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A hybrid prognostic model applied to SOFC prognostics
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 3
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A hybrid prognostic model applied to SOFC prognostics Xiaojuan Wu*, Qianwen Ye, Junhao Wang School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
article info
abstract
Article history:
Poor durability is one of the major hurdles for Solid Oxide Fuel Cell (SOFC) commerciali-
Received 23 June 2017
zation. Prognostic technology is an important approach to improve system durability.
Received in revised form
However, the current prognostic methods for fuel cells are mainly applied to proton ex-
12 August 2017
change membrane fuel cell (PEMFC) systems, moreover, there are still shortages of recent
Accepted 17 August 2017
prognostic algorithms. Therefore, an improved prognostic model is developed to predict
Available online xxx
the remaining useful life of the SOFC in this study, which combines a hidden semi-Mark model (HSMM) with an empirical model. To build the hybrid prognostic model, an HSMM
Keywords:
and an empirical model are firstly built. The merit and demerit of the respective prognostic
Solid oxide fuel cell (SOFC)
methodology are then analyzed. According to the analysis results, the hybrid prognostic
Hybrid prognostic model
model is proposed and applied to six sets of SOFC run-to-failure data. The results show the
Hidden semi-Markov model (HSMM)
proposed prognostic model has a higher prediction accuracy and a faster forecasting speed
Empirical model
compared with the existed approaches for SOFC prognostics.
Prognostic
© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Solid Oxide Fuel Cell (SOFC) is an electro-chemical device, which can convert chemical energy into electrical energy. Due to its low emission and high efficiency, SOFC is considered to be a promising generation technology [1]. Nevertheless, because of inadequate operational states, impurities in gases and materials deterioration, poor long-term performance is one of the major hurdles for the commercialization of SOFC [2]. In order to improve system's durability, in this study prognostic technology is proposed to predict the future condition of a system. According to International Standard Organization(ISO), prognostic is defined as “the estimation of the operating time before failure and the risk of existence” [3]. Based on the ISO standard, it allows to define the remaining
useful life, which is “the estimation of the time between the current moment and the moment when the monitored system is considered as failed ” [4]. Thus, the objective of prognostic is to estimate the remaining useful life of the system to be functional. Various prognostic methods have been successful applied in the fuel cell systems, and they can be divided into two types of approaches: model-based and data-based approach. Model driven approach uses mathematical equations to describe the degradation process of the system, which requires a precise knowledge of the system failure mechanisms [5]. A physicsbased model was firstly built, and then unscented kalman filter was proposed to capture the degradation of the proton exchange membrane fuel cell (PEMFC) [6]. A first-order mathematical model was established to estimate the remaining useful of the PEMFC [7]. A power degradation model
* Corresponding author. E-mail address: [email protected] (X. Wu). http://dx.doi.org/10.1016/j.ijhydene.2017.08.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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was presented based on a detailed understanding of the degradation phenomena [8]. Data-based approach is also named a black box method, for it has no direct link with the physical phenomenon occurred in the system. In this case, the monitored historical data is employed to discuss the degradation process of the system [5]. Data driven prognostic approach can be classified into two categories: 1) degradation modeling; 2) direct prediction modeling. For the degradation modeling, a degrading signal is firstly estimated, such as voltage or power. The remaining useful life of the system is then calculated when the degrading signal reaches a pre-defined failure threshold. Empirical models were built to follow the power degradation due to time varying parameters, and then the residual life of the PEMFC was predicted when the power intersected the failure threshold [9]. Four empirical models were used to predict the power degradation trend of the PEMFC [10]. Five empirical models based on weighted mean was developed to estimate the voltage [11]. Three empirical models of the voltage drop were proposed for PEMFC prognostic [12]. Summation WaveletExtreme Learning Machine algorithm was presented to estimate the voltage degradation of the PEMFC and then the residual life was predicted [13]. An echo state network was reported to forecast the voltage degradation of PEMFC [14]. An adaptive neuro-fuzzy inference system was studied to estimate the PEMFC voltage [15]. Using an improved relevance vector machine, the PEMFC degradation was predicted [16]. Based on the group method of data handling and the wavelet analysis, a short-term prognostics method was developed to predict the voltage for the PEMFC [17]. Using a neural network model, the SOFC voltage degradation was estimated [18]. Direct prognostic modeling can predict the remaining useful life of the system directly, by finding the similarity between the observed data and the training data. The approach does not define a failure threshold, and directly learns from the data. A hidden semi-Markov model (HSMM) was exploited to predict the residual life of the SOFC by the present author [19]. Despite the great progress in prognostic technique for the fuel cell, the existing literature still has several drawbacks:
from the training data, the prognostic accuracy may not be high. To address the above issues, a hybrid prognostic model based on data-driven approach is presented to perform the remaining useful life prediction for the SOFC, which integrates an HSMM with an empirical model of degradation. As described above, using the empirical model, it is time consuming to predict the remaining useful life; nevertheless, using the HSMM method, the prediction accuracy strongly depends on the similarity between the test and training data. The hybrid prognostic model can exploit the strengths and eliminate the weaknesses of the respective prognostic methodology, rather than continuing to select between the individual prognostic approach [20]. When the degradation trend of the test data is similar with the training data, the HSMM method is used to predict the residual life for the SOFC, which can avoid rebuilding the prognostic model when new data is provided and improve the prognostic speed. Otherwise, the empirical model which can improve the prediction accuracy is employed for SOFC prognostic. The main contributions of this paper are summarized below: * The proposed prognostic algorithm not only guarantees a higher prediction accuracy, but also improves the prognostic speed compared to the existed prognostic approaches. * The proposed hybrid prognostic model is applied to the SOFC. To the best of our knowledge, only two articles previously studied the SOFC prognostic technique. The paper hereafter is organized as follows. Section Problem formulation explains SOFC prognostic problem. In Section SOFC prognostic using the individual model, the HSMM and the empirical model are respectively presented for SOFC prognostic. According to their own advantages and disadvantages, the hybrid model is proposed to predict the remaining useful life of the SOFC in Section SOFC prognostic using the hybrid model. Section Results draws the conclusion.
Problem formulation * Using the model-based prognostic approach, it is a difficult task to build the degradation model to reflect the degradation process of the fuel cell, since the fuel cell system is a complex multi physics system, which involves mechanical, electric, thermal, fluidic and electrochemistry phenomena. Moreover, the system is a time and space multiscale system. * The degradation modeling is a very time-consuming process, because the models use the past degradation signal to predict the future value, which implies that if new data is available, the prognostic model should be rebuilt. Moreover, to obtain a precise prediction model, a group of models with various initialization is generally needed to be trained. * The direct prognostic modeling depends on the similarity between the test and training data. For example, using the HSMM, if the drop trend of the test data is much different
For the SOFC anode, different kinds of fuels can be considered. Nevertheless, practical fuels often contain chlorine compounds at 100 ppm or higher concentration, especially in coal gas [21,22]. Degradation is occurred in the SOFC system when a high concentration of Cl2 is supplied in the anode [21,22]. Therefore, it is necessary to discuss the influence of Cl2 poisoning on the SOFC performance. Since the ambient air is continuously supplied to the cathode, it can not ignore the influence of water vapor in the air on the cathode performance to test long-term durability of the SOFC. Ref. [21,23] demonstrated a high concentration of water vapor supplied in the cathode could lead to the degradation of the SOFC performance. When the SOFC contains the impurities, such as Cl2 at the anode or water vapor at the cathode, it generally experiences several health states (good, medium, bad, etc) to reach failure, which is illustrated in Fig. 1.
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 3
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Fig. 1 e Health state transitions diagram for the SOFC.
Prognostics and Health Management (PHM) is developed to guarantee system's safe long-term operation and reduce maintenance cost. To achieve this goal, PHM is generally performed by three main stages:data acquisition, prognostic, and decision making. Data acquiring part is to gather useful data which can reflect the degradation change in the system. According to the acquired data, prognostic is employed to predict the future condition and calculate the remaining useful life of the system. The decision making module is used to take a proper maintenance on the system at the right time to extend its life. This study focuses on the first two stages of PHM described hereafter: * Acquiring data Cl2 poisoning or water vapor poisoning may lead to a decrease in voltage [21], therefore voltage is selected as the prognostic indicator to describe the SOFC degradation process. The voltage signal is firstly extracted using sensors. Furthermore, the raw data collected by the sensors is processed to be used in the prognostic model, which will be explained in Section Data preparing. * Prognostic A hybrid prognostic model based on an empirical model and an HSMM is developed to estimate the progression of the SOFC health condition and predict the remaining useful life. When the degradation trend between the test and training data is similar, the HSMM approach is presented for SOFC prognostic, which is clarified in Section HSMM method for SOFC prognostic. Otherwise, the empirical model is employed to predict the voltage decrease, which is given in Fig. 2. The SOFC is defined as failure when the voltage reaches the failure threshold Vfailure . Therefore, the remaining useful life of the SOFC is the difference between the failure life tfailure and the current moment tcurrent . The empirical model for SOFC prognostic is explained in Section Empirical model for SOFC prognostic.
SOFC prognostic using the individual model In order to build the hybrid prognostic model, an HSMM and an empirical model are respectively established in this section.
Fig. 2 e The remaining useful life illustration.
Data preparing To implement anode and cathode poisoning tests, six electrolyte-supported single SOFC cells were employed. Electrolyte plates were made of 10 mol% SC2O3-1mol% CeO289 mol% ZrO2, and the thickness was 200 mm. Electrode area was 8 mm 8 mm and Pt mesh was used as the current collector. Anode layer had double layer structures. The first layer was the mixture of 56 wt% NiO and 44 wt% ScSZ, while the second layer was the mixture of 80 wt% NiO and 20 wt% ScSZ. Cathode was the mixture of LSM and ScSZ with a weight ratio of 1:1. More details about the six single SOFC cells can be found in Refs. [22,23]. For the electrochemical measurements of anode poisoning, the anode gas was 3 vol% humidified H2 containing Cl2 at 100 ppm, 400 ppm and 1000 ppm, and the cathode gas was supplied with dry air. The SOFC operated at a constant current density of 0.2Acm2 with a constant temperature of 1073 K. The degradation process was measured for 150 h, and three groups of voltage with Cl2 concentration at 100 ppm, 400 ppm and 1000 ppm were gathered. The anode poisoning data used for prognostic is displayed by the solid lines in Fig. 3(a) [22]. The voltage with 1000 ppm Cl2 is employed for the HSMM training, whereas the training requires to be made under each concentration using the empirical model. To carry out the cathode poisoning test, the anode gas was 3 vol% humidified H2 and the cathode was the humidified air with 3 vol%, 5 vol% and 10 vol% water vapor. The SOFC operated at a constant current density of 0.2 Acm2, and the operating temperature was 1073 K. The degradation process was measured for 1000 h, and three sets of voltage degradation data with 3 vol%, 5 vol%, 10 vol% water vapor in air were collected. The cathode poisoning data used for prognostic is given by the solid lines in Fig. 3(b) [23]. The voltage with 10 vol % of water vapor is used to train the HSMM, however, it is necessary to train an empirical model under each water vapor concentration. In order to be learned more accurately by the prognostic model, the raw voltage data is processed applying a moving average filter algorithm [24]. The filtered data is described by
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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number N is selected as three. Each state of the HSMM represents a health state of the SOFC. Using the Baum-Welch algorithm [25], the HSMM in Eq. (1) is trained. The degradation state estimation generated by the HSMM is given in Fig. 4(a). The voltage from 1.02 V to 0.96 V is represented by H1, which indicates that the SOFC is in the normal state. The voltage from 0.96 V to 0.90 V is denoted as H2, which means that the SOFC is in the level-1 defect state. The voltage from 0.90 V to 0.82 V is described by H3, which implies the SOFC is in the level-2 defect state (failure). The estimated parameters of the HSMM are given as follows:
1.02 1 0.98
100ppm Cl
2
SOFC voltage(V)
0.96 0.94 0.92 0.9 0.88
1000ppm Cl
400ppm Cl
2
2
0.84 0.82
3 0 1 2 3 2 3 m1 ; s 1 1 0 1 0 a11 a12 a13 A ¼ 4 a21 a22 a23 5 ¼ 4 0 0 1 5; p ¼ @ 0 A; 4 m2 ; s2 5 0 0 0 1 a31 a32 a33 m3 ; s 3 3 2 34; 2:8 ¼ 4 44:5; 1:1 103 5h 72; 0 2
0.86
0
50
100
150
Time(h)
(a) Under anode poisoning [22]
(2)
0.94 0.92 3 vol%
2) Under cathode poisoning
0.9
SOFC voltage(V)
0.88
Under the cathode poisoning, the voltage with 10 vol% of water vapor is employed to train the HSMM, and the estimated degradation trend is presented in Fig. 4(b). H1 means the SOFC normal state, and the SOFC voltage is varied from 0.89 V to 0.85 V. H2 indicates level-1 defect state, and the voltage changes from 0.85 V to 0.80 V. level-2 defect state (failure state) is represented by H3, and the voltage varies from 0.80 V to 0.75 V. Under the cathode poisoning, the estimated parameters of the HSMM are shown as follows:
0.86 5 vol%
0.84 0.82 0.8
10 vol%
0.78 0.76 0.74
2
0
100
200
300
400
500 600 Time(h)
700
800
900
1000
(b) Under cathode poisoning [23] Fig. 3 e Data used for SOFC prognostics. the dashed lines in Fig. 3, which reveals a monotonic decrease of the SOFC voltage.
a11 A ¼ 4 a21 a31 2 460; ¼ 4 160; 380;
0 1 2 3 3 2 3 m1 ; s 1 1 0 1 0 a13 4 A @ 5 4 5 a23 ¼ 0 0 1 ; p ¼ 0 ; m2 ; s2 5 0 0 0 1 a33 m3 ; s 3 3 0:0107 0:5 104 5h 0
a12 a22 a32
(3)
Estimate the remaining useful life for the SOFC 1) Under anode poisoning
HSMM method for SOFC prognostic The HSMM is general expressed by Ref. [25]: l ¼ f ðN; M; A; B; p; PÞ
(1)
where, durational probability P is defined to follow a Gaussian function distribution in this study. It usually needs two stages to predict the remaining useful life by the HSMM: 1) training an HSMM which is able to reflect the SOFC degradation process; 2) estimating the SOFC remaining useful life.
The main physical equations are given below, but further details can be retrieved from the reference papers [19,26]. Assuming the SOFC is identified at the i th health state(i ¼ 1; 2; 3), the remaining useful life of the SOFC is calculated as follows [17]: RULHSMM;i ¼ ti þ
aij @mj þ
N X
1 ajk mk A
(4)
k¼jþ1
where, ti ¼
In the case of anode poisoning, the voltage with 1000 ppm Cl2 is employed to train the HSMM. The SOFC is defined to go through three health states to reach failure: normal, level-1 defect, and level-2 defect(failure). Therefore, the HSMM state
0
j¼iþ1
Train an HSMM to represent the SOFC degraded process 1) Under anode poisoning
N X
Di X ðDi tÞ Pðsi =OÞ
(5)
t¼1
where, aij and mj are obtained from Eq. (2). ti is the remaining duration time at the i th health state. According to Eq. (2), the maximum duration Di in the i th health state is respectively 34 h, 44.5 h and 72 h under anode poisoning. Pðsi =OÞis the probability that the single state si generates the observation O,
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Voltage(V) Health state
1.02
SOFC voltage(V)
0.95 Normal state(H ) 1
0.9
Level-1 defect state(H ) 2
0.82
Level-2 defect state(H ) 3
0.75
0
50
100
150
Time(h)
(a) Under anode poisoning 0.92 Voltage(V) Health state
SOFC voltage(V)
0.87
Normal state(H ) 1
0.82 Level-1 defect state(H ) 2
0.77 Level-2 defect state(H ) 3
0.72
0
100
200
300
400
500 Time(h)
600
700
800
900
1000
(b) Under cathode poisoning Fig. 4 e SOFC voltage degradation trend prediction. which is obtained using the Viterbi algorithm [27]. i is the current health state of the SOFC. Through calculating the loglikelihoods of the test samples under three various health states, the current health state of the test sample can be identified [28]. Further detailed identification process can be referred to our previous work [19]. Fig. 5 (a), (b) and (c) give the identified results for fourteen sets of random voltage observation data under various Cl2 concentrations. The circles reflect the predicted current health states of the 14 test samples, and the Asterisks indicate the real health states. The number of correctly identified data is all 14 under three various Cl2 concentrations, and the accuracy ratio is 100%. Further, according to Eqs. (4-5), the remaining useful life of the 14 test samples under different Cl2 concentrations is calculated, which is presented by the solid squares in Fig. 6 (a),
(b) and (c). Using cubic interpolation method [29], the predicted results of the 14 test samples are connected to form the predicted curve of the SOFC residual life, which is given by the thick dashed line in Fig. 6(a),(b) and (c). The solid lines describe the real remaining useful life of the SOFC. For example, if the current moment is 10 h, the real remaining useful life of the SOFC is 140 h since the total life is assumed to be 150 h. By the analogy, the real residual life is 130 h when the current life is 20 h. The dashed and dash-dotted lines are respectively the upper and lower bounds, which represent 15% above or below the real residual life. The prediction is evaluated with a classical prognostic metric:v performance metrics [12]. If the prediction enters in an interval of ±v around the real remaining useful life, it is considered as good estimation. In this study, v is chosen as 15%. Under 100 ppm Cl2, the prediction result is good
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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Predicted state Real state
Predicted state Real state
H
3
H
Health State
Health State
3
H
2
H
H
2
H
1
1
0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
14
0
1
2
(a) under Cl2 100ppm
3
4 5 6 Sample Index
7
8
Predicted state Real state H
H
3
3
Health State
Health State
10
(d) under 3vol % water vapor Predicted state Real state
H
2
H
2
H
H
1
1
0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
0
14
1
2
3
4 5 6 Sample Index
7
8
9
10
(e) under 5vol % water vapor
(b) under Cl2 400ppm Predicted state Real state
Predicted state Real state H
H
3
Health State
3
Health State
9
H
2
H
2
H
1
H
1
0 0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
14
(c) under Cl2 1000ppm
1
2
3
4 5 6 Sample Index
7
8
9
10
(f) under 10vol % water vapor
Fig. 5 e The predicted current health state by the HSMM.
at the initial stage. However, after 60 h, the error between the predicted remaining useful life and the real one is beyond 15%. Under 400 ppm and 1000 ppm Cl2, the accuracy of the prediction is hopeful. To check the prediction performance, Root Mean Square Error (RMSE) is employed to quantify the difference between the predicted remaining useful life and its real target, which is shown in Table 1. The RMSEs are respectively 12.84 h, 4.07 h and 3.52 h under Cl2 concentrations at 100 ppm, 400 ppm and 1000 ppm. The results once again demonstrate that the HSMM method is effective for the SOFC voltage with 400 ppm and 1000 ppm Cl2, however, it is not valid for the test data under 100 ppm Cl2. Moreover, using the HSMM method, the remaining useful life of the SOFC is predicted with only a couple of minutes of prep time. 2) Under cathode poisoning Ten random test samples are respectively selected under 3 vol%, 5 vol% and 10 vol% water vapor. In the same way, the
current health states of the ten test data are identified, which are given in Fig. 5(d),(e)and (f). The Asterisks and circles respectively indicate the real and predicted health states for the ten test samples. The predicted accuracy is respectively 90%, 90%and 100% under 3 vol%, 5 vol% and 10 vol% water vapor. Based on the identified current health state and Eqs. (45), the remaining useful life of the ten test samples are calculated, which are given by the solid squares in Fig. 6(d), (e) and (f). Linking the predicted results using cubic interpolation algorithm, the prognostic results are obtained, which are presented by the thick dashed lines in Fig. 6(d),(e) and (f). Under 3 vol% water vapor, the prediction result is good before 550 h, however, the predicted remaining useful life is beyond 15% lower bound after 550 h. Under 5 vol% and 10 vol% water vapor, the prediction accuracy is hopeful. For the 1000-h long test data, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are respectively 38.79 h, 24.19 h and 16.67 h under 3 vol%, 5 vol% and 10 vol% water vapor.
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Fig. 6 e SOFC prognostic using the HSMM method.
Empirical model for SOFC prognostic According to the reference paper [9], the voltage degradation trend follows the empirical model: c VðtÞ ¼ a þ bt þ þ d logðtÞ t
(6)
where, t is time. During the voltage prediction process, the following constraints are considered: dVt s0 dt
(7)
Vtcurrent > Vðtcurrent þiÞ ; i2Zþ
(8)
b tþh Vfailure V
(9)
b t is the predicted voltage at time t. Vt where, V current is the real b ðt voltage at the current time tcurrent , and V current þiÞ is the predicted voltage at time tcurrent þ i. Eqs. (7) and (8) reflect the SOFC aging
process is irreversible degradation, and Eq. (9) guarantees that the prediction trend reaches the failure threshold. It generally needs two steps to predict the remaining useful life of the SOFC using the empirical prognostic model:1) for each test sample, training a degradation model in Eq. (6) which is able to predict the SOFC voltage evolution; 2) estimating the SOFC remaining useful life.
Train empirical models 1) Under anode poisoning Various lengths of data are employed to learn the model in Eq. (6). In this study, the data is gathered from 10 h to 140 h with a step of 10 h. Therefore, 14 empirical models are supposed to be learned. With a single prediction, it is not easy to obtain an accurate model in Eq. (6) which is constraint with Eqs. (7)e(9). Therefore, using gradient descent algorithm, 50 groups of models with various parameters initialization are trained under each length of
Table 1 e Error between the predicted residual life and its real remaining useful life.
Anode poisoning (100 ppm) Anode poisoning (400 ppm) Anode poisoning (1000 ppm) Cathode poisoning (3 vol%) Cathode poisoning (5 vol%) Cathode poisoning (10 vol%)
RMSE with HSMM (hours)
RMSE with empirical model (hours)
RMSE with hybrid model (hours)
12.84 4.07 3.52 38.79 24.19 16.67
4.35 4.44 4.01 21.20 39.35 51.36
2.86 4.29 3.52 20.65 28.48 16.67
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training data. The median of the 50 models from ensemble is regarded as the SOFC voltage degradation model. Fig. 7(a) and (b), and (c) describe the voltage degradation trend under 14 various initial time for 100 ppm, 400 ppm and 1000 ppm Cl2. The solid line describes the filtered voltage, and the left dashed lines depict the predicted voltage under the different length of training data used during prognostics learning. For the 14 various initial time, the RMSEs between the real SOFC voltage and the predicted one are less than 0.0035 V,0.0075 V and 0.011 V respectively under 100 ppm, 400 ppm and 1000 ppm Cl2. However, it took several hours to obtain the model in Eq. (6), for 50 group of models have been trained with various parameters initialization under each length of training data. Especially for short training data, it spent nearly 8 h to obtain the prediction model in Eq. (6). 2) Under cathode poisoning Under cathode poisoning, the data is collected from 100 h to 900 h with an interval of every 100 h. Thus, 9 empirical models are needed to be learned. Using the gradient-descent algorithm, the trained results under the 9 various initial time are given in Fig. 7 (d),(e) and (f). The RMSEs between the real SOFC voltage and the predicted one are respectively less than 0.0044 V, 0.0066 V and 0.016 V under the water vapor concentrations at 3 vol%, 5 vol% and 10 vol%. Nevertheless, it also took a lot of time to obtain the empirical model in Eq. (6), especially for less training data.
Predict the remaining useful life using the empirical model 1) Under anode poisoning In this study, the SOFC failure criteria is defined as follows: when the voltage reaches a pre-defined failure threshold Vfailure , the SOFC system fails. Therefore, the remaining useful life of the SOFC is calculated as follows: RULEMP ¼ arg VfailureðtÞ tcurrent
(10)
where, argðVfailureðtÞ Þrepresents the time that the SOFC voltage reaches the voltage threshold Vfailure . In the case of 100 ppm Cl2, the voltage threshold Vfailure is 0.936 V from Fig. 3 (a). For the initial 10 h long test sample, the current time tcurrent is 10 h, and the time that the voltage intersects 0.936 V is 138 h according to the predicted voltage given in Fig. 7 (a). Thus, according to Eq. (10), the left time is 128 h for the first test sample, which is marked by the first solid square in Fig. 8 (a). By this analogy, the remaining useful life for the left 13 various length of training data is calculated. Using the cubic interpolation method, the 14 consecutive solid squares are jointed to form the thick dashed line in Fig. 8 (a), which describes the predicted residual life of the SOFC under Cl2 concentration at 100 ppm. The solid line describes the actual remaining useful life of the SOFC. The dashed and dashdotted lines are respectively the upper and lower bounds, which represent 15% above or below the real residual life. The simulation results show the prediction with the empirical model is within the bounds under Cl2 concentration at 100 ppm.
By the same way, the remaining useful life for the SOFC voltage with 400 ppm and 1000 ppm Cl2 is predicted, which is shown in Fig. 8(b) and (c). Using the empirical model, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are respectively 4.35 h, 4.44 h and 4.01 h under 100 ppm, 400 ppm and 1000 ppm Cl2. Compared with the predicted results using the HSMM method, the prediction accuracy of the two methods is very close under 400 ppm and 1000 ppm Cl2. Nevertheless, in the case of 100 ppm Cl2, it is obvious that the prediction precision with the empirical model is higher than the HSMM method. In the aspect of the prognostic speed, the empirical model is a very time-consuming prognostic method compared with HSMM. With only a couple of minutes of prep time, the remaining useful life can be predicted using the HSMM method, however, it took several hours to predict the residual life with the empirical model. For each test data, an empirical model is needed to be built, moreover 50 models with various parameters initialization are needed to be trained to obtain the accurate empirical model. 2) Under cathode poisoning Based on the predicted voltage under 9 various length of training data(shown in Fig. 7 (d,e,f)), the remaining useful life of the SOFC is calculated, which is given by the thick dashed lines in Fig. 8(d), (e) and (f). The solid squares in these figures indicate the remaining useful life of the 9 test samples. For example, under 3 vol% water vapor, the failure voltage threshold Vfailure is 0.865 V from Fig. 3(b). For the initial 100 h long test sample, the time that the voltage reaches 0.865 V is 1048 h, which is indicated by Fig. 7(d). Therefore, the remaining useful life is 948 h using Eq. (10), which is marked by the first solid square in Fig. 8(d). By the same way, for the left 8 different length of training data, the residual life can be calculated. Using the cubic interpolation method, the predicted results of the 9 test samples are connected to obtain the SOFC remaining useful life under 3 vol% water vapor, which is depicted by the thick dashed line in Fig. 8(d). The prediction result with the empirical model is hopeful under 3 vol% water vapor. Similarly, the remaining useful life under 5 vol% and 10 vol % water vapor is predicted, which is given in Fig. 8(e) and (f). Using the empirical model, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are 21.20 h, 39.35 h and 51.36 h respectively under 3 vol%, 5 vol % and 10 vol% water vapor. Compared with the predicted results with the HSMM method, it is obvious that the prediction accuracy with the empirical model is higher than the HSMM method under 3 vol% water vapor. However, in the case of 5 vol% and 10 vol% water vapor, the HSMM method offers more effective prediction performance. Moreover, in comparison with the HSMM method, the prognostic speed of the empirical model is too much slower.
SOFC prognostic using the hybrid model The proposed hybrid prognostic model The above two types of prognostic methods have their own advantages and disadvantages.
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Fig. 7 e Predicting results for different length of data.
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Fig. 8 e SOFC prognostic using the empirical model.
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1) For the HSMM method, the prediction accuracy strongly depends on the data similarity. If the drop trend of the test voltage is alike to the training voltage, the HSMM can forecast the test data with a high accuracy. Otherwise, it will lead to a low accuracy. Under anode poisoning, the training data with the HSMM method is the SOFC voltage with 1000 ppm Cl2. The drop trend of the test data under 100 ppm Cl2 has a great difference with the training data, however, the voltage drop trend with 400 ppm Cl2 is similar with the training data. In the case of cathode poisoning, the training data is the SOFC voltage with 10 vol% water vapor, which is similar with the voltage under 5 vol% water vapor, nevertheless, different from the voltage under 3 vol% water vapor. From Fig. 6 and Table 1, using the HSMM method, the prediction results under 400 ppm Cl2 and 5 vol% water vapor are hopeful, however, the results under 100 ppm Cl2 and 3 vol% water vapor are not good. 2) Using the empirical model, the prediction under Cl2 at 100 ppm concentration and 3 vol% water vapor is hopeful according to Fig. 8 and Table 1, which can eliminate the weakness of the HSMM method. However, the empirical model is a very time-consuming prognostic method, which has been explained before. According to the above analysis, the hybrid prognostic model is designed as follows: RULi;Final ¼ a$RULi;HSMM þ ð1 aÞ$RULi;EMP
(11)
where, RULi;Final is the predicted remaining useful life at the i th time by the hybrid prognostic model. RULi;HSMM and RULi;EMP are respectively the predicted remaining useful life of the SOFC by the HSMM method and the empirical mode at the i th time, which have been obtained from Section SOFC prognostic using the individual model. a is a weighting factor, which is calculated by: a¼
0 b > 0:7 1 b 0:7
(12)
where, t current P VðiÞtest Vði 1Þtest i¼tcurrent 10 1 b¼ t P current VðiÞtrain Vði 1Þtrain i¼t 10
(13)
current
where, VðiÞtest and VðiÞtrain are the voltage of the test and training samples at the i th hour. b is an index, which can reflect the similarity between the predicted data and the training sample. The smaller this value, the greater the similarity. When the drop trend of the test data has a great difference with the training data, i.e.b > 0:7, the empirical model is employed for SOFC prognostic, which has a higher prognostic accuracy than the HSMM approach. When the difference of the degradation trend between the test and training data is slight, i.e.b 0:7, the HSMM method is applied to SOFC prognostic, which provides faster prediction rate and better prediction precision than the empirical model.
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Results 1) Under anode poisoning Various lengths of data are employed to validate the model in Eq. (11), which are collected from 1 h to 150 h with a step of 1 h. Therefore, 150 sets of data are gathered to test the proposed hybrid prognostic model, and the predicted results for the SOFC anode poisoning are given in Fig. 9 (a),(b) and (c). The thick dashed lines indicate the predicted results with the hybrid prognostic model, and the solid lines present the real residual life. The dashed and dash-dotted lines stand for the upper and lower bounds, which represent 15% above or below the real residual life. When the Cl2 concentration is 100 ppm, the index b is less than 0.7 before 29 h, and after that is greater than 0.7. Thus, the HSMM method is employed to predict the remaining useful life when the test data is before 29 h, and the empirical model is used for SOFC prognostic after that. The prediction accuracy of the hybrid model is higher than the individual method. Besides, the prediction rate of the hybrid model is much faster than the empirical model, for 20% of the test samples can be predicted using the HSMM method. Under Cl2 concentration at 400 ppm, when the test data is between 19 and 38 h, the index b is larger than 0.7, which means that the empirical model is used to predict the residual life in this case. Otherwise, the index b is smaller than 0.7, and the HSMM method is proposed for SOFC prognostic. The prediction of the hybrid model is close to the individual model. Moreover, the hybrid model improves the prognostic speed compared with the empirical model, for 87% of the test samples are predicted by the HSMM method. In the case of 1000 ppm Cl2, the HSMM method is employed for SOFC prognostic, for the index b is less than 0.7 at each prognostic time. Therefore, the prediction accuracy with the hybrid model is identical with the HSMM method. The RMSEs between the real residual life and the measured one using the hybrid model are respectively 2.86 h, 4.29 h and 3.52 h under 100 ppm, 400 ppm and 1000 ppm Cl2, which are given in Table 1. In most cases, the prediction error of the hybrid model is less than that of the individual model. Moreover, in comparison with the empirical model, the hybrid model improves the prognostic speed, for some of the test samples are predicted by the HSMM method. 2) Under cathode poisoning Under cathode poisoning, the data is collected from 1 h to 1000 h with a step of 1 h, and the prediction results using the hybrid model are presented in Fig. 9(d),(e) and (f). The thick dashed and solid lines respectively reflect the predicted results with the hybrid prognostic model and the real residual life. The dashed and dash-dotted lines are respectively the upper and lower bounds, which represent 15% above or below the real remaining useful life. In the case of 3 vol% water vapor, the index b is mostly greater than 0.7. Therefore, the empirical model is mainly employed for SOFC prognostic, and the prediction result with
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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Fig. 9 e SOFC prognostic using the hybrid model. the hybrid prognostic model is similar with the empirical model. Under 5 vol% water vapor, the index b for 44% of the total test samples is larger than 0.7, and the left is smaller than 0.7. The empirical model combined with the HSMM is used for SOFC prognostic, and the prediction accuracy of the hybrid model is close to the HSMM method, while higher than the empirical model. When the water vapor concentration is 10 vol%, the index b is less than 0.7 at each prognostic time. Therefore, the HSMM is employed to predict the remaining useful life for the SOFC, and the prediction result with the hybrid prognostic model is identical with the HSMM method. Using the hybrid model, the RMSEs between the real remaining useful life and the measured one are respectively 20.65 h, 28.48 h and 16.67 h under 3 vol%, 5 vol% and 10 vol% water vapor. On the whole, the prediction error of the hybrid model is smaller than that of the individual model. Compared with Fig. 6, Figs. 8 and 9, the hybrid model not only guarantees the prediction accuracy, but also improves the prognostic speed. The hybrid model is an effective method with rapid forecasting speed and a high precision.
Conclusions In order to improve system reliability, the hybrid prognostic model is proposed for SOFC prognostic in this study, which consists of the HSMM and the empirical model. The proposed hybrid model is conducted on six groups of SOFC experimental data, and the main results are described as follows:
1) In the case of 100 ppm, 400 ppm and 1000 ppm Cl2, the RMSEs between the predicted remaining useful life and its real target are respectively 2.86 h, 4.29 h and 3.52 h using the hybrid prognostic model, which are mostly less than that of the individual model. Moreover, since some of the test samples are predicted by the HSMM, the hybrid model improves the prognostic speed compared with the empirical model. 2) Under 3 vol%, 5 vol% and 10 vol% of water vapor, the RMSEs are respectively 20.65 h, 28.48 h and 16.67 h using the hybrid model, which are smaller than that of the individual model on the whole. The results show the approach needs less time and achieves a higher prediction accuracy compared with the individual model presented previously. In future, if more failure data can be gathered, the proposed hybrid prognostic model can be applied to predict other degradation such as those due to Siloxane poisoning and redox cycling, etc.
Acknowledgments This work is supported by National Natural Science Foundation of China (No. 61304114)
Nomenclature aij A
State transition probability from health statesi to health statesj Probability distribution of state transition
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B Di M N si tcurrent tfailure Vfailure mi si p
Probability distribution of observation symbol Maximum duration in health statesi Observation symbol number in each state Number of health states in an HSMM The i-th health state in an HSMM Current life of the SOFC Failure life of the SOFC Pre-defined failure threshold Mean of duration in health statesi Variance of duration in health statesi Initial state probability distribution
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A hybrid prognostic model applied to SOFC prognostics Xiaojuan Wu*, Qianwen Ye, Junhao Wang School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
article info
abstract
Article history:
Poor durability is one of the major hurdles for Solid Oxide Fuel Cell (SOFC) commerciali-
Received 23 June 2017
zation. Prognostic technology is an important approach to improve system durability.
Received in revised form
However, the current prognostic methods for fuel cells are mainly applied to proton ex-
12 August 2017
change membrane fuel cell (PEMFC) systems, moreover, there are still shortages of recent
Accepted 17 August 2017
prognostic algorithms. Therefore, an improved prognostic model is developed to predict
Available online xxx
the remaining useful life of the SOFC in this study, which combines a hidden semi-Mark model (HSMM) with an empirical model. To build the hybrid prognostic model, an HSMM
Keywords:
and an empirical model are firstly built. The merit and demerit of the respective prognostic
Solid oxide fuel cell (SOFC)
methodology are then analyzed. According to the analysis results, the hybrid prognostic
Hybrid prognostic model
model is proposed and applied to six sets of SOFC run-to-failure data. The results show the
Hidden semi-Markov model (HSMM)
proposed prognostic model has a higher prediction accuracy and a faster forecasting speed
Empirical model
compared with the existed approaches for SOFC prognostics.
Prognostic
© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Solid Oxide Fuel Cell (SOFC) is an electro-chemical device, which can convert chemical energy into electrical energy. Due to its low emission and high efficiency, SOFC is considered to be a promising generation technology [1]. Nevertheless, because of inadequate operational states, impurities in gases and materials deterioration, poor long-term performance is one of the major hurdles for the commercialization of SOFC [2]. In order to improve system's durability, in this study prognostic technology is proposed to predict the future condition of a system. According to International Standard Organization(ISO), prognostic is defined as “the estimation of the operating time before failure and the risk of existence” [3]. Based on the ISO standard, it allows to define the remaining
useful life, which is “the estimation of the time between the current moment and the moment when the monitored system is considered as failed ” [4]. Thus, the objective of prognostic is to estimate the remaining useful life of the system to be functional. Various prognostic methods have been successful applied in the fuel cell systems, and they can be divided into two types of approaches: model-based and data-based approach. Model driven approach uses mathematical equations to describe the degradation process of the system, which requires a precise knowledge of the system failure mechanisms [5]. A physicsbased model was firstly built, and then unscented kalman filter was proposed to capture the degradation of the proton exchange membrane fuel cell (PEMFC) [6]. A first-order mathematical model was established to estimate the remaining useful of the PEMFC [7]. A power degradation model
* Corresponding author. E-mail address: [email protected] (X. Wu). http://dx.doi.org/10.1016/j.ijhydene.2017.08.114 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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was presented based on a detailed understanding of the degradation phenomena [8]. Data-based approach is also named a black box method, for it has no direct link with the physical phenomenon occurred in the system. In this case, the monitored historical data is employed to discuss the degradation process of the system [5]. Data driven prognostic approach can be classified into two categories: 1) degradation modeling; 2) direct prediction modeling. For the degradation modeling, a degrading signal is firstly estimated, such as voltage or power. The remaining useful life of the system is then calculated when the degrading signal reaches a pre-defined failure threshold. Empirical models were built to follow the power degradation due to time varying parameters, and then the residual life of the PEMFC was predicted when the power intersected the failure threshold [9]. Four empirical models were used to predict the power degradation trend of the PEMFC [10]. Five empirical models based on weighted mean was developed to estimate the voltage [11]. Three empirical models of the voltage drop were proposed for PEMFC prognostic [12]. Summation WaveletExtreme Learning Machine algorithm was presented to estimate the voltage degradation of the PEMFC and then the residual life was predicted [13]. An echo state network was reported to forecast the voltage degradation of PEMFC [14]. An adaptive neuro-fuzzy inference system was studied to estimate the PEMFC voltage [15]. Using an improved relevance vector machine, the PEMFC degradation was predicted [16]. Based on the group method of data handling and the wavelet analysis, a short-term prognostics method was developed to predict the voltage for the PEMFC [17]. Using a neural network model, the SOFC voltage degradation was estimated [18]. Direct prognostic modeling can predict the remaining useful life of the system directly, by finding the similarity between the observed data and the training data. The approach does not define a failure threshold, and directly learns from the data. A hidden semi-Markov model (HSMM) was exploited to predict the residual life of the SOFC by the present author [19]. Despite the great progress in prognostic technique for the fuel cell, the existing literature still has several drawbacks:
from the training data, the prognostic accuracy may not be high. To address the above issues, a hybrid prognostic model based on data-driven approach is presented to perform the remaining useful life prediction for the SOFC, which integrates an HSMM with an empirical model of degradation. As described above, using the empirical model, it is time consuming to predict the remaining useful life; nevertheless, using the HSMM method, the prediction accuracy strongly depends on the similarity between the test and training data. The hybrid prognostic model can exploit the strengths and eliminate the weaknesses of the respective prognostic methodology, rather than continuing to select between the individual prognostic approach [20]. When the degradation trend of the test data is similar with the training data, the HSMM method is used to predict the residual life for the SOFC, which can avoid rebuilding the prognostic model when new data is provided and improve the prognostic speed. Otherwise, the empirical model which can improve the prediction accuracy is employed for SOFC prognostic. The main contributions of this paper are summarized below: * The proposed prognostic algorithm not only guarantees a higher prediction accuracy, but also improves the prognostic speed compared to the existed prognostic approaches. * The proposed hybrid prognostic model is applied to the SOFC. To the best of our knowledge, only two articles previously studied the SOFC prognostic technique. The paper hereafter is organized as follows. Section Problem formulation explains SOFC prognostic problem. In Section SOFC prognostic using the individual model, the HSMM and the empirical model are respectively presented for SOFC prognostic. According to their own advantages and disadvantages, the hybrid model is proposed to predict the remaining useful life of the SOFC in Section SOFC prognostic using the hybrid model. Section Results draws the conclusion.
Problem formulation * Using the model-based prognostic approach, it is a difficult task to build the degradation model to reflect the degradation process of the fuel cell, since the fuel cell system is a complex multi physics system, which involves mechanical, electric, thermal, fluidic and electrochemistry phenomena. Moreover, the system is a time and space multiscale system. * The degradation modeling is a very time-consuming process, because the models use the past degradation signal to predict the future value, which implies that if new data is available, the prognostic model should be rebuilt. Moreover, to obtain a precise prediction model, a group of models with various initialization is generally needed to be trained. * The direct prognostic modeling depends on the similarity between the test and training data. For example, using the HSMM, if the drop trend of the test data is much different
For the SOFC anode, different kinds of fuels can be considered. Nevertheless, practical fuels often contain chlorine compounds at 100 ppm or higher concentration, especially in coal gas [21,22]. Degradation is occurred in the SOFC system when a high concentration of Cl2 is supplied in the anode [21,22]. Therefore, it is necessary to discuss the influence of Cl2 poisoning on the SOFC performance. Since the ambient air is continuously supplied to the cathode, it can not ignore the influence of water vapor in the air on the cathode performance to test long-term durability of the SOFC. Ref. [21,23] demonstrated a high concentration of water vapor supplied in the cathode could lead to the degradation of the SOFC performance. When the SOFC contains the impurities, such as Cl2 at the anode or water vapor at the cathode, it generally experiences several health states (good, medium, bad, etc) to reach failure, which is illustrated in Fig. 1.
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
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Fig. 1 e Health state transitions diagram for the SOFC.
Prognostics and Health Management (PHM) is developed to guarantee system's safe long-term operation and reduce maintenance cost. To achieve this goal, PHM is generally performed by three main stages:data acquisition, prognostic, and decision making. Data acquiring part is to gather useful data which can reflect the degradation change in the system. According to the acquired data, prognostic is employed to predict the future condition and calculate the remaining useful life of the system. The decision making module is used to take a proper maintenance on the system at the right time to extend its life. This study focuses on the first two stages of PHM described hereafter: * Acquiring data Cl2 poisoning or water vapor poisoning may lead to a decrease in voltage [21], therefore voltage is selected as the prognostic indicator to describe the SOFC degradation process. The voltage signal is firstly extracted using sensors. Furthermore, the raw data collected by the sensors is processed to be used in the prognostic model, which will be explained in Section Data preparing. * Prognostic A hybrid prognostic model based on an empirical model and an HSMM is developed to estimate the progression of the SOFC health condition and predict the remaining useful life. When the degradation trend between the test and training data is similar, the HSMM approach is presented for SOFC prognostic, which is clarified in Section HSMM method for SOFC prognostic. Otherwise, the empirical model is employed to predict the voltage decrease, which is given in Fig. 2. The SOFC is defined as failure when the voltage reaches the failure threshold Vfailure . Therefore, the remaining useful life of the SOFC is the difference between the failure life tfailure and the current moment tcurrent . The empirical model for SOFC prognostic is explained in Section Empirical model for SOFC prognostic.
SOFC prognostic using the individual model In order to build the hybrid prognostic model, an HSMM and an empirical model are respectively established in this section.
Fig. 2 e The remaining useful life illustration.
Data preparing To implement anode and cathode poisoning tests, six electrolyte-supported single SOFC cells were employed. Electrolyte plates were made of 10 mol% SC2O3-1mol% CeO289 mol% ZrO2, and the thickness was 200 mm. Electrode area was 8 mm 8 mm and Pt mesh was used as the current collector. Anode layer had double layer structures. The first layer was the mixture of 56 wt% NiO and 44 wt% ScSZ, while the second layer was the mixture of 80 wt% NiO and 20 wt% ScSZ. Cathode was the mixture of LSM and ScSZ with a weight ratio of 1:1. More details about the six single SOFC cells can be found in Refs. [22,23]. For the electrochemical measurements of anode poisoning, the anode gas was 3 vol% humidified H2 containing Cl2 at 100 ppm, 400 ppm and 1000 ppm, and the cathode gas was supplied with dry air. The SOFC operated at a constant current density of 0.2Acm2 with a constant temperature of 1073 K. The degradation process was measured for 150 h, and three groups of voltage with Cl2 concentration at 100 ppm, 400 ppm and 1000 ppm were gathered. The anode poisoning data used for prognostic is displayed by the solid lines in Fig. 3(a) [22]. The voltage with 1000 ppm Cl2 is employed for the HSMM training, whereas the training requires to be made under each concentration using the empirical model. To carry out the cathode poisoning test, the anode gas was 3 vol% humidified H2 and the cathode was the humidified air with 3 vol%, 5 vol% and 10 vol% water vapor. The SOFC operated at a constant current density of 0.2 Acm2, and the operating temperature was 1073 K. The degradation process was measured for 1000 h, and three sets of voltage degradation data with 3 vol%, 5 vol%, 10 vol% water vapor in air were collected. The cathode poisoning data used for prognostic is given by the solid lines in Fig. 3(b) [23]. The voltage with 10 vol % of water vapor is used to train the HSMM, however, it is necessary to train an empirical model under each water vapor concentration. In order to be learned more accurately by the prognostic model, the raw voltage data is processed applying a moving average filter algorithm [24]. The filtered data is described by
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number N is selected as three. Each state of the HSMM represents a health state of the SOFC. Using the Baum-Welch algorithm [25], the HSMM in Eq. (1) is trained. The degradation state estimation generated by the HSMM is given in Fig. 4(a). The voltage from 1.02 V to 0.96 V is represented by H1, which indicates that the SOFC is in the normal state. The voltage from 0.96 V to 0.90 V is denoted as H2, which means that the SOFC is in the level-1 defect state. The voltage from 0.90 V to 0.82 V is described by H3, which implies the SOFC is in the level-2 defect state (failure). The estimated parameters of the HSMM are given as follows:
1.02 1 0.98
100ppm Cl
2
SOFC voltage(V)
0.96 0.94 0.92 0.9 0.88
1000ppm Cl
400ppm Cl
2
2
0.84 0.82
3 0 1 2 3 2 3 m1 ; s 1 1 0 1 0 a11 a12 a13 A ¼ 4 a21 a22 a23 5 ¼ 4 0 0 1 5; p ¼ @ 0 A; 4 m2 ; s2 5 0 0 0 1 a31 a32 a33 m3 ; s 3 3 2 34; 2:8 ¼ 4 44:5; 1:1 103 5h 72; 0 2
0.86
0
50
100
150
Time(h)
(a) Under anode poisoning [22]
(2)
0.94 0.92 3 vol%
2) Under cathode poisoning
0.9
SOFC voltage(V)
0.88
Under the cathode poisoning, the voltage with 10 vol% of water vapor is employed to train the HSMM, and the estimated degradation trend is presented in Fig. 4(b). H1 means the SOFC normal state, and the SOFC voltage is varied from 0.89 V to 0.85 V. H2 indicates level-1 defect state, and the voltage changes from 0.85 V to 0.80 V. level-2 defect state (failure state) is represented by H3, and the voltage varies from 0.80 V to 0.75 V. Under the cathode poisoning, the estimated parameters of the HSMM are shown as follows:
0.86 5 vol%
0.84 0.82 0.8
10 vol%
0.78 0.76 0.74
2
0
100
200
300
400
500 600 Time(h)
700
800
900
1000
(b) Under cathode poisoning [23] Fig. 3 e Data used for SOFC prognostics. the dashed lines in Fig. 3, which reveals a monotonic decrease of the SOFC voltage.
a11 A ¼ 4 a21 a31 2 460; ¼ 4 160; 380;
0 1 2 3 3 2 3 m1 ; s 1 1 0 1 0 a13 4 A @ 5 4 5 a23 ¼ 0 0 1 ; p ¼ 0 ; m2 ; s2 5 0 0 0 1 a33 m3 ; s 3 3 0:0107 0:5 104 5h 0
a12 a22 a32
(3)
Estimate the remaining useful life for the SOFC 1) Under anode poisoning
HSMM method for SOFC prognostic The HSMM is general expressed by Ref. [25]: l ¼ f ðN; M; A; B; p; PÞ
(1)
where, durational probability P is defined to follow a Gaussian function distribution in this study. It usually needs two stages to predict the remaining useful life by the HSMM: 1) training an HSMM which is able to reflect the SOFC degradation process; 2) estimating the SOFC remaining useful life.
The main physical equations are given below, but further details can be retrieved from the reference papers [19,26]. Assuming the SOFC is identified at the i th health state(i ¼ 1; 2; 3), the remaining useful life of the SOFC is calculated as follows [17]: RULHSMM;i ¼ ti þ
aij @mj þ
N X
1 ajk mk A
(4)
k¼jþ1
where, ti ¼
In the case of anode poisoning, the voltage with 1000 ppm Cl2 is employed to train the HSMM. The SOFC is defined to go through three health states to reach failure: normal, level-1 defect, and level-2 defect(failure). Therefore, the HSMM state
0
j¼iþ1
Train an HSMM to represent the SOFC degraded process 1) Under anode poisoning
N X
Di X ðDi tÞ Pðsi =OÞ
(5)
t¼1
where, aij and mj are obtained from Eq. (2). ti is the remaining duration time at the i th health state. According to Eq. (2), the maximum duration Di in the i th health state is respectively 34 h, 44.5 h and 72 h under anode poisoning. Pðsi =OÞis the probability that the single state si generates the observation O,
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Voltage(V) Health state
1.02
SOFC voltage(V)
0.95 Normal state(H ) 1
0.9
Level-1 defect state(H ) 2
0.82
Level-2 defect state(H ) 3
0.75
0
50
100
150
Time(h)
(a) Under anode poisoning 0.92 Voltage(V) Health state
SOFC voltage(V)
0.87
Normal state(H ) 1
0.82 Level-1 defect state(H ) 2
0.77 Level-2 defect state(H ) 3
0.72
0
100
200
300
400
500 Time(h)
600
700
800
900
1000
(b) Under cathode poisoning Fig. 4 e SOFC voltage degradation trend prediction. which is obtained using the Viterbi algorithm [27]. i is the current health state of the SOFC. Through calculating the loglikelihoods of the test samples under three various health states, the current health state of the test sample can be identified [28]. Further detailed identification process can be referred to our previous work [19]. Fig. 5 (a), (b) and (c) give the identified results for fourteen sets of random voltage observation data under various Cl2 concentrations. The circles reflect the predicted current health states of the 14 test samples, and the Asterisks indicate the real health states. The number of correctly identified data is all 14 under three various Cl2 concentrations, and the accuracy ratio is 100%. Further, according to Eqs. (4-5), the remaining useful life of the 14 test samples under different Cl2 concentrations is calculated, which is presented by the solid squares in Fig. 6 (a),
(b) and (c). Using cubic interpolation method [29], the predicted results of the 14 test samples are connected to form the predicted curve of the SOFC residual life, which is given by the thick dashed line in Fig. 6(a),(b) and (c). The solid lines describe the real remaining useful life of the SOFC. For example, if the current moment is 10 h, the real remaining useful life of the SOFC is 140 h since the total life is assumed to be 150 h. By the analogy, the real residual life is 130 h when the current life is 20 h. The dashed and dash-dotted lines are respectively the upper and lower bounds, which represent 15% above or below the real residual life. The prediction is evaluated with a classical prognostic metric:v performance metrics [12]. If the prediction enters in an interval of ±v around the real remaining useful life, it is considered as good estimation. In this study, v is chosen as 15%. Under 100 ppm Cl2, the prediction result is good
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Predicted state Real state
Predicted state Real state
H
3
H
Health State
Health State
3
H
2
H
H
2
H
1
1
0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
14
0
1
2
(a) under Cl2 100ppm
3
4 5 6 Sample Index
7
8
Predicted state Real state H
H
3
3
Health State
Health State
10
(d) under 3vol % water vapor Predicted state Real state
H
2
H
2
H
H
1
1
0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
0
14
1
2
3
4 5 6 Sample Index
7
8
9
10
(e) under 5vol % water vapor
(b) under Cl2 400ppm Predicted state Real state
Predicted state Real state H
H
3
Health State
3
Health State
9
H
2
H
2
H
1
H
1
0 0
1
2
3
4
5
6 7 8 Sample Index
9
10
11
12
13
14
(c) under Cl2 1000ppm
1
2
3
4 5 6 Sample Index
7
8
9
10
(f) under 10vol % water vapor
Fig. 5 e The predicted current health state by the HSMM.
at the initial stage. However, after 60 h, the error between the predicted remaining useful life and the real one is beyond 15%. Under 400 ppm and 1000 ppm Cl2, the accuracy of the prediction is hopeful. To check the prediction performance, Root Mean Square Error (RMSE) is employed to quantify the difference between the predicted remaining useful life and its real target, which is shown in Table 1. The RMSEs are respectively 12.84 h, 4.07 h and 3.52 h under Cl2 concentrations at 100 ppm, 400 ppm and 1000 ppm. The results once again demonstrate that the HSMM method is effective for the SOFC voltage with 400 ppm and 1000 ppm Cl2, however, it is not valid for the test data under 100 ppm Cl2. Moreover, using the HSMM method, the remaining useful life of the SOFC is predicted with only a couple of minutes of prep time. 2) Under cathode poisoning Ten random test samples are respectively selected under 3 vol%, 5 vol% and 10 vol% water vapor. In the same way, the
current health states of the ten test data are identified, which are given in Fig. 5(d),(e)and (f). The Asterisks and circles respectively indicate the real and predicted health states for the ten test samples. The predicted accuracy is respectively 90%, 90%and 100% under 3 vol%, 5 vol% and 10 vol% water vapor. Based on the identified current health state and Eqs. (45), the remaining useful life of the ten test samples are calculated, which are given by the solid squares in Fig. 6(d), (e) and (f). Linking the predicted results using cubic interpolation algorithm, the prognostic results are obtained, which are presented by the thick dashed lines in Fig. 6(d),(e) and (f). Under 3 vol% water vapor, the prediction result is good before 550 h, however, the predicted remaining useful life is beyond 15% lower bound after 550 h. Under 5 vol% and 10 vol% water vapor, the prediction accuracy is hopeful. For the 1000-h long test data, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are respectively 38.79 h, 24.19 h and 16.67 h under 3 vol%, 5 vol% and 10 vol% water vapor.
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Fig. 6 e SOFC prognostic using the HSMM method.
Empirical model for SOFC prognostic According to the reference paper [9], the voltage degradation trend follows the empirical model: c VðtÞ ¼ a þ bt þ þ d logðtÞ t
(6)
where, t is time. During the voltage prediction process, the following constraints are considered: dVt s0 dt
(7)
Vtcurrent > Vðtcurrent þiÞ ; i2Zþ
(8)
b tþh Vfailure V
(9)
b t is the predicted voltage at time t. Vt where, V current is the real b ðt voltage at the current time tcurrent , and V current þiÞ is the predicted voltage at time tcurrent þ i. Eqs. (7) and (8) reflect the SOFC aging
process is irreversible degradation, and Eq. (9) guarantees that the prediction trend reaches the failure threshold. It generally needs two steps to predict the remaining useful life of the SOFC using the empirical prognostic model:1) for each test sample, training a degradation model in Eq. (6) which is able to predict the SOFC voltage evolution; 2) estimating the SOFC remaining useful life.
Train empirical models 1) Under anode poisoning Various lengths of data are employed to learn the model in Eq. (6). In this study, the data is gathered from 10 h to 140 h with a step of 10 h. Therefore, 14 empirical models are supposed to be learned. With a single prediction, it is not easy to obtain an accurate model in Eq. (6) which is constraint with Eqs. (7)e(9). Therefore, using gradient descent algorithm, 50 groups of models with various parameters initialization are trained under each length of
Table 1 e Error between the predicted residual life and its real remaining useful life.
Anode poisoning (100 ppm) Anode poisoning (400 ppm) Anode poisoning (1000 ppm) Cathode poisoning (3 vol%) Cathode poisoning (5 vol%) Cathode poisoning (10 vol%)
RMSE with HSMM (hours)
RMSE with empirical model (hours)
RMSE with hybrid model (hours)
12.84 4.07 3.52 38.79 24.19 16.67
4.35 4.44 4.01 21.20 39.35 51.36
2.86 4.29 3.52 20.65 28.48 16.67
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training data. The median of the 50 models from ensemble is regarded as the SOFC voltage degradation model. Fig. 7(a) and (b), and (c) describe the voltage degradation trend under 14 various initial time for 100 ppm, 400 ppm and 1000 ppm Cl2. The solid line describes the filtered voltage, and the left dashed lines depict the predicted voltage under the different length of training data used during prognostics learning. For the 14 various initial time, the RMSEs between the real SOFC voltage and the predicted one are less than 0.0035 V,0.0075 V and 0.011 V respectively under 100 ppm, 400 ppm and 1000 ppm Cl2. However, it took several hours to obtain the model in Eq. (6), for 50 group of models have been trained with various parameters initialization under each length of training data. Especially for short training data, it spent nearly 8 h to obtain the prediction model in Eq. (6). 2) Under cathode poisoning Under cathode poisoning, the data is collected from 100 h to 900 h with an interval of every 100 h. Thus, 9 empirical models are needed to be learned. Using the gradient-descent algorithm, the trained results under the 9 various initial time are given in Fig. 7 (d),(e) and (f). The RMSEs between the real SOFC voltage and the predicted one are respectively less than 0.0044 V, 0.0066 V and 0.016 V under the water vapor concentrations at 3 vol%, 5 vol% and 10 vol%. Nevertheless, it also took a lot of time to obtain the empirical model in Eq. (6), especially for less training data.
Predict the remaining useful life using the empirical model 1) Under anode poisoning In this study, the SOFC failure criteria is defined as follows: when the voltage reaches a pre-defined failure threshold Vfailure , the SOFC system fails. Therefore, the remaining useful life of the SOFC is calculated as follows: RULEMP ¼ arg VfailureðtÞ tcurrent
(10)
where, argðVfailureðtÞ Þrepresents the time that the SOFC voltage reaches the voltage threshold Vfailure . In the case of 100 ppm Cl2, the voltage threshold Vfailure is 0.936 V from Fig. 3 (a). For the initial 10 h long test sample, the current time tcurrent is 10 h, and the time that the voltage intersects 0.936 V is 138 h according to the predicted voltage given in Fig. 7 (a). Thus, according to Eq. (10), the left time is 128 h for the first test sample, which is marked by the first solid square in Fig. 8 (a). By this analogy, the remaining useful life for the left 13 various length of training data is calculated. Using the cubic interpolation method, the 14 consecutive solid squares are jointed to form the thick dashed line in Fig. 8 (a), which describes the predicted residual life of the SOFC under Cl2 concentration at 100 ppm. The solid line describes the actual remaining useful life of the SOFC. The dashed and dashdotted lines are respectively the upper and lower bounds, which represent 15% above or below the real residual life. The simulation results show the prediction with the empirical model is within the bounds under Cl2 concentration at 100 ppm.
By the same way, the remaining useful life for the SOFC voltage with 400 ppm and 1000 ppm Cl2 is predicted, which is shown in Fig. 8(b) and (c). Using the empirical model, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are respectively 4.35 h, 4.44 h and 4.01 h under 100 ppm, 400 ppm and 1000 ppm Cl2. Compared with the predicted results using the HSMM method, the prediction accuracy of the two methods is very close under 400 ppm and 1000 ppm Cl2. Nevertheless, in the case of 100 ppm Cl2, it is obvious that the prediction precision with the empirical model is higher than the HSMM method. In the aspect of the prognostic speed, the empirical model is a very time-consuming prognostic method compared with HSMM. With only a couple of minutes of prep time, the remaining useful life can be predicted using the HSMM method, however, it took several hours to predict the residual life with the empirical model. For each test data, an empirical model is needed to be built, moreover 50 models with various parameters initialization are needed to be trained to obtain the accurate empirical model. 2) Under cathode poisoning Based on the predicted voltage under 9 various length of training data(shown in Fig. 7 (d,e,f)), the remaining useful life of the SOFC is calculated, which is given by the thick dashed lines in Fig. 8(d), (e) and (f). The solid squares in these figures indicate the remaining useful life of the 9 test samples. For example, under 3 vol% water vapor, the failure voltage threshold Vfailure is 0.865 V from Fig. 3(b). For the initial 100 h long test sample, the time that the voltage reaches 0.865 V is 1048 h, which is indicated by Fig. 7(d). Therefore, the remaining useful life is 948 h using Eq. (10), which is marked by the first solid square in Fig. 8(d). By the same way, for the left 8 different length of training data, the residual life can be calculated. Using the cubic interpolation method, the predicted results of the 9 test samples are connected to obtain the SOFC remaining useful life under 3 vol% water vapor, which is depicted by the thick dashed line in Fig. 8(d). The prediction result with the empirical model is hopeful under 3 vol% water vapor. Similarly, the remaining useful life under 5 vol% and 10 vol % water vapor is predicted, which is given in Fig. 8(e) and (f). Using the empirical model, the RMSEs between the predicted and real remaining useful life are presented in Table 1, which are 21.20 h, 39.35 h and 51.36 h respectively under 3 vol%, 5 vol % and 10 vol% water vapor. Compared with the predicted results with the HSMM method, it is obvious that the prediction accuracy with the empirical model is higher than the HSMM method under 3 vol% water vapor. However, in the case of 5 vol% and 10 vol% water vapor, the HSMM method offers more effective prediction performance. Moreover, in comparison with the HSMM method, the prognostic speed of the empirical model is too much slower.
SOFC prognostic using the hybrid model The proposed hybrid prognostic model The above two types of prognostic methods have their own advantages and disadvantages.
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Fig. 7 e Predicting results for different length of data.
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Fig. 8 e SOFC prognostic using the empirical model.
10
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 3
1) For the HSMM method, the prediction accuracy strongly depends on the data similarity. If the drop trend of the test voltage is alike to the training voltage, the HSMM can forecast the test data with a high accuracy. Otherwise, it will lead to a low accuracy. Under anode poisoning, the training data with the HSMM method is the SOFC voltage with 1000 ppm Cl2. The drop trend of the test data under 100 ppm Cl2 has a great difference with the training data, however, the voltage drop trend with 400 ppm Cl2 is similar with the training data. In the case of cathode poisoning, the training data is the SOFC voltage with 10 vol% water vapor, which is similar with the voltage under 5 vol% water vapor, nevertheless, different from the voltage under 3 vol% water vapor. From Fig. 6 and Table 1, using the HSMM method, the prediction results under 400 ppm Cl2 and 5 vol% water vapor are hopeful, however, the results under 100 ppm Cl2 and 3 vol% water vapor are not good. 2) Using the empirical model, the prediction under Cl2 at 100 ppm concentration and 3 vol% water vapor is hopeful according to Fig. 8 and Table 1, which can eliminate the weakness of the HSMM method. However, the empirical model is a very time-consuming prognostic method, which has been explained before. According to the above analysis, the hybrid prognostic model is designed as follows: RULi;Final ¼ a$RULi;HSMM þ ð1 aÞ$RULi;EMP
(11)
where, RULi;Final is the predicted remaining useful life at the i th time by the hybrid prognostic model. RULi;HSMM and RULi;EMP are respectively the predicted remaining useful life of the SOFC by the HSMM method and the empirical mode at the i th time, which have been obtained from Section SOFC prognostic using the individual model. a is a weighting factor, which is calculated by: a¼
0 b > 0:7 1 b 0:7
(12)
where, t current P VðiÞtest Vði 1Þtest i¼tcurrent 10 1 b¼ t P current VðiÞtrain Vði 1Þtrain i¼t 10
(13)
current
where, VðiÞtest and VðiÞtrain are the voltage of the test and training samples at the i th hour. b is an index, which can reflect the similarity between the predicted data and the training sample. The smaller this value, the greater the similarity. When the drop trend of the test data has a great difference with the training data, i.e.b > 0:7, the empirical model is employed for SOFC prognostic, which has a higher prognostic accuracy than the HSMM approach. When the difference of the degradation trend between the test and training data is slight, i.e.b 0:7, the HSMM method is applied to SOFC prognostic, which provides faster prediction rate and better prediction precision than the empirical model.
11
Results 1) Under anode poisoning Various lengths of data are employed to validate the model in Eq. (11), which are collected from 1 h to 150 h with a step of 1 h. Therefore, 150 sets of data are gathered to test the proposed hybrid prognostic model, and the predicted results for the SOFC anode poisoning are given in Fig. 9 (a),(b) and (c). The thick dashed lines indicate the predicted results with the hybrid prognostic model, and the solid lines present the real residual life. The dashed and dash-dotted lines stand for the upper and lower bounds, which represent 15% above or below the real residual life. When the Cl2 concentration is 100 ppm, the index b is less than 0.7 before 29 h, and after that is greater than 0.7. Thus, the HSMM method is employed to predict the remaining useful life when the test data is before 29 h, and the empirical model is used for SOFC prognostic after that. The prediction accuracy of the hybrid model is higher than the individual method. Besides, the prediction rate of the hybrid model is much faster than the empirical model, for 20% of the test samples can be predicted using the HSMM method. Under Cl2 concentration at 400 ppm, when the test data is between 19 and 38 h, the index b is larger than 0.7, which means that the empirical model is used to predict the residual life in this case. Otherwise, the index b is smaller than 0.7, and the HSMM method is proposed for SOFC prognostic. The prediction of the hybrid model is close to the individual model. Moreover, the hybrid model improves the prognostic speed compared with the empirical model, for 87% of the test samples are predicted by the HSMM method. In the case of 1000 ppm Cl2, the HSMM method is employed for SOFC prognostic, for the index b is less than 0.7 at each prognostic time. Therefore, the prediction accuracy with the hybrid model is identical with the HSMM method. The RMSEs between the real residual life and the measured one using the hybrid model are respectively 2.86 h, 4.29 h and 3.52 h under 100 ppm, 400 ppm and 1000 ppm Cl2, which are given in Table 1. In most cases, the prediction error of the hybrid model is less than that of the individual model. Moreover, in comparison with the empirical model, the hybrid model improves the prognostic speed, for some of the test samples are predicted by the HSMM method. 2) Under cathode poisoning Under cathode poisoning, the data is collected from 1 h to 1000 h with a step of 1 h, and the prediction results using the hybrid model are presented in Fig. 9(d),(e) and (f). The thick dashed and solid lines respectively reflect the predicted results with the hybrid prognostic model and the real residual life. The dashed and dash-dotted lines are respectively the upper and lower bounds, which represent 15% above or below the real remaining useful life. In the case of 3 vol% water vapor, the index b is mostly greater than 0.7. Therefore, the empirical model is mainly employed for SOFC prognostic, and the prediction result with
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Fig. 9 e SOFC prognostic using the hybrid model. the hybrid prognostic model is similar with the empirical model. Under 5 vol% water vapor, the index b for 44% of the total test samples is larger than 0.7, and the left is smaller than 0.7. The empirical model combined with the HSMM is used for SOFC prognostic, and the prediction accuracy of the hybrid model is close to the HSMM method, while higher than the empirical model. When the water vapor concentration is 10 vol%, the index b is less than 0.7 at each prognostic time. Therefore, the HSMM is employed to predict the remaining useful life for the SOFC, and the prediction result with the hybrid prognostic model is identical with the HSMM method. Using the hybrid model, the RMSEs between the real remaining useful life and the measured one are respectively 20.65 h, 28.48 h and 16.67 h under 3 vol%, 5 vol% and 10 vol% water vapor. On the whole, the prediction error of the hybrid model is smaller than that of the individual model. Compared with Fig. 6, Figs. 8 and 9, the hybrid model not only guarantees the prediction accuracy, but also improves the prognostic speed. The hybrid model is an effective method with rapid forecasting speed and a high precision.
Conclusions In order to improve system reliability, the hybrid prognostic model is proposed for SOFC prognostic in this study, which consists of the HSMM and the empirical model. The proposed hybrid model is conducted on six groups of SOFC experimental data, and the main results are described as follows:
1) In the case of 100 ppm, 400 ppm and 1000 ppm Cl2, the RMSEs between the predicted remaining useful life and its real target are respectively 2.86 h, 4.29 h and 3.52 h using the hybrid prognostic model, which are mostly less than that of the individual model. Moreover, since some of the test samples are predicted by the HSMM, the hybrid model improves the prognostic speed compared with the empirical model. 2) Under 3 vol%, 5 vol% and 10 vol% of water vapor, the RMSEs are respectively 20.65 h, 28.48 h and 16.67 h using the hybrid model, which are smaller than that of the individual model on the whole. The results show the approach needs less time and achieves a higher prediction accuracy compared with the individual model presented previously. In future, if more failure data can be gathered, the proposed hybrid prognostic model can be applied to predict other degradation such as those due to Siloxane poisoning and redox cycling, etc.
Acknowledgments This work is supported by National Natural Science Foundation of China (No. 61304114)
Nomenclature aij A
State transition probability from health statesi to health statesj Probability distribution of state transition
Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 3
B Di M N si tcurrent tfailure Vfailure mi si p
Probability distribution of observation symbol Maximum duration in health statesi Observation symbol number in each state Number of health states in an HSMM The i-th health state in an HSMM Current life of the SOFC Failure life of the SOFC Pre-defined failure threshold Mean of duration in health statesi Variance of duration in health statesi Initial state probability distribution
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Please cite this article in press as: Wu X, et al., A hybrid prognostic model applied to SOFC prognostics, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.114