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Predicting air pollutant emissions from a medical incinerator using grey model and neural network
Applied Mathematical Modelling xxx (2014) xxx–xxx
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Predicting air pollutant emissions from a medical incinerator using grey model and neural network Tzu-Yi Pai a,⇑, Huang-Mu Lo b, Terng-Jou Wan c, Li Chen d, Pei-Shan Hung b, Hsuan-Hao Lo b, Wei-Jia Lai b, Hsin-Yi Lee c a Master Program of Environmental Education and Management, Department of Science Application and Dissemination, National Taichung University of Education, Taichung 40306, Taiwan, ROC b Department of Environmental Engineering and Management, Chaoyang University of Technology, Wufeng, Taichung 41349, Taiwan, ROC c Department of Environmental and Safety Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan, ROC d General Education Center, Shuzen College of Medicine and Management, Luju, Kaohsiung City 82144, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 17 December 2010 Received in revised form 29 March 2014 Accepted 16 September 2014 Available online xxxx Keywords: Grey model Artificial neural network Medical incinerator Air pollutant emission Control parameters
a b s t r a c t This paper represents the first study to use the grey model (GM) for predicting CO2, SO2 and O2 in the emissions from a medical incinerator. The artificial neural network (ANN) was also employed for comparison. Four control parameters were served as the input variables. The results indicated that two control parameters of temperature highly influenced air pollutant emissions. The minimum mean absolute percentage errors of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2 could be achieved using GMs, meanwhile the minimum root mean squared errors for three air pollutant were 0.1660, 2.4521 and 0.2112. The control parameters could be applied to the prediction of air pollutant emissions. It also revealed that GM could predict the air pollutant emissions even though emission data were not sufficient. Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction Treatment and disposal of waste become more important in Taiwan because the amount of waste generated from households, business and industries is steadily increasing every year with the expansion of population. The more acceptable waste disposal process in the past decades was landfill, but this process encountered serious challenge because the available cites for landfill became less and less. To overcome the difficulties, the Environmental Protection Administration (EPA) of Taiwan has adopted a strategy in which incineration is adopted as the primary method of treatment and landfill as a supplement. Among the waste, medical waste is defined as hazardous waste and strict treatment and disposal is required. If incineration is adopted for treatment of medical waste, the air pollutant emissions must meet the Waste Incinerator Air Pollutant Emissions Standards (WIAPES). In order to save cost, the investigation of air pollutant emissions from incinerator is only carried out to meet WIAPES, so their investigation data are few and incomplete compared with general study cases. Under this situation, the air pollutant emissions cannot be predicted appropriately using some numerical models, especially mechanism models. Some soft computation techniques, such as artificial neural network (ANN), in which the mechanism reactions can be ignored are available presently and applied in prediction of air pollutant emissions. Although ANN can predict the air pollutant emissions from incinerators successfully, many data are required for further calculation [1–5].
⇑ Corresponding author. Tel.: +886 4 22183541; fax: +886 4 22183540. E-mail address: [email protected] (T.-Y. Pai). http://dx.doi.org/10.1016/j.apm.2014.09.017 0307-904X/Ó 2014 Elsevier Inc. All rights reserved.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Due to the fact that only few parameters are selected for regulation in WIAPES, it is necessary to adopt a suitable method to present these limited data appropriately. In order to gain consistent results from the investigation data and predict the air pollutant emissions, the grey system theory (GST) is a suitable method. The GST proposed by Deng [6,7] can resolve the problem of incomplete data and has been applied in our previous works [8–16]. GST focuses on the relational analysis, model establishment, and prediction of the indefinite and incomplete information. It requires only a small amount of data and the better prediction results can be obtained. There are many analysis methods in GST including grey model (GM). GM can be used to establish the relationship between many sequences of data and its coefficients can be used to evaluate which sequence of data influences system extraordinarily. GM was adopted for forecasting the effluent quality from different wastewater treatment plant and good results were obtained in our previous study [9]. However, the incinerator temperature not only affects the air pollutant species but also affects the concentrations due to the expansion or shrinkage of air volume. The air pollutant emissions are more complicated. Therefore the better operation strategy of medical incinerator could be found out if the relation between the control parameters and air pollutant emissions can be established. The objectives of this study are listed as follows. (1) Employ GM to determine the control parameters of a medical incinerator which highly influenced air pollutant emissions. (2) Utilize GM to establish the emitted CO2, SO2 and O2 characteristics, subsequently to forecast the air pollutant emissions. (3) Furthermore, a comparison between the proposed GM model and traditional ANN was also made to evaluate the performance. 2. Materials and methods 2.1. Treatment process The medical incinerator located in middle of Taiwan was selected for study. The type of this medical incinerator was fixed bed and batch feeding was adopted. Its maximum designed handling capacity (MDHC, maximum weight of waste fed into the incinerator per batch) and maximum designed feeding rate (MDFR, maximum designed handling capacity divided by batch time) was 9 tons per day and 375 kg hr1, respectively. The MDHC and MDFR was fixed value and determined in accordance with incinerator function and mass balance. Although MDHC and MDFR was fixed values, the handling capacity (HC, weight of waste fed into the incinerator per batch) and feeding rate (FR, handling capacity divided by batch time) varied with daily hauling amount of medical waste and operation time. Both HC and FR reflected the operation and performance of the medical incinerator. Therefore, the control parameters including HC, FR, temperature of first stage (Temp1) and temperature of second stage (Temp2) were used as the input variables. The output variables included effluent CO2, SO2 and O2. These compounds were continuously monitored using a gas analyzer (SIEMENS, ULTRAMAT 23). The control parameters and air pollutant emission data in one day were recorded and investigated. They were sampled and investigated every 5 min and their total number was 78. Among the total number of data, the number for training and testing (predicting) was 68 and 10, respectively. 2.2. Grey modeling process When system information is not sufficient, GM can be created to describe the behavior of the few outputs using fewer (at least 4) system information. Through accumulated generating operation (AGO), the disorderly data may be converted into exponentially orderly form such that the system behavior can be characterized using a first-order differential equation. Solving the differential equation may yield a time relative solution for prediction. By means of inverse accumulated generating operation (IAGO), the prediction can be transformed back to the sequence of original series. A grey modeling process is described as follows. Assume that the original series of data with n samples is expressed as: X{0} = (x(0)(1), x(0)(2), . . . , x(0)(n)), where the superscription (0) of X(0) represents the original series. Let X(1) be the first-order AGO of X(0), whose elements are generated from P X(0): X(1) = (x(1)(1), x(1)(2), . . . , x(1)(n)), where xð1Þ ðkÞ ¼ ki¼1 xð0Þ ðiÞ; for k ¼ 1; 2; . . . ; n. Further operation of AGO can be conP ducted to derive the r-order AGO series, X(r): X{r} = (x(r)(1), x(r)(2), . . . , x(r)(n)), where xðrÞ ðkÞ ¼ ki¼1 xðr1Þ ðiÞ; for k ¼ 1; 2; . . . ; n. The IAGO is the inverse operation of AGO. It converts the AGO-operational series back to the one lower order form. The operation of IAGO for the first-order series is described as follows: x(0)(1) = x(1)(1) and x(0)(k) = x(1)(k) x(1)(k 1) for k = 2, 3, . . . , n. Extending this representation to the IAGO of r-order series, the following form can be obtained, x(r1)(k) = xr(k) xr(k 1) for k = 2, 3, . . . , n. The tendency of AGO can be approximated by an exponential function. Its dynamic behavior is analogous to a form of differential equation. Therefore grey model GM (h, N) adopts an n-order differential equation to fit the AGO-operational series. The parameters h and N in GM (h, N) denotes the order and the number of variables in the relative differential equation, respectively. The GM (h, N) can be generally expressed as ðiÞ ð1Þ h N X X d x1 ð1Þ ai ¼ bj xj ðkÞ; ðiÞ dt i¼0 j¼2
ð1Þ
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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where the parameter a is the developing coefficient and b is the grey input. In this study, different types of GM were adopted, i.e. GM (1, N), GM (1, 1) and rolling GM (1, 1) (RGM (1, 1)). GM (1, N). In accordance with the definition of GM (h, N), GM (1, N) is the one that the order in grey differential equation is equal to 1 and expressed as follows: ð0Þ
ð1Þ
x1 ðkÞ þ az1 ðkÞ ¼
N X ð1Þ ð1Þ ð1Þ ð1Þ bj xj ðkÞ ¼ b2 x2 ðkÞ þ b3 x3 ðkÞ þ þ bN xN ðkÞ;
ð2Þ
j¼2 ð1Þ
ð1Þ
ð1Þ
where z1 ðkÞ ¼ 0:5x1 ðk 1Þ þ 0:5x1 ðkÞ k = 2, 3, 4, . . . , n. Expanding Eq. (2), the following equation can be obtained: ð0Þ
ð1Þ
ð1Þ
ð1Þ
x1 ð2Þ þ az1 ð2Þ ¼ b2 x2 ð2Þ þ þ bN xN ð2Þ ð0Þ x1 ð3Þ
þ
ð1Þ az1 ð3Þ
ð0Þ
¼ .. .
ð1Þ
ð1Þ b2 x2 ð3Þ
ð1Þ
þ þ bN xN ð3Þ
ð1Þ
ð3Þ
ð1Þ
x1 ðnÞ þ az1 ðnÞ ¼ b2 x2 ðnÞ þ þ bN xN ðnÞ Transforming Eq. (3) into the matrix form, the following equation can be derived:
32 3 a 7 6 7 6 ð0Þ 6 x ð3Þ 7 6 zð1Þ ð3Þ xð1Þ ð3Þ xð1Þ ð3Þ 76 b2 7 7 N 2 7 6 1 76 6 1 6 . 7 7 6 . 7¼6 6 .. .. 74 .. 7 6 . 7 6 5 5 4 . 5 4 . . ð0Þ ð1Þ ð1Þ ð1Þ b N x1 ðnÞ z1 ðnÞ x2 ðnÞ xN ðnÞ 2
ð0Þ
x1 ð2Þ
3
2
ð1Þ
ð1Þ
ð1Þ
z1 ð2Þ x2 ð2Þ xN ð2Þ
ð4Þ
Then the coefficients can be calculated by solving matrix, h = (BTB)1BTY,
2
a
3
2
ð0Þ
x1 ð2Þ
3
2
ð1Þ
ð1Þ
ð1Þ
z1 ð2Þ x2 ð2Þ xN ð2Þ
3
7 7 6 ð0Þ 6 ð1Þ 6b 7 6 x ð3Þ 7 6 z ð3Þ xð1Þ ð3Þ xð1Þ ð3Þ 7 6 27 N 2 7 7 6 1 6 1 7 where h ¼ 6 Y ¼ B ¼ 7: 6 . 7 6 6 .. 7 .. .. 7 6 . 7 6 4 . 5 5 4 . 5 4 . . ð0Þ ð1Þ ð1Þ ð1Þ bN x1 ðnÞ z1 ðnÞ x2 ðnÞ xN ðnÞ The h values represent the weight of comparative series to the referential series. In addition, the GM (1, N) model can be used for prediction and described as:
^x1ð0Þ ðkÞ ¼
N X ð1Þ ð1Þ bj xj ðkÞ az1 ðkÞ:
ð5Þ
j¼2
When adopting GM (1, N), 2 parameters with higher weights (GM1N2-1), 3 parameters with higher weights (GM1N3-1) and all 4 parameters (GM1N4-1) were taken as the comparative series, respectively. Thus N was equal to 3, 4, and 5, respectively. The GM (1, N) established in this study represented the relationship between air pollutant emissions and control parameters with different weights. GM (0, N). According to the definition of GM (h, N), GM (0, N) is that the order in grey differential equation is equal to 0 and defined as follows: ð1Þ
az1 ðkÞ ¼
N X ð1Þ ð1Þ ð1Þ ð1Þ bj xj ðkÞ ¼ b2 x2 ðkÞ þ b3 x3 ðkÞ þ þ bN xN ðkÞ:
ð6Þ
j¼2
Expanding Eq. (6), Eq. (7) can be obtained as follows: ð1Þ
ð1Þ
ð1Þ
ð1Þ
ð1Þ
ð1Þ
az1 ð2Þ ¼ b2 x2 ð2Þ þ þ bN xN ð2Þ; az1 ð3Þ ¼ b2 x2 ð3Þ þ þ bN xN ð3Þ; .. . ð1Þ
ð1Þ
ð7Þ
ð1Þ
az1 ðnÞ ¼ b2 x2 ðnÞ þ þ bN xN ðnÞ; Converting Eq. (7) into the form of matrix, the following equation is derived:
2
ð1Þ
z1 ð2Þ
3
2
ð1Þ
ð1Þ
x2 ð2Þ xN ð2Þ
32 b2 3 a
7 6 76 7 6 ð1Þ 6 z ð3Þ 7 6 xð1Þ ð3Þ xð1Þ ð3Þ 76 b3 7 N 7 6 2 76 a 7 6 1 ¼ 6 . 7 6 . 6 7: . . 7 76 . 7 6 . 7 6 . . . 4 . 5 4 . . . 54 .. 5 ð1Þ
z1 ðnÞ
ð1Þ
ð1Þ
x2 ðnÞ xN ðnÞ
ð8Þ
bN a
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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^ T BÞ ^ 1 B ^ T Y, ^ Then the coefficients can be determined by solving matrix, ^ h ¼ ðB
2 b2 3 a b3 a
2
ð1Þ
z1 ð2Þ
3
2
ð1Þ
ð1Þ
x2 ð2Þ xN ð2Þ
3
7 7 6 7 6 ð1Þ 6 ð1Þ ð1Þ 7 6 7 6 z ð3Þ 7 6 7 ^ 6 x2 ð3Þ xN ð3Þ 7 6 7 6 1 ¼6 . where ^h ¼ 6 . 7 Y^ ¼ 6 . 7 B 7: . . 6 . 7 6 . 7 6 . .. .. 7 5 4 . 5 4 . 5 4 . bN a
ð1Þ
z1 ðnÞ
ð1Þ
ð1Þ
x2 ðnÞ xN ðnÞ
The ^ h values are the weight of comparative series to the referential series. GM (1, 1). If the number of comparative series was reduced further, the model was simplified to GM (1, 1). All time series values of one specific air pollutant were used to establish GM (1, 1). Then the established GM (1, 1) was used for prediction. RGM (1, 1). In GM (1, 1), all time series values of one specific air pollutant were used to establish GM (1, 1). While in RGM (1, 1), the time series data of specific air pollutant used to establish model were traditionally the 4 data before the point which was considered to be predicted. That is, the model had to be established every time step and only 4 data were used for model establishment. The control parameter of medical incinerator was ignored in both GM (1, 1) and RGM (1, 1). 2.3. ANN The ANN approach mimics the important operation features of human nervous system and attempts to solve problems by using information gained from past experience on new problems. In order to mimic the human brain, many simple computational elements called artificial neurons are connected by variable weights in the ANN. By mimicking the hierarchical network structure of interconnected neurons, an ANN can deal with complex computation. Among many different types of structures, the multi-layer perceptron structure is commonly adopted. A neural network model typically consists of three independent layers: input, hidden, and output layers. Each layer is comprised of several operating neurons. Input neurons receive the input variable values and store the scaled input values, subsequently the output neurons assign the calculated results into output layer. The hidden layer performs an interface for fully interconnecting input and output layers. The pattern of hidden layer can be either multiple layers or a single layer. Each neuron is connected to every neuron in adjacent layers by a connection weight, which estimates the strength of the relationship between two connected neurons. Each neuron sums all of the input values and the sum is transformed into an output value based on the activation, or transfer, function. For prediction problems, a supervised learning algorithm is often used for training the network to relate input data to output data. The back-propagation algorithm is widely used for training multi-layer neural networks. The algorithm generally uses a gradient search technique (the steepest gradient descent method) to minimize the error between the desired and the actual network outputs [17–20]. In this study, the ANN consisted of three independent layers: input, hidden, and output layers. To compare with GM, 2 parameters with higher weights (ANN2-1), 3 parameters with higher weights (ANN3-1) and all 4 parameters (ANN4-1) were taken as the input layer variables, respectively. Meanwhile each air pollutant emission, i.e. CO2, SO2 and O2, was the single output layer variable. The hidden layer was comprised of 10 operating neurons. The number and speed of training was 10,000 and 0.1, respectively. The calculation was carried out using MATLAB. 2.4. Error analysis In order to evaluate the prediction performance of GM and ANN, the mean absolute percentage error (MAPE) and root mean squared error (RMSE) were employed, given by
MAPE ¼
n 1X obsi prei 100%; n i¼1 obsi
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X 2 RMSE ¼ t ðobsi prei Þ ; n i¼1
ð9Þ
ð10Þ
where obsi and prei are the observed value and prediction value, respectively. 2.5. Weights of control parameters According to Eq. (8), the weights (^ h) between the air pollutant emissions (CO2, SO2 and O2) and 4 different control parameters (HC, FR, Temp1, and Temp2) were calculated as shown in Table 1. The weights of CO2 were in the order: Temp2 (0.7352) > Temp1 (0.1509) > FR (0.1378) > HC (0.0337). Those of SO2 were in the order: Temp1 (2.1014) > Temp2 (1.3978) > FR and HC (0.0197). Those of O2 were in the order: Temp1 (1.5064) > Temp2 (0.7631) > FR (0.3279) > HC (0.1026). Based on the results of GM (0, N), the selected input variables in three types of GM (1, N) (GM1N2-1, GM1N3-1 and GM1N4-1) and in three types of ANN (ANN2-1, ANN3-1 and ANN3-1) were shown in Table 2. Figs. 1 and 2 depict their structures. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx Table 1 The weights between the air pollutant emissions and different control parameters.
CO2 SO2 O2
HC
FR
Temp1
Temp2
0.0337 0.0197 0.1026
0.1378 0.0197 0.3279
0.1509 2.1014 1.5064
0.7352 1.3978 0.7631
Table 2 The selected input variables in GM and ANN. GM
Input variables
ANN
Input variables
CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp2, Temp1 Temp2, Temp1, FR Temp2, Temp1, FR, HC All CO2 for training Previous 4 CO2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp2, Temp1 Temp2, Temp1, FR Temp2, Temp1, FR, HC
SO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC All SO2 for training Previous 4 SO2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC
O2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC All O2 for training Previous 4 O2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC
3. Results and discussion 3.1. Variation of control parameters and emissions The number of data investigated in one day was totally 78, as shown in Fig. 3. Among the total number of data, the number for model establishing (or training) and predicting (testing) was 68 and 10, respectively.
Fig. 1. The structure diagram of GM.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Hidden layer
Input layer
Output layer
1 Highest weight
2 3
. . . . . . . . . .
2nd higher weight
ANN2-1
3rd higher weight
ANN3-1
ANN4-1
4th higher weight
CO2 SO2 Single flue gas O2
10 Fig. 2. The structure diagram of ANN.
3.2. Simulation of CO2 Fig. 4(a)–(h) depicts the simulation results using GM1N2-1, GM1N3-1, GM1N4-1, GM (1, 1), RGM (1, 1), ANN2-1, ANN3-1, and ANN4-1, respectively. All MAPE and RMSE values are shown in Tables 3 and 4. The 1st to 68th values were used for establishing model, 69th to 78th values were used for evaluating prediction performance. As shown in Table 3, when establishing model, MAPEs between the prediction and observation of CO2 were 52.52%, 53.81%, 49.69% and 5.88% using GM1N21, GM1N3-1, GM1N4-1, and GM (1, 1), respectively. The RMSEs fell in the range of 0.2890 to 2.0897. The MAPEs were 3.19%, 2.86% and 2.58% using ANN2-1, ANN3-1, and ANN4-1, respectively. The RMSEs were between 0.1291 and 0.1561 using different ANN. For CO2 prediction, the MAPEs varied within the range of 3.70% to 38.43% when adopting GMs, but they were between 4.93% and 5.44% when using three types of ANN. The RMSEs lay between 0.1660 and 1.3983 for GM, but they were between 0.2216 and 0.2368 for ANN. In GMs, the MAPE of 3.70% was found to be the lowest when using RGM (1, 1) to predict CO2. This value was lower than those of ANN2-1, ANN3-1, and ANN4-1 by 1.64%, 1.23% and 1.74%, respectively.
3.3. Simulation of SO2
HC (kg), Temp 1, Temp 2 (OC)
1000
50
800
40
600
30
400
20
200
10
0
0 0
50
100
150
200 250 Time (min)
300
350
400
FR (kg/hr), CO 2 (%), SO2 (ppm), O 2 (%)
Fig. 5(a)–(h) shows the simulation results of SO2. From Table 3, MAPEs of SO2 were 35.94%, 36.04%, 30.57% and 11.68% using GM1N2-1, GM1N3-1, GM1N4-1, and GM (1, 1), respectively for establishing model. The RMSEs were between
HC Temp1 Temp2 FR CO2 SO2 O2
Fig. 3. Variation of control parameters and emissions.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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oncentration (%)
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
20
Obs_CO2
15
GM1N2-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(a) 20
Obs_CO2
15
GM1N3-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(b) 20
Obs_CO2
15
GM1N4-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(c) 20
Obs_CO2
15
GM(1,1)
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(d) 20
Obs_CO2
15
RGM(1, 1)
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
(e) Fig. 4. Simulation results of CO2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
4.8188 and 14.3231. The MAPEs were 9.99%, 10.17%, and 8.71%, meanwhile the RMSEs were 4.2884, 4.3123 and 3.7710, respectively using ANN2-1, ANN3-1, and ANN4-1. For SO2 prediction, the MAPEs were between 6.11% and 41.25% when using five different types of GMs, but they were between 13.11% and 16.16% when using three types of ANN. The RMSEs were between 2.4521 and 16.8717 when five types of GMs were used, but they were between 5.3214 and 6.6138 when using ANN. In GMs, the MAPE of 6.11% was found to be the lowest when using RGM (1, 1) to predict SO2. This value was less than those of ANN2-1, ANN3-1, and ANN4-1 by 10.05%, 9.53% and 7.00%, respectively. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
Concentration (%)
8
20
Obs_CO2
15
ANN2-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(f) 20
Obs_CO2
15
ANN3-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(g) 20
Obs_CO2
15
ANN4-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
(h) Fig. 4 (continued)
Table 3 MAPEs between the simulation and observation values using different GM and ANN. CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1) ANN2-1 ANN3-1 ANN4-1
SO2
O2
Establishment of model (%)
Prediction of model (%)
Establishment of model (%)
Prediction of model (%)
Establishment of model (%)
Prediction of model (%)
52.52 53.81 49.69 5.88 3.70 3.19 2.86 2.58
38.30 38.43 23.94 4.64
35.94 36.04 30.57 11.68 6.11 9.99 10.17 8.71
38.65 41.25 21.28 14.38
34.43 34.88 32.25 2.11 1.08 1.82 1.51 1.40
54.06 54.19 42.08 1.08
5.34 4.93 5.44
16.16 15.64 13.11
3.16 1.63 1.64
Table 4 RMSEs between the simulation and observation values using different GM and ANN. CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1) ANN2-1 ANN3-1 ANN4-1
SO2
O2
Establishment of model
Prediction of model
Establishment of model
Prediction
Establishment of model
Prediction of model
2.0564 2.0897 1.9232 0.2890 0.1660 0.1561 0.1449 0.1291
1.3869 1.3983 0.8944 0.2156
14.3179 14.3231 12.0163 4.8188 2.4521 4.2884 4.3123 3.7710
16.1072 16.8717 10.1774 5.8572
5.9392 5.9728 5.5637 0.4089 0.2112 0.3599 0.3150 0.2915
9.0659 9.0788 7.0745 0.2433
0.2230 0.2216 0.2368
6.6138 6.4437 5.3214
0.5515 0.2960 0.3253
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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RGM(1, 1)
150
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Time (min)
(e) Fig. 5. Simulation results of SO2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
3.4. Simulation of O2 The simulation results of O2 are shown in Fig. 6. According to Table 3, when using GM1N2-1, GM1N3-1, GM1N4-1, and GM (1, 1) to establish models, the MAPEs between the simulation and observation values of O2 were between 2.11% and 34.88%. The RMSEs fell between 0.4089 and 5.9728. When using ANN2-1, ANN3-1, and ANN4-1, they were 1.82%, 1.51% and 1.40%, respectively. The RMSEs were 0.3599, 0.3150, and 0.2915, respectively. For O2 prediction, the MAPEs were between 1.08% and 54.19% when using five types of GMs, but they were between 1.63% and 3.16% when three types of ANN were used. The RMSEs were between 0.2112 and 9.0788 when using GMs for prediction, Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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ANN2-1
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(f) 100 80 60 40 20 0
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Time (min)
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(g) 100 80 60 40 20 0
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ANN4-1
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Time (min)
(h) Fig. 5 (continued)
but they fell in the range of 0.2960 and 0.5515 when using ANN. In GMs, the MAPE of 1.08% was the lowest when GM (1, 1) and RGM (1, 1) were adopted to forecast O2. This value was lower than those of ANN2-1, ANN3-1, and ANN4-1 by 2.08%, 0.55% and 0.56%, respectively. Five GMs were utilized to predict the air pollutant emissions from the medical incinerator in this study. The application could be classified into two patterns. GM1N2-1, GM1N3-1, and GM1N4-1 belonged to the first pattern of application, GM (1, 1) and RGM (1, 1) belonged to the second pattern. In the first pattern, the relationship between air pollutant emissions and control parameters was established, and the control parameters were regarded as the input variables to predict air pollutant emissions. In the second pattern, only air pollutant emissions were used to establish GMs. In the first pattern of application, the MAPE values of CO2 using GM1N4-1 (49.69%) were lower than those of GM1N2-1 (52.52%) and GM1N3-1 (53.81%) when establishing model, its value (23.94%) was also lower than those of GM1N2-1 (38.30%) and GM1N3-1 (38.43%) when predicting. The MAPE value of SO2 using GM1N4-1 (30.57%) was lower than those of GM1N2-1 (35.94%) and GM1N3-1 (36.04%) when establishing model, meanwhile its value (21.28%) was lower than those of GM1N2-1 (38.65%) and GM1N3-1 (41.25%) when predicting. The MAPE values of O2 using GM1N4-1 (32.25% for establishment and 42.08% for prediction) were lower than those of GM1N2-1 (34.43% for establishment and 54.06% for prediction) and GM1N3-1 (34.88% for establishment and 54.19% for prediction) when establishing and predicting model. For the second pattern, when forecasting CO2, the MAPE value using GM (1, 1) was higher than that of RGM (1, 1). When forecasting SO2, the value using GM (1, 1) was also higher than that of RGM (1, 1). The MAPE value using GM (1, 1) was the same as that of RGM (1, 1) when forecasting O2. It indicated that the predicting capability of RGM (1, 1) prevailed GM (1, 1). Three types of ANN were also employed in this study. When forecasting CO2, the MAPE value using ANN4-1 (4.93%) was the lowest. But its predicting value was still higher than those of GM (1, 1) and RGM (1, 1) by 0.29% and 1.23%, respectively. When forecasting SO2, the MAPE value using ANN4-1 (13.11% for prediction) was the lowest. But this value was still higher than that of RGM (1, 1) by 7.00%. When forecasting O2, the MAPE value using ANN3-1 (1.63% for prediction) was the lowest. This value was higher than those of GM (1, 1) and RGM (1, 1) by 0.55%. Comparable observations were similarly made by Ionescu and Candau [5]. Ionescu and Candau [5] compared different types of ANN by which the air pollutant emission from a re-heating furnace of the iron and steel industry was predicted. They found that the RMSEs of NO2 lay between 7.48 and 26.3 when training and they were between 10.39 and 26.93 when forecasting. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Obs_O2
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GM1N2-1
T rain
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(a) 40
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GM1N3-1
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GM(1,1)
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Time (min)
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(d) 40
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30
RGM(1, 1)
T rain
Predict
20 10 0 0
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Time (min)
(e) Fig. 6. Simulation results of O2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
In this study, when using GMs, the minimum MAPEs of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2, respectively could be achieved, meanwhile the minimum RMSEs were 0.1660, 2.4521 and 0.2112. Although a good performance could be achieved using ANN too, they required a large amount of data for establishing model. Contrarily, GM only required less data (at least 4 data) and the prediction performance was even better than those of ANN. Therefore, GM could be applied successfully in predicting the air pollutant emissions when the information was insufficient. It also indicated that the control parameters could be utilized on the prediction of air pollutant emissions.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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(h) Fig. 6 (continued)
4. Conclusions Five types of GM were employed to predict the CO2, SO2 and O2 from an incinerator. The ANN was also used for comparing. The simulation results can be drawn as follows. According to GM (0, N), two control parameters of temperature, i.e. Temp1 and Temp2, highly influenced air pollutant emissions. When using GMs, the minimum MAPEs of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2 could be achieved, respectively, meanwhile the minimum RMSEs were 0.1660, 2.4521 and 0.2112, respectively. A good performance could be achieved using ANN too, but they required abundant data for training. Contrarily, GM only required a small quantity of data (at least 4 data) and the prediction performance was even better than those of ANN. In the first pattern of application, the MAPE of CO2 for GM1N4-1 (49.69%) was lower when establishing model, its value (23.94%) was also lower when predicting. The MAPE values of SO2 using GM1N4-1 were lower either for establishing model (30.57%) or prediction (21.28%). The MAPE values of O2 using GM1N4-1 (32.25% for establishment and 42.08% for prediction) were lower when establishing model and predicting. In the second pattern, the MAPE value for CO2 and SO2 using GM (1, 1) was greater than those of RGM (1, 1). For O2 prediction, the MAPE value using GM (1, 1) was the same as that of RGM (1, 1). It indicated that the predicting capability of RGM (1, 1) prevailed GM (1, 1). The air pollutant emissions could be successfully predicted by application of control parameters. It also showed that GM could forecast the air pollutant emission variation when the emission data was insufficient. After successful prediction, it is suggested that the GM models can be employed to find out the best design or operation strategy for medical incinerator air emission control using the optimization methods in the future study.
Acknowledgments The authors are grateful to the National Science Council of Taiwan, ROC for financial support under the grant number NSC 101-3113-S-324-001. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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References [1] T. Slanvetpan, R.B. Barat, J.G. Stevens, Process control of a laboratory combustor using artificial neural networks, Comput. Chem. Eng. 27 (11) (2003) 1605–1616. [2] L.E. Olcese, B.M. Toselli, A method to estimate emission rates from industrial stacks based on neural networks, Chemosphere 57 (7) (2004) 691–696. [3] W.Z. Lu, W.J. Wang, Potential assessment of the ‘‘support vector machine’’ method in forecasting ambient air pollutant trends, Chemosphere 59 (5) (2005) 693–701. [4] D. Wang, W.Z. Lu, Interval estimation of urban ozone level and selection of influential factors by employing automatic relevance determination model, Chemosphere 62 (10) (2006) 1600–1611. [5] A. Ionescu, Y. Candau, Air pollutant emissions prediction by process modelling – application in the iron and steel industry in the case of a re-heating furnace, Environ. Model. Software 22 (9) (2007) 1362–1371. [6] J. Deng, The Foundation of Grey Theory, Huazhang University of Science and Technology Press, Wuhan, China, 2002. [7] J. Deng, The Primary Methods of Grey System Theory, Huazhang University of Science and Technology Press, Wuhan, China, 2005. [8] T.Y. Pai, K. Hanaki, H.H. Ho, C.M. Hsieh, Using grey system theory to evaluate transportation on air quality trends in Japan, Transp. Res. D: Transp. Environ. 12 (3) (2007) 158–166. [9] T.Y. Pai, Y.P. Tsai, H.M. Lo, C.H. Tsai, C.Y. Lin, Grey and neural network prediction of suspended solids and chemical oxygen demand in hospital wastewater treatment plant effluent, Comput. Chem. Eng. 31 (10) (2007) 1272–1281. [10] T.Y. Pai, Grey and neural network prediction of effluent from the wastewater treatment plant of industrial park using influent quality, Environ. Eng. Sci. 25 (5) (2008) 757–766. [11] T.Y. Pai, R.J. Chiou, H.H. Wen, Evaluating impact level of different factors in environmental impact assessment for incinerator plants using GM (1, N) model, Waste Manage. 28 (10) (2008) 1915–1922. [12] T.Y. Pai, S.H. Chuang, H.H. Ho, L.F. Yu, H.C. Su, H.C. Hu, Predicting performance of grey and neural network in industrial effluent using online monitoring parameters, Process Biochem. 43 (2) (2008) 199–205. [13] T.Y. Pai, S.H. Chuang, T.J. Wan, H.M. Lo, Y.P. Tsai, H.C. Su, L.F. Yu, H.C. Hu, P.J. Sung, Comparisons of grey and neural network prediction of industrial park wastewater effluent using influent quality and online monitoring parameters, Environ. Monit. Assess. 146 (1–3) (2008) 51–66. [14] T.Y. Pai, K.L. Lin, J.L. Shie, T.C. Chang, B.Y. Chen, Predicting the co-melting temperatures of municipal solid waste incinerator fly ash and sewage sludge ash using grey model and neural network, Waste Manage. Res. 29 (3) (2011) 284–293. [15] T.Y. Pai, C.L. Ho, S.W. Chen, H.M. Lo, P.J. Sung, S.W. Lin, W.J. Lai, S.C. Tseng, S.P. Ciou, J.L. Kuo, J.T. Kao, Using seven types of GM (1, 1) model to forecast hourly particulate matter concentration in Banciao City of Taiwan, Water Air Soil Poll. 217 (1–4) (2011) 25–33. [16] T.Y. Pai, K. Hanaki, R.J. Chiou, Forecasting hourly roadside particulate matter in Taipei County of Taiwan based on first-order and one-variable grey model, CLEAN-Soil Air Water 41 (8) (2013) 737–742. [17] T.Y. Pai, T.J. Wan, S.T. Hsu, T.C. Chang, Y.P. Tsai, C.Y. Lin, H.C. Su, L.F. Yu, Using fuzzy inference system to improve neural network for predicting hospital wastewater treatment plant effluent, Comput. Chem. Eng. 33 (7) (2009) 1272–1278. [18] T.Y. Pai, S.C. Wang, C.F. Chiang, H.C. Su, L.F. Yu, P.J. Sung, C.Y. Lin, H.C. Hu, Improving neural network prediction of effluent from biological wastewater treatment plant of industrial park using fuzzy learning approach, Bioprocess Biosyst. Eng. 32 (6) (2009) 781–790. [19] T.Y. Pai, P.Y. Yang, S.C. Wang, H.M. Lo, C.F. Chiang, J.L. Kuo, H.H. Chu, H.C. Su, L.F. Yu, H.C. Hu, Y.H. Chang, Predicting effluent from the wastewater treatment plant of industrial park based on fuzzy network and influent quality, Appl. Math. Model. 35 (8) (2011) 3674–3684. [20] T.Y. Pai, K. Hanaki, H.C. Su, L.F. Yu, A 24-h forecast of oxidant concentration in Tokyo using neural network and fuzzy learning approach, CLEAN-Soil Air Water 41 (8) (2013) 729–736.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm
Predicting air pollutant emissions from a medical incinerator using grey model and neural network Tzu-Yi Pai a,⇑, Huang-Mu Lo b, Terng-Jou Wan c, Li Chen d, Pei-Shan Hung b, Hsuan-Hao Lo b, Wei-Jia Lai b, Hsin-Yi Lee c a Master Program of Environmental Education and Management, Department of Science Application and Dissemination, National Taichung University of Education, Taichung 40306, Taiwan, ROC b Department of Environmental Engineering and Management, Chaoyang University of Technology, Wufeng, Taichung 41349, Taiwan, ROC c Department of Environmental and Safety Engineering, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan, ROC d General Education Center, Shuzen College of Medicine and Management, Luju, Kaohsiung City 82144, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 17 December 2010 Received in revised form 29 March 2014 Accepted 16 September 2014 Available online xxxx Keywords: Grey model Artificial neural network Medical incinerator Air pollutant emission Control parameters
a b s t r a c t This paper represents the first study to use the grey model (GM) for predicting CO2, SO2 and O2 in the emissions from a medical incinerator. The artificial neural network (ANN) was also employed for comparison. Four control parameters were served as the input variables. The results indicated that two control parameters of temperature highly influenced air pollutant emissions. The minimum mean absolute percentage errors of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2 could be achieved using GMs, meanwhile the minimum root mean squared errors for three air pollutant were 0.1660, 2.4521 and 0.2112. The control parameters could be applied to the prediction of air pollutant emissions. It also revealed that GM could predict the air pollutant emissions even though emission data were not sufficient. Ó 2014 Elsevier Inc. All rights reserved.
1. Introduction Treatment and disposal of waste become more important in Taiwan because the amount of waste generated from households, business and industries is steadily increasing every year with the expansion of population. The more acceptable waste disposal process in the past decades was landfill, but this process encountered serious challenge because the available cites for landfill became less and less. To overcome the difficulties, the Environmental Protection Administration (EPA) of Taiwan has adopted a strategy in which incineration is adopted as the primary method of treatment and landfill as a supplement. Among the waste, medical waste is defined as hazardous waste and strict treatment and disposal is required. If incineration is adopted for treatment of medical waste, the air pollutant emissions must meet the Waste Incinerator Air Pollutant Emissions Standards (WIAPES). In order to save cost, the investigation of air pollutant emissions from incinerator is only carried out to meet WIAPES, so their investigation data are few and incomplete compared with general study cases. Under this situation, the air pollutant emissions cannot be predicted appropriately using some numerical models, especially mechanism models. Some soft computation techniques, such as artificial neural network (ANN), in which the mechanism reactions can be ignored are available presently and applied in prediction of air pollutant emissions. Although ANN can predict the air pollutant emissions from incinerators successfully, many data are required for further calculation [1–5].
⇑ Corresponding author. Tel.: +886 4 22183541; fax: +886 4 22183540. E-mail address: [email protected] (T.-Y. Pai). http://dx.doi.org/10.1016/j.apm.2014.09.017 0307-904X/Ó 2014 Elsevier Inc. All rights reserved.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Due to the fact that only few parameters are selected for regulation in WIAPES, it is necessary to adopt a suitable method to present these limited data appropriately. In order to gain consistent results from the investigation data and predict the air pollutant emissions, the grey system theory (GST) is a suitable method. The GST proposed by Deng [6,7] can resolve the problem of incomplete data and has been applied in our previous works [8–16]. GST focuses on the relational analysis, model establishment, and prediction of the indefinite and incomplete information. It requires only a small amount of data and the better prediction results can be obtained. There are many analysis methods in GST including grey model (GM). GM can be used to establish the relationship between many sequences of data and its coefficients can be used to evaluate which sequence of data influences system extraordinarily. GM was adopted for forecasting the effluent quality from different wastewater treatment plant and good results were obtained in our previous study [9]. However, the incinerator temperature not only affects the air pollutant species but also affects the concentrations due to the expansion or shrinkage of air volume. The air pollutant emissions are more complicated. Therefore the better operation strategy of medical incinerator could be found out if the relation between the control parameters and air pollutant emissions can be established. The objectives of this study are listed as follows. (1) Employ GM to determine the control parameters of a medical incinerator which highly influenced air pollutant emissions. (2) Utilize GM to establish the emitted CO2, SO2 and O2 characteristics, subsequently to forecast the air pollutant emissions. (3) Furthermore, a comparison between the proposed GM model and traditional ANN was also made to evaluate the performance. 2. Materials and methods 2.1. Treatment process The medical incinerator located in middle of Taiwan was selected for study. The type of this medical incinerator was fixed bed and batch feeding was adopted. Its maximum designed handling capacity (MDHC, maximum weight of waste fed into the incinerator per batch) and maximum designed feeding rate (MDFR, maximum designed handling capacity divided by batch time) was 9 tons per day and 375 kg hr1, respectively. The MDHC and MDFR was fixed value and determined in accordance with incinerator function and mass balance. Although MDHC and MDFR was fixed values, the handling capacity (HC, weight of waste fed into the incinerator per batch) and feeding rate (FR, handling capacity divided by batch time) varied with daily hauling amount of medical waste and operation time. Both HC and FR reflected the operation and performance of the medical incinerator. Therefore, the control parameters including HC, FR, temperature of first stage (Temp1) and temperature of second stage (Temp2) were used as the input variables. The output variables included effluent CO2, SO2 and O2. These compounds were continuously monitored using a gas analyzer (SIEMENS, ULTRAMAT 23). The control parameters and air pollutant emission data in one day were recorded and investigated. They were sampled and investigated every 5 min and their total number was 78. Among the total number of data, the number for training and testing (predicting) was 68 and 10, respectively. 2.2. Grey modeling process When system information is not sufficient, GM can be created to describe the behavior of the few outputs using fewer (at least 4) system information. Through accumulated generating operation (AGO), the disorderly data may be converted into exponentially orderly form such that the system behavior can be characterized using a first-order differential equation. Solving the differential equation may yield a time relative solution for prediction. By means of inverse accumulated generating operation (IAGO), the prediction can be transformed back to the sequence of original series. A grey modeling process is described as follows. Assume that the original series of data with n samples is expressed as: X{0} = (x(0)(1), x(0)(2), . . . , x(0)(n)), where the superscription (0) of X(0) represents the original series. Let X(1) be the first-order AGO of X(0), whose elements are generated from P X(0): X(1) = (x(1)(1), x(1)(2), . . . , x(1)(n)), where xð1Þ ðkÞ ¼ ki¼1 xð0Þ ðiÞ; for k ¼ 1; 2; . . . ; n. Further operation of AGO can be conP ducted to derive the r-order AGO series, X(r): X{r} = (x(r)(1), x(r)(2), . . . , x(r)(n)), where xðrÞ ðkÞ ¼ ki¼1 xðr1Þ ðiÞ; for k ¼ 1; 2; . . . ; n. The IAGO is the inverse operation of AGO. It converts the AGO-operational series back to the one lower order form. The operation of IAGO for the first-order series is described as follows: x(0)(1) = x(1)(1) and x(0)(k) = x(1)(k) x(1)(k 1) for k = 2, 3, . . . , n. Extending this representation to the IAGO of r-order series, the following form can be obtained, x(r1)(k) = xr(k) xr(k 1) for k = 2, 3, . . . , n. The tendency of AGO can be approximated by an exponential function. Its dynamic behavior is analogous to a form of differential equation. Therefore grey model GM (h, N) adopts an n-order differential equation to fit the AGO-operational series. The parameters h and N in GM (h, N) denotes the order and the number of variables in the relative differential equation, respectively. The GM (h, N) can be generally expressed as ðiÞ ð1Þ h N X X d x1 ð1Þ ai ¼ bj xj ðkÞ; ðiÞ dt i¼0 j¼2
ð1Þ
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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where the parameter a is the developing coefficient and b is the grey input. In this study, different types of GM were adopted, i.e. GM (1, N), GM (1, 1) and rolling GM (1, 1) (RGM (1, 1)). GM (1, N). In accordance with the definition of GM (h, N), GM (1, N) is the one that the order in grey differential equation is equal to 1 and expressed as follows: ð0Þ
ð1Þ
x1 ðkÞ þ az1 ðkÞ ¼
N X ð1Þ ð1Þ ð1Þ ð1Þ bj xj ðkÞ ¼ b2 x2 ðkÞ þ b3 x3 ðkÞ þ þ bN xN ðkÞ;
ð2Þ
j¼2 ð1Þ
ð1Þ
ð1Þ
where z1 ðkÞ ¼ 0:5x1 ðk 1Þ þ 0:5x1 ðkÞ k = 2, 3, 4, . . . , n. Expanding Eq. (2), the following equation can be obtained: ð0Þ
ð1Þ
ð1Þ
ð1Þ
x1 ð2Þ þ az1 ð2Þ ¼ b2 x2 ð2Þ þ þ bN xN ð2Þ ð0Þ x1 ð3Þ
þ
ð1Þ az1 ð3Þ
ð0Þ
¼ .. .
ð1Þ
ð1Þ b2 x2 ð3Þ
ð1Þ
þ þ bN xN ð3Þ
ð1Þ
ð3Þ
ð1Þ
x1 ðnÞ þ az1 ðnÞ ¼ b2 x2 ðnÞ þ þ bN xN ðnÞ Transforming Eq. (3) into the matrix form, the following equation can be derived:
32 3 a 7 6 7 6 ð0Þ 6 x ð3Þ 7 6 zð1Þ ð3Þ xð1Þ ð3Þ xð1Þ ð3Þ 76 b2 7 7 N 2 7 6 1 76 6 1 6 . 7 7 6 . 7¼6 6 .. .. 74 .. 7 6 . 7 6 5 5 4 . 5 4 . . ð0Þ ð1Þ ð1Þ ð1Þ b N x1 ðnÞ z1 ðnÞ x2 ðnÞ xN ðnÞ 2
ð0Þ
x1 ð2Þ
3
2
ð1Þ
ð1Þ
ð1Þ
z1 ð2Þ x2 ð2Þ xN ð2Þ
ð4Þ
Then the coefficients can be calculated by solving matrix, h = (BTB)1BTY,
2
a
3
2
ð0Þ
x1 ð2Þ
3
2
ð1Þ
ð1Þ
ð1Þ
z1 ð2Þ x2 ð2Þ xN ð2Þ
3
7 7 6 ð0Þ 6 ð1Þ 6b 7 6 x ð3Þ 7 6 z ð3Þ xð1Þ ð3Þ xð1Þ ð3Þ 7 6 27 N 2 7 7 6 1 6 1 7 where h ¼ 6 Y ¼ B ¼ 7: 6 . 7 6 6 .. 7 .. .. 7 6 . 7 6 4 . 5 5 4 . 5 4 . . ð0Þ ð1Þ ð1Þ ð1Þ bN x1 ðnÞ z1 ðnÞ x2 ðnÞ xN ðnÞ The h values represent the weight of comparative series to the referential series. In addition, the GM (1, N) model can be used for prediction and described as:
^x1ð0Þ ðkÞ ¼
N X ð1Þ ð1Þ bj xj ðkÞ az1 ðkÞ:
ð5Þ
j¼2
When adopting GM (1, N), 2 parameters with higher weights (GM1N2-1), 3 parameters with higher weights (GM1N3-1) and all 4 parameters (GM1N4-1) were taken as the comparative series, respectively. Thus N was equal to 3, 4, and 5, respectively. The GM (1, N) established in this study represented the relationship between air pollutant emissions and control parameters with different weights. GM (0, N). According to the definition of GM (h, N), GM (0, N) is that the order in grey differential equation is equal to 0 and defined as follows: ð1Þ
az1 ðkÞ ¼
N X ð1Þ ð1Þ ð1Þ ð1Þ bj xj ðkÞ ¼ b2 x2 ðkÞ þ b3 x3 ðkÞ þ þ bN xN ðkÞ:
ð6Þ
j¼2
Expanding Eq. (6), Eq. (7) can be obtained as follows: ð1Þ
ð1Þ
ð1Þ
ð1Þ
ð1Þ
ð1Þ
az1 ð2Þ ¼ b2 x2 ð2Þ þ þ bN xN ð2Þ; az1 ð3Þ ¼ b2 x2 ð3Þ þ þ bN xN ð3Þ; .. . ð1Þ
ð1Þ
ð7Þ
ð1Þ
az1 ðnÞ ¼ b2 x2 ðnÞ þ þ bN xN ðnÞ; Converting Eq. (7) into the form of matrix, the following equation is derived:
2
ð1Þ
z1 ð2Þ
3
2
ð1Þ
ð1Þ
x2 ð2Þ xN ð2Þ
32 b2 3 a
7 6 76 7 6 ð1Þ 6 z ð3Þ 7 6 xð1Þ ð3Þ xð1Þ ð3Þ 76 b3 7 N 7 6 2 76 a 7 6 1 ¼ 6 . 7 6 . 6 7: . . 7 76 . 7 6 . 7 6 . . . 4 . 5 4 . . . 54 .. 5 ð1Þ
z1 ðnÞ
ð1Þ
ð1Þ
x2 ðnÞ xN ðnÞ
ð8Þ
bN a
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T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
^ T BÞ ^ 1 B ^ T Y, ^ Then the coefficients can be determined by solving matrix, ^ h ¼ ðB
2 b2 3 a b3 a
2
ð1Þ
z1 ð2Þ
3
2
ð1Þ
ð1Þ
x2 ð2Þ xN ð2Þ
3
7 7 6 7 6 ð1Þ 6 ð1Þ ð1Þ 7 6 7 6 z ð3Þ 7 6 7 ^ 6 x2 ð3Þ xN ð3Þ 7 6 7 6 1 ¼6 . where ^h ¼ 6 . 7 Y^ ¼ 6 . 7 B 7: . . 6 . 7 6 . 7 6 . .. .. 7 5 4 . 5 4 . 5 4 . bN a
ð1Þ
z1 ðnÞ
ð1Þ
ð1Þ
x2 ðnÞ xN ðnÞ
The ^ h values are the weight of comparative series to the referential series. GM (1, 1). If the number of comparative series was reduced further, the model was simplified to GM (1, 1). All time series values of one specific air pollutant were used to establish GM (1, 1). Then the established GM (1, 1) was used for prediction. RGM (1, 1). In GM (1, 1), all time series values of one specific air pollutant were used to establish GM (1, 1). While in RGM (1, 1), the time series data of specific air pollutant used to establish model were traditionally the 4 data before the point which was considered to be predicted. That is, the model had to be established every time step and only 4 data were used for model establishment. The control parameter of medical incinerator was ignored in both GM (1, 1) and RGM (1, 1). 2.3. ANN The ANN approach mimics the important operation features of human nervous system and attempts to solve problems by using information gained from past experience on new problems. In order to mimic the human brain, many simple computational elements called artificial neurons are connected by variable weights in the ANN. By mimicking the hierarchical network structure of interconnected neurons, an ANN can deal with complex computation. Among many different types of structures, the multi-layer perceptron structure is commonly adopted. A neural network model typically consists of three independent layers: input, hidden, and output layers. Each layer is comprised of several operating neurons. Input neurons receive the input variable values and store the scaled input values, subsequently the output neurons assign the calculated results into output layer. The hidden layer performs an interface for fully interconnecting input and output layers. The pattern of hidden layer can be either multiple layers or a single layer. Each neuron is connected to every neuron in adjacent layers by a connection weight, which estimates the strength of the relationship between two connected neurons. Each neuron sums all of the input values and the sum is transformed into an output value based on the activation, or transfer, function. For prediction problems, a supervised learning algorithm is often used for training the network to relate input data to output data. The back-propagation algorithm is widely used for training multi-layer neural networks. The algorithm generally uses a gradient search technique (the steepest gradient descent method) to minimize the error between the desired and the actual network outputs [17–20]. In this study, the ANN consisted of three independent layers: input, hidden, and output layers. To compare with GM, 2 parameters with higher weights (ANN2-1), 3 parameters with higher weights (ANN3-1) and all 4 parameters (ANN4-1) were taken as the input layer variables, respectively. Meanwhile each air pollutant emission, i.e. CO2, SO2 and O2, was the single output layer variable. The hidden layer was comprised of 10 operating neurons. The number and speed of training was 10,000 and 0.1, respectively. The calculation was carried out using MATLAB. 2.4. Error analysis In order to evaluate the prediction performance of GM and ANN, the mean absolute percentage error (MAPE) and root mean squared error (RMSE) were employed, given by
MAPE ¼
n 1X obsi prei 100%; n i¼1 obsi
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X 2 RMSE ¼ t ðobsi prei Þ ; n i¼1
ð9Þ
ð10Þ
where obsi and prei are the observed value and prediction value, respectively. 2.5. Weights of control parameters According to Eq. (8), the weights (^ h) between the air pollutant emissions (CO2, SO2 and O2) and 4 different control parameters (HC, FR, Temp1, and Temp2) were calculated as shown in Table 1. The weights of CO2 were in the order: Temp2 (0.7352) > Temp1 (0.1509) > FR (0.1378) > HC (0.0337). Those of SO2 were in the order: Temp1 (2.1014) > Temp2 (1.3978) > FR and HC (0.0197). Those of O2 were in the order: Temp1 (1.5064) > Temp2 (0.7631) > FR (0.3279) > HC (0.1026). Based on the results of GM (0, N), the selected input variables in three types of GM (1, N) (GM1N2-1, GM1N3-1 and GM1N4-1) and in three types of ANN (ANN2-1, ANN3-1 and ANN3-1) were shown in Table 2. Figs. 1 and 2 depict their structures. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx Table 1 The weights between the air pollutant emissions and different control parameters.
CO2 SO2 O2
HC
FR
Temp1
Temp2
0.0337 0.0197 0.1026
0.1378 0.0197 0.3279
0.1509 2.1014 1.5064
0.7352 1.3978 0.7631
Table 2 The selected input variables in GM and ANN. GM
Input variables
ANN
Input variables
CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp2, Temp1 Temp2, Temp1, FR Temp2, Temp1, FR, HC All CO2 for training Previous 4 CO2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp2, Temp1 Temp2, Temp1, FR Temp2, Temp1, FR, HC
SO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC All SO2 for training Previous 4 SO2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC
O2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1)
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC All O2 for training Previous 4 O2 before predicted point
ANN2-1 ANN3-1 ANN4-1
Temp1, Temp2 Temp1, Temp2, FR Temp1, Temp2, FR, HC
3. Results and discussion 3.1. Variation of control parameters and emissions The number of data investigated in one day was totally 78, as shown in Fig. 3. Among the total number of data, the number for model establishing (or training) and predicting (testing) was 68 and 10, respectively.
Fig. 1. The structure diagram of GM.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Hidden layer
Input layer
Output layer
1 Highest weight
2 3
. . . . . . . . . .
2nd higher weight
ANN2-1
3rd higher weight
ANN3-1
ANN4-1
4th higher weight
CO2 SO2 Single flue gas O2
10 Fig. 2. The structure diagram of ANN.
3.2. Simulation of CO2 Fig. 4(a)–(h) depicts the simulation results using GM1N2-1, GM1N3-1, GM1N4-1, GM (1, 1), RGM (1, 1), ANN2-1, ANN3-1, and ANN4-1, respectively. All MAPE and RMSE values are shown in Tables 3 and 4. The 1st to 68th values were used for establishing model, 69th to 78th values were used for evaluating prediction performance. As shown in Table 3, when establishing model, MAPEs between the prediction and observation of CO2 were 52.52%, 53.81%, 49.69% and 5.88% using GM1N21, GM1N3-1, GM1N4-1, and GM (1, 1), respectively. The RMSEs fell in the range of 0.2890 to 2.0897. The MAPEs were 3.19%, 2.86% and 2.58% using ANN2-1, ANN3-1, and ANN4-1, respectively. The RMSEs were between 0.1291 and 0.1561 using different ANN. For CO2 prediction, the MAPEs varied within the range of 3.70% to 38.43% when adopting GMs, but they were between 4.93% and 5.44% when using three types of ANN. The RMSEs lay between 0.1660 and 1.3983 for GM, but they were between 0.2216 and 0.2368 for ANN. In GMs, the MAPE of 3.70% was found to be the lowest when using RGM (1, 1) to predict CO2. This value was lower than those of ANN2-1, ANN3-1, and ANN4-1 by 1.64%, 1.23% and 1.74%, respectively.
3.3. Simulation of SO2
HC (kg), Temp 1, Temp 2 (OC)
1000
50
800
40
600
30
400
20
200
10
0
0 0
50
100
150
200 250 Time (min)
300
350
400
FR (kg/hr), CO 2 (%), SO2 (ppm), O 2 (%)
Fig. 5(a)–(h) shows the simulation results of SO2. From Table 3, MAPEs of SO2 were 35.94%, 36.04%, 30.57% and 11.68% using GM1N2-1, GM1N3-1, GM1N4-1, and GM (1, 1), respectively for establishing model. The RMSEs were between
HC Temp1 Temp2 FR CO2 SO2 O2
Fig. 3. Variation of control parameters and emissions.
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oncentration (%)
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
20
Obs_CO2
15
GM1N2-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(a) 20
Obs_CO2
15
GM1N3-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(b) 20
Obs_CO2
15
GM1N4-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(c) 20
Obs_CO2
15
GM(1,1)
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(d) 20
Obs_CO2
15
RGM(1, 1)
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
(e) Fig. 4. Simulation results of CO2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
4.8188 and 14.3231. The MAPEs were 9.99%, 10.17%, and 8.71%, meanwhile the RMSEs were 4.2884, 4.3123 and 3.7710, respectively using ANN2-1, ANN3-1, and ANN4-1. For SO2 prediction, the MAPEs were between 6.11% and 41.25% when using five different types of GMs, but they were between 13.11% and 16.16% when using three types of ANN. The RMSEs were between 2.4521 and 16.8717 when five types of GMs were used, but they were between 5.3214 and 6.6138 when using ANN. In GMs, the MAPE of 6.11% was found to be the lowest when using RGM (1, 1) to predict SO2. This value was less than those of ANN2-1, ANN3-1, and ANN4-1 by 10.05%, 9.53% and 7.00%, respectively. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
Concentration (%)
8
20
Obs_CO2
15
ANN2-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(f) 20
Obs_CO2
15
ANN3-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(g) 20
Obs_CO2
15
ANN4-1
T rain
Predict
10 5 0 0
50
100
150
200
250
300
350
400
Time (min)
(h) Fig. 4 (continued)
Table 3 MAPEs between the simulation and observation values using different GM and ANN. CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1) ANN2-1 ANN3-1 ANN4-1
SO2
O2
Establishment of model (%)
Prediction of model (%)
Establishment of model (%)
Prediction of model (%)
Establishment of model (%)
Prediction of model (%)
52.52 53.81 49.69 5.88 3.70 3.19 2.86 2.58
38.30 38.43 23.94 4.64
35.94 36.04 30.57 11.68 6.11 9.99 10.17 8.71
38.65 41.25 21.28 14.38
34.43 34.88 32.25 2.11 1.08 1.82 1.51 1.40
54.06 54.19 42.08 1.08
5.34 4.93 5.44
16.16 15.64 13.11
3.16 1.63 1.64
Table 4 RMSEs between the simulation and observation values using different GM and ANN. CO2
GM1N2-1 GM1N3-1 GM1N4-1 GM (1, 1) RGM (1, 1) ANN2-1 ANN3-1 ANN4-1
SO2
O2
Establishment of model
Prediction of model
Establishment of model
Prediction
Establishment of model
Prediction of model
2.0564 2.0897 1.9232 0.2890 0.1660 0.1561 0.1449 0.1291
1.3869 1.3983 0.8944 0.2156
14.3179 14.3231 12.0163 4.8188 2.4521 4.2884 4.3123 3.7710
16.1072 16.8717 10.1774 5.8572
5.9392 5.9728 5.5637 0.4089 0.2112 0.3599 0.3150 0.2915
9.0659 9.0788 7.0745 0.2433
0.2230 0.2216 0.2368
6.6138 6.4437 5.3214
0.5515 0.2960 0.3253
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Concentration (ppm)
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
100 80 60 40 20 0
Obs_SO2
0
50
100
GM1N2-1
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(a) 100 80 60 40 20 0
Obs_SO2
0
50
100
GM1N3-1
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(b) 100 80 60 40 20 0
Obs_SO2
0
50
100
GM1N4-1
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(c) 100 80 60 40 20 0
Obs_SO2
0
50
100
GM(1,1)
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(d) 100 80 60 40 20 0
Obs_SO2
0
50
100
RGM(1, 1)
150
200
250
T rain
300
Predict
350
400
Time (min)
(e) Fig. 5. Simulation results of SO2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
3.4. Simulation of O2 The simulation results of O2 are shown in Fig. 6. According to Table 3, when using GM1N2-1, GM1N3-1, GM1N4-1, and GM (1, 1) to establish models, the MAPEs between the simulation and observation values of O2 were between 2.11% and 34.88%. The RMSEs fell between 0.4089 and 5.9728. When using ANN2-1, ANN3-1, and ANN4-1, they were 1.82%, 1.51% and 1.40%, respectively. The RMSEs were 0.3599, 0.3150, and 0.2915, respectively. For O2 prediction, the MAPEs were between 1.08% and 54.19% when using five types of GMs, but they were between 1.63% and 3.16% when three types of ANN were used. The RMSEs were between 0.2112 and 9.0788 when using GMs for prediction, Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
Concentration (ppm)
10
100 80 60 40 20 0
Obs_SO2
0
50
100
ANN2-1
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(f) 100 80 60 40 20 0
Obs_SO2
0
50
100
ANN3-1
150
200
250
T rain
300
Predict
350
400
Time (min)
Concentration (ppm)
(g) 100 80 60 40 20 0
Obs_SO2
0
50
100
ANN4-1
150
200
250
T rain
300
Predict
350
400
Time (min)
(h) Fig. 5 (continued)
but they fell in the range of 0.2960 and 0.5515 when using ANN. In GMs, the MAPE of 1.08% was the lowest when GM (1, 1) and RGM (1, 1) were adopted to forecast O2. This value was lower than those of ANN2-1, ANN3-1, and ANN4-1 by 2.08%, 0.55% and 0.56%, respectively. Five GMs were utilized to predict the air pollutant emissions from the medical incinerator in this study. The application could be classified into two patterns. GM1N2-1, GM1N3-1, and GM1N4-1 belonged to the first pattern of application, GM (1, 1) and RGM (1, 1) belonged to the second pattern. In the first pattern, the relationship between air pollutant emissions and control parameters was established, and the control parameters were regarded as the input variables to predict air pollutant emissions. In the second pattern, only air pollutant emissions were used to establish GMs. In the first pattern of application, the MAPE values of CO2 using GM1N4-1 (49.69%) were lower than those of GM1N2-1 (52.52%) and GM1N3-1 (53.81%) when establishing model, its value (23.94%) was also lower than those of GM1N2-1 (38.30%) and GM1N3-1 (38.43%) when predicting. The MAPE value of SO2 using GM1N4-1 (30.57%) was lower than those of GM1N2-1 (35.94%) and GM1N3-1 (36.04%) when establishing model, meanwhile its value (21.28%) was lower than those of GM1N2-1 (38.65%) and GM1N3-1 (41.25%) when predicting. The MAPE values of O2 using GM1N4-1 (32.25% for establishment and 42.08% for prediction) were lower than those of GM1N2-1 (34.43% for establishment and 54.06% for prediction) and GM1N3-1 (34.88% for establishment and 54.19% for prediction) when establishing and predicting model. For the second pattern, when forecasting CO2, the MAPE value using GM (1, 1) was higher than that of RGM (1, 1). When forecasting SO2, the value using GM (1, 1) was also higher than that of RGM (1, 1). The MAPE value using GM (1, 1) was the same as that of RGM (1, 1) when forecasting O2. It indicated that the predicting capability of RGM (1, 1) prevailed GM (1, 1). Three types of ANN were also employed in this study. When forecasting CO2, the MAPE value using ANN4-1 (4.93%) was the lowest. But its predicting value was still higher than those of GM (1, 1) and RGM (1, 1) by 0.29% and 1.23%, respectively. When forecasting SO2, the MAPE value using ANN4-1 (13.11% for prediction) was the lowest. But this value was still higher than that of RGM (1, 1) by 7.00%. When forecasting O2, the MAPE value using ANN3-1 (1.63% for prediction) was the lowest. This value was higher than those of GM (1, 1) and RGM (1, 1) by 0.55%. Comparable observations were similarly made by Ionescu and Candau [5]. Ionescu and Candau [5] compared different types of ANN by which the air pollutant emission from a re-heating furnace of the iron and steel industry was predicted. They found that the RMSEs of NO2 lay between 7.48 and 26.3 when training and they were between 10.39 and 26.93 when forecasting. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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Concentration (%)
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
40
Obs_O2
30
GM1N2-1
T rain
Predict
20 10 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(a) 40
Obs_O2
30
GM1N3-1
T rain
Predict
20 10 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(b) 40
Obs_O2
30
GM1N4-1
T rain
Predict
20 10 0 0
50
100
150
200
250
300
350
400
Time (min)
Concentration (%)
(c) 40
Obs_O2
30
T rain
GM(1,1)
Predict
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(e) Fig. 6. Simulation results of O2. (a) GM1N2-1 (b) GM1N3-1 (c) GM1N4-1 (d) GM (1, 1) (e) RGM (1, 1) (f) ANN2-1 (g) ANN3-1 (h) ANN4-1.
In this study, when using GMs, the minimum MAPEs of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2, respectively could be achieved, meanwhile the minimum RMSEs were 0.1660, 2.4521 and 0.2112. Although a good performance could be achieved using ANN too, they required a large amount of data for establishing model. Contrarily, GM only required less data (at least 4 data) and the prediction performance was even better than those of ANN. Therefore, GM could be applied successfully in predicting the air pollutant emissions when the information was insufficient. It also indicated that the control parameters could be utilized on the prediction of air pollutant emissions.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
T.-Y. Pai et al. / Applied Mathematical Modelling xxx (2014) xxx–xxx
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(h) Fig. 6 (continued)
4. Conclusions Five types of GM were employed to predict the CO2, SO2 and O2 from an incinerator. The ANN was also used for comparing. The simulation results can be drawn as follows. According to GM (0, N), two control parameters of temperature, i.e. Temp1 and Temp2, highly influenced air pollutant emissions. When using GMs, the minimum MAPEs of 3.70%, 6.11% and 1.08% for CO2, SO2 and O2 could be achieved, respectively, meanwhile the minimum RMSEs were 0.1660, 2.4521 and 0.2112, respectively. A good performance could be achieved using ANN too, but they required abundant data for training. Contrarily, GM only required a small quantity of data (at least 4 data) and the prediction performance was even better than those of ANN. In the first pattern of application, the MAPE of CO2 for GM1N4-1 (49.69%) was lower when establishing model, its value (23.94%) was also lower when predicting. The MAPE values of SO2 using GM1N4-1 were lower either for establishing model (30.57%) or prediction (21.28%). The MAPE values of O2 using GM1N4-1 (32.25% for establishment and 42.08% for prediction) were lower when establishing model and predicting. In the second pattern, the MAPE value for CO2 and SO2 using GM (1, 1) was greater than those of RGM (1, 1). For O2 prediction, the MAPE value using GM (1, 1) was the same as that of RGM (1, 1). It indicated that the predicting capability of RGM (1, 1) prevailed GM (1, 1). The air pollutant emissions could be successfully predicted by application of control parameters. It also showed that GM could forecast the air pollutant emission variation when the emission data was insufficient. After successful prediction, it is suggested that the GM models can be employed to find out the best design or operation strategy for medical incinerator air emission control using the optimization methods in the future study.
Acknowledgments The authors are grateful to the National Science Council of Taiwan, ROC for financial support under the grant number NSC 101-3113-S-324-001. Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017
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References [1] T. Slanvetpan, R.B. Barat, J.G. Stevens, Process control of a laboratory combustor using artificial neural networks, Comput. Chem. Eng. 27 (11) (2003) 1605–1616. [2] L.E. Olcese, B.M. Toselli, A method to estimate emission rates from industrial stacks based on neural networks, Chemosphere 57 (7) (2004) 691–696. [3] W.Z. Lu, W.J. Wang, Potential assessment of the ‘‘support vector machine’’ method in forecasting ambient air pollutant trends, Chemosphere 59 (5) (2005) 693–701. [4] D. Wang, W.Z. Lu, Interval estimation of urban ozone level and selection of influential factors by employing automatic relevance determination model, Chemosphere 62 (10) (2006) 1600–1611. [5] A. Ionescu, Y. Candau, Air pollutant emissions prediction by process modelling – application in the iron and steel industry in the case of a re-heating furnace, Environ. Model. Software 22 (9) (2007) 1362–1371. [6] J. Deng, The Foundation of Grey Theory, Huazhang University of Science and Technology Press, Wuhan, China, 2002. [7] J. Deng, The Primary Methods of Grey System Theory, Huazhang University of Science and Technology Press, Wuhan, China, 2005. [8] T.Y. Pai, K. Hanaki, H.H. Ho, C.M. Hsieh, Using grey system theory to evaluate transportation on air quality trends in Japan, Transp. Res. D: Transp. Environ. 12 (3) (2007) 158–166. [9] T.Y. Pai, Y.P. Tsai, H.M. Lo, C.H. Tsai, C.Y. Lin, Grey and neural network prediction of suspended solids and chemical oxygen demand in hospital wastewater treatment plant effluent, Comput. Chem. Eng. 31 (10) (2007) 1272–1281. [10] T.Y. Pai, Grey and neural network prediction of effluent from the wastewater treatment plant of industrial park using influent quality, Environ. Eng. Sci. 25 (5) (2008) 757–766. [11] T.Y. Pai, R.J. Chiou, H.H. Wen, Evaluating impact level of different factors in environmental impact assessment for incinerator plants using GM (1, N) model, Waste Manage. 28 (10) (2008) 1915–1922. [12] T.Y. Pai, S.H. Chuang, H.H. Ho, L.F. Yu, H.C. Su, H.C. Hu, Predicting performance of grey and neural network in industrial effluent using online monitoring parameters, Process Biochem. 43 (2) (2008) 199–205. [13] T.Y. Pai, S.H. Chuang, T.J. Wan, H.M. Lo, Y.P. Tsai, H.C. Su, L.F. Yu, H.C. Hu, P.J. Sung, Comparisons of grey and neural network prediction of industrial park wastewater effluent using influent quality and online monitoring parameters, Environ. Monit. Assess. 146 (1–3) (2008) 51–66. [14] T.Y. Pai, K.L. Lin, J.L. Shie, T.C. Chang, B.Y. Chen, Predicting the co-melting temperatures of municipal solid waste incinerator fly ash and sewage sludge ash using grey model and neural network, Waste Manage. Res. 29 (3) (2011) 284–293. [15] T.Y. Pai, C.L. Ho, S.W. Chen, H.M. Lo, P.J. Sung, S.W. Lin, W.J. Lai, S.C. Tseng, S.P. Ciou, J.L. Kuo, J.T. Kao, Using seven types of GM (1, 1) model to forecast hourly particulate matter concentration in Banciao City of Taiwan, Water Air Soil Poll. 217 (1–4) (2011) 25–33. [16] T.Y. Pai, K. Hanaki, R.J. Chiou, Forecasting hourly roadside particulate matter in Taipei County of Taiwan based on first-order and one-variable grey model, CLEAN-Soil Air Water 41 (8) (2013) 737–742. [17] T.Y. Pai, T.J. Wan, S.T. Hsu, T.C. Chang, Y.P. Tsai, C.Y. Lin, H.C. Su, L.F. Yu, Using fuzzy inference system to improve neural network for predicting hospital wastewater treatment plant effluent, Comput. Chem. Eng. 33 (7) (2009) 1272–1278. [18] T.Y. Pai, S.C. Wang, C.F. Chiang, H.C. Su, L.F. Yu, P.J. Sung, C.Y. Lin, H.C. Hu, Improving neural network prediction of effluent from biological wastewater treatment plant of industrial park using fuzzy learning approach, Bioprocess Biosyst. Eng. 32 (6) (2009) 781–790. [19] T.Y. Pai, P.Y. Yang, S.C. Wang, H.M. Lo, C.F. Chiang, J.L. Kuo, H.H. Chu, H.C. Su, L.F. Yu, H.C. Hu, Y.H. Chang, Predicting effluent from the wastewater treatment plant of industrial park based on fuzzy network and influent quality, Appl. Math. Model. 35 (8) (2011) 3674–3684. [20] T.Y. Pai, K. Hanaki, H.C. Su, L.F. Yu, A 24-h forecast of oxidant concentration in Tokyo using neural network and fuzzy learning approach, CLEAN-Soil Air Water 41 (8) (2013) 729–736.
Please cite this article in press as: T.-Y. Pai et al., Predicting air pollutant emissions from a medical incinerator using grey model and neural network, Appl. Math. Modell. (2014), http://dx.doi.org/10.1016/j.apm.2014.09.017