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Application of BP neural network to the prediction of coal ash melting characteristic temperature
Fuel 260 (2020) 116324
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Full Length Article
Application of BP neural network to the prediction of coal ash melting characteristic temperature ⁎
T
⁎
Wang Lianga, Guangwei Wanga, , Xiaojun Ninga, , Jianliang Zhanga,b, Yanjiang Lia, Chunhe Jianga, Nan Zhanga a b
School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Melting characteristic temperature Blast furnace injection Deformation temperature Linear regression Factsage BP neural network
The characteristic temperature of coal ash melting strongly influences the blast furnace injection process. The coal ash deformation temperature (DT) is determined by its chemical composition, but relationship between the two remains uncertain. In this paper, the traditional linear regression, Factsage calculation, and back-propagation (BP) neural network calculation are used to predict the coal ash deformation temperature. The results show that the melting characteristic temperature of coal ash has a great relationship with the coal ash composition. The linear regression can predict the change trend of coal ash deformation temperature, but the prediction results are not very satisfactory. The calculation results of Factsage show a great deviation from the experimental values. The prediction results of the BP neural network can achieve good accuracy, and the maximum relative average error of prediction results is 6.67%. This also illustrates the feasibility of using the BP network prediction model in predicting coal ash deformation temperature.
1. Introduction As one of the world's three major energy sources, the use of coal resources is reflected in many industries. At present, China's coal resource consumption accounts for more than 50% of its total energy consumption [1,2]. The industrial structure of China's coal consumption is diversified, but it is mainly concentrated in the power, steel, building materials, chemical and other industries [3,4]. Coal is a very complex substance whose chemical composition mainly includes five elements (carbon, hydrogen, oxygen, nitrogen and sulfur) and a small amount of mineral components. Through the difference of these components, the performance index of coal can be preliminarily judged, and then a series of experiments can be conducted to determine the performance of different coal types [5,6]. In the process of using coal resources, the power, steel, and other industries are very concerned about the combustion performance and gasification performance indicators of coal [7,8]. During the combustion and gasification of pulverized coal, the fixed carbon in the coal participates in the chemical reaction, the volatile matter evaporates and disappears upon heating, and the mineral composition in the ash also changes. In most industrial conditions, the ambient temperature is generally higher than 1000 °C, which is enough to facilitate the physical
⁎
and chemical changes of minerals in coal. Given that various types of coal have different mineral components, the presence of certain minerals at high temperatures causes the liquid phase to appear earlier and adhere on the surface of the equipment, this phenomenon known as “slagging” [9,10]. In order to quantitatively characterize the slagging performance of coal ash, four characteristic temperatures were proposed to characterize the melting characteristics of coal ash: deformation temperature (DT), softening temperature (ST), hemispherical temperature (HT), and flow temperature (FT) [11]. When the temperature reaches DT, the coal ash begins to melt and produces a certain viscosity. When the temperature reaches ST, the viscosity of the coal ash further increases, and the surface of the equipment becomes sticky. When the temperature reaches FT, the adhesion phenomenon is already very severe, and a large amount of liquid phase exists at this time. HT is generally not used to indicate the slagging process. The process of pulverized coal injection into the blast furnace is usually accompanied by the blowing of hot air. In order to ensure that the pulverized coal is smoothly injected into the blast furnace without slagging, the DT temperature of the coal ash must be higher than the hot air temperature [12]. Although extensive research has been conducted on the relationship between coal ash components and AFT [13–15], there is no universally accepted method for predicting the AFT, so it is necessary to
Corresponding authors. E-mail addresses: [email protected] (G. Wang), [email protected] (X. Ning).
https://doi.org/10.1016/j.fuel.2019.116324 Received 22 May 2019; Received in revised form 25 July 2019; Accepted 30 September 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 Ash composition analysis of 28 samples. Samples
SiO2
Al2O3
CaO
Fe2O3
SO3
K2O
TiO2
MgO
MnO
Others
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
48.781 50.855 49.482 34.459 50.739 51.163 35.204 48.213 26.078 32.441 49.707 41.435 35.233 29.139 27.470 33.186 53.657 51.281 31.209 41.656 45.550 55.477 24.273 39.071 34.816 47.986 43.322 35.239
41.138 23.559 21.274 16.193 23.224 22.944 16.792 22.986 14.005 17.862 23.285 19.949 18.634 14.258 13.476 15.923 21.943 24.591 18.804 18.110 21.889 25.715 14.413 11.789 18.048 12.976 47.275 51.549
2.005 8.140 11.740 26.214 10.599 10.065 28.059 11.856 37.383 23.625 11.576 18.056 25.342 27.946 31.752 26.888 9.232 8.053 19.610 14.814 11.612 7.538 27.299 16.616 20.698 7.900 2.505 3.597
2.772 6.304 6.523 8.519 6.132 6.484 7.185 7.055 7.126 8.016 6.601 8.553 10.639 9.157 9.770 8.191 4.488 6.153 14.336 8.531 8.928 4.346 12.170 17.831 12.137 20.139 1.662 1.747
2.147 7.275 7.184 11.483 5.345 5.573 9.947 6.563 14.096 16.633 4.884 8.765 5.134 15.471 12.748 11.691 5.514 6.613 14.215 12.941 8.201 2.843 17.049 10.452 11.263 6.957 2.895 3.940
0.631 1.979 1.783 0.824 1.810 1.775 0.558 1.547 0.232 0.266 1.692 0.959 0.297 0.614 0.252 0.742 2.656 2.013 0.380 1.318 1.588 1.831 0.244 0.365 0.367 0.116 0.449 0.925
1.707 1.056 1.006 0.623 0.976 0.964 0.833 0.908 0.436 0.680 0.886 0.882 0.800 0.714 0.670 0.710 0.753 0.922 0.863 0.764 0.852 0.886 0.920 0.730 0.875 0.767 1.482 1.972
— 0.452 0.690 1.114 0.743 0.623 0.729 0.445 — — 0.871 0.759 1.282 2.075 2.806 1.986 0.815 — — 1.554 0.883 0.886 2.429 2.121 0.998 2.707 — —
0.026 0.135 0.102 0.217 0.158 0.168 0.322 0.180 0.422 0.274 0.170 0.210 0.280 0.345 0.398 0.312 0.134 0.129 0.245 0.188 0.148 0.072 0.228 0.440 0.254 0.103 0.027 0.018
0.793 0.245 0.216 0.354 0.274 0.241 0.371 0.247 0.222 0.203 0.328 0.432 2.358 0.281 0.658 0.371 0.808 0.245 0.338 0.124 0.349 0.406 0.975 0.585 0.544 0.349 0.383 1.013
Fig. 1. The schematic of ash melting characteristic temperature measuring device.
find a suitable method through research. By summarizing the previous research results, it can be found that some studies have been carried out on the prediction of the melting characteristic temperature of coal ash. For example, Xiao et al. [12] predicted the deformation temperature of coal ash by using the GWOSVM model and found that the model has certain prediction accuracy. Cheng et al. [16] developed a back-propagation (BP) neural network model to accurately predict the ignition temperature and activation energy of 16 coals, and achieved good prediction results. Yu et al. [10] discovered the relationship between chemical composition and softening temperature of coal ash through numerous research, and derived a higher precision softening temperature prediction formula. Dyk et al. [17,18] established a thermodynamic model of ash fusion behavior through the Factsage thermodynamics software, which can accurately predict the ash fusion temperature. Shi et al. [19] estimated the liquidus temperature of coal ash through molecular dynamics and thermodynamic simulation, before finally deriving a calculation formula with high precision. Tambe et al. [20] predicted the coal ash melting temperature based on the computational intelligence model and achieved good prediction results. From the abovementioned results, we can see that many research methods have been proposed for predicting the
Fig. 2. BP network topology.
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Table 2 Chemical composition of coal ash.
DT ST HT FT
1300
Samples
AO
BO
B/A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
91.63 75.47 71.76 51.28 74.94 75.07 52.83 72.11 40.52 50.98 73.88 62.27 54.67 44.11 41.62 49.82 76.35 76.79 50.88 60.53 68.29 82.08 39.61 51.59 53.74 61.73 92.08 88.76
5.41 16.88 20.74 36.67 19.28 18.95 36.53 20.90 44.74 31.91 20.74 28.33 37.56 39.79 44.58 37.81 17.19 16.22 34.33 26.22 23.01 14.60 42.14 36.93 34.20 30.86 4.62 6.27
0.06 0.22 0.29 0.72 0.26 0.25 0.69 0.29 1.10 0.63 0.28 0.45 0.69 0.90 1.07 0.76 0.23 0.21 0.67 0.43 0.34 0.18 1.06 0.72 0.64 0.50 0.05 0.07
Temperature (
)
1250 1200 1150 1100 1050 1000 950 2
4
6
8
10
12
14
16
18
20
22
24
26
28
Sample number Fig. 3. The melting characteristic temperature of coal ash.
collected for the convenience of the subsequent experimental contents. 2.2. Experimental method The X-ray fluorescence spectroscopy (XRF) of an EDX8000 (X-ray tube power: 50 kV, 1 mA) was used to measure the main components and content of the coal ash samples. The test results are shown in Table 1. The collected coal ash samples were measured for ash fusion characteristic temperature, and the measurement method was carried out according to the Chinese standard GB/T 219-2008. The schematic of the ash fusion characteristic temperature measuring device is shown in Fig. 1. First, the sample was formed into a triangular pyramid shape, and then placed in the ash melting point tester. When the temperature was lower than 800 °C, the heating rate of the device was 20 °C/min, and when the temperature was higher than 800 °C, the heating rate was 10 °C/min. The maximum heating temperature set in this experiment is 1400 °C. The data was collected 10 times per minute during the heating process, and the temperature values of the DT, ST, HT, and FT of the coal ash were automatically read and saved according to the change of the shape of the gray cone. After the experiment was completed, the results were checked by playing back the recorded images to ensure the accuracy of the read results.
temperature of coal ash melting characteristics. Among these, the most commonly used methods are empirical formulas, software prediction, and mathematical modeling. As a mathematical model with simple principle and high calculation accuracy, BP neural network has been applied in many fields. However, the BP neural network model is rarely used in the literature to predict the deformation temperature of coal ash. In this study, we use BP neural network to predict the deformation temperature of coal ash and verify the accuracy of the prediction results. In this study, linear regression, Factsage calculation, and BP network calculation are all used to predict the coal ash melting temperature. The goal is to develop a predictive model that is simple to operate, computationally efficient, and highly accurate. First, the linear correlation between the coal ash deformation temperature and the ash composition was studied by the linear regression of experimental results. Then, through the Factsage software calculation, the experimental and calculation results are compared and analyzed to assess the feasibility of the proposed research method. Finally, a new BP network model is introduced, that can accurately predict the melting point of coal ash without specifying the relationship between input and output variables. By comparing these results, the most accurate and reliable prediction model is obtained. Given that the ash melting point experiment has a certain timeliness, the development of the model provides a simple and effective method for selecting coal for blast furnace.
2.3. Prediction method In this study, linear regression, Factsage calculation, and the BP neural network model were used to predict the deformation temperature of coal ash. A linear regression method was used to determine whether there is a significant linear relationship between the deformation temperature of coal ash and its composition. Using the Factsage thermodynamics software, the total mass was set to 100 g, the FToxid database was selected, and the Equilib module was used to calculate the formation target phase temperature and the precipitate target phase temperature of the coal ash. Afterwards, the calculated results were compared with the experimental results. Using the BP neural network model, simulated the human brain's thinking mode to learn some data, and then adjusted the parameters to make the prediction model achieve higher precision. Finally, the computer was also used to verify the model prediction results.
2. Test contents and method 2.1. Preparation of samples All coal samples used in this study were sourced from Shaanxi Province, China. Due to the large differences in particle size distribution of the raw coal samples, these were crushed and ground so that those with a particle size of 1 mm or less can be screened. The coal ash sample was prepared by referring to the ash component in the Chinese standard GB/T212-2008. The crucible containing pulverized coal was placed in a muffle furnace and heated to 815 °C for 2 h until the coal powder was completely burned and turned to ash. Then these samples were
2.4. Introduction to the principle of the BP neural network The BP neural network is an algorithm for error back propagation training with a multi-layer network structure. The BP neural network learns the use of the steepest descent method, and the network 3
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DT Linear fit of DT
(a)
1250
y=-0.26x+1123.41
y=0.32x+1095.81
)
1150
Temperature (
)
DT Linear fit of DT
1200
1200
Temperature (
(b)
1250
1100 1050
1150 1100 1050
1000
1000
950
950 40
50
60
70
80
90
100
10
20
30
40
50
Basic oxide content (%)
Acid oxide content (%) DT Linear fit of DT
(c)
1250
0
Temperature (
)
1200
y=-20.05x+1126.25
1150 1100 1050 1000 950 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ratio of basic oxide to acidic oxide Fig. 4. Relationship between chemical composition and DT temperature. (a) Acid oxide; (b) Basic oxide; (c) Ratio of basic oxide to acidic oxide.
DT FT FTPT PTPT
1800 1700
Temperature (
)
1600 1500 1400 1300 1200 1100 1000 900
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Samples Fig. 5. Factsage software calculation results.
connection weight coefficients and thresholds are automatically adjusted by the back-propagation of the output error, thereby minimizing the error value of the network to achieve the desired error. The BP neural network used in this study has a three-layer network structure, consisting of an input layer, a hidden layer, and an output layer, each composed of a plurality of neurons that can be calculated in parallel. The connection between the hidden layer and the input layer are connected by an activation function. For example, in the case where the
Fig. 6. Flow chart of BP network model establishment.
input layer is 8, the relationship between a certain neuron n of the hidden layer and the input layer data can be characterized by the following formula:
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0.06
in Fig. 4. As shown in Fig. 4(a), the linear fit of the DT temperature of the coal ash to the AO content is positively correlated, that is, as the AO content increases, the DT temperature also increases gradually, and a small portion of the sample deviates from the fitting result. Meanwhile, Fig. 4(b) shows that as the BO content increases, the DT temperature of the coal ash decreases. There is a negative correlation between the linear fit of DT temperature and BO content, and the results of most samples are near the fitting results. Figure (c) shows the fitting results of B/A and DT. As can be seen, as the B/A value increases, the DT temperature gradually decreases, also showing a significant negative correlation trend. This is consistent with the conclusions of past studies [9,21,22]. Fig. 4 also shows that, in addition to the points near the fitting result, many points are also not around the fitting result, and the deviation is large. In order to quantitatively analyze the accuracy of the linear regression, the DT of the coal ash was calculated based on the linear regression result, and the differences between the calculated and experimental results are listed in Table S1. As shown in the table, the calculation results obtained by the three linear regressions are close to the experimental results, and the deviation of most of the calculation results is less than 100 °C. The maximum differences among the three linear regression results are 147.93 °C, 151.06 °C and 146.16 °C, respectively, and the corresponding maximum deviation rates are 15.38%, 15.70%, and 15.19%, respectively. In general, the linear regression method can be used to predict the temperature of coal ash DT, but the stability of the calculation results is poor given that the maximum deviation is about 15%. From the above analysis, it can be seen that there is an uncertain relationship between DT and chemical composition. Therefore, this method can be used to predict the change trend of coal ash deformation temperature, although it may still be difficult to accurately predict the deformation temperature of coal ash.
logsig tansig
0.05
MSE
0.04
0.03
0.02
0.01
0.00 0
5
10
15
20
25
30
Number of neurons Fig. 7. The effect of different activation functions on the error. 8
fn =
∑ wni·Xi i=1
(1)
where n is a neuron in the hidden layer and i is the number of input layers. At the same time, the output layer and the hidden layer are also connected by an indeterminate activation function. The topology used in this experiment is shown in Fig. 2. As can be seen, the red wireframe in the figure represents the three-layer network structure, and the blue arrows indicate the corresponding relationship. 3. Results and discussion 3.1. Analysis of the ash melting characteristic temperature results
3.3. Factsage prediction of coal ash melting point
The coal ash components of 28 types of coal based on the XRF test results are listed in Table 1. The other columns in Table 1 indicate the addition of oxides having a very small amount of a part of the test results. As shown in Table 1, the SiO2, Al2O3, CaO, and Fe2O3 contents of all coal ash selected range between 24% and 56%, 11% and 52%, 2% and 38%, and 1% and 21%, respectively. In addition, the SO3 content ranges between 2% and 18%, the K2O and MgO contents are below 3%, and TiO2 content is below 2%. The slagging index is used to evaluate the tendency of slagging. According to some previously proposed criteria, the chemical components in coal ash are classified into acidic oxides (AO) and basic oxides (BO). The AO, the BO, and the ratio of the basic oxides to the acidic oxides (B/A) is listed in Table 2. As can be seen, the AO includes (SiO2, Al2O3, TiO2), and the BO includes (CaO, Fe2O3, K2O, MgO). Fig. 3 shows the experimental results of the ash melting temperatures of 28 kinds of coals. As shown in the figure, the four melting characteristic temperatures of different types of coal ash have basically the same trend: the ST, HT, and FT temperatures have the same trend change as the DT changes. The experimentally measured coal ash DT temperature ranges between 962 °C and 1230 °C, the ST temperature range is between 992 °C and 1242 °C, the HT temperature range is between 1036 °C and 1249 °C, and the FT temperature range is between 1058 °C and 1316 °C.
The formation target phase temperature (FTPT) and the precipitate target phase temperature (PTPT) of coal ash can be calculated by using the Factsage thermodynamic calculation software. The chemical composition of coal ash is encoded into the software for calculation, and the calculation results are shown in Fig. 5. As can be seen, the calculated FTPT and PTPT temperatures are very similar to the trends of DT and FT. As the DT changes, the other three temperatures also change accordingly. In order to quantitatively analyze the accuracy of the calculation results obtained by the Factsage software, these were compared with the experimental results and the results are listed in Table S2. From the data listed in the table, it can also be found that the FTPT temperature curve is above the DT temperature curve, the value of the DT temperatures of the 28 types of coal ash is calculated to be 1116 °C, and the average value of FTPT is 1265 °C. The difference between the average of the calculated results and the average of the experimental results is 149 °C, which is quite huge. The maximum value of the difference between the calculated and the experimental values is 328° C, and the maximum value of the deviation between the calculated and the experimental values is 32%. On the one hand, the gas content in the coal ash cannot be used as an input. Hence, the inputted coal ash component deviates from the XRF result, resulting in the calculation result indicating a large deviation from the experimental result. On the other hand, the software itself has some drawbacks, and it is still in the process of continuous updating and upgrading, and this may have contributed to the deviation between the calculation result and the experimental result. These results indicate the difficult of accurately predicting the DT of the coal ash by using Factsage. In order to obtain more accurate calculation results, more reasonable research methods should thus be adopted.
3.2. Linear regression analysis According to previous studies [9,21,22], the acidic and basic metal oxides in coal ash have the effects of increasing and decreasing the melting temperature of coal ash, respectively The acidic oxide, the basic oxide, and the ratio of the basic metal oxide to the acidic metal oxide in the coal ash are respectively plotted with DT, and the results are shown 5
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 8. The effect of training function on the average absolute error value. (a) Traingd; (b) Traingda; (c) Traingdm; (d) Trainlm; (e) Trainrp; (f) Traincgb.
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Table 3 BP network structure parameters. Number
Structural parameters
Ranges
Application value
1 2 3 4 5 6 7 8 9 10 11
Input variable Number of hidden layers Learning rate Initial weight Number of hidden layer nodes Training function Implicit layer transfer function Output layer transfer function Momentum factor Maximum number of training steps Allowable error range
≥1 ≥0 0.01–0.7 −1 to 1 1–30 Traingd, Traingda, Traingdm, Trainlm, Trainrp, Traincgb Logsig, Tansig purelin 0.9 10,000 1 * 10−6
8 1 0.05 −1 to 1 27 traincgb logsig purelin 0.9 10,000 1 * 10−6
stability of BP network training results. When the MSE reaches the minimum value, the BP network's setting parameters becomes the optimal network structure. Fig. 7 shows the relationship between the number of transfer functions and neurons in the hidden layer. As can be seen, regardless of whether the transfer function of the hidden layer is “tansig” or “logsig”, the MSE value gradually converges close to zero as the number of neurons increases. When the hidden layer transfer function is “tansig”, the measured MSE value of the measurement is usually smaller. Fig. 7 also shows that when the transfer function of the hidden layer is “tansig” the number of neurons is 27, the MSE thus reaches a minimum. Therefore, the hidden layer transfer function used in this experiment is “tansig” and the number of neurons in the hidden layer is 27. The commonly used BP network training functions include: “trainlm”, “reaingd”, “traingda”, “traingdm”, “traincgb” and “trainrp”. The results of the Mean Squared Error values generated using different training functions are shown in Fig. 8. As can be seen from the figure, when the three training functions of “traingd”, “traingda”, and “traingdm” are used, there is no convergence after 10,000 times of training. When the “trainlm” function is selected for training, the training result reaches 1 × 10−6 precision, but this does not mean that it has reached convergence. It can be seen from the figure, as the number of training steps increases, the MSE suddenly drops; this phenomenon is called overtraining. Convergence is achieved when training is performed using the function “trainrp” and “traincgb”. Clearly, when training with the function “traincgb”, the convergence rate is better than that obtained when training with the function “trainrp”. The best training function among all those in “traincgb”, which is used in this study. In order to obtain good prediction accuracy, the other parameters of the BP network structure must be appropriately adjusted. The range of values of some parameters used in the BP network structure and the values in this experiment are listed in Table 3. The learning rate usually set to range between 0.01 and 0.7. If the learning rate is too high, the results become unstable, whereas if the learning rate is too low, the network convergence becomes slow. After the experimental calculation, the learning rate is set to 0.05 in this study. In order to facilitate the calculation, the input data must be normalized to within the range between 0 and 1. In this study, the momentum factor is taken as 0.9, the maximum number of training steps is 10,000, and the allowable error is 1 × 10−6. Samples No. 1 to No. 22 were used as learning samples, and the modeling method was used to predict the deformation temperature of samples No. 23 to No. 28. The prediction results and errors are listed in Table 4. As shown in the table, the difference between the calculated and experimental values of the six samples is small. The maximum difference is 75 °C, and the maximum relative error is 6.67%, indicating that the BP network has higher prediction accuracy for DT of coal ash. The maximum error of the BP network is 6.67%, which is much better than the 15% rate of the linear regression results and 32% of the Factsage prediction results. This superior value which also shows that
Table 4 Comparison of predicted and calculated values. DT
23
24
25
26
27
28
Actual value (°C) Calculated (°C) Difference (°C) Error (%)
1122 1096 26 2.32
1139 1074 65 5.71
1146 1179 33 2.88
1125 1050 75 6.67
1138 1115 23 2.02
1129 1058 71 6.29
3.4. BP network prediction model In recent years, the BP neural network has been widely used due to its high prediction accuracy, simple structure, and good self-learning, self-organization, and self-adaptive capabilities. Here, the parameters of the network structure are automatically adjusted through the back propagation of the error. For a given input, the most desirable output is produced. In the case of uncertain internal mechanisms and linkages, the BP neural network is considered a highly accurate model method. The relationship between the chemical composition of coal ash and its deformation temperature has remained uncertain. Therefore, the BP neural network model is used to solve this problem. The flow chart of the BP network modeling and parameter optimization is shown in Fig. 6. As can be seen from the figure, the process is performed from top to bottom, and there are two feedbacks at the output. First, after analyzing the problem, the input and output are determined, after which the sample is normalized, in order to facilitate accurate calculation and reduce the error. Next is the determination of the network structure, the initialization of the weights and the establishment of the training network. Before outputting the result, whether the calculation result converges quickly and reaches the prediction accuracy should be determined. Moreover, it is also important to assess whether the error of the output result satisfies the set range and to output the result only if both conditions are simultaneously; otherwise, the network needs to be trained again. As shown in Fig. 6, a flow chart of the BP neural network is described in detail. The problem that this research aims to resolve has to do with the deformation temperature of coal ash, and its input components comprising the eight chemical components present in coal ash. The samples are the 28 kinds of Shaanxi coal shown in Table 1. After determining the problem of the study and selecting the samples, the most important step is the determination of the network structure, which requires the determination of the training function, transfer function, learning rate, training steps, and allowable error range to be used in the calculation process. The functions of these parameters have been introduced in previous studies [23–25]. The number of neurons in the hidden layer is between 1 and 30, and the transfer function of the hidden layer typically uses “tansig” or “logsig”. The BP neural network is trained by changing the number of neurons in the hidden layer under different transfer function conditions. Mean Squared Error (MSE) is often used to evaluate the degree of dispersion of a set of data. In this study, MSE was used to assess the 7
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the BP algorithm predicts the ash melting point result with high accuracy and reliability.
[5]
4. Conclusion [6]
In this study, three methods were used to predict the DT temperature of coal ash based on the relationship between the composition and the melting characteristic temperature of coal ash. The DT value of the coal ash was determined by using a device that measured the coal ash melting characteristic temperature. When the DT temperature was predicted by linear regression and Factsage calculation, the maximum deviations were 15% and 32%, respectively, which produced large deviations. Based on the knowledge that the BP network does not need to establish the relationship between the input and output, the results can be accurately predicted. Therefore, a three-layer BP neural network model with eight input functions was developed to predict the deformation temperature of coal ash. Through the continuous selflearning of the BP network, the maximum relative error calculated from the model is 6.67%, which is much lower than the results obtained by linear regression and Factsage calculation. This finding thus proves the accuracy of the prediction results obtained using the proposed method. Therefore, the BP network structure can be considered as a very effective method for predicting coal ash DT and may be used effectively in future industrial applications.
[7]
[8]
[9] [10] [11] [12]
[13] [14] [15] [16]
[17]
Acknowledgement
[18]
This work was supported by the Natural Science Foundation for Young Scientists of China (No. 51804026), and the Young Elite Scientists Sponsorship Program By China Association for Science and Technology (2017QNRC001).
[19]
[20]
Appendix A. Supplementary data [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.fuel.2019.116324.
[22] [23]
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studies on co-gasification of petroleum coke and biomass char blends. Energy 2017;131:27–40. Li K, Khanna R, Zhang J, Barati M, Liu Z, Xu T, et al. Comprehensive investigation of various structural features of bituminous coals using advanced analytical techniques. Energ Fuel 2015;29(11):7178–89. Van Dyk J, Keyser M. Influence of discard mineral matter on slag–liquid formation and ash melting properties of coal–A FACTSAGETM simulation study. Fuel 2014;116:834–40. Wang G, Zhang J, Shao J, Liu Z, Zhang G, Xu T, et al. Thermal behavior and kinetic analysis of co-combustion of waste biomass/low rank coal blends. Energ Convers Manage 2016;124:414–26. Wang G, Zhang J, Huang X, Liang X, Ning X, Li R. Co-gasification of petroleum cokebiomass blended char with steam at temperatures of 1173–1373 K. Appl Therm Eng 2018;137:678–88. Liu B, He Q, Jiang Z, Xu R, Hu B. Relationship between coal ash composition and ash fusion temperatures. Fuel 2013;105:293–300. Yu L, Wang L, Li P. Study on prediction models of biomass ash softening temperature based on ash composition. J Energy Inst 2014;87(3):215–9. ASTM D. 87: Standard Test Method for Fusibility of Coal and Coke Ash. 1985 Annual Book of Standards. 1857;5. Xiao H, Chen Y, Dou C, Ru Y, Cai L, Zhang C, et al. Prediction of ash-deformation temperature based on grey-wolf algorithm and support-vector machine. Fuel 2019;241:304–10. Luan C, You C, Zhang D. An experimental investigation into the characteristics and deposition mechanism of high-viscosity coal ash. Fuel 2014;119:14–20. Song WJ, Tang LH, Zhu XD, Wu YQ, Zhu ZB, Koyama S. Effect of coal ash composition on ash fusion temperatures. Energy Fuel 2009;24(1):182–9. Li Q, Zhang Y, Meng A, Li L, Li G. Study on ash fusion temperature using original and simulated biomass ashes. Fuel Process Technol 2013;107:107–12. Cheng J, Wang X, Si T, Zhou F, Zhou J, Cen K. Ignition temperature and activation energy of power coal blends predicted with back-propagation neural network models. Fuel 2016;173:230–8. Jak E. Prediction of coal ash fusion temperatures with the F∗ A∗ C∗ T thermodynamic computer package. Fuel 2002;81(13):1655–68. Kumar N, Venugopal R, Soren S, Chakravarty S, Sahu R, Mishra P. Application of FactSage to predict ash melting behavior. Conference Application of FactSage to predict ash melting behavior. CSIR-CIMFR Dhanbad, p. 541–48. Shi W, Dai X, Bai J, Kong L, Xu J, Li X, et al. A new method of estimating the liquidus temperature of coal ash slag using ash composition. Chem Eng Sci 2018;175:278–85. Tambe SS, Naniwadekar M, Tiwary S, Mukherjee A, Das TB. Prediction of coal ash fusion temperatures using computational intelligence based models. Int J Coal Sci Technol 2018;5(4):486–507. Wei B, Wang X, Tan H, Zhang L, Wang Y, Wang Z. Effect of silicon–aluminum additives on ash fusion and ash mineral conversion of Xinjiang high-sodium coal. Fuel 2016;181:1224–9. Wang D, Liang Q, Gong X, Liu H, Liu X. Influence of coal blending on ash fusion property and viscosity. Fuel 2017;189:15–22. Yang FS, Wei BL, Zhou AN, Lin MQ, Zhang HJ, Wang H, et al. Prediction of Coal Ash Fusion Characteristics of Blending Coals for Gasification Based on Genetic Algorithm and BP Neural Network. Conference Prediction of Coal Ash Fusion Characteristics of Blending Coals for Gasification Based on Genetic Algorithm and BP Neural Network. Atlantis Press. Vasseghian Y, Heidari N, Ahmadi M, Zahedi G, Mohsenipour AA. Simultaneous ash and sulfur removal from bitumen: experiments and neural network modeling. Fuel Process Technol 2014;125:79–85. Wang G, Xu T, Wang X. Error compensation of coal mine paste filling weighing system based on BP neural network. Coal Mine Machinery 2014;35(6):198–9.
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Full Length Article
Application of BP neural network to the prediction of coal ash melting characteristic temperature ⁎
T
⁎
Wang Lianga, Guangwei Wanga, , Xiaojun Ninga, , Jianliang Zhanga,b, Yanjiang Lia, Chunhe Jianga, Nan Zhanga a b
School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: Melting characteristic temperature Blast furnace injection Deformation temperature Linear regression Factsage BP neural network
The characteristic temperature of coal ash melting strongly influences the blast furnace injection process. The coal ash deformation temperature (DT) is determined by its chemical composition, but relationship between the two remains uncertain. In this paper, the traditional linear regression, Factsage calculation, and back-propagation (BP) neural network calculation are used to predict the coal ash deformation temperature. The results show that the melting characteristic temperature of coal ash has a great relationship with the coal ash composition. The linear regression can predict the change trend of coal ash deformation temperature, but the prediction results are not very satisfactory. The calculation results of Factsage show a great deviation from the experimental values. The prediction results of the BP neural network can achieve good accuracy, and the maximum relative average error of prediction results is 6.67%. This also illustrates the feasibility of using the BP network prediction model in predicting coal ash deformation temperature.
1. Introduction As one of the world's three major energy sources, the use of coal resources is reflected in many industries. At present, China's coal resource consumption accounts for more than 50% of its total energy consumption [1,2]. The industrial structure of China's coal consumption is diversified, but it is mainly concentrated in the power, steel, building materials, chemical and other industries [3,4]. Coal is a very complex substance whose chemical composition mainly includes five elements (carbon, hydrogen, oxygen, nitrogen and sulfur) and a small amount of mineral components. Through the difference of these components, the performance index of coal can be preliminarily judged, and then a series of experiments can be conducted to determine the performance of different coal types [5,6]. In the process of using coal resources, the power, steel, and other industries are very concerned about the combustion performance and gasification performance indicators of coal [7,8]. During the combustion and gasification of pulverized coal, the fixed carbon in the coal participates in the chemical reaction, the volatile matter evaporates and disappears upon heating, and the mineral composition in the ash also changes. In most industrial conditions, the ambient temperature is generally higher than 1000 °C, which is enough to facilitate the physical
⁎
and chemical changes of minerals in coal. Given that various types of coal have different mineral components, the presence of certain minerals at high temperatures causes the liquid phase to appear earlier and adhere on the surface of the equipment, this phenomenon known as “slagging” [9,10]. In order to quantitatively characterize the slagging performance of coal ash, four characteristic temperatures were proposed to characterize the melting characteristics of coal ash: deformation temperature (DT), softening temperature (ST), hemispherical temperature (HT), and flow temperature (FT) [11]. When the temperature reaches DT, the coal ash begins to melt and produces a certain viscosity. When the temperature reaches ST, the viscosity of the coal ash further increases, and the surface of the equipment becomes sticky. When the temperature reaches FT, the adhesion phenomenon is already very severe, and a large amount of liquid phase exists at this time. HT is generally not used to indicate the slagging process. The process of pulverized coal injection into the blast furnace is usually accompanied by the blowing of hot air. In order to ensure that the pulverized coal is smoothly injected into the blast furnace without slagging, the DT temperature of the coal ash must be higher than the hot air temperature [12]. Although extensive research has been conducted on the relationship between coal ash components and AFT [13–15], there is no universally accepted method for predicting the AFT, so it is necessary to
Corresponding authors. E-mail addresses: [email protected] (G. Wang), [email protected] (X. Ning).
https://doi.org/10.1016/j.fuel.2019.116324 Received 22 May 2019; Received in revised form 25 July 2019; Accepted 30 September 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
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Table 1 Ash composition analysis of 28 samples. Samples
SiO2
Al2O3
CaO
Fe2O3
SO3
K2O
TiO2
MgO
MnO
Others
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
48.781 50.855 49.482 34.459 50.739 51.163 35.204 48.213 26.078 32.441 49.707 41.435 35.233 29.139 27.470 33.186 53.657 51.281 31.209 41.656 45.550 55.477 24.273 39.071 34.816 47.986 43.322 35.239
41.138 23.559 21.274 16.193 23.224 22.944 16.792 22.986 14.005 17.862 23.285 19.949 18.634 14.258 13.476 15.923 21.943 24.591 18.804 18.110 21.889 25.715 14.413 11.789 18.048 12.976 47.275 51.549
2.005 8.140 11.740 26.214 10.599 10.065 28.059 11.856 37.383 23.625 11.576 18.056 25.342 27.946 31.752 26.888 9.232 8.053 19.610 14.814 11.612 7.538 27.299 16.616 20.698 7.900 2.505 3.597
2.772 6.304 6.523 8.519 6.132 6.484 7.185 7.055 7.126 8.016 6.601 8.553 10.639 9.157 9.770 8.191 4.488 6.153 14.336 8.531 8.928 4.346 12.170 17.831 12.137 20.139 1.662 1.747
2.147 7.275 7.184 11.483 5.345 5.573 9.947 6.563 14.096 16.633 4.884 8.765 5.134 15.471 12.748 11.691 5.514 6.613 14.215 12.941 8.201 2.843 17.049 10.452 11.263 6.957 2.895 3.940
0.631 1.979 1.783 0.824 1.810 1.775 0.558 1.547 0.232 0.266 1.692 0.959 0.297 0.614 0.252 0.742 2.656 2.013 0.380 1.318 1.588 1.831 0.244 0.365 0.367 0.116 0.449 0.925
1.707 1.056 1.006 0.623 0.976 0.964 0.833 0.908 0.436 0.680 0.886 0.882 0.800 0.714 0.670 0.710 0.753 0.922 0.863 0.764 0.852 0.886 0.920 0.730 0.875 0.767 1.482 1.972
— 0.452 0.690 1.114 0.743 0.623 0.729 0.445 — — 0.871 0.759 1.282 2.075 2.806 1.986 0.815 — — 1.554 0.883 0.886 2.429 2.121 0.998 2.707 — —
0.026 0.135 0.102 0.217 0.158 0.168 0.322 0.180 0.422 0.274 0.170 0.210 0.280 0.345 0.398 0.312 0.134 0.129 0.245 0.188 0.148 0.072 0.228 0.440 0.254 0.103 0.027 0.018
0.793 0.245 0.216 0.354 0.274 0.241 0.371 0.247 0.222 0.203 0.328 0.432 2.358 0.281 0.658 0.371 0.808 0.245 0.338 0.124 0.349 0.406 0.975 0.585 0.544 0.349 0.383 1.013
Fig. 1. The schematic of ash melting characteristic temperature measuring device.
find a suitable method through research. By summarizing the previous research results, it can be found that some studies have been carried out on the prediction of the melting characteristic temperature of coal ash. For example, Xiao et al. [12] predicted the deformation temperature of coal ash by using the GWOSVM model and found that the model has certain prediction accuracy. Cheng et al. [16] developed a back-propagation (BP) neural network model to accurately predict the ignition temperature and activation energy of 16 coals, and achieved good prediction results. Yu et al. [10] discovered the relationship between chemical composition and softening temperature of coal ash through numerous research, and derived a higher precision softening temperature prediction formula. Dyk et al. [17,18] established a thermodynamic model of ash fusion behavior through the Factsage thermodynamics software, which can accurately predict the ash fusion temperature. Shi et al. [19] estimated the liquidus temperature of coal ash through molecular dynamics and thermodynamic simulation, before finally deriving a calculation formula with high precision. Tambe et al. [20] predicted the coal ash melting temperature based on the computational intelligence model and achieved good prediction results. From the abovementioned results, we can see that many research methods have been proposed for predicting the
Fig. 2. BP network topology.
2
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Table 2 Chemical composition of coal ash.
DT ST HT FT
1300
Samples
AO
BO
B/A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
91.63 75.47 71.76 51.28 74.94 75.07 52.83 72.11 40.52 50.98 73.88 62.27 54.67 44.11 41.62 49.82 76.35 76.79 50.88 60.53 68.29 82.08 39.61 51.59 53.74 61.73 92.08 88.76
5.41 16.88 20.74 36.67 19.28 18.95 36.53 20.90 44.74 31.91 20.74 28.33 37.56 39.79 44.58 37.81 17.19 16.22 34.33 26.22 23.01 14.60 42.14 36.93 34.20 30.86 4.62 6.27
0.06 0.22 0.29 0.72 0.26 0.25 0.69 0.29 1.10 0.63 0.28 0.45 0.69 0.90 1.07 0.76 0.23 0.21 0.67 0.43 0.34 0.18 1.06 0.72 0.64 0.50 0.05 0.07
Temperature (
)
1250 1200 1150 1100 1050 1000 950 2
4
6
8
10
12
14
16
18
20
22
24
26
28
Sample number Fig. 3. The melting characteristic temperature of coal ash.
collected for the convenience of the subsequent experimental contents. 2.2. Experimental method The X-ray fluorescence spectroscopy (XRF) of an EDX8000 (X-ray tube power: 50 kV, 1 mA) was used to measure the main components and content of the coal ash samples. The test results are shown in Table 1. The collected coal ash samples were measured for ash fusion characteristic temperature, and the measurement method was carried out according to the Chinese standard GB/T 219-2008. The schematic of the ash fusion characteristic temperature measuring device is shown in Fig. 1. First, the sample was formed into a triangular pyramid shape, and then placed in the ash melting point tester. When the temperature was lower than 800 °C, the heating rate of the device was 20 °C/min, and when the temperature was higher than 800 °C, the heating rate was 10 °C/min. The maximum heating temperature set in this experiment is 1400 °C. The data was collected 10 times per minute during the heating process, and the temperature values of the DT, ST, HT, and FT of the coal ash were automatically read and saved according to the change of the shape of the gray cone. After the experiment was completed, the results were checked by playing back the recorded images to ensure the accuracy of the read results.
temperature of coal ash melting characteristics. Among these, the most commonly used methods are empirical formulas, software prediction, and mathematical modeling. As a mathematical model with simple principle and high calculation accuracy, BP neural network has been applied in many fields. However, the BP neural network model is rarely used in the literature to predict the deformation temperature of coal ash. In this study, we use BP neural network to predict the deformation temperature of coal ash and verify the accuracy of the prediction results. In this study, linear regression, Factsage calculation, and BP network calculation are all used to predict the coal ash melting temperature. The goal is to develop a predictive model that is simple to operate, computationally efficient, and highly accurate. First, the linear correlation between the coal ash deformation temperature and the ash composition was studied by the linear regression of experimental results. Then, through the Factsage software calculation, the experimental and calculation results are compared and analyzed to assess the feasibility of the proposed research method. Finally, a new BP network model is introduced, that can accurately predict the melting point of coal ash without specifying the relationship between input and output variables. By comparing these results, the most accurate and reliable prediction model is obtained. Given that the ash melting point experiment has a certain timeliness, the development of the model provides a simple and effective method for selecting coal for blast furnace.
2.3. Prediction method In this study, linear regression, Factsage calculation, and the BP neural network model were used to predict the deformation temperature of coal ash. A linear regression method was used to determine whether there is a significant linear relationship between the deformation temperature of coal ash and its composition. Using the Factsage thermodynamics software, the total mass was set to 100 g, the FToxid database was selected, and the Equilib module was used to calculate the formation target phase temperature and the precipitate target phase temperature of the coal ash. Afterwards, the calculated results were compared with the experimental results. Using the BP neural network model, simulated the human brain's thinking mode to learn some data, and then adjusted the parameters to make the prediction model achieve higher precision. Finally, the computer was also used to verify the model prediction results.
2. Test contents and method 2.1. Preparation of samples All coal samples used in this study were sourced from Shaanxi Province, China. Due to the large differences in particle size distribution of the raw coal samples, these were crushed and ground so that those with a particle size of 1 mm or less can be screened. The coal ash sample was prepared by referring to the ash component in the Chinese standard GB/T212-2008. The crucible containing pulverized coal was placed in a muffle furnace and heated to 815 °C for 2 h until the coal powder was completely burned and turned to ash. Then these samples were
2.4. Introduction to the principle of the BP neural network The BP neural network is an algorithm for error back propagation training with a multi-layer network structure. The BP neural network learns the use of the steepest descent method, and the network 3
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DT Linear fit of DT
(a)
1250
y=-0.26x+1123.41
y=0.32x+1095.81
)
1150
Temperature (
)
DT Linear fit of DT
1200
1200
Temperature (
(b)
1250
1100 1050
1150 1100 1050
1000
1000
950
950 40
50
60
70
80
90
100
10
20
30
40
50
Basic oxide content (%)
Acid oxide content (%) DT Linear fit of DT
(c)
1250
0
Temperature (
)
1200
y=-20.05x+1126.25
1150 1100 1050 1000 950 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ratio of basic oxide to acidic oxide Fig. 4. Relationship between chemical composition and DT temperature. (a) Acid oxide; (b) Basic oxide; (c) Ratio of basic oxide to acidic oxide.
DT FT FTPT PTPT
1800 1700
Temperature (
)
1600 1500 1400 1300 1200 1100 1000 900
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Samples Fig. 5. Factsage software calculation results.
connection weight coefficients and thresholds are automatically adjusted by the back-propagation of the output error, thereby minimizing the error value of the network to achieve the desired error. The BP neural network used in this study has a three-layer network structure, consisting of an input layer, a hidden layer, and an output layer, each composed of a plurality of neurons that can be calculated in parallel. The connection between the hidden layer and the input layer are connected by an activation function. For example, in the case where the
Fig. 6. Flow chart of BP network model establishment.
input layer is 8, the relationship between a certain neuron n of the hidden layer and the input layer data can be characterized by the following formula:
4
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0.06
in Fig. 4. As shown in Fig. 4(a), the linear fit of the DT temperature of the coal ash to the AO content is positively correlated, that is, as the AO content increases, the DT temperature also increases gradually, and a small portion of the sample deviates from the fitting result. Meanwhile, Fig. 4(b) shows that as the BO content increases, the DT temperature of the coal ash decreases. There is a negative correlation between the linear fit of DT temperature and BO content, and the results of most samples are near the fitting results. Figure (c) shows the fitting results of B/A and DT. As can be seen, as the B/A value increases, the DT temperature gradually decreases, also showing a significant negative correlation trend. This is consistent with the conclusions of past studies [9,21,22]. Fig. 4 also shows that, in addition to the points near the fitting result, many points are also not around the fitting result, and the deviation is large. In order to quantitatively analyze the accuracy of the linear regression, the DT of the coal ash was calculated based on the linear regression result, and the differences between the calculated and experimental results are listed in Table S1. As shown in the table, the calculation results obtained by the three linear regressions are close to the experimental results, and the deviation of most of the calculation results is less than 100 °C. The maximum differences among the three linear regression results are 147.93 °C, 151.06 °C and 146.16 °C, respectively, and the corresponding maximum deviation rates are 15.38%, 15.70%, and 15.19%, respectively. In general, the linear regression method can be used to predict the temperature of coal ash DT, but the stability of the calculation results is poor given that the maximum deviation is about 15%. From the above analysis, it can be seen that there is an uncertain relationship between DT and chemical composition. Therefore, this method can be used to predict the change trend of coal ash deformation temperature, although it may still be difficult to accurately predict the deformation temperature of coal ash.
logsig tansig
0.05
MSE
0.04
0.03
0.02
0.01
0.00 0
5
10
15
20
25
30
Number of neurons Fig. 7. The effect of different activation functions on the error. 8
fn =
∑ wni·Xi i=1
(1)
where n is a neuron in the hidden layer and i is the number of input layers. At the same time, the output layer and the hidden layer are also connected by an indeterminate activation function. The topology used in this experiment is shown in Fig. 2. As can be seen, the red wireframe in the figure represents the three-layer network structure, and the blue arrows indicate the corresponding relationship. 3. Results and discussion 3.1. Analysis of the ash melting characteristic temperature results
3.3. Factsage prediction of coal ash melting point
The coal ash components of 28 types of coal based on the XRF test results are listed in Table 1. The other columns in Table 1 indicate the addition of oxides having a very small amount of a part of the test results. As shown in Table 1, the SiO2, Al2O3, CaO, and Fe2O3 contents of all coal ash selected range between 24% and 56%, 11% and 52%, 2% and 38%, and 1% and 21%, respectively. In addition, the SO3 content ranges between 2% and 18%, the K2O and MgO contents are below 3%, and TiO2 content is below 2%. The slagging index is used to evaluate the tendency of slagging. According to some previously proposed criteria, the chemical components in coal ash are classified into acidic oxides (AO) and basic oxides (BO). The AO, the BO, and the ratio of the basic oxides to the acidic oxides (B/A) is listed in Table 2. As can be seen, the AO includes (SiO2, Al2O3, TiO2), and the BO includes (CaO, Fe2O3, K2O, MgO). Fig. 3 shows the experimental results of the ash melting temperatures of 28 kinds of coals. As shown in the figure, the four melting characteristic temperatures of different types of coal ash have basically the same trend: the ST, HT, and FT temperatures have the same trend change as the DT changes. The experimentally measured coal ash DT temperature ranges between 962 °C and 1230 °C, the ST temperature range is between 992 °C and 1242 °C, the HT temperature range is between 1036 °C and 1249 °C, and the FT temperature range is between 1058 °C and 1316 °C.
The formation target phase temperature (FTPT) and the precipitate target phase temperature (PTPT) of coal ash can be calculated by using the Factsage thermodynamic calculation software. The chemical composition of coal ash is encoded into the software for calculation, and the calculation results are shown in Fig. 5. As can be seen, the calculated FTPT and PTPT temperatures are very similar to the trends of DT and FT. As the DT changes, the other three temperatures also change accordingly. In order to quantitatively analyze the accuracy of the calculation results obtained by the Factsage software, these were compared with the experimental results and the results are listed in Table S2. From the data listed in the table, it can also be found that the FTPT temperature curve is above the DT temperature curve, the value of the DT temperatures of the 28 types of coal ash is calculated to be 1116 °C, and the average value of FTPT is 1265 °C. The difference between the average of the calculated results and the average of the experimental results is 149 °C, which is quite huge. The maximum value of the difference between the calculated and the experimental values is 328° C, and the maximum value of the deviation between the calculated and the experimental values is 32%. On the one hand, the gas content in the coal ash cannot be used as an input. Hence, the inputted coal ash component deviates from the XRF result, resulting in the calculation result indicating a large deviation from the experimental result. On the other hand, the software itself has some drawbacks, and it is still in the process of continuous updating and upgrading, and this may have contributed to the deviation between the calculation result and the experimental result. These results indicate the difficult of accurately predicting the DT of the coal ash by using Factsage. In order to obtain more accurate calculation results, more reasonable research methods should thus be adopted.
3.2. Linear regression analysis According to previous studies [9,21,22], the acidic and basic metal oxides in coal ash have the effects of increasing and decreasing the melting temperature of coal ash, respectively The acidic oxide, the basic oxide, and the ratio of the basic metal oxide to the acidic metal oxide in the coal ash are respectively plotted with DT, and the results are shown 5
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 8. The effect of training function on the average absolute error value. (a) Traingd; (b) Traingda; (c) Traingdm; (d) Trainlm; (e) Trainrp; (f) Traincgb.
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Table 3 BP network structure parameters. Number
Structural parameters
Ranges
Application value
1 2 3 4 5 6 7 8 9 10 11
Input variable Number of hidden layers Learning rate Initial weight Number of hidden layer nodes Training function Implicit layer transfer function Output layer transfer function Momentum factor Maximum number of training steps Allowable error range
≥1 ≥0 0.01–0.7 −1 to 1 1–30 Traingd, Traingda, Traingdm, Trainlm, Trainrp, Traincgb Logsig, Tansig purelin 0.9 10,000 1 * 10−6
8 1 0.05 −1 to 1 27 traincgb logsig purelin 0.9 10,000 1 * 10−6
stability of BP network training results. When the MSE reaches the minimum value, the BP network's setting parameters becomes the optimal network structure. Fig. 7 shows the relationship between the number of transfer functions and neurons in the hidden layer. As can be seen, regardless of whether the transfer function of the hidden layer is “tansig” or “logsig”, the MSE value gradually converges close to zero as the number of neurons increases. When the hidden layer transfer function is “tansig”, the measured MSE value of the measurement is usually smaller. Fig. 7 also shows that when the transfer function of the hidden layer is “tansig” the number of neurons is 27, the MSE thus reaches a minimum. Therefore, the hidden layer transfer function used in this experiment is “tansig” and the number of neurons in the hidden layer is 27. The commonly used BP network training functions include: “trainlm”, “reaingd”, “traingda”, “traingdm”, “traincgb” and “trainrp”. The results of the Mean Squared Error values generated using different training functions are shown in Fig. 8. As can be seen from the figure, when the three training functions of “traingd”, “traingda”, and “traingdm” are used, there is no convergence after 10,000 times of training. When the “trainlm” function is selected for training, the training result reaches 1 × 10−6 precision, but this does not mean that it has reached convergence. It can be seen from the figure, as the number of training steps increases, the MSE suddenly drops; this phenomenon is called overtraining. Convergence is achieved when training is performed using the function “trainrp” and “traincgb”. Clearly, when training with the function “traincgb”, the convergence rate is better than that obtained when training with the function “trainrp”. The best training function among all those in “traincgb”, which is used in this study. In order to obtain good prediction accuracy, the other parameters of the BP network structure must be appropriately adjusted. The range of values of some parameters used in the BP network structure and the values in this experiment are listed in Table 3. The learning rate usually set to range between 0.01 and 0.7. If the learning rate is too high, the results become unstable, whereas if the learning rate is too low, the network convergence becomes slow. After the experimental calculation, the learning rate is set to 0.05 in this study. In order to facilitate the calculation, the input data must be normalized to within the range between 0 and 1. In this study, the momentum factor is taken as 0.9, the maximum number of training steps is 10,000, and the allowable error is 1 × 10−6. Samples No. 1 to No. 22 were used as learning samples, and the modeling method was used to predict the deformation temperature of samples No. 23 to No. 28. The prediction results and errors are listed in Table 4. As shown in the table, the difference between the calculated and experimental values of the six samples is small. The maximum difference is 75 °C, and the maximum relative error is 6.67%, indicating that the BP network has higher prediction accuracy for DT of coal ash. The maximum error of the BP network is 6.67%, which is much better than the 15% rate of the linear regression results and 32% of the Factsage prediction results. This superior value which also shows that
Table 4 Comparison of predicted and calculated values. DT
23
24
25
26
27
28
Actual value (°C) Calculated (°C) Difference (°C) Error (%)
1122 1096 26 2.32
1139 1074 65 5.71
1146 1179 33 2.88
1125 1050 75 6.67
1138 1115 23 2.02
1129 1058 71 6.29
3.4. BP network prediction model In recent years, the BP neural network has been widely used due to its high prediction accuracy, simple structure, and good self-learning, self-organization, and self-adaptive capabilities. Here, the parameters of the network structure are automatically adjusted through the back propagation of the error. For a given input, the most desirable output is produced. In the case of uncertain internal mechanisms and linkages, the BP neural network is considered a highly accurate model method. The relationship between the chemical composition of coal ash and its deformation temperature has remained uncertain. Therefore, the BP neural network model is used to solve this problem. The flow chart of the BP network modeling and parameter optimization is shown in Fig. 6. As can be seen from the figure, the process is performed from top to bottom, and there are two feedbacks at the output. First, after analyzing the problem, the input and output are determined, after which the sample is normalized, in order to facilitate accurate calculation and reduce the error. Next is the determination of the network structure, the initialization of the weights and the establishment of the training network. Before outputting the result, whether the calculation result converges quickly and reaches the prediction accuracy should be determined. Moreover, it is also important to assess whether the error of the output result satisfies the set range and to output the result only if both conditions are simultaneously; otherwise, the network needs to be trained again. As shown in Fig. 6, a flow chart of the BP neural network is described in detail. The problem that this research aims to resolve has to do with the deformation temperature of coal ash, and its input components comprising the eight chemical components present in coal ash. The samples are the 28 kinds of Shaanxi coal shown in Table 1. After determining the problem of the study and selecting the samples, the most important step is the determination of the network structure, which requires the determination of the training function, transfer function, learning rate, training steps, and allowable error range to be used in the calculation process. The functions of these parameters have been introduced in previous studies [23–25]. The number of neurons in the hidden layer is between 1 and 30, and the transfer function of the hidden layer typically uses “tansig” or “logsig”. The BP neural network is trained by changing the number of neurons in the hidden layer under different transfer function conditions. Mean Squared Error (MSE) is often used to evaluate the degree of dispersion of a set of data. In this study, MSE was used to assess the 7
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the BP algorithm predicts the ash melting point result with high accuracy and reliability.
[5]
4. Conclusion [6]
In this study, three methods were used to predict the DT temperature of coal ash based on the relationship between the composition and the melting characteristic temperature of coal ash. The DT value of the coal ash was determined by using a device that measured the coal ash melting characteristic temperature. When the DT temperature was predicted by linear regression and Factsage calculation, the maximum deviations were 15% and 32%, respectively, which produced large deviations. Based on the knowledge that the BP network does not need to establish the relationship between the input and output, the results can be accurately predicted. Therefore, a three-layer BP neural network model with eight input functions was developed to predict the deformation temperature of coal ash. Through the continuous selflearning of the BP network, the maximum relative error calculated from the model is 6.67%, which is much lower than the results obtained by linear regression and Factsage calculation. This finding thus proves the accuracy of the prediction results obtained using the proposed method. Therefore, the BP network structure can be considered as a very effective method for predicting coal ash DT and may be used effectively in future industrial applications.
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[8]
[9] [10] [11] [12]
[13] [14] [15] [16]
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Acknowledgement
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This work was supported by the Natural Science Foundation for Young Scientists of China (No. 51804026), and the Young Elite Scientists Sponsorship Program By China Association for Science and Technology (2017QNRC001).
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Appendix A. Supplementary data [21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.fuel.2019.116324.
[22] [23]
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