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Assessing slagging propensity of coal from their slagging indices
Journal of the Energy Institute xxx (2017) 1e9
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Journal of the Energy Institute journal homepage: http://www.journals.elsevier.com/journal-of-the-energyinstitute
Assessing slagging propensity of coal from their slagging indices Xiaoqiang Wen a, b, *, Yang Xu b, Jianguo Wang b a b
Simulation Center, Northeast Electric Power University, Jilin, China Department of Automation, Northeast Electric Power University, Jilin, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 March 2017 Received in revised form 2 June 2017 Accepted 6 June 2017 Available online xxx
Energy production by coal combustion is the most commonly used energy technology. At this time, the correlation between the existing coal slagging indices and the actual observations made in most conventional boilers is poor. Some of the conventional test results and empirical ratios frequently offer misleading information, especially, when their use is extended to other coals or blends. For better understanding of the coal properties related to slagging problems, here a multi-variable regression (MR) analysis equation to predict slagging propensity and new models based on multi-resolution wavelet neural network (MWNN) and vague sets are proposed. Coal samples collected from a wide range of Chinese power plants are evaluated. The results of predictions correlate well with the reported field performance of the coals and the new models offer better predictive capability for understanding the field slagging observations than the conventional indices. The methods proposed here provide an encouraging development towards the search for a generic technique of assessing the slagging potential of pulverized coals/blends in boilers. © 2017 Energy Institute. Published by Elsevier Ltd. All rights reserved.
Keywords: Coal Slagging index MR MWNN Vague sets
1. Introduction The combustion of pulverized coal in power stations is expected to continue to be used for electricity generation for many years to come. In pulverized coal combustion, slagging and ash deposition are a set of the serious operational problems associated with power station boilers [1]. Slagging itself affects not only the heat transfer in the boiler, but also leads to mechanical damages and failures of the water/ steam cycle [2]. The general features of ash deposition in boilers are still not fully understood, but it is generally agreed that inertial impaction, thermophoresis, heterogeneous reactions and condensation are the major pathways for ash particle transport to the boiler walls [3]. Many attempts have been made to accurately predict slagging tendency in boilers [19], such as empirical indices [4,5], new indices [1,6], numerical simulation [2,3,6e9], mechanism modeling [10,11] and so on. Traditionally, empirical indices have been used to predict coal deposition tendencies, and they are still widely used due to their easy application, in spite of their shortcomings [4]. The standard test for ash fusion temperatures (AFT) was originally devised for assessing the clinker formation of ash from lump coal in stoker boilers [1]. There are still many other conventional empirical slagging indices, such as base to acid ratio [5], iron oxide percentage [4] and silica ratio derived from the chemical analysis of coal ash [4,5]. Angela [5] and Ruhul [12] provided abundant information about definitions and practical use of many of these indices. However, it has been shown, for example, by Jenkins et al. [13] and Degereji et al. [3] that so far, there is no single slagging index that is suitable to predict the slagging tendencies for a variety of coals. The applicability of such indices is mainly restricted to the particular coals for which they were obtained, and that their success rate is very low when trying to predict the slagging behavior for new coals. As a consequence, there is a need to question research findings that predict the slagging and fouling tendencies based on some of these indices [5]. Here, we propose new models to assess the slagging propensity of coals based on some indices. The evaluation of the different approaches is invariably done by comparing predictions with experimental observations on slagging behavior.
* Corresponding author. Simulation Center, Northeast Electric Power University, Jilin, China. E-mail address: [email protected] (X. Wen). http://dx.doi.org/10.1016/j.joei.2017.06.005 1743-9671/© 2017 Energy Institute. Published by Elsevier Ltd. All rights reserved.
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2. Materials and methodology 2.1. Database Here, in order to develop a comprehensive model, a wide range of coal samples which come from 50 coal mines in China's 18 provinces [14], including anthracite, lean coal, soft coal, lignite according to GB/T5751-2009 [15], are considered. For data selection process, similarity analysis is performed. After an analysis, the potential outliers are eliminated. After this process, 157 data of coal samples are selected to use in this study. This data set is separated randomly into two subsets as 120 for training and rest for testing purposes. The statistical characteristics of all the samples are shown in Table 1. 2.2. Multi-resolution wavelet neural network (MWNN) 2.2.1. Characteristics of orthogonal wavelets The close subspace {Vj} (j2Z, the number of closed-loop subspace) which belong to the square integrable space L2 has these features [20]:
consistency and monotony: Vj 3Vjþ1 gradual progress:
\
Vj ¼ f0g;
j2Z
[
(1)
Vj ¼ L2 ðRÞ
(2)
j2Z
f ðtÞ2Vj ⇔f 2j t 2V0
(3)
f ðtÞ2V0 0f ðt nÞ2V0
(4)
there must be {f(tn)} (f2V0), being the orthogonal basis of V0 (j, k2Z, the number of the orthogonal basis):
n Vj ¼ span fj;k
o j fj;k ðtÞ ¼ 22 f 2j t n ; ðj; k2ZÞ
n Wj ¼ span jj;k
j
o
jj;k ðtÞ ¼ 22 j 2j t n
(5)
; ðj; k2ZÞ
(6)
f(x) and J(x) have the relationship: fðxÞ ¼
X
hk fð2x kÞ
(7)
gk fð2x kÞ
(8)
k
jðxÞ ¼
X k
Table 1 The number of samples and ranges of analyses for different provinces. Province
N
Minimum
Maximum
Mean
Std. dev
Anhui Beijing Fujian Guizhou Hebei Henan Heilongjiang Hubei Jilin Jiangsu Jiangxi Ningxia Qinghai Yunnan Chongqing Shanxi Xinjiang Guangxi
8 7 8 10 6 10 2 9 13 8 9 7 8 9 12 10 10 11
1026a/67.6b/2.7c/0.2d 1070a/52.8b/1.5c/0.1d 1190a/73.0b/1.4c/0.1d 1130a/19.9b/1.1c/0.1d 1115a/60.3b/1.1c/0.1d 1210a/62.2b/1.1c/0.1d 1320a/67.5b/1.5c/0.2d 1150a/47.3b/1.1c/0.2d 1130a/29.1b/1.1c/0.1d 1170a/83.3b/1.9c/0.1d 1245a/22.9b/0.8c/0.1d 1270a/20.3b/1.3c/0.2d 1100a/62.5b/1.2c/0.2d 1120a/67.4b/1.1c/0.1d 1020a/61.0b/1.2c/0.1d 1040a/19.6b/1.1c/0.1d 1270a/53.2b/1.0c/0.1d 1100a/32.2b/1.4c/0.1d
1476a/86.4b/10.6c/0.4d 1500a/91.5b/3.2c/0.7d 1500a/86.7b/2.9c/0.3d 1500a/91.9b/3.4c/3.0d 1500a/83.2b/6.9c/0.4d 1500a/93.3b/2.8c/0.4d 1460a/80.8b/1.6c/0.3d 1370a/79.7b/2.9c/0.9d 1500a/91.3b/2.5c/1.3d 1450a/90.2b/3.3c/0.6d 1480a/93.5b/3.8c/1.8d 1340a/80.9b/2.8c/2.5d 1385a/80.3b/11.0c/0.5d 1500a/86.8b/3.3c/0.4d 1500a/86.0b/3.5c/0.5d 1580a/84.4b/9.4c/1.8d 1700a/91.4b/1.7c/0.5d 1500a/87.0b/8.1c/1.4d
1363a/77.3b/4.5c/0.3d 1306a/74.3b/2.3c/0.3d 1346a/79.1b/2.2c/0.2d 1333a/64.7b/2.1c/0.9d 1328a/72.2b/2.5c/0.3d 1379a/77.7b/1.8c/0.2d 1390a/74.2b/1.5c/0.2d 1226a/61.9b/2.1c/0.5d 1375a/72.8b/1.6c/0.3d 1349a/82.1b/2.5c/0.2d 1334a/58.0b/2.4c/0.8d 1296a/41.5b/1.7c/1.4d 1224a/70.1b/3.9c/0.3d 1386a/81.3b/2.0c/0.2d 1323a/78.4b/2.4c/0.2d 1303a/65.7b/3.2c/0.4d 1443a/73.3b/1.3c/0.2d 1288a/73.2b/3.0c/0.4d
164.4a/6.6b/2.5c/0.1d 183.8a/13.0b/0.7c/0.2d 111.1a/4.5b/0.6c/0.1d 151.1a/27.5b/0.8c/1.2d 147.4a/8.5b/2.3c/0.1d 116.5a/10.4b/0.6c/0.1d 99.0a/9.4b/0.1c/0.1d 65.2a/12.2b/0.7c/0.2d 132.4a/15.6b/0.5c/0.3d 86.5a/10.8b/0.3c/0.2d 69.4a/30.8b/1.2c/0.7d 23.2a/22.9b/0.5c/0.9d 107.3a/7.0b/3.1c/0.1d 150.3a/6.1b/0.7c/0.1d 143.9a/8.7b/0.9c/0.1d 180.7a/23.5b/2.4c/0.5d 135.4a/12.1b/0.2c/0.1d 136.5a/17.1b/1.8c/0.4d
a b c d
Classification of slagging tendency LS
MS
SS
3 3 3 4 2 4 1 1 7 4 1 0 1 6 5 4 5 4
2 1 3 1 2 5 1 3 4 3 3 2 1 3 4 2 3 1
3 3 2 5 2 1 0 5 2 1 5 5 6 0 3 4 2 6
Softening temperature (ST). Silica ratio (SR). Silica to alumina ratio (SAR). Basic to acid oxides ratio (BAOR); LS e Low slagging, MS e Medium slagging, SS e Severe slagging.
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3
wherein gk ¼ ð1Þk hð1kÞ (k ¼ 1,2, …,n), and /3Vj1 3Vj 3Vjþ1 3/. Within the same scale, wavelet function and scaling function are orthogonal (Vj⊥Wj):
Z
jj;k ðtÞ,fj;k ðtÞdt ¼ 0 ðj; k2Z; the number of the orthogonal basisÞ
(9)
2.2.2. Theory of multi-scale spaces Depending on multi-resolution analysis, we have: V0 ¼ W1 4 V1 ¼ W1 4 W2 4 V2 ¼ … ¼ W1 4 W2 4 W3 4 … 4 Wj 4 Vj (j ¼ 1,2, …,n), in which, Vj1 ¼ Wj4Vj, and f(t) and f(t) are the scaling function and wavelet function, respectively. Subspaces W1, W2, W3, …, Vj are orthogonal to each other. Based on the features of wavelet function and the scaling function in the frequency domain, we define the entire domain in which the discrete sequence distributes as V0. After the first decomposition, V0 is divided into two parts with the same width: low frequency space V1 and high frequency space W1. We can conclude that these two spaces must be orthogonal because the wavelet function is orthogonal to the scaling function. After another decomposition, low frequency part V1 is divided into the low frequency space V2 and high frequency space W2. These are the multi-scale spaces based on multi-resolution analysis. Therefore, after we set the scale parameter J which also means the top resolution, any nonlinear function f(x) 2 L2(R) can be transformed into (j, g, e, k2Z):
f ðxÞ ¼
n X
Cj;g fðxÞ þ
e1 J 2X n X
e Dk;g 22 j 2e x
(10)
e¼1 k¼1
j¼1
wherein Cj,g is the weight between the jth neuron with the scaling function of the hidden layer and the gth neuron of the output layer, and Dk,g is the weight between the kth neuron with the wavelet function of the hidden layer and the gth neuron of the output layer. 2.2.3. Establishment and topological structure of MWNN Depending on the multi-scale orthogonal decomposition of the wavelet and the framework basis of the feed forward neural network, a MWNN is established with three layers comprising m nodes in the input layer, n basic nodes in the hidden layer, and g nodes in the output layer. When the scale parameter J is 0, the top resolution of MWNN is 0. The scaling function is set as the activation function of neurons in the hidden layer when the network can approximately aim the contour of the target function, we have the transfer function as below:
f ðxÞ ¼
n X
02
Cj;g 2 f 2
0
j¼1
m X
! Wi;j xi aj
(11)
i¼1
where x is the input vector; Wi,j is the weight between the ith neuron of input layer and the jth neuron with the scaling function of hidden layer; aj is the threshold of the jth neuron with the scaling function of the hidden layer; Cj,g is the weight between the jth neuron with the scaling function of the hidden layer and the gth neuron of the output layer. If the result is not good, increase the scale parameter J, so set J be 1 which means the top resolution of the net work is 1. Add n neurons with the activation function of the wavelet into the hidden layer to approximate part of the details of the aimed function, when the network comprise hidden neurons with the resolutions of 0 and 1. The transfer function is what below:
f ðxÞ ¼
n X
Cj;g 22 f 20 0
j¼1
m X
! Wi;j xi aj
þ
i¼1
n X
Dk;g 22 j 21 1
m X
! Vi;k xi bk
(12)
i¼1
k¼1
where Vi,k is the weight between the ith neuron of the input layer and the kth neuron with the wavelet function of the hidden layer; Dk,g is the weight between the kth neuron with the wavelet function of the hidden layer and the gth neuron of the output layer; bk is the threshold of the kth neuron with the wavelet function of the hidden layer. If the network did not achieve a desirable result, continue to increase scale parameter J. Let J be 2. Add another 2n neurons with the wavelet function added to the hidden layer. Then we have hidden neurons resolutions of 0, 1 and 2. The transfer function is below:
f ðxÞ ¼
n X
02
Cj;g 2 f 2
j¼1
0
m X
! Wi;j xi aj
i¼1
þ
n X
12
Dk;g 2 j 2
1
m X
! Vi;k xi bk
i¼1
k¼1
þ
2n X k¼1
22
Dk;g 2 j 2
2
m X
! Vi;k xi bk
(13)
i¼1
Thus, each time that scale parameter increases, add 2J1n neurons to approximate more details of the aimed function on a gradual basis. If we keep increasing the scale parameter until the best result is reached, we will achieve the following transfer equation when the scale parameter is J:
f ðxÞ ¼
n X j¼1
Cj;g f
m X i¼1
! Wi;j xi aj
þ
e1 J 2X n X
e¼1 k¼1
2e
Dk;g 2 j 2
e
m X
! Vi;k xi bk
(14)
i¼1
This is the way to approximate the aimed function from contour to details. If the simulation result is not desirable enough, keep adding a squad of neurons with higher resolution into the network. When we get to the scale parameter of J, the n basic neurons with scaling function and the added n þ 2n þ 22n þ … 2J1n neurons with wavelet function in different resolution spaces will approximate the aimed function simultaneously.
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The proposed MWNN is based on the framework of feed forward neural network (Fig. 1). A number of neurons with the activation function of Meyer scaling function are set in the basic space of resolution 0 of the hidden layer; neurons in the dashed line are squads of neurons with activation function of Meyer wavelet function in different resolution spaces [18]. A bunch of neurons of the higher resolution are added to the net work each time when ascending the scale parameter J. Thus, after the scale parameter J is determined, all the neurons of different resolutions are in charge of approximating the aimed function in different resolution. Since the neurons are mapped to different resolution spaces, the corresponding weights and thresholds are mapped to different resolution spaces as well, which means that all the parameters of the network will be trained in different magnitudes and determines the MWNN will not be trapped to the local minimum. However, it is not greater the scale parameter J, the better the result will be achieved, because the neuron number of each bunch added to the hidden layer grows exponentially. If we keep increasing the scale parameter J, you can see the number of neurons which are about to be added to the network will be fairly huge. Although there is no conflict among each bunch of neurons in hidden layer, there will be chaos within the huge bunch of neurons, which will make it too hard for the network to adjust all the weights and thresholds, both the convergence time and performance result will be affected. That is why it is necessary to determine the scale parameter J as well as the top resolution of the network. 3. Results and discussions 3.1. Multi-variable regression (MR) In this study, a MR analysis is also proposed to predict the slagging tendency of the test samples. 76.4% of total data (120 samples) are used for developing the MR model. Rest 23.6% data (37 samples) are used to evaluate the prediction efficacy of the model. The linear relationship between the dependent variable and independent variables is as follows:
y ¼ 7:3563 0:0037x1 0:0137x2 þ 0:1657x3 þ 0:2580x4 ;
R2 ¼ 0:83
(15)
wherein y is dependent variable (the slagging tendency); x1, x2, x3 and x4 are independent variables including softening temperature (ST) [26], Silica ratio (SR) [4], Silica to alumina ratio (SAR) [4], and basic to acid oxides ratio (BAOR) [4]. When developing the MR model, we make the following definition for the input values according to the degrees of slagging tendency (DST): 1- low slagging (LS) tendency, 2- medium slagging (MS) tendency and 3- severe slagging (SS) tendency. Thus, the outputs of the MR model are: 0.5e1.5 for LS, 1.5e2.5 for MS and 2.5e3.5 for SS. By the least square mathematical method (Pearson correlation), the correlation coefficients among the single index (ST, SR, SAR and BAOR.) are determined (Table 2). Results indicate that there is a negative correlation between ST/SR and DST (r: 0.80 and 0.67 respectively), and a positive correlation between SAR/BAOR and DST (r: 0.54 and 0.36 respectively). The results are in good agreement with the coefficients of Eq. (15).
Fig. 1. Topological structure of MWNN. Table 2 Correlation coefficients for input variables and the DST value. Variables
DST
ST
SR
SAR
BAOR
DST ST SR SAR BAOR
1 0.795 0.671 0.358 0.543
0.795 1 0.415 0.242 0.260
0.671 0.415 1 0.079 0.901
0.358 0.242 0.079 1 0.021
0.543 0.260 0.901 0.021 1
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According to the definitions above, the prediction results are shown in Fig. 2. Here, the prediction results in terms of the four conventional empirical slagging indices are shown in Table 3. Obviously, the estimating accuracy of the MR model is higher than that of the conventional empirical index. One of the important reasons is: the conventional indices do not take into account the other influencing factors derived from the chemical analysis of coal ash and hence could not be reliably correlated with actual slagging potential of the coals tested. Compared with the conventional indices, the MR model provides a better tool for assessing coal slagging. Besides, according to the definition of the DST, we could lead to the conclusion: for the ST and SR, the bigger the values of the indices are, the lower the DST are; and for the SAR and BAOR, the results are just the opposite. The bigger the values of the indices are, the lower the DST are. Here, the former is called “anisotropic property”, and the latter is called “isotropic property”. Thus the ST and SR are anisotropic indices and the SAR and BAOR are isotropic indices. The coefficients in Eq. (15) are as follows: 0.0037(ST), 0.0137(SR), 0.1657 (SAR) and 0.2580 (BAOR). The coefficients of the anisotropic indices (ST and SR) are negative and the ones of the isotropic indices (SAR and BAOR) are positive. The results are in a good agreement with the definition of the anisotropic/isotropic indices above. It is interesting to note that the increase/decrease of the indices is significant: the former (ST and SR) will lead to a decrease/increase in the slagging potential of the coals and the latter (SAR and BAOR) will lead to an increase/decrease in the slagging potential of the coals. In order to lower the potential of the coals, the output of Eq. (15) should be as follows:
y ¼ 7:3563 0:0037x1 0:0137x2 þ 0:1657x3 þ 0:2580x4 < 1:5
(16)
A B > 5:8563
(17)
wherein A ¼ (0.0037x1 þ 0.0137x2), the sum of the anisotropic indices, and B ¼ (0.1657x3 þ 0.2580x4), the sum of the isotropic indices. 3.2. MWNN First, determine the top resolution of MWNN, and set n basic neurons in hidden layer of 2 when the scale parameter J is 0. The two error criteria Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) are shown in Table 5. The network does not achieve a good result because there are only 2 (2Jþ1, J ¼ 0) neurons in hidden layer with activation function of Meyer scaling function. MAPE converge to 0.4773 and RMSE converge to 0.8116 after six hundred iterations when both of them have reached the plateau. Then, increase the scale parameter J to 1, there will be 4(2Jþ1, J ¼ 1) neurons with activation function of Meyer wavelet function in hidden layer. Go on to increase the scale parameter J, and gather all the information of the process of scale parameter determination, so we have Table 5 below. From Table 5 we know that, when the scale parameter J is 7, MWNN gains the best performance: the number of training samples in wrong region is 10. The prediction results are shown in Table 6.
Fig. 2. Prediction results of MR model.
Table 3 Prediction results in terms of conventional empirical indices and MR model. Index/MR
Samples in wrong region (for training data)
Samples in wrong region (for testing data)
Samples in correct region (for total data)
ST SR SAR BAOR MR
33 41 52 33 19
11 13 22 15 13
113 103 83 109 125
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X. Wen et al. / Journal of the Energy Institute xxx (2017) 1e9 Table 4 Thresholds of the indices. Indices
Vupper
Vlower
Vcenter
ST ( C) BAOR SAR SR (%)
1390 0.206 1.87 78.8
1260 0.400 2.65 66.1
1330 0.350 2.10 70.0
Table 5 Result of different scale parameters J in the training data batch simulation. Scale parameter J
0
1
2
3
4
5
6
7
8
N of hidden neurons N of parameters need to be optimized
2 10 26 0.477 0.812 0.262 0.609 82 51 41.3 44.4 1000 900
4 20 52 0.209 0.511 0.258 0.666 29 46 40.8 50.2 800 700
8 40 104 0.152 0.362 0.190 0.463 11 30 40.0 52.0 600 500
16 80 208 0.150 0.367 0.002 0.332 15 16 50.7 70.4 500 400
32 160 416 0.145 0.343 0.104 0.298 12 14 65.6 94.5 400 300
64 320 832 0.143 0.367 0.123 0.292 17 6 113.6 177.6 400 300
128 640 1664 0.160 0.378 0.123 0.315 13 13 159.6 236.0 300 200
256 1280 3328 0.182 0.404 0.124 0.339 10 10 202.0 224.0 200 100
512 2560 6656 0.189 0.422 0.124 0.339 18 14 205.0 368.0 100 80
MWNN MWNNVS Samples in wrong region (for training data) Time consuming/s Iterations when reaching the plateau
MWNN MWNNVS MAPE RMSE MAPE RMSE MWNN MWNNVS MWNN MWNNVS MWNN MWNNVS
Table 6 Prediction results by various methods. methods
Samples in correct region (for training data)
Samples in correct region (for testing data)
Accuracy for total data (%)
ST MR BP RBF Mexihat Meyer MWNN (J ¼ 7) MWNNVS (J ¼ 5)
87 101 108 69 109 97 110 114
26 24 29 17 20 18 31 29
72.0 79.6 87.3 54.8 82.2 73.2 89.8 91.1
3.3. MWNN based on vague sets (MWNNVS) and discussion The vague set provides a kind of new tool for knowledge representation. It is clearly to give the representation of the degree and scope, and supply a good description to the thing's attribute from the form to the contents. However, in many situations, the concept is misty and distinguished, and causes people's understanding to the concept impossibly and completely accurate. For example, let A be a vague set with the truth-membership function tA and false-membership function fA respectively. If [tA, 1fA] ¼ [0.5, 0.7], then we can see that tA ¼ 0.5, fA ¼ 0.3, and the hesitancy degree mA ¼ 1tAfA ¼ 0.2. This result can be interpreted as ‘‘the vote for resolution is 5 for pro, 3 for con, and 2 for abstention” [16,17]. Now, we rebuild the MWNN based on Vague sets. Step 1: calculation of tx, fx and mx According to the concept and set operations of Vague Sets, firstly we should calculate the vague values. To calculate tx, fx and mx, the fuzzy membership function is introduced, which is shown in Fig. 3. The thresholds of the four indices are shown in Table 4 [10]. Without loss of
Fig. 3. Membership grade function.
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Fig. 4. Number of trees (MWNNVS) for different scale parameter J in training stage.
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X. Wen et al. / Journal of the Energy Institute xxx (2017) 1e9
generality, let tx be LS tendency, fx be medium and mx be severe. The assumption is arbitrary and it will not influence the results of evaluation. Take the ST as an example: if the ST is 1290 C, which is between 1330 C (Vcenter) and 1260 C (Vlower), so tx is 0.0, fx is 0.429 and mx is 0.571 according to the equations as follows:
8 > > > <
0 x 1330 tx ¼ > 60 > > : 1
mx ¼
8 0 > > > > x 1260 > > > < 70 > 1390 x > > > > 60 > > : 1
8 > > > <
0 1330 x fx ¼ > 70 > > : 1
x < 1330 1330 x 1390
(20)
x > 1390 x < 1260 1260 x 1330 (21) 1330 < x 1390 x > 1390 x < 1330 1260 x 1330
(22)
x < 1260
Step 2: MWNNVS model. According to step 1, there are 3 input variables for each index, so the number of the total input variables in the MWNNVS model is 12. Training results and testing results (Tables 5 and 6) show that the MWNNVS could estimate the slagging potential of the coals quite satisfactorily when the scale parameter J is 5. Here the back propagation (BP) neural network [21], radical basis function (RBF) neural network [22], Mexihat wavelet neural network [23e25], Meyer wavelet neural network [23e25] are also built. The comparison results are shown in Table 6. From Table 6, we know that the MWNNVS has the highest prediction accuracy for total data. Table 5 also shows the training processes: if the scale parameter J is 0, there are 10 parameters (26 parameters for MWNNVS) that need to be optimized, the network doesn't achieve a good result because there are only two neurons in hidden layer with activation function of Meyer scaling function. The time spent in training is 43.1s (44.4s for MWNNVS). MAPE and RMSE have reached the plateau after 1000 iterations for MWNN model (900 iterations for MWNNVS model). When the scale parameter J continues to increase, the curves of MAPE and RMSE are shown in Fig. 4 under the same training iterations. So we can draw a conclusion from Fig. 4 and Table 5 that: the number of hidden layer nodes has grown exponentially, but the training time does not have the same tendency of exponent increase. That is to say, the training iterations are gradually shortened along with the growth of the scale parameter J (Table 5). The conventional single slagging index has low accuracy in predicting and judging the coal DST. One of the most important reasons is that they do not have an overall consideration of the conventional indices derived from chemical composition of ash for Chinese coals and hence could not be reliably correlated with actual field performance. Here provides a better method for assessing coal DST. Besides, there are still some coal samples that have not been predicted and judged correctly (Table 6). It is because the slagging phenomena in boilers not only depends on coal quality but also the boiler design such as volumetric heat loading and operational regimes like excess air, fineness of coal particles etc [1]. Therefore, in order to make the best use of the new method, some related index, such as the dimensionless average furnace temperature, the dimensionless inscribed circle diameter in furnace and so on should be introduced into the model as the influencing factors. 4. Conclusions The conventional single slagging index has low accuracy in predicting and judging the coal DST. The new models proposed here could offer better predictive capability for understanding the field slagging observations than the conventional indices. In order to make the best use of the new models, some related index, such as the particularities of the raw materials used, combustion technologies and operating conditions and so on, should also be introduced into the models as the influencing factors. Acknowledgment The authors are thankful to the support of Science and technology development plan of Jilin City (201464061), National Natural Science Foundation of China (51176028,51476025) and the KEY Scientific and Technological Project of Jilin Province of China (20150203001SF). References [1] A. Lawrence, R. Kumar, K. Nandakumar, K. Narayanan, A novel tool for assessing slagging propensity of coals in PF boilers, Fuel 87 (2008) 946e950. [2] W. Christoph, K. Benjamin, B. Gundula, et al., Evaluation, comparison and validation of deposition criteria for numerical simulation of slagging, Appl. Energy 93 (2012) 184e192. [3] M.U. Degereji, D.B. Ingham, L. Ma, M. Pourkashanian, A. Williams, Prediction of ash slagging propensity in a pulverized coal combustion furnace, Fuel 101 (2012) 171e178. [4] J. Barroso, J. Ballester, A. Pina, Study of coal ash deposition in an entrained flow reactor: assessment of traditional and alternative slagging indices, Fuel Process. Technol. 88 (2007) 865e876.
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[5] G.M. Angela, M.S. Jesus, C. Manuel, et al., Critical review of predictive coefficients for biomass ash deposition tendency, J. Energy Inst. 89 (2016) 1e15. [6] M.U. Degereji, S.R. Gubba, D.B. Ingham, et al., Predicting the slagging potential of co-fired coal with sewage sludge and wood biomass, Fuel 108 (2013) 550e556. [7] M.P. Kurowski, H. Spliethoff, Deposition and slagging in an entrained-flow gasifier with focus on heat transfer, reactor design and flow dynamics with SPH, Fuel Process. Technol. 152 (2016) 147e155. [8] I. Ye, C. Ryu, Numerical modeling of slag flow and heat transfer on the wall of an entrained coal gasifier, Fuel 150 (2015) 64e74. [9] D.P. Bi, Q.L. Guan, W.W. Xuan, J.S. Zhang, Combined slag flow model for entrained flow gasification, Fuel 150 (2015) 565e572. [10] A.B. Arafat, J. Naser, Modelling of slag deposition and flow characteristics of coal combustion under oxy-firing condition in a 550 MW tangentially fired furnace, Appl. Therm. Eng. 106 (2016) 221e235. [11] T.A. Erickson, S.E. Allan, D.P. McCollor, et al., Modeling of fouling and slagging in coal-fired utility boilers, Fuel Process. Technol. 44 (1995) 155e171. [12] R.A. Mozumder, A.I. Laskar, Prediction of unconfined compressive strength of geopolymer stabilized clayey soil using artificial neural network, Comput. Geotechnics 69 (2015) 291e300. [13] B.M. Jenkins, L.L. Baxter, T.R.J. Miles, T.R. Miles, Combustion properties of biomass, Fuel Process Technol. 54 (1998) 17e46. [14] http://www.sxcoal.com/. [15] http://www.sac.gov.cn/. [16] J. Ye, Using an improved measure function of vague sets for multicriteria fuzzy decision-making, Expert Syst. Appl. 37 (2010) 4706e4709. [17] W.Y. Zeng, Y.B. Zhao, Y.D. Gu, Similarity measure for vague sets based on implication functions, Knowledge-Based Syst. 94 (2016) 124e131. [18] W.J. William, C.D. Jeffrey, The square root raised cosine wavelet and its relation to the meyer functions, IEEE Trans. Signal Process. 49 (2001) 248e251. [19] S.C. Yang, A study of prediction slagging for utility PC boiler based on fuzzy theory, J. Shanghai Univ. Electr. Power 18 (2002) 47e52. [20] C.P. Yan, Construction of Y. Meyer wavelet, J. Zhejiang Univ. Sci. Technol. 18 (2006) 177e179. [21] Z.M. Xu, X.Q. Wen, J.L. Zheng, et al., Cooling water fouling resistance prediction of plate heat exchanger based on partial least-squares regression, CIESC J. 62 (2011) 1531e1536. [22] X.Q. Wen, Z.M. Xu, L.F. Sun, Study on the state of slag on coal-fired boilers based on RBF neural network, J. China Coal Soc. 35 (2010) 218e222. [23] http://wenku.baidu.com/. [24] W. Zhou, Advanced Technique of Wavelet Analysis in MATLAB, Xidian University Press, Xi’an, 2006. [25] Z.Z. Zheng, P. Shen, X.H. Yang, et al., Wavelet Transform and the Application of Matlab Toolbox, Seismological Press, Beijing, 2001. [26] T.F. Wall, et al., Inorganic transformations and ash deposition during combustion, in: Engineering Foundation Conference. New Hampshire, 1995.
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Contents lists available at ScienceDirect
Journal of the Energy Institute journal homepage: http://www.journals.elsevier.com/journal-of-the-energyinstitute
Assessing slagging propensity of coal from their slagging indices Xiaoqiang Wen a, b, *, Yang Xu b, Jianguo Wang b a b
Simulation Center, Northeast Electric Power University, Jilin, China Department of Automation, Northeast Electric Power University, Jilin, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 March 2017 Received in revised form 2 June 2017 Accepted 6 June 2017 Available online xxx
Energy production by coal combustion is the most commonly used energy technology. At this time, the correlation between the existing coal slagging indices and the actual observations made in most conventional boilers is poor. Some of the conventional test results and empirical ratios frequently offer misleading information, especially, when their use is extended to other coals or blends. For better understanding of the coal properties related to slagging problems, here a multi-variable regression (MR) analysis equation to predict slagging propensity and new models based on multi-resolution wavelet neural network (MWNN) and vague sets are proposed. Coal samples collected from a wide range of Chinese power plants are evaluated. The results of predictions correlate well with the reported field performance of the coals and the new models offer better predictive capability for understanding the field slagging observations than the conventional indices. The methods proposed here provide an encouraging development towards the search for a generic technique of assessing the slagging potential of pulverized coals/blends in boilers. © 2017 Energy Institute. Published by Elsevier Ltd. All rights reserved.
Keywords: Coal Slagging index MR MWNN Vague sets
1. Introduction The combustion of pulverized coal in power stations is expected to continue to be used for electricity generation for many years to come. In pulverized coal combustion, slagging and ash deposition are a set of the serious operational problems associated with power station boilers [1]. Slagging itself affects not only the heat transfer in the boiler, but also leads to mechanical damages and failures of the water/ steam cycle [2]. The general features of ash deposition in boilers are still not fully understood, but it is generally agreed that inertial impaction, thermophoresis, heterogeneous reactions and condensation are the major pathways for ash particle transport to the boiler walls [3]. Many attempts have been made to accurately predict slagging tendency in boilers [19], such as empirical indices [4,5], new indices [1,6], numerical simulation [2,3,6e9], mechanism modeling [10,11] and so on. Traditionally, empirical indices have been used to predict coal deposition tendencies, and they are still widely used due to their easy application, in spite of their shortcomings [4]. The standard test for ash fusion temperatures (AFT) was originally devised for assessing the clinker formation of ash from lump coal in stoker boilers [1]. There are still many other conventional empirical slagging indices, such as base to acid ratio [5], iron oxide percentage [4] and silica ratio derived from the chemical analysis of coal ash [4,5]. Angela [5] and Ruhul [12] provided abundant information about definitions and practical use of many of these indices. However, it has been shown, for example, by Jenkins et al. [13] and Degereji et al. [3] that so far, there is no single slagging index that is suitable to predict the slagging tendencies for a variety of coals. The applicability of such indices is mainly restricted to the particular coals for which they were obtained, and that their success rate is very low when trying to predict the slagging behavior for new coals. As a consequence, there is a need to question research findings that predict the slagging and fouling tendencies based on some of these indices [5]. Here, we propose new models to assess the slagging propensity of coals based on some indices. The evaluation of the different approaches is invariably done by comparing predictions with experimental observations on slagging behavior.
* Corresponding author. Simulation Center, Northeast Electric Power University, Jilin, China. E-mail address: [email protected] (X. Wen). http://dx.doi.org/10.1016/j.joei.2017.06.005 1743-9671/© 2017 Energy Institute. Published by Elsevier Ltd. All rights reserved.
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2
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2. Materials and methodology 2.1. Database Here, in order to develop a comprehensive model, a wide range of coal samples which come from 50 coal mines in China's 18 provinces [14], including anthracite, lean coal, soft coal, lignite according to GB/T5751-2009 [15], are considered. For data selection process, similarity analysis is performed. After an analysis, the potential outliers are eliminated. After this process, 157 data of coal samples are selected to use in this study. This data set is separated randomly into two subsets as 120 for training and rest for testing purposes. The statistical characteristics of all the samples are shown in Table 1. 2.2. Multi-resolution wavelet neural network (MWNN) 2.2.1. Characteristics of orthogonal wavelets The close subspace {Vj} (j2Z, the number of closed-loop subspace) which belong to the square integrable space L2 has these features [20]:
consistency and monotony: Vj 3Vjþ1 gradual progress:
\
Vj ¼ f0g;
j2Z
[
(1)
Vj ¼ L2 ðRÞ
(2)
j2Z
f ðtÞ2Vj ⇔f 2j t 2V0
(3)
f ðtÞ2V0 0f ðt nÞ2V0
(4)
there must be {f(tn)} (f2V0), being the orthogonal basis of V0 (j, k2Z, the number of the orthogonal basis):
n Vj ¼ span fj;k
o j fj;k ðtÞ ¼ 22 f 2j t n ; ðj; k2ZÞ
n Wj ¼ span jj;k
j
o
jj;k ðtÞ ¼ 22 j 2j t n
(5)
; ðj; k2ZÞ
(6)
f(x) and J(x) have the relationship: fðxÞ ¼
X
hk fð2x kÞ
(7)
gk fð2x kÞ
(8)
k
jðxÞ ¼
X k
Table 1 The number of samples and ranges of analyses for different provinces. Province
N
Minimum
Maximum
Mean
Std. dev
Anhui Beijing Fujian Guizhou Hebei Henan Heilongjiang Hubei Jilin Jiangsu Jiangxi Ningxia Qinghai Yunnan Chongqing Shanxi Xinjiang Guangxi
8 7 8 10 6 10 2 9 13 8 9 7 8 9 12 10 10 11
1026a/67.6b/2.7c/0.2d 1070a/52.8b/1.5c/0.1d 1190a/73.0b/1.4c/0.1d 1130a/19.9b/1.1c/0.1d 1115a/60.3b/1.1c/0.1d 1210a/62.2b/1.1c/0.1d 1320a/67.5b/1.5c/0.2d 1150a/47.3b/1.1c/0.2d 1130a/29.1b/1.1c/0.1d 1170a/83.3b/1.9c/0.1d 1245a/22.9b/0.8c/0.1d 1270a/20.3b/1.3c/0.2d 1100a/62.5b/1.2c/0.2d 1120a/67.4b/1.1c/0.1d 1020a/61.0b/1.2c/0.1d 1040a/19.6b/1.1c/0.1d 1270a/53.2b/1.0c/0.1d 1100a/32.2b/1.4c/0.1d
1476a/86.4b/10.6c/0.4d 1500a/91.5b/3.2c/0.7d 1500a/86.7b/2.9c/0.3d 1500a/91.9b/3.4c/3.0d 1500a/83.2b/6.9c/0.4d 1500a/93.3b/2.8c/0.4d 1460a/80.8b/1.6c/0.3d 1370a/79.7b/2.9c/0.9d 1500a/91.3b/2.5c/1.3d 1450a/90.2b/3.3c/0.6d 1480a/93.5b/3.8c/1.8d 1340a/80.9b/2.8c/2.5d 1385a/80.3b/11.0c/0.5d 1500a/86.8b/3.3c/0.4d 1500a/86.0b/3.5c/0.5d 1580a/84.4b/9.4c/1.8d 1700a/91.4b/1.7c/0.5d 1500a/87.0b/8.1c/1.4d
1363a/77.3b/4.5c/0.3d 1306a/74.3b/2.3c/0.3d 1346a/79.1b/2.2c/0.2d 1333a/64.7b/2.1c/0.9d 1328a/72.2b/2.5c/0.3d 1379a/77.7b/1.8c/0.2d 1390a/74.2b/1.5c/0.2d 1226a/61.9b/2.1c/0.5d 1375a/72.8b/1.6c/0.3d 1349a/82.1b/2.5c/0.2d 1334a/58.0b/2.4c/0.8d 1296a/41.5b/1.7c/1.4d 1224a/70.1b/3.9c/0.3d 1386a/81.3b/2.0c/0.2d 1323a/78.4b/2.4c/0.2d 1303a/65.7b/3.2c/0.4d 1443a/73.3b/1.3c/0.2d 1288a/73.2b/3.0c/0.4d
164.4a/6.6b/2.5c/0.1d 183.8a/13.0b/0.7c/0.2d 111.1a/4.5b/0.6c/0.1d 151.1a/27.5b/0.8c/1.2d 147.4a/8.5b/2.3c/0.1d 116.5a/10.4b/0.6c/0.1d 99.0a/9.4b/0.1c/0.1d 65.2a/12.2b/0.7c/0.2d 132.4a/15.6b/0.5c/0.3d 86.5a/10.8b/0.3c/0.2d 69.4a/30.8b/1.2c/0.7d 23.2a/22.9b/0.5c/0.9d 107.3a/7.0b/3.1c/0.1d 150.3a/6.1b/0.7c/0.1d 143.9a/8.7b/0.9c/0.1d 180.7a/23.5b/2.4c/0.5d 135.4a/12.1b/0.2c/0.1d 136.5a/17.1b/1.8c/0.4d
a b c d
Classification of slagging tendency LS
MS
SS
3 3 3 4 2 4 1 1 7 4 1 0 1 6 5 4 5 4
2 1 3 1 2 5 1 3 4 3 3 2 1 3 4 2 3 1
3 3 2 5 2 1 0 5 2 1 5 5 6 0 3 4 2 6
Softening temperature (ST). Silica ratio (SR). Silica to alumina ratio (SAR). Basic to acid oxides ratio (BAOR); LS e Low slagging, MS e Medium slagging, SS e Severe slagging.
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wherein gk ¼ ð1Þk hð1kÞ (k ¼ 1,2, …,n), and /3Vj1 3Vj 3Vjþ1 3/. Within the same scale, wavelet function and scaling function are orthogonal (Vj⊥Wj):
Z
jj;k ðtÞ,fj;k ðtÞdt ¼ 0 ðj; k2Z; the number of the orthogonal basisÞ
(9)
2.2.2. Theory of multi-scale spaces Depending on multi-resolution analysis, we have: V0 ¼ W1 4 V1 ¼ W1 4 W2 4 V2 ¼ … ¼ W1 4 W2 4 W3 4 … 4 Wj 4 Vj (j ¼ 1,2, …,n), in which, Vj1 ¼ Wj4Vj, and f(t) and f(t) are the scaling function and wavelet function, respectively. Subspaces W1, W2, W3, …, Vj are orthogonal to each other. Based on the features of wavelet function and the scaling function in the frequency domain, we define the entire domain in which the discrete sequence distributes as V0. After the first decomposition, V0 is divided into two parts with the same width: low frequency space V1 and high frequency space W1. We can conclude that these two spaces must be orthogonal because the wavelet function is orthogonal to the scaling function. After another decomposition, low frequency part V1 is divided into the low frequency space V2 and high frequency space W2. These are the multi-scale spaces based on multi-resolution analysis. Therefore, after we set the scale parameter J which also means the top resolution, any nonlinear function f(x) 2 L2(R) can be transformed into (j, g, e, k2Z):
f ðxÞ ¼
n X
Cj;g fðxÞ þ
e1 J 2X n X
e Dk;g 22 j 2e x
(10)
e¼1 k¼1
j¼1
wherein Cj,g is the weight between the jth neuron with the scaling function of the hidden layer and the gth neuron of the output layer, and Dk,g is the weight between the kth neuron with the wavelet function of the hidden layer and the gth neuron of the output layer. 2.2.3. Establishment and topological structure of MWNN Depending on the multi-scale orthogonal decomposition of the wavelet and the framework basis of the feed forward neural network, a MWNN is established with three layers comprising m nodes in the input layer, n basic nodes in the hidden layer, and g nodes in the output layer. When the scale parameter J is 0, the top resolution of MWNN is 0. The scaling function is set as the activation function of neurons in the hidden layer when the network can approximately aim the contour of the target function, we have the transfer function as below:
f ðxÞ ¼
n X
02
Cj;g 2 f 2
0
j¼1
m X
! Wi;j xi aj
(11)
i¼1
where x is the input vector; Wi,j is the weight between the ith neuron of input layer and the jth neuron with the scaling function of hidden layer; aj is the threshold of the jth neuron with the scaling function of the hidden layer; Cj,g is the weight between the jth neuron with the scaling function of the hidden layer and the gth neuron of the output layer. If the result is not good, increase the scale parameter J, so set J be 1 which means the top resolution of the net work is 1. Add n neurons with the activation function of the wavelet into the hidden layer to approximate part of the details of the aimed function, when the network comprise hidden neurons with the resolutions of 0 and 1. The transfer function is what below:
f ðxÞ ¼
n X
Cj;g 22 f 20 0
j¼1
m X
! Wi;j xi aj
þ
i¼1
n X
Dk;g 22 j 21 1
m X
! Vi;k xi bk
(12)
i¼1
k¼1
where Vi,k is the weight between the ith neuron of the input layer and the kth neuron with the wavelet function of the hidden layer; Dk,g is the weight between the kth neuron with the wavelet function of the hidden layer and the gth neuron of the output layer; bk is the threshold of the kth neuron with the wavelet function of the hidden layer. If the network did not achieve a desirable result, continue to increase scale parameter J. Let J be 2. Add another 2n neurons with the wavelet function added to the hidden layer. Then we have hidden neurons resolutions of 0, 1 and 2. The transfer function is below:
f ðxÞ ¼
n X
02
Cj;g 2 f 2
j¼1
0
m X
! Wi;j xi aj
i¼1
þ
n X
12
Dk;g 2 j 2
1
m X
! Vi;k xi bk
i¼1
k¼1
þ
2n X k¼1
22
Dk;g 2 j 2
2
m X
! Vi;k xi bk
(13)
i¼1
Thus, each time that scale parameter increases, add 2J1n neurons to approximate more details of the aimed function on a gradual basis. If we keep increasing the scale parameter until the best result is reached, we will achieve the following transfer equation when the scale parameter is J:
f ðxÞ ¼
n X j¼1
Cj;g f
m X i¼1
! Wi;j xi aj
þ
e1 J 2X n X
e¼1 k¼1
2e
Dk;g 2 j 2
e
m X
! Vi;k xi bk
(14)
i¼1
This is the way to approximate the aimed function from contour to details. If the simulation result is not desirable enough, keep adding a squad of neurons with higher resolution into the network. When we get to the scale parameter of J, the n basic neurons with scaling function and the added n þ 2n þ 22n þ … 2J1n neurons with wavelet function in different resolution spaces will approximate the aimed function simultaneously.
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The proposed MWNN is based on the framework of feed forward neural network (Fig. 1). A number of neurons with the activation function of Meyer scaling function are set in the basic space of resolution 0 of the hidden layer; neurons in the dashed line are squads of neurons with activation function of Meyer wavelet function in different resolution spaces [18]. A bunch of neurons of the higher resolution are added to the net work each time when ascending the scale parameter J. Thus, after the scale parameter J is determined, all the neurons of different resolutions are in charge of approximating the aimed function in different resolution. Since the neurons are mapped to different resolution spaces, the corresponding weights and thresholds are mapped to different resolution spaces as well, which means that all the parameters of the network will be trained in different magnitudes and determines the MWNN will not be trapped to the local minimum. However, it is not greater the scale parameter J, the better the result will be achieved, because the neuron number of each bunch added to the hidden layer grows exponentially. If we keep increasing the scale parameter J, you can see the number of neurons which are about to be added to the network will be fairly huge. Although there is no conflict among each bunch of neurons in hidden layer, there will be chaos within the huge bunch of neurons, which will make it too hard for the network to adjust all the weights and thresholds, both the convergence time and performance result will be affected. That is why it is necessary to determine the scale parameter J as well as the top resolution of the network. 3. Results and discussions 3.1. Multi-variable regression (MR) In this study, a MR analysis is also proposed to predict the slagging tendency of the test samples. 76.4% of total data (120 samples) are used for developing the MR model. Rest 23.6% data (37 samples) are used to evaluate the prediction efficacy of the model. The linear relationship between the dependent variable and independent variables is as follows:
y ¼ 7:3563 0:0037x1 0:0137x2 þ 0:1657x3 þ 0:2580x4 ;
R2 ¼ 0:83
(15)
wherein y is dependent variable (the slagging tendency); x1, x2, x3 and x4 are independent variables including softening temperature (ST) [26], Silica ratio (SR) [4], Silica to alumina ratio (SAR) [4], and basic to acid oxides ratio (BAOR) [4]. When developing the MR model, we make the following definition for the input values according to the degrees of slagging tendency (DST): 1- low slagging (LS) tendency, 2- medium slagging (MS) tendency and 3- severe slagging (SS) tendency. Thus, the outputs of the MR model are: 0.5e1.5 for LS, 1.5e2.5 for MS and 2.5e3.5 for SS. By the least square mathematical method (Pearson correlation), the correlation coefficients among the single index (ST, SR, SAR and BAOR.) are determined (Table 2). Results indicate that there is a negative correlation between ST/SR and DST (r: 0.80 and 0.67 respectively), and a positive correlation between SAR/BAOR and DST (r: 0.54 and 0.36 respectively). The results are in good agreement with the coefficients of Eq. (15).
Fig. 1. Topological structure of MWNN. Table 2 Correlation coefficients for input variables and the DST value. Variables
DST
ST
SR
SAR
BAOR
DST ST SR SAR BAOR
1 0.795 0.671 0.358 0.543
0.795 1 0.415 0.242 0.260
0.671 0.415 1 0.079 0.901
0.358 0.242 0.079 1 0.021
0.543 0.260 0.901 0.021 1
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5
According to the definitions above, the prediction results are shown in Fig. 2. Here, the prediction results in terms of the four conventional empirical slagging indices are shown in Table 3. Obviously, the estimating accuracy of the MR model is higher than that of the conventional empirical index. One of the important reasons is: the conventional indices do not take into account the other influencing factors derived from the chemical analysis of coal ash and hence could not be reliably correlated with actual slagging potential of the coals tested. Compared with the conventional indices, the MR model provides a better tool for assessing coal slagging. Besides, according to the definition of the DST, we could lead to the conclusion: for the ST and SR, the bigger the values of the indices are, the lower the DST are; and for the SAR and BAOR, the results are just the opposite. The bigger the values of the indices are, the lower the DST are. Here, the former is called “anisotropic property”, and the latter is called “isotropic property”. Thus the ST and SR are anisotropic indices and the SAR and BAOR are isotropic indices. The coefficients in Eq. (15) are as follows: 0.0037(ST), 0.0137(SR), 0.1657 (SAR) and 0.2580 (BAOR). The coefficients of the anisotropic indices (ST and SR) are negative and the ones of the isotropic indices (SAR and BAOR) are positive. The results are in a good agreement with the definition of the anisotropic/isotropic indices above. It is interesting to note that the increase/decrease of the indices is significant: the former (ST and SR) will lead to a decrease/increase in the slagging potential of the coals and the latter (SAR and BAOR) will lead to an increase/decrease in the slagging potential of the coals. In order to lower the potential of the coals, the output of Eq. (15) should be as follows:
y ¼ 7:3563 0:0037x1 0:0137x2 þ 0:1657x3 þ 0:2580x4 < 1:5
(16)
A B > 5:8563
(17)
wherein A ¼ (0.0037x1 þ 0.0137x2), the sum of the anisotropic indices, and B ¼ (0.1657x3 þ 0.2580x4), the sum of the isotropic indices. 3.2. MWNN First, determine the top resolution of MWNN, and set n basic neurons in hidden layer of 2 when the scale parameter J is 0. The two error criteria Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) are shown in Table 5. The network does not achieve a good result because there are only 2 (2Jþ1, J ¼ 0) neurons in hidden layer with activation function of Meyer scaling function. MAPE converge to 0.4773 and RMSE converge to 0.8116 after six hundred iterations when both of them have reached the plateau. Then, increase the scale parameter J to 1, there will be 4(2Jþ1, J ¼ 1) neurons with activation function of Meyer wavelet function in hidden layer. Go on to increase the scale parameter J, and gather all the information of the process of scale parameter determination, so we have Table 5 below. From Table 5 we know that, when the scale parameter J is 7, MWNN gains the best performance: the number of training samples in wrong region is 10. The prediction results are shown in Table 6.
Fig. 2. Prediction results of MR model.
Table 3 Prediction results in terms of conventional empirical indices and MR model. Index/MR
Samples in wrong region (for training data)
Samples in wrong region (for testing data)
Samples in correct region (for total data)
ST SR SAR BAOR MR
33 41 52 33 19
11 13 22 15 13
113 103 83 109 125
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X. Wen et al. / Journal of the Energy Institute xxx (2017) 1e9 Table 4 Thresholds of the indices. Indices
Vupper
Vlower
Vcenter
ST ( C) BAOR SAR SR (%)
1390 0.206 1.87 78.8
1260 0.400 2.65 66.1
1330 0.350 2.10 70.0
Table 5 Result of different scale parameters J in the training data batch simulation. Scale parameter J
0
1
2
3
4
5
6
7
8
N of hidden neurons N of parameters need to be optimized
2 10 26 0.477 0.812 0.262 0.609 82 51 41.3 44.4 1000 900
4 20 52 0.209 0.511 0.258 0.666 29 46 40.8 50.2 800 700
8 40 104 0.152 0.362 0.190 0.463 11 30 40.0 52.0 600 500
16 80 208 0.150 0.367 0.002 0.332 15 16 50.7 70.4 500 400
32 160 416 0.145 0.343 0.104 0.298 12 14 65.6 94.5 400 300
64 320 832 0.143 0.367 0.123 0.292 17 6 113.6 177.6 400 300
128 640 1664 0.160 0.378 0.123 0.315 13 13 159.6 236.0 300 200
256 1280 3328 0.182 0.404 0.124 0.339 10 10 202.0 224.0 200 100
512 2560 6656 0.189 0.422 0.124 0.339 18 14 205.0 368.0 100 80
MWNN MWNNVS Samples in wrong region (for training data) Time consuming/s Iterations when reaching the plateau
MWNN MWNNVS MAPE RMSE MAPE RMSE MWNN MWNNVS MWNN MWNNVS MWNN MWNNVS
Table 6 Prediction results by various methods. methods
Samples in correct region (for training data)
Samples in correct region (for testing data)
Accuracy for total data (%)
ST MR BP RBF Mexihat Meyer MWNN (J ¼ 7) MWNNVS (J ¼ 5)
87 101 108 69 109 97 110 114
26 24 29 17 20 18 31 29
72.0 79.6 87.3 54.8 82.2 73.2 89.8 91.1
3.3. MWNN based on vague sets (MWNNVS) and discussion The vague set provides a kind of new tool for knowledge representation. It is clearly to give the representation of the degree and scope, and supply a good description to the thing's attribute from the form to the contents. However, in many situations, the concept is misty and distinguished, and causes people's understanding to the concept impossibly and completely accurate. For example, let A be a vague set with the truth-membership function tA and false-membership function fA respectively. If [tA, 1fA] ¼ [0.5, 0.7], then we can see that tA ¼ 0.5, fA ¼ 0.3, and the hesitancy degree mA ¼ 1tAfA ¼ 0.2. This result can be interpreted as ‘‘the vote for resolution is 5 for pro, 3 for con, and 2 for abstention” [16,17]. Now, we rebuild the MWNN based on Vague sets. Step 1: calculation of tx, fx and mx According to the concept and set operations of Vague Sets, firstly we should calculate the vague values. To calculate tx, fx and mx, the fuzzy membership function is introduced, which is shown in Fig. 3. The thresholds of the four indices are shown in Table 4 [10]. Without loss of
Fig. 3. Membership grade function.
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X. Wen et al. / Journal of the Energy Institute xxx (2017) 1e9
Fig. 4. Number of trees (MWNNVS) for different scale parameter J in training stage.
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8
X. Wen et al. / Journal of the Energy Institute xxx (2017) 1e9
generality, let tx be LS tendency, fx be medium and mx be severe. The assumption is arbitrary and it will not influence the results of evaluation. Take the ST as an example: if the ST is 1290 C, which is between 1330 C (Vcenter) and 1260 C (Vlower), so tx is 0.0, fx is 0.429 and mx is 0.571 according to the equations as follows:
8 > > > <
0 x 1330 tx ¼ > 60 > > : 1
mx ¼
8 0 > > > > x 1260 > > > < 70 > 1390 x > > > > 60 > > : 1
8 > > > <
0 1330 x fx ¼ > 70 > > : 1
x < 1330 1330 x 1390
(20)
x > 1390 x < 1260 1260 x 1330 (21) 1330 < x 1390 x > 1390 x < 1330 1260 x 1330
(22)
x < 1260
Step 2: MWNNVS model. According to step 1, there are 3 input variables for each index, so the number of the total input variables in the MWNNVS model is 12. Training results and testing results (Tables 5 and 6) show that the MWNNVS could estimate the slagging potential of the coals quite satisfactorily when the scale parameter J is 5. Here the back propagation (BP) neural network [21], radical basis function (RBF) neural network [22], Mexihat wavelet neural network [23e25], Meyer wavelet neural network [23e25] are also built. The comparison results are shown in Table 6. From Table 6, we know that the MWNNVS has the highest prediction accuracy for total data. Table 5 also shows the training processes: if the scale parameter J is 0, there are 10 parameters (26 parameters for MWNNVS) that need to be optimized, the network doesn't achieve a good result because there are only two neurons in hidden layer with activation function of Meyer scaling function. The time spent in training is 43.1s (44.4s for MWNNVS). MAPE and RMSE have reached the plateau after 1000 iterations for MWNN model (900 iterations for MWNNVS model). When the scale parameter J continues to increase, the curves of MAPE and RMSE are shown in Fig. 4 under the same training iterations. So we can draw a conclusion from Fig. 4 and Table 5 that: the number of hidden layer nodes has grown exponentially, but the training time does not have the same tendency of exponent increase. That is to say, the training iterations are gradually shortened along with the growth of the scale parameter J (Table 5). The conventional single slagging index has low accuracy in predicting and judging the coal DST. One of the most important reasons is that they do not have an overall consideration of the conventional indices derived from chemical composition of ash for Chinese coals and hence could not be reliably correlated with actual field performance. Here provides a better method for assessing coal DST. Besides, there are still some coal samples that have not been predicted and judged correctly (Table 6). It is because the slagging phenomena in boilers not only depends on coal quality but also the boiler design such as volumetric heat loading and operational regimes like excess air, fineness of coal particles etc [1]. Therefore, in order to make the best use of the new method, some related index, such as the dimensionless average furnace temperature, the dimensionless inscribed circle diameter in furnace and so on should be introduced into the model as the influencing factors. 4. Conclusions The conventional single slagging index has low accuracy in predicting and judging the coal DST. The new models proposed here could offer better predictive capability for understanding the field slagging observations than the conventional indices. In order to make the best use of the new models, some related index, such as the particularities of the raw materials used, combustion technologies and operating conditions and so on, should also be introduced into the models as the influencing factors. Acknowledgment The authors are thankful to the support of Science and technology development plan of Jilin City (201464061), National Natural Science Foundation of China (51176028,51476025) and the KEY Scientific and Technological Project of Jilin Province of China (20150203001SF). References [1] A. Lawrence, R. Kumar, K. Nandakumar, K. Narayanan, A novel tool for assessing slagging propensity of coals in PF boilers, Fuel 87 (2008) 946e950. [2] W. Christoph, K. Benjamin, B. Gundula, et al., Evaluation, comparison and validation of deposition criteria for numerical simulation of slagging, Appl. Energy 93 (2012) 184e192. [3] M.U. Degereji, D.B. Ingham, L. Ma, M. Pourkashanian, A. Williams, Prediction of ash slagging propensity in a pulverized coal combustion furnace, Fuel 101 (2012) 171e178. [4] J. Barroso, J. Ballester, A. Pina, Study of coal ash deposition in an entrained flow reactor: assessment of traditional and alternative slagging indices, Fuel Process. Technol. 88 (2007) 865e876.
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Please cite this article in press as: X. Wen, et al., Assessing slagging propensity of coal from their slagging indices, Journal of the Energy Institute (2017), http://dx.doi.org/10.1016/j.joei.2017.06.005