fig.2 The Structure of Main Neural Network
As shown in Fig.2, the input layer nodes are values of sensor 1~n from time t-1 to t-p, H1~Hm are the hidden layer nodes, O1~On are the output nodes at the time of t. Here, we define the error of the main net as
2
1( )
n
i ii
MNNERR y o=
= −∑ (1)
Where y1~yn are corresponding to the output values of sensor 1~n at the time of t. Besides, the ith sensor is corresponding to sub net i(i=1~n), similarly, the specific structure of the ith sub net is shown in Fig.3.
4.2. Fault Diagnosis and Signals Reconstruction Process
When all the sensors are in order, the inputs of the main net are the output values of sensor 1~n from time t-1 to t-p, and their output values at time t are taken as the outputs of the main net, then it is trained with algorithm until convergence. As to the training of the ith sub net(i=1~n), the output values of the other n-1 sensors from time t-i to t-p except the ith sensor are its inputs, the practical value at time t of the ith sensor
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is its output. Thus, the outputs of both main net and sub nets 1~n are equal to pracitcal valid values, i.e. both MNNERR and SNNERR are close to 0.
H1 H2 Hk…H3
t-1 … t-p t-1 … t-p t-1 … t-p
Sensor 1 Sensor 2 Sensor n… Sensor i
Odi
Algorithm
Calculation of SNNERR
yi+
-
Output layer
Hidden layer
Input layer
Weight
Threshold
Fig.3 The Structure of ith Sub Neural Network
In Fig.3, the signs have the same meaning as those in Fig.2, and we define the error of the ith sub net as SNNERR=yi-Odi (2) Taking the fault of the ith sensor at time k for example, its output values from time k-1 to k-p are normal,
so the outputs of the main net at time k are accurate, but compared with its practical valide value, MNNERR still exists. Accordingly, as to the ith sub net the output values of the other n-1 sensors from time t-i to t-p except the ith sensor are also precise, thus, SNNERR is much bigger than 0. At this moment, both of the inputs and outputs of the other n-1 kinds of sub net are normal. So if both MNNERR and SNNERR exceed the threshold set and they will last for a certain time, we can decide the faults of multi-sensor. In order to confirm the fault of the specific the ith sub sensor, its SNNERR is the judgement basis, and the output signal of the ith sensor is replaced by the output of its corresponding ith sub net, based on these reconstructed values, the inputs and outputs of both the main net and sub net 1~n are updated in time.
4.3. Training Algorithm of Two-level Neural Networks
The basic training algorithm of neural networks is the standarded Back Propagation(BP) algorithm, which reaches the minimum square error by regulating its weights and thresholds with gradient descending method, but it has obvious disadvantages such as slow convergence speed, local minimum and poor generalization even though it is improved with momentum gene and learning rate. In this paper, we adopt Levenberg-Marquardt(noted LM) algorithm [12,13] to optimize the regulation of weights and thresholds of traditional BP neural network:
X(k+1)=X(k)+∩X (3)
Where X(k) is the vector made up of weights and thresholds at the kth time of iterative operation, X(k+1) is the updated one at the (k+1)th time, ∩X is a vector defined by formula 4.
∩X=-|∇2E(x)|-1∇E(x) (4)
Where ∇2E(x) is the Hessian matrix of training error index function E(x), ∇E(x) is the gradient. E(x) is
2
1
( ) (1 / 2 ) ( )N
ii
E x e x=
= ∑ (5)
Where e(x) is the training error, in addition, we can come to the conclution shown by formula 6 and 7:
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∇E(x)=JT(x)e(x) (6)
∇2E(x)=JT(x)e(x)+S(x) (7)
Where 2
1
( ) ( ) ( )N
i ii
S x e x e x=
= ∇∑ , J(x) is Jacobian matrix [14].
Based on Gauss-Newton algorithm [15], formula 4 is transformed into formula 9. ∩X=-[JT(x)J(x)]-1J(x)e(x) (8)
Accordingly, formula 4 can be transformed into formula 9 with LM algorithm stated above. ∩X=-[JT(x)J(x)+ μI]-1J(x)e(x) (9)
Where μ is a positive constant, I is the unit matrix. LM algorithm is equal to Gauss-Newton algorithm When μ is 0, contrarily, if μ is large enough, LM algorithm is close to BP algorithm, the closer it reaches the error objective after each iterative operation, the smaller μ is, and the more likely LM algorithm is to be Gauss-Newton algorithm which has fast compution and exclusive precision when it approaches the minimal error. In theory, LM algorithm has distinct advantages over BP algorithm, thus, we employ it in the training of both the main net and sub nets 1~n, its detailed steps are presented in [12, 13, 14].
5. Simulation and Discussion
5.1. Training of Two-level Neural Networks
To set up the mechanism model of fuel cell system and analyse its dynamic performance, the sensors in Fig.1 or even more will be fixed. But for the costs cutting and structure simplifying of system, to monitor its basic working states, sensors P1~P5, T2~T4, A1, A2, U, H and C are the elementary combination unit applied in this paper. As indicated in section 2, among them sensors P2, P4, T4, U and A1 are the essential ones, based on the redundancy relations among one another(which can be proven by Fig.4), they are selected as the simulated objectives which are corresponding to sub net 1~5 respectively.
According to Fig.2 and Fig.3 above, the output number of the main net is 5, and the output number of sub net 1~5 is 1. In this paper, we chose the delayed gene p of both the main net and sub net 1~5 to be 3(in pracitical work the interval sampled time of sensors’ output signals is 100ms), so the input number of the main net is 15, while the input number of sub net 1~5 is 12.
Fig.4 gives the real-time curves of P2, P4, T4, V and A1 with different output power Pout, in which P1 is kept stable at 7Bar, and the ripple of P2 is caused by the aperiodic opening of exhaust valve. To train both the main net and sub net 1~5, 2100 different groups of data in Fig.4 are selected and the ripple of P2 is filtered with bubbling filter method.
Fig.5 gives the training results of the main net and sub net 5 with LM algorithm, as to both the main net and sub net 1~5, the hidden function is tansig, the training goal is set at 0.001. In addition, the output layer function is logsig. As to training of sub net 1~4 in Fig.2, sub net 5 is taken for an example to represent them for their similar training performance with quick convergence, its hidden layer number is 16, while the hidden layer number of the main net is 21. Obviously, the main net quickly converges to the goal after 17 epochs, and the sub nets converge to the training goal only after 9 epochs.
To compare the performance of LM algorithm with BP algorithm in the training of the main net and sub net 5, Fig.6 gives the training errors, in which relavant simulattion setting parameters are kept the same as
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those in the training with LM algorithm. Comparing Fig.5 with Fig.6, LM algorithm has overwhelming advantages over BP algorithm in the training of two-level neural networks.
Fig.4 The Curves of Relavant Variables with Different Output Power
a. Training of the Main Net b. Training of Sub Net 5
Fig.5 Training of Two-level Neural Networks with LM Algorithm
5.2. Example
Based on the trained two-level neural networks model above, In this section, the instance that only a sensor goes wrong at each time is considered, for the sake of representation, the fault of sensor A1 is presented as an example. Fig.7 gives the comparison between the practical output of sensor A1 with prediction of sub net 5 after normalization, from 191s to 214s the output of sensor A1 increases overly because of its offset fault while the outputs of the other 4 sensors are valid, the prediction of sub net 5 keeps relatively stable within a certain range of the valid value. What is more, the errors of the main net and sub net 5 increse from almost 0 to 0.1 and 0.01 respectively at the time of 191s, while the errors of the other 4 sub nets are close to 0 all the time(for the limitation of paper length, they are not given directly). So if the thresholds of both the main net and sub net 5 are set at 0.005 and 0.05 respectively, the faults of sensors A1 can be easily detected in time. In this case, from the time 191s on, the false output of sensor A1 can be substituted by the prediction of sub net 5, which realizes the fault-tolerant control performance of the multi-sensor system.
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a. Training of the Main Net b.Training of Sub Net 5
Fig.6 Training of Two-level Neural Networks with BP Algorithm
Based on the same method above, as to the simulation results of sensors P2, P4, T4 and U(omitted for the pages length limitation), when their undetected faults occur, the maximal errors of the main net and sub net 1~4 are shown in table, thus, if we set the error thresholds of the main net and sub net 1~5 at 0.005 and 0.05 respectively, we can easily figure out sensors faults once MNNERR and SNNERR exceed them.
Fig.7 The Errors and Prediction of Neural Networks
Table 1 Maximal Errors of The Main Net and Sub Net 1~4
Max Errors P2 P4 T4 U
MNNERR 0.98 1.12 1.07 1.09
SNNERR 0.99 1.08 1.01 1.04
6. Conclusion
In this paper, we proposed a two-level neural networks based method for the real-time diagnosis and fault-tolerant control of sensors P2, P4, T4, U and A1, and the threshold errors of main net and sub nets are set at 0.005 and 0.05 respectively to detect the faults of each sensor, once MNNERR and SNNERR exceed them, we can detect the fault of the relevant sensor and substitute the invalid signals with the predictive output of its corresponding sub net. We applied the method above in practice for months, the experimental results also showed that it can quickly detect the sensor faults and enhance the fault-tolerant control performance of the whole system. It can also provide an instructional alternative to the reliability and safety research of other complicated non-linear systems with large nunbers of sensors.
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Acknowledgement
This work is supported by the High-Tech Research and Development Program of China (863 Program) (NO.2006AA11A133 and NO.2008AA05Z105) and the National Natural Science Foundation of China(NO.60705032/F30605 and NO.61004018/F030102).
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