The cycle life prediction of Mg-based hydrogen storage alloys by artificial neural network

international journal of hydrogen energy 34 (2009) 1931–1936

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The cycle life prediction of Mg-based hydrogen storage alloys by artificial neural network Qifeng Tiana,b,d,*, Yao Zhangc,**, Yuanxin Wua,b, Zhicheng Tanc a

Key Laboratory for Green Chemical Process of Ministry of Education, Wuhan Institute of Technology, Wuhan 430073, China Hubei Key Laboratory of Novel Reactor and Green Chemical Technology, Wuhan Institute of Technology, Wuhan 430073, China c Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China d Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 b

article info

abstract

Article history:

Mg-based hydrogen storage alloys are a type of promising cathode material of Nickel-Metal

Received 1 April 2008

Hydride (Ni-MH) batteries. But inferior cycle life is their major shortcoming. Many

Received in revised form

methods, such as element substitution, have been attempted to enhance its life. However,

5 October 2008

these methods usually require time-consuming charge–discharge cycle experiments to

Accepted 30 November 2008

obtain a result. In this work, we suggested a cycle life prediction method of Mg-based

Available online 24 January 2009

hydrogen storage alloys based on artificial neural network, which can be used to predict its cycle life rapidly with high precision. As a result, the network can accurately estimate the

Keywords:

normalized discharge capacities vs. cycles (after the fifth cycle) for Mg0.8Ti0.1M0.1Ni (M ¼ Ti,

Cycle life

Al, Cr, etc.) and Mg0.9  xTi0.1PdxNi (x ¼ 0.04–0.1) alloys in the training and test process,

Artificial neural network

respectively. The applicability of the model was further validated by estimating the cycle

Mg-based hydrogen storage alloys

life of Mg0.9Al0.08Ce0.02Ni alloys and Nd5Mg41–Ni composites. The predicted results agreed well with experimental values, which verified the applicability of the network model in the estimation of discharge cycle life of Mg-based hydrogen storage alloys. Crown Copyright ª 2008 Published by Elsevier Ltd on behalf of International Association for Hydrogen Energy. All rights reserved.

1.

Introduction

Mg-based hydrogen storage alloys are a type of promising cathode material for Ni-MH batteries owing to their significant advantages, such as high discharge capacities, abundant reserves, low cost, etc. Many electrochemical studies about such alloys were reported in previous decades by Lei et al. [1], Liu et al. [2] and Nohara et al. [3]. The major problem hindering the application of this kind of alloy may be attributed to its inferior cycle life. Recently the partial substitution of Ti for Mg in MgNi alloys attracted more attention, as can be seen in Ye

et al. [4], Zhang et al. [5], Han et al. [6] and Ruggeri et al. [7]. It was found that the Ti substitution inhibited the capacity degradation effectively. We also reported on the improved cycle life of Pd partially substituted Mg–Ti–Ni alloys due to the excellent anti-corrosion performances of Pd [8,9]. In the development of qualified electrode alloys, a cyclic charge–discharge test is a standard method to measure its discharge capacities and cycle life. This kind of test is timeconsuming. For example, the test time of a new electrode alloy with discharge current density of 100 mA/g will exceed 100 h in its initial 20 charge–discharge cycles. Even much more time

* Corresponding author. Key Laboratory for Green Chemical Process of Ministry of Education, Wuhan Institute of Technology, 693 Xiongchu Road, Wuhan 430073, China. Tel.: þ86 27 8719 4509; fax: þ86 27 8719 4465. ** Corresponding author. E-mail addresses: [email protected] (Q. Tian), [email protected] (Y. Zhang). 0360-3199/$ – see front matter Crown Copyright ª 2008 Published by Elsevier Ltd on behalf of International Association for Hydrogen Energy. All rights reserved. doi:10.1016/j.ijhydene.2008.11.077

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will be taken if the discharge current density is lower or the cycle life is longer. To accelerate the research and development of novel electrode materials, a new method, which can predict the discharge capacities variation along with cycles based on the limited experimental data, is urgently needed. As to the prediction of cycle life of Mg-based hydrogen storage alloys, Sun et al. [10] and Liu et al. [11] utilized a capacity deterioration model, which was based on the oxidation kinetics of Mg-based amorphous alloys, to predict the cycle life of partially substituted MgNi electrode alloys. But they only reported the prediction results of the above alloys in the initial 10 cycles, even though the predicted value agreed well with the experimental ones. To the best of our knowledge, above literatures are the only reports about the prediction of cycle life of Mg-based hydrogen storage alloys up to date. Because of the non-linear relationship between battery voltage and discharge time, it is hard to describe the functional relationship of these variants using only one equation. In this case, artificial neural networks (ANNs) seem to be suitable for modeling non-linear processes by means of a large-scale parallel-distributed information processing system, which contains many interconnected neurons. It may be helpful in predicting battery capacity variations during the long discharge time. ANNs are mathematical systems that can simulate the signal transfer of biological neural networks. They are composed of processing elements (neurons) organized in layers. Most neural networks used in practice are back-propagation (BP) neural networks. A typical BP neural network consists of the input, the hidden, and the output layers. Every layer is composed of neurons. The interconnections of the input layer with the hidden layer, and the hidden layer with the output layer are transfer functions, which are used to get the output. The activation of a neuron is defined as the sum of the weighted input signals to that neuron, which is used as an independent variable of the transfer functions. The goal of training the network is to change the weights and bias between the neurons in a direction that minimizes the mean square error function MSE (Mean Square Error) as follows:

MSE ¼

2 1 X X ypk  tpk 2 p k

can be utilized to predict the state of charge (SOC) of the battery. The estimation accuracy is relatively high when compared with experimental results. Similarly, Shen et al. also predicted the available capacities of lead–acid [12,13,17,18] and Nickel-Metal Hydride (Ni-MH) batteries [19] with artificial neural network in the last few years. The prediction results agreed well with experimental value. However, up to now most researchers have only predicted battery available capacities using different discharge currents, voltages and temperatures as input parameters. There are few reports about the prediction of the battery or electrode’s cycle life from initial discharge behaviors of the batteries or electrodes, which is very important for developing qualified electrode materials. Based on the importance of Mg-based hydrogen storage alloys in Ni-MH batteries and the advantages of artificial neural networks in the prediction of battery performance, we proposed a three-layer BP neural network to model the nonlinear relationship of discharge capacities versus cycle number in the present work. The proposed network was used to estimate the cycle life of Mg–Ti–M–Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn, Pd) studied by us. The cyclic discharge performances of Mg0.9Al0.08Ce0.02Ni ternary alloys, Nd5Mg41 – 150 wt.% Ni and Nd5Mg41 – 200 wt.% Ni composites reported by other researchers were used to verify the correctness of the proposed artificial neural network model. The discharge cycle number of accurate prediction ranged from 20 to 80 according to various discharge performances for alloys.

2.

Experimental

2.1.

The preparation of alloys and test of its cycle life

The Mg-based hydrogen storage alloys Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) and Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1) were prepared by ball milling as described in our previous work [8,9]. The main structures of the alloys were determined as amorphous phase by X-ray diffraction (XRD) as noted in the above papers. The preparations and tests on the electrodes were the same as in our previous work.

(1)

The MSE of a network is defined as the squared differences between the targets t and the outputs y of the output neurons summed over p training patterns and k output nodes. In this work, the MSE, or the convergence tolerance, was set as 105 according to Shen et al. [12,13]. In recent years, ANNs have been used for predicting battery characteristics by many researchers. Yang et al. [14] used ANNs to predict the individual cell performance in a longstring lead/acid peak-shaving battery. The maximum overall prediction accuracy achieved in their study was 80.6%. Using a three-layer back-propagation (BP) neural network, Karami et al. [15] modeled and predicted voltage and available capacities at different currents and times of discharge in Zn–polyaniline bipolar rechargeable batteries with a very low prediction error. Monfared et al. [16] used a two-layer network to estimate the equivalent circuit parameters of lead–acid batteries, which

2.2. The artificial neural network modeling and prediction The cycle life data of Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys were used to train the network and those of Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1) alloys were used to test the validation of the proposed network. Because the discharge capacity is lower than 200 mAh/g after 20 cycles for Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) alloys, the discharge capacities in 20 cycles were recorded and used to train the neural network model. The initial five discharge capacities of the above electrode alloys were used as input vectors and the discharge capacities from the sixth to 20th cycles were used as output in the training process. As to the test process, the discharge capacities of Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1), Mg0.9Al0.08Ce0.02Ni alloys and Nd5Mg41 – 150 wt.% Ni, Nd5Mg41 – 200 wt.% Ni composites in the initial

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five cycles were also used as input vectors; the discharge capacities of following cycles were used as outputs of the network. The number of predicted cycles depends on the cycle life behaviors of the above alloys or composites, respectively. The performance of the network was tested by comparing the network output with the experimental values (after the initial five cycles) of the test samples. The training and test of the neural network were run in MATLAB environment. The computation was realized by the neural network toolbox in MATLAB.

3.

Results and discussion

3.1. The cycle life of Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys The cycle life of Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys is presented in Fig. 1. From the figure, one can see that the cycle life of substituted Mg-based electrode alloys was partially improved due to the substitution of some elements other than Ti. As to the effects of enhancing cycle life, Al was found to be the most effective and V was the second. Liu et al. [20] and Rongeat and Roue´ [21,22] have confirmed the synergetic effect between Ti and Al that improves the cyclic stability of the MgNi-based metal hydride electrode. Iwakura et al. [23] also reported that the decay of discharge capacity with increasing cycle number was suppressed by partial substitution with either Ti or V, and the alloy partially substituted with both Ti and V exhibited further improved cycle performance. Our experimental results were consistent with these reports.

3.2. The network structure, normalization of the input vector and transfer functions According to Kolmogorov’s theorem in Haykin’s book [24], a three-layer (input-hidden-output) feed-forward neural network is capable of approximating most functions if the number of neurons in hidden layer was chosen properly. In

Discharge Capacity (mAh/g)

500 M=Ti M=Al M=Cr M=Cu M=Fe M=Si M=V M=Zn M=Zr M=Mn

400

300

addition, the number of neurons in hidden layer can be 2n þ 1 if there are n input neurons in the input layer. Because of the requirements of the MATLAB Neural Network Toolbox, the number of columns in the input vector must be the same as that of the output vector and the amount of input/output neurons must be the same as the number of rows in the input/output vectors (every row vector works as a neuron). In order to conform to the above rules and simplify problems, we used a row vector, which contains the several normalized discharge capacities of several initial cycles, as input vector. That means the number of input neurons is one. After comparing the convergence performance of the network, we selected the initial five normalized discharge capacities as the input vector and the other 15 discharge capacities as output vector as to training data sets. Therefore, the architecture of the artificial neural network chosen was as an 1  3  3 three-layer back-propagation network, hereinto, one is the number of input neuron representing the discharge capacities of initial five cycles, the discharge capacities from the sixth to 20th cycle as target output, which is a 5  3 matrix. The sixth to 10th discharge capacities consist of the first row vector and the 11th to 15th discharge capacities are the second row vector in the matrix. The 16th to 20th discharge capacities take the place of the third row vector. Therefore, the amount of neurons in the hidden layer and output layers are all 3 according to above 2n þ 1 rule. As to the testing process, the number of neurons in the output layer was adjusted accordingly since the cycle life of alloys or composites in the test sets were longer than that of the training sets. But the number of neurons in the hidden layer is kept all the same because the input neuron is one during the whole processes. The configuration of the proposed neural network model is depicted in Fig. 2. In the figure, P is denoted as the input vector (the discharge capacities of the initial five cycles for each electrode alloy), while h1, h2, .hm and T1, T2, .Tn represent the neurons in the hidden layer and output layer, respectively. To train the NN model using the BP algorithm effectively, the input should be preprocessed appropriately. For the BP algorithm using the sigmoid function which is suitable to fit non-linear processes, the input and output should always be in the interval between 0 and 1. There are several ways to accomplish normalization, and the method chosen depends on the application. In this paper, the raw training data are normalized by the same method as used by Shen et al. [18]. That is (2) Cnor ¼ ðC  Cmin Þ=ðCmax  Cmin Þ

h1 T1 h2 T2

200

100

P

0

4

8

12

16

20

Cycle Number Fig. 1 – The cycle life of Mg0.8Ti0.1M0.1Ni (M [ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys.

. . . . . .

. . .

Tn

hm Fig. 2 – The configuration of the proposed neural network model.

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where Cnor is the normalized value, Cmax and Cmin are the maximum and minimum discharge capacities in the discharge cycle, respectively and C is the discharge capacities along with different cycles. The outputs were also ranged from 0 to 1 because the input vectors were normalized in the above range. Since the range of the input and output of the network was set from 0 to 1, the following function

0.7 M=Ti M=Al M=Cr M=Cu M=Fe M=Si M=V M=Zn M=Zr M=Mn

0.6

Prediction Value

0.5 0.4 0.3

  f ðxÞ ¼ 2= 1 þ e2x  1

(3)

0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Experimental Value Fig. 3 – The comparison of predicted values with experimental results of normalized discharge capacities from the 6th to 20th cycle for Mg0.8Ti0.1M0.1Ni (M [ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys.

a

as used by Chan et al. [17] was chosen as transfer function between the input-hidden layer and the hidden-output layer because the calculated results of the function were also ranged from 0 to 1, which was accordant with the above range. x is the independent variable for the transfer function, that is to say, x denotes the input vector and calculation results of the hidden layer, respectively.

3.3.

The training algorithm of the neural network is a numerical process, which determines the weights and the biases in neurons with the target of minimizing the error to less than

c

0.7 R2=0.9996

0.8 R2=0.9998 0.7

0.6

0.6

Prediction Value

0.5

Prediction Value

The training algorithm and results

0.4 0.3 0.2

0.5 0.4 0.3 0.2

0.1

0.1

0.0

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0

0.7

0.1

0.2

Experimental Value

b

d 0.5

0.3

0.4

0.5

0.6

0.7

0.8

Experimental Value 0.5 R2=0.9994

R2=0.9997 0.4

Prediction Value

Prediction Value

0.4 0.3 0.2 0.1

0.3

0.2

0.1

0.0

0.0 0.0

0.1

0.2

0.3

Experimental Value

0.4

0.5

0.0

0.1

0.2

0.3

0.4

0.5

Experimental Value

Fig. 4 – The comparison of predicted values with experimental results of normalized discharge capacities after the fifth cycle for Mg0.9 L xTi0.1PdxNi (x [ 0.04, 0.06, 0.08, 0.1) electrode alloys, (a) Mg0.86Ti0.1Pd0.04Ni; (b) Mg0.84Ti0.1Pd0.06Ni; (c) Mg0.82Ti0.1Pd0.08Ni; (d) Mg0.8Ti0.1Pd0.1Ni.

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0.6

Prediction Value

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Experimental Value Fig. 5 – The comparison of predicted values with experimental results of normalized discharge capacities after the fifth cycle for Mg0.9Al0.08Ce0.02Ni electrode alloys.

the MSE. During the training process, the treated training data is incorporated to improve the generality of the network. As Lin et al. [25] pointed out, the process of optimizing the parameters of the neural network is performed by the Levenberg–Marquardt algorithm, one of the improved backpropagation (BP) algorithms. This algorithm is a variation of Newton’s method designed for minimizing functions that are sums of squares of other non-linear functions. So, it is well suited to minimize the error function as defined in Eq. (1). As to Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys, the normalized discharge capacities from the 6th to 20th cycles were calculated with the above neural network model and training algorithm, using the normalized discharge capacities of the initial five cycles as the input vector. Fig. 3 shows a comparison between the predicted discharge capacities and experimental results based on the normalized value. As can be seen from the figure, the prediction data has a good compatibility with the corresponding experimental data. Therefore, the model can be used to predict the cycle life of Mg0.8Ti0.1M0.1Ni (M ¼ Ti, Al, Cr, Cu, Fe, Si, V, Zn, Zr, Mn) electrode alloys with very low prediction error.

3.4.

The test of the neural network model

The performance of the trained neural network was tested by comparing the predicted normalized discharge capacities (after the fifth cycle) of Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1) electrode alloys with the experimental data. As noticed above, the amount of neurons in the output layer were adjusted accordingly because the cycle life of the Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1) alloys were improved greatly compared with those in the training sets. Among these alloys, the cycle life of Mg0.8Ti0.1Pd0.1Ni alloy can achieve 80 cycles as reported in our previous paper [8], which is rather longer than that of the training data sets. Fig. 4 gives the comparison of the prediction results and the experimental data for the normalized discharge capacities of Mg0.9  xTi0.1PdxNi (x ¼ 0.04, 0.06, 0.08, 0.1) electrode

alloys. It can be seen from figure that there is good agreement between the results of the predicted and experimental data in the test data sets. In order to further verify the validation of the neural network model, other two examples were used to prove its correctness. Feng et al. [26] reported 100-h milled Mg0.9Al0.08Ce0.02Ni alloys possessed the best cycle life in their work. Using the above method, the normalized discharge capacities after the fifth cycle of Mg0.9Al0.08Ce0.02Ni electrode alloys were predicted accurately with the trained neural network in this work. The comparison of the predicted value and experimental data was illustrated in Fig. 5. In addition, Lu et al. [27] found that the capacity retention of ball-milled Nd5Mg41 – 150 wt.% Ni and Nd5Mg41 – 200 wt.% Ni composites falls to 40% and 24% after 20 cycles, respectively. The result indicates that the addition of the large amount of metallic Ni can improve the cycle behavior to some extent. As can be seen in Fig. 6, the trained neural network model was also utilized to estimate the cycle life of the above composites successfully. Even though the types of alloys in the above two papers are different than ours, the estimation accuracy can be relatively high. Therefore, the proposed neural network model can be applied to estimate the cycle life of Mgbased hydrogen storage electrode alloys. In addition, it is

a 0.30 R2 = 0.9999 0.25

Prediction Value

R2 = 0.9999

0.20 0.15 0.10 0.05 0.00 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Experimental Value

b Prediction Value

0.7

0.16

R2 = 0.9961

0.12

0.08

0.04

0.00 0.00

0.04

0.08

0.12

0.16

Experimental Value Fig. 6 – The comparison of predicted values with experimental results of normalized discharge capacities after the fifth cycle for ball-milling Nd5Mg41 alloys with x wt.% (x [ 150, 200) Ni composites, (a) x [ 150, (b) x [ 200.

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noteworthy to point out that one can achieve very high accuracy of prediction with the model on the condition that the training processes were only preceded within the 6th to 20th discharge cycles, while the charge–discharge cycles in the test data sets were longer than the former.

4.

Conclusions

A discharge cycle life prediction model based on artificial neural network (ANN) was successfully constructed and used to estimate the discharge capacities along with cycles for Mgbased hydrogen storage alloys. Given the data of several initial discharge cycles, the model can predict the discharge capacities up to 80 cycles accurately. The predicted values agreed well with the experimental results, which verified the validity of the proposed neural network model.

Acknowledgements This work is supported by Youths Science Foundation of Wuhan Institute of Technology (Q200801). The authors are also grateful to Mr. Markus Karahka from Dalhousie University of Canada for his correction on the writing.

references

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