Deep Bidirectional Learning Machine for Predicting NOx Emissions

Article pubs.acs.org/EF

Deep Bidirectional Learning Machine for Predicting NOx Emissions and Boiler Efficiency from a Coal-Fired Boiler Guo-Qiang Li,*,†,‡ Xiao-Bin Qi,† Keith C. C. Chan,‡ and Bin Chen† †

Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao, Hebei 066004, People’s Republic of China ‡ Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon 999077, Hong Kong ABSTRACT: Combustion optimization is one of the effective techniques to enhance boiler efficiency and reduce nitrogen oxide (NOx) emissions from coal-fired boilers. A precise NOx emission model and a boiler efficiency model are the basis of implementing real-time combustion optimization and are required. In this study, to obtain very precise models and make full use of abundant real-time operational data easily collected from supervisory information systems (SIS), a novel deep learning algorithm called a deep bidirectional learning machine (DBLM) is proposed to set up the correlation between NOx emissions, boiler efficiency, and operational parameters from a 300 MW circulating fluidized bed boiler (CFBB). Experimental results indicate that, in comparison to other recently published state-of-the-art modeling methods, the models built by DBLM could own much better generalization performance and high repeatability, which may be a better choice for modeling NOx emissions and efficiency in achieving boiler combustion optimization and improving power plant performance.

1. INTRODUCTION With the development of the economy and growing worldwide attention paid to environmental protection, how to reduce pollutant emissions under keeping or improving boiler efficiency is an important and urgent problem to be solved for most power plants in China. To protect our living environment, a very stringent pollutant emission standard was addressed to power plants by the Ministry of Environmental Protection of China on July 1, 2014. With NOx emissions taken as an example, the maximum NOx emission is limited to 100 mg/Nm3. Combustion optimization technology is an effective and economic method to improve boiler efficiency and reduce pollutant emissions from coal-fired boilers.1,2 The reduction of NOx emissions and the improvement of the boiler efficiency could be achieved by tuning adjustable operational parameters of a boiler, such as primary air, secondary air, coal feed quantity, etc.3,4 However, the optimization of operational parameters has heavily relied on the correlations between both NOx emissions and boiler efficiency and operational parameters.5,6 Therefore, precise and rapid prediction models of NOx emissions and boiler efficiency are required for improving power plant performance.7 However, because the combustion process of a boiler in power plants is a very complex multi-variable strong coupling nonlinear system, it is very difficult to set up accurate mathematical models by mechanism modeling methods. As a result of abundant real-time operational information easily collected from supervisory information systems (SIS) in power plants, many researchers have been committed to building the system model of the combustion process of coal-fired boilers by machine-learning methods, which could achieve very good nonlinear fitting and generalization abilities. In ref 8, a globally enhanced general regression neural network (GE-GRNN) is proposed and employed to predict multiple emissions [NOx and loss on ignition (LOI) of fly ash] from a 600 MW utility © XXXX American Chemical Society

boiler in an online environment. In ref 9, a generalized regression neural network is employed to set up a NOx emission model, which shows better generalization performance. Support vector regression (SVR) optimized by ant colony optimization (ACO) is adopted to build an efficient NOx emission model of a coal-fired utility boiler.10 In ref 11, teaching−learning-based optimization (TLBO) is employed to optimize the hyperparameters of the least squares support vector machine (LS-SVM) to build a NOx emission model of a 330 MW coal-fired boiler. An enhanced general regression neural network (enhanced-GRNN) is employed to predict the coal mass flow rate, NOx emission concentration, and fly ash LOI percentage, and an artificial bee colony (ABC) is used to optimize the operational parameters.12 Booth and Roland apply an online real-time neural network to several commercially operating coal-fired boilers and reduce NOx emissions up to 60% and unburned carbon in ash up to 30%, meanwhile improving the heat rate up to 2% overall.13 In addition, there are many published research studies to predict pollutant emissions.14−19 However, although the support vector machine (SVM) and the traditional neural networks could achieve good generalization performance in the above applications, training SVMs is a very slow process and becomes a bottleneck for large data sets because the kernel matrix would grow quadratically with the size of the training set and training traditional neural networks would suffer from the problems of iterative computing and being time-consuming, especially when traditional gradient descent methods are employed. Therefore, it is essential to thoroughly study novel neural network topologies or learning algorithms to further develop the applications of neural networks on power plants. Received: May 16, 2017 Revised: August 29, 2017

A

DOI: 10.1021/acs.energyfuels.7b01415 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels

Figure 1. Structure of the DBLM, where bij is the bias of the jth neuron of the ith hidden layer and ci is the bias of the ith neuron of the output layer.

output parameters, the number of hidden neurons is m. Then, the output G of the hidden layer could be obtained by eq 1

For this study, to establish precise correlations between the boiler efficiency, NOx emissions, and operational parameters, a large amount of real-time data (28 801 cases with 28 attribute parameters) is collected from the SIS of a 300 MW circulating fluidized bed boiler (CFBB) in a power plant. In the present paper, a novel deep neural network, which is called a deep bidirectional learning machine (DBLM), is proposed to set up the prediction models of the boiler efficiency and NOx emissions based on collected operational parameters from the 300 MW CFBB. A model comparison study including twohidden-layer extreme learning machine (TELM),20 improved extreme learning machine based on principal component analysis (P-ELM),21 and least squares fast learning network (LSFLN)22 modeling approaches, which are three variants of the extreme learning machine (ELM),23,24 is presented. Results of the model comparison study reveal that, for the analyzed 300 MW CFBB, the model based on DBLM could better predict the boiler efficiency and NOx emissions than the other three methods. The rest of this study is organized as follows: in section 2, the ELM is reviewed in brief. A DBLM is proposed in section 3. Modeling boiler efficiency and NOx emissions and experimental comparisons are given in section 4. Finally, section 5 summarizes the conclusions of this paper.

⎡ g (b1 + W1x1) ⋯ g (b1 + W1xN ) ⎤ ⎥ ⎢ ⋱ ⋮ G = ⎢⋮ ⎥ ⎥ ⎢ ⎣ g (bm + Wmx1) ⋯ g (bm + WmxN )⎦

(1)

in which g(·) is the activation function of the hidden neurons, bi is the bias of the ith hidden neuron, and Wi is the input weights that connect the ith hidden neuron and all input neurons. The output of ELM could be computed by the following formula Y = Gβ

(2)

in which β is the output weights. According to the least squares method, the output weights β could be analytically calculated by ̃ − Y || = minβ||βGY || ||β G

(3)

β ̃ = YG+

(4)

+

where G is the Moore−Penrose (MP) generalized inverse of G.

3. DEEP BIDIRECTIONAL LEARNING MACHINE (DBLM) In this section, a novel DBLM based on the ELM is proposed, whose structure is given in Figure 1. The learning process of the DBLM is described in detail as follows: We suppose that there are N distinct samples {X, Y}, in which xi = [xi1, xi2, ..., xin]T ∈ Rn is the n-dimensional feather vector of the ith sample and yi = [yi1, yi2, ..., yim]T ∈ Rm is the corresponding m-dimension output vector. In DBLM, there are one input layer with n neurons, one output layer with m neurons, and k hidden layers, which own L1, L2, ..., Li, ..., Lk − 1, Lk hidden neurons with b1, b2, ..., bi, ..., bk − 1, bk hidden bias vectors, respectively. Wi is a Li×Li − 1 weight matrix connecting between the neurons of the (i − 1)th hidden layers and the neurons of the ith hidden layers. When i = 1, L0 equals the

2. EXTREME LEARNING MACHINE (ELM) The ELM, which was proposed in 2006, is a single-hidden-layer forward neural network (SLFNN), which overcomes disadvantages of traditional neural networks, such as problems of iterative computing, the time-consuming problem, local optimum, etc. In the learning process of ELM, its input weights and hidden biases are randomly generated, and the output weights are analytically determined by the least squares method. We simply review the learning process of ELM as follows: If we suppose N training samples {X, Y}, in which xi = [xi1, xi2, ..., xin]T ∈ Rn, n-dimensional feather vector, are the input parameters of ELM and yi = [yi1, yi2, ..., yil ]T ∈ Rl are the l B


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Energy & Fuels number n of input layer neurons; that is to say, W1 is a L1×n input weight matrix connecting between input neurons and the neurons of the first hidden layers. β is a m×Lk output weight matrix connecting between the neurons of the kth hidden layer and the output neurons with their biases c = [c1, c2, ..., cl]T. f i(·) and g(·) are the activation functions of the neurons of the ith hidden layer and the output neurons, respectively. Then, the mathematical model of the DBLM could be described as ⎧ H1 = f (W 1X + b1) 1 ⎪ ⎪ 2 2 1 2 ⎪ H = f2 (W H + b ) ⎪ ⎨⋮ ⎪ k ⎪ H = fk (W kH k − 1 + bk ) ⎪ ⎪ Y = g (β H k + c ) ⎩

⎡ f (b k + W kH k − 1) ⋯ f (b k + W kH k − 1) ⎤ 1 1 1 N k 1 ⎢ k 1 ⎥ k ⎢ ⎥ ⋱ ⋮ H = ⋮ ⎢ ⎥ ⎢ f (b Lk + W Lk H1k − 1) ⋯ f (b Lk + W Lk HNk− 1)⎥ ⎣ k k ⎦ k k k k ⎛⎡ k ⎞ k k−1 ⋯ b1k + W1kHNk− 1 ⎤⎟ ⎜⎢b1 + W1 H1 ⎥ ⎥⎟ ⋱ ⋮ = fk ⎜⎢⋮ ⎜⎢ ⎥⎟ ⎜⎢ b k + W k H k − 1 ⋯ b k + W k H k − 1 ⎥⎟ L L N L L N ⎣ ⎦⎠ ⎝ k k k k = fk (WP) (7)

⎡W k W k ⋯ W k ⎤ 2 Lk ⎥ ⎢ 1 W=⎢ k k k ⎥ ⎣b1 b2 ⋯ b Lk ⎦

T

⎡ ⎤ ⎢ H1k − 1 H2k − 1 ⋯ HNk− 1⎥ P=⎢ ⎥ ⋯ 1 1 ⎢1 ⎥ ⎣ ⎦

(5)

As seen from Figure 1 and eq 5, the DBLM is one of multilayer neural networks. As we know, multilayer neural networks do not perform very well when only trained using the back propagation (BP) algorithm; therefore, most deep neural networks are initialized using layer-wise unsupervised learning and fine-tuning the whole or part neural networks with the BP algorithm. In this study, DBLM adopts layer-wise unsupervised learning to initialize all of the weights by a novel weight computational method, which will be given in the following section. In addition, in contest to traditional deep neural networks, the DBLM does not require fine-tuning. To determine all weights and biases, the whole network of DBLM is divided into two parts: The first part is from the input layer to the (k − 1)th hidden layer, and the second part is from the (k − 1)th hidden layer to the output layer. For the first part, it could be thought of the stacked auto-encoder; therefore, the structure of any adjacent two layers could be transformed into a single-hidden-layer feedforward neural network (SLFN), whose output data are equal to input data. For example, panels a and b of Figure 1 show examples how to transform a two-layer network into a three-layer network SLFN. For the second part, it owns three layers and could be thought of as a SLFN, whose input is the output of the (k − 1)th hidden layer and output is the output of the network of the whole DBLM, as shown as Figure 1c. In this study, the determination of weights of the transformed SLFNs (panels a and b of Figure 1) in the first part is the same as that of the SLFN in the second part. Therefore, to uniformly express how to determine weights and biases, we take the SLFN (Figure 1c) in the second part for example. 3.1. Determine the Input Weights and Biases of a SLFN. According to eq 5and Figure 1c, the output of the DBLM could be rewritten as ⎛ ⎡ k ⎤⎞ Y = g (βH + cI ) = g ⎜[ β c ]⎢ H ⎥⎟ ⎣ I ⎦⎠ ⎝

and

Wki

(8)

bki

where and are the weight connecting all input neurons and the ith neuron of the kth hidden layer and the bias of the ith neuron of the kth hidden layer, respectively, Hki − 1 is the output vector containing Lk output values of the neurons of the kth hidden layer for the ith input sample. Hk is the hidden output matrix of the kth hidden layer, and I = [1, 1, ..., 1]1×N. For an invertible activation function g(·), eq 6 could be rewritten as the following formula:

βH k = g −1(Y ) − cI

(9)

If we suppose that the output weight β and the bias c are known, then Hk could be calculated by ||βH̃ k − [g −1(Y ) − cI ]|| = ||βH̃ k − g −1(Y ) + cI || = min H k ||βH k − g −1(Y ) + cI ||

(10)

The minimum norm least squares solution of eq 10 could be obtained by H̃ k = β +(g −1(Y ) − cI ) = fk (WP)

(11)

For an invertible activation function f k(·) of the kth hidden layer, eq 11 could be rewritten as WP = f k−1 (H̃ k) = f k−1 (β +(g −1(Y ) − cI ))

(12)

f −1 k (·)

where is the invertible function of f k(·). Then, the minimum norm least squares solution of eq 12 could be obtained by ̃ − f −1 (H̃ k)|| = ||WP ̃ − f −1 (β +(g −1(Y ) − cI ))| ||WP k k | = minW ||WP − f k−1 (β +(g −1(Y ) − cI ))|| k

(13) k

The combination matrix containing W and biases b could be analytically calculated by

k

(6) C

W̃ = f −1 (β +(g −1(Y ) − cI ))P+

(14)

k ⎧ ⎪ W = W̃ (1: Lk , 1: Lk − 1) ⎨ ⎪ k ⎩b = W̃ (1: Lk , Lk − 1 + 1)

(15) DOI: 10.1021/acs.energyfuels.7b01415 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels However, in the initialization of the learning process, the output weight β and biases c are unknown. Therefore, we can randomly assign the values for β and c under the following two conditions. The conditions are (1) the range of randomassigned values should be located in between 0 and 1 and (2) the rank of β should equals to min{m, Lk}. When there are negative values before the computation of the invertible −1 functions f −1 k ( ) and g ( ), their absolute values would take the place of these negative values to keep the presence of invertible computation. This cannot affect the performance of DBLM because we will recalculate the output weight β and the biases c in the following section, which would take the place of the randomly assigned β and c. Here, it is note that, for the first part of the DBLM, the biases of the output layer should be set as zero because the output data are the input data. 3.2. Determination of the Output Weights and Biases. After determination of Wk and bk, the DBLM could be thought of as a linear system. Therefore, the output weights β and biases c could be analytically determined by ⎛ ⎡ k ⎤⎞ g ⎜γ ⎢̃ H ⎥⎟ − Y ⎝ ⎣ I ⎦⎠

⎛ ⎡ k ⎤⎞ = min γ g ⎜γ ⎢ H ⎥⎟ − Y ⎝ ⎣ I ⎦⎠

Table 1. Differences between the DBLM and ELM difference

⎡ k⎤ = min γ γ ⎢ H ⎥ − f −1 (Y ) ⎣I ⎦

initialization

randomly generated input weights and hidden biases randomly initialized values

multiple-hidden-layer feedforward neural network randomly generated output weightsa determined by least squares methodsa redetermined by the third least squaresa used 3 timesa

determined by once least squares used only once

Take Figure 1c for example to state the differences. bInput weights containing hidden biases.

temperature (1 and 2), distribution flow of secondary air (A and B), air preheater secondary air outlet air temperature (A and B), total flow of secondary air, limestone powder conveying motor current (1 and 2), unburned carbon in flue dust (A and B), flue gas oxygen content, flue gas temperature, outlet temperature of slag cooler (1−4), boiler efficiency, and NOx emissions. The ranges of these parameters during the sampling period and measurement units are given in Table 2, and some

(16)

Table 2. Parameter Ranges of a 300 MW CFBB during the Sampling Period variable

(17)

range

load (%) coal quantity of coal feeder (1−4) (t/h) primary air flow of burner inlet (A and B) (kNm3/h) primary air temperature of burner inlet (A and B) (°C) primary air fan inlet temperature (1 and 2) (°C) distribution flow of secondary air (A and B) (kNm3/h) air preheater secondary air outlet air temperature (A and B) (°C) total flow of secondary air (kNm3/h) limestone powder conveying motor current (1 and 2) (A) unburned carbon in flue dust (A and B) (%) flue gas oxygen content (%) flue gas temperature (°C) outlet temperature of slag cooler (1−4) (°C) boiler efficiency (%) NOx emissions (mg/Nm3)

(18)

where H = [(Hk)T IT]T. Then, the output weight and output biases could be calculated by the following formula: ⎧ ̃ m , 1: Lk ) ⎪ β = γ (1: ⎨ ⎪ ̃ m , Lk + 1) ⎩ c = γ (1:

single-hidden-layer feedforward neural network

a

The combination matrix γ could be calculated by ⎡ k ⎤+ γ ̃ = f − 1 (Y ) ⎢ H ⎥ = f − 1 ( Y ) H + ⎣I ⎦

DBLM

structure

input weightsb output weights least squares

where γ = [β c]. For an invertible activation function g( ), the combination matrix γ could be analytically determined by eq 17. ⎡ k⎤ γ ⎢̃ H ⎥ − f −1 (Y ) ⎣I ⎦

ELM

(19)

As seen from the above learning process, the DBLM could be thought of as one variant of the ELM. The training of the DBLM can be made without iteratively tuning their weights (containing biases) similar to the ELM, which is the main difference from traditional neural networks; in addition, the least squares method is adopted to determine their weights (containing biases), which could make the weights (containing biases) be the minimum norm solutions. However, there are some differences between the DBLM and ELM, which are listed in Table 1.

52.80−86.03 22.25−57.92 66.82−537.16 241.32−268.16 23.39−32.85 42.53−709.69 243.74−278.23 125.66−955.23 73.12−192.48 from −0.04a to 1.80 3.75−8.68 141.23−155.18 23.07−105.73 89.37−92.30 78.88−191.87

a

Negative values indicate that its corresponding equipment did not work when collecting these data.

collected samples are given in Table 3. In addition, it is noted that these samples are collected under the same kind of coal during the sample period; therefore, the impact of the coal properties was neglected. In this study, the focus is to set up correlations between the operational parameters and the boiler efficiency as well as NOx emissions by the proposed DBLM. The parameters boiler efficiency and NOx emissions would be taken as the outputs of the DBLM, and other 26 operational parameters would be taken as the input parameters of the DBLM. 4.2. Results and Comparisons. All evaluations are carried out by means of the Matlab 2016b computational environment

4. MODELING BOILER EFFICIENCY AND NOX EMISSIONS 4.1. Data Preparation. In this section, we adopt the data collected from a 300 MW CFBB under operational conditions of an actual power plant. As a result of the limits of the field equipment and structure and sampling techniques, 28 801 samples with 28 attribute parameters are collected. The 28 attribute parameters are load (%), coal quantity of coal feeder (1−4), primary air flow of burner inlet (A and B), primary air temperature of burner inlet (A and B), primary air fan inlet D


load

1

A

261.574 261.574 261.574 ⋮ 258.262 257.499 258.679 268.17 ⋮ 278.228

1 2 3 ⋮ 5101 9910 13120 20127 ⋮ 28801

251.811 251.811 251.811 ⋮ 250.419 246.566 246.566 253.963 ⋮ 265.512

B

64.504 41.163 64.617 40.972 64.513 40.926 ⋮ ⋮ 53.93 28.617 78.037 50.605 82.563 54.841 85.363 44.371 ⋮ ⋮ 82.661 44.258 air preheater secondary air outlet air temperature

number

1 2 3 ⋮ 5101 9910 13120 20127 ⋮ 28801

number

3 37.222 37.351 37.254 ⋮ 28.547 50.777 55.354 44.518 ⋮ 44.349

6.527 6.527 6.527 ⋮ 8.68 6.309 5.798 3.755 ⋮ 4.947

flue gas oxygen content

37.152 36.911 37.188 ⋮ 28.642 50.531 54.918 44.552 ⋮ 44.137

2

coal quantity of coal feeder A

1 85.673 85.33 85.635 ⋮ 88.267 102.495 99.672 105.508 ⋮ 90.708

2 101.961 102.151 102.075 ⋮ 104.44 97.04 97.04 107.835 ⋮ 108.674

A

A 0.794 0.794 0.794 ⋮ 1.236 1.652 1.652 1.671 ⋮ 1.799

B 0.275 0.222 0.165 ⋮ 0.185 0.293 0.391 0.206 ⋮ 0.087

143.5 143.5 143.5 ⋮ 148.192 144.233 144.736 148.512 ⋮ 155.172

flue gas temperature

249.961 249.961 249.961 ⋮ 247.926 245.536 246.595 255.271 ⋮ 266.494

B

primary air temperature of burner inlet

279.677 252.341 256.103 252.341 321.102 252.341 ⋮ ⋮ 227.037 249.545 327.739 247.726 363.671 248.958 345.59 256.766 ⋮ ⋮ 344.904 268.142 unburned carbon in flue dust

B

primary air flow of burner inlet 36.735 233.445 36.485 244.66 36.708 222.002 ⋮ ⋮ 28.564 178.059 50.545 366.646 54.827 283.796 44.451 314.464 ⋮ ⋮ 44.216 346.735 limestone powder conveying motor current

4

Table 3. Some Samples Collected from a 300 MW CFBB

2 23.393 23.393 23.393 ⋮ 28.916 31.153 31.153 31.515 ⋮ 32.499

187.099 165.357 168.218 ⋮ 99.558 506.847 531.927 651.51 ⋮ 385.738

A

2 37.04 37.04 37.04 ⋮ 31.75 46.065 46.065 47.427 ⋮ 50.442

3 58.203 56.162 56.162 ⋮ 31.604 81.052 78.357 68.687 ⋮ 32.709

34.54 34.54 34.54 ⋮ 32.4 32.562 32.562 32.729 ⋮ 33.943

4

226.388 263.579 224.291 ⋮ 74.764 413.583 542.035 455.447 ⋮ 415.872

B

distribution flow of secondary air

outlet temperature of slag cooler 33.958 33.958 33.958 ⋮ 31.721 31.254 31.254 31.05 ⋮ 32.307

1

25.004 25.004 25.185 ⋮ 28.671 31.011 31.011 31.05 ⋮ 30.83

1

primary air fan inlet temperature

90.98 91.02 91.07 ⋮ 89.58 90.67 90.75 91.37 ⋮ 92.29

efficiency

154.410 155.859 153.647 ⋮ 155.783 141.745 132.972 97.116 ⋮ 121.071

NOx emissions

351.239 335.221 318.761 ⋮ 166.637 681.947 745.398 816.637 ⋮ 509.911

total flow of secondary air

Energy & Fuels Article

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Energy & Fuels Table 4. Performance Comparison for NOx Emissions and the Boiler Efficiency output NOx emissions

performance index RMSE

R

efficiency

2

RMSE

R

2

minimum maximum mean SD minimum maximum mean SD minimum maximum mean SD minimum maximum mean SD

PELM

TELM

12.966 2.4808 × 106 1.3317 × 105 4.9127 × 105 0.0004 0.7633 0.3932 0.3285 6.8123 122.82 0.2995 24.091 0.0005 0.4593 0.2943 0.1474

17.438 20.069 19.981 0.4803 0.0008 0.6429 0.0341 0.1173 0.2433 817.28 59.128 0.1286 0.0004 0.6924 0.0351 0.1245

LSFLN 7.2978 7.3072 7.2987 2.6523 0.9315 0.9314 0.9315 5.1607 0.0536 0.0536 0.0536 6.7654 0.9873 0.9873 0.9873 4.9993

DBLM

× 10−3

× 10−5

× 10−8

× 10−8

3.5816 3.8217 3.7327 0.0618 0.9817 0.9839 0.9825 5.7966 × 10−4 0.0531 0.0539 0.0533 1.9723 × 10−4 0.9871 0.9875 0.9874 9.3146 × 10−5

Figure 2. Comparison between actual measured and predicted NOx emissions on the testing data set for the DBLM.

running on a computer with Windows 10 (64 bit), 3.16 GHz CPU, and 4 GB RAM. In this study, to state the superiority of the proposed DBLM, another three recently published outstanding algorithms (TELM,20 PELM,21 and LSFLN22) are employed to set up the models of NOx emissions and the boiler efficiency of the above 300 MW CFBB. It should be noted that, before modeling, all samples are divided into two parts: half (14 401 samples) of all samples are taken as training samples, and the rest (14 400 samples) of the samples are taken as test samples. In addition, for single-hidden-layer feedforward neural networks (PELM and LSFLN), the “sig” function is taken as the activation function of hidden neurons. For TELM, although it is a two-hidden-layer feedforward neural network, the number of two hidden neurons is equal and their hidden activation functions are set as the “sig” function. For the DBLM, although

it is a multiple-hidden-layer neural network, here, it is set as a two-hidden-layer neural network, and the activation functions for two hidden layers are set as “linear” and “sig”. To keep a watchful eye to the generalization performance of each algorithm, each algorithm used in the experiments is uniformly assigned a number of hidden neurons, which varies from 15 to 300 by the step of 15. Moreover, 30 trials are carried out for each algorithm with a given number of hidden neurons. The performance evaluation criteria selected for the comparative study is the maximum, minimum, mean, and standard deviation (SD) of the accuracy quantified in terms of the root mean square error (RMSE) and R2 for the problems. In this section, all raw data are directly used by each algorithm to set up prediction models for NOx emissions and the boiler efficiency of the 300 MW CFBB. The experimental results of the above four algorithms are reported in Table 4. F


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Figure 3. Comparison between actual measured and predicted efficiency on the testing data set for the DBLM.

Figure 4. Performance of the DBLM varies with the number of hidden neurons for the NOx emissions.

For the LSFLN, its average RMSE and R2 would reduce and improve, respectively, with the increase of the number of hidden neurons, until the number achieves 45. When the number is more than 45, its best performance would stay the same. According to the best results, we could know that the LSFLN could predict NOx emissions and the boiler efficiency very well with less hidden neurons, especially for boiler efficiency. For the DBLM, the average RMSEs obtained by the DBLM could achieve 3.7327 and 0.533 and average R2 of 98.25 and 98.74% for NOx emissions and the boiler efficiency, respectively. In addition, Figures 2 and 3 illustrate the comparisons between the actual measured NOx emissions

According to experiments and Table 4, the models built by regardless of TELM or PELM do not very well predict the NOx emissions and the boiler efficiency. The average RMSE and R2 obtained by both of them could not become better with the increase of the number of hidden neurons but worse sometimes. In 30 runs for a certain set number of hidden neurons, their RMSEs and R2 sometimes achieve 103−106 and 10−2−10−4, respectively. Therefore, we could think that both of them are not suitable to be employed to build the models of NOx emissions and the boiler efficiency under the situation that the raw data are not processed. G


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Figure 5. Performance of the DBLM varies with the number of hidden neurons for the boiler efficiency

Table 6. Performance Comparison of the DBLM with/without Cross-Validation DBLM with 3-fold cross-validation DBLM without cross-validation output NOx emissions

performance index RMSE

R2

efficiency

RMSE

R2

minimum maximum mean SD minimum maximum mean SD minimum maximum mean SD minimum maximum mean SD

DBLM with 10-fold cross-validation

validation

validation

test

test

mean

optimum

test

mean

optimum

3.5816 3.8217 3.7327 0.0618 0.9817 0.9839 0.9825 5.7966 × 10−4 0.0531 0.0539 0.0533 1.9723 × 10−4 0.9871 0.9875 0.9874 9.3146 × 10−5

3.6429 3.6909 3.6579 0.0221 0.9829 0.9834 0.9833 2.0544 × 10−4 0.0534 0.0537 0.0535 1.1593 × 10−4 0.9873 0.9874 0.9873 5.5802 × 10−5

3.7435 3.8832 3.8029 0.0376 0.9811 0.9825 0.9819 3.6826 × 10−4 0.0554 0.0557 0.0555 7.4607 × 10−4 0.9862 0.9864 0.9863 4.1760 × 10−5

3.6487 3.8196 3.7308 0.0642 0.9818 0.9838 0.9826 4.6051 × 10−4 0.0514 0.0544 0.0534 7.8340 × 10−4 0.9869 0.9885 0.9876 3.8961 × 10−5

3.6220 3.7526 3.6879 0.0271 0.9824 0.9836 0.9830 2.5140 × 10−4 0.0534 0.0536 0.0536 8.4218 × 10−4 0.9874 0.9873 0.9873 4.0867 × 10−5

3.7407 3.8301 3.7810 0.0234 0.9816 0.9824 0.9821 2.2375 × 10−4 0.0552 0.0555 0.0554 8.2112 × 10−4 0.9862 0.9864 0.9863 4.9955 × 10−5

3.5086 3.6993 3.6057 0.04695 0.9830 0.9851 0.9840 5.0366 × 10−4 0.0479 0.0522 0.0506 9.9915 × 10−4 0.9879 0.9896 0.9888 4.8307 × 10−5

and the predicted NOx emissions by the DBLM and between the actual boiler efficiency and the predicted boiler efficiency by the DBLM on the testing data set, respectively. It is easy to see that almost all of the data have been fallen in a diagonal distribution along with the perfect line, where predicted values are equal to actual values. It means that both NOx emissions and the efficiency could be predicted with good accuracy by the DBLM for both testing data sets. In comparison to the other three methods, the DBLM shows the best generalization performance with better repeatability. As seen from Figures 4 and 5, regardless of NOx emissions or the boiler efficiency, their R2 would improve with the increase of the number of two hidden neurons. For NOx emissions, the improvement of the performance mainly depends upon the increase of the number of the second hidden neurons; when the DBLM achieves the best performance, the numbers of neurons of two hidden layers are 300 and 300. For the boiler efficiency, the improvement of the performance mainly depends upon the increase of the number of the first hidden neurons; when the DBLM achieves

the best performance, the number of two-hidden-layer neurons are 45 and 30. In addition, for NOx emissions, the mean training time is 11.9339 s and its SD is 0.5767 and the mean testing time (the response time for testing samples) is 1.0646 s for 14 400 testing samples and its SD is 0.0861. For the boiler efficiency, the mean training time is 11.1995 s and its SD is 0.3147 and the mean testing time (the response time for testing samples) is 1.0443 s for 14 400 testing samples and its SD is 0.0363. According to the response times (1.0646 s of NOx emissions and 1.0443 s of the boiler efficiency for 14 400 samples), we could know that the response time of the DBLM is very quick and could meet the needs of power plants. In addition, to further state the generalization performance of the DBLM, we adopted 3- and 10-fold cross-validations to train the DBLM model. Here, the above training samples (14 401 samples) would be divided into two parts according to the above k-fold (k = 3 or 10) cross-validation, training set and validation set, and the above test samples are still taken as the testing set. The numbers of neurons of two-hidden-layers are H


Energy & Fuels

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still set as 300. A total of 30 trials are still carried out. Results obtained by the DBLM with k-fold cross-validation are given in Table 6. In Table 6, for the validation set, the mean is the mean value of k validation results for one trial and the optimum is the best of the k values (for RMSE, optimum is the minimum value, and for R2, optimum is the maximum value). As seen from Table 6, we could know that, for NOx emissions, the obtained best mean RMSE and R2 is the DBLM with 3-fold cross-validation, the next is the DBLM without cross validation, and the last is the DBLM with 10-fold cross-validation. Although the 3-fold cross-validation could improve the generalization performance, the 10-fold crossvalidation would make the DBLM own a little worse generalization ability. Therefore, an appropriate k-fold crossvalidation will improve the performance of the DBLM. In addition, according to the obtained values, we could know that the results obtained by all three methods (DBLM without cross-validation and DBLM with 3- and 10-fold crossvalidation) could achieve satisfactory results and meet the needs of power plants. For boiler efficiency, the results (mean values of R2 and RMSE) obtained by all of the methods are very similar and the SD achieves 10−5 and 10−4 for R2 and RMSE, respectively, which are very small for efficiency and NOx emissions. In addition, the difference between maximum and minimum is very small. Therefore, all three methods could own high repeatability. The DBLM with k-fold cross-validation does not improve the generalization ability but increases the training time for boiler efficiency. This cross-validation experiment could reflect that the DBLM owns very good generalization ability from the side. Therefore, we conclude that the proposed DBLM with better repeatability could not only predict NOx emissions very well but also predict the boiler efficiency. The DBLM could be taken as an effective machine-learning tool for the prediction of pollutant emissions.

Article

AUTHOR INFORMATION

Corresponding Author

*Telephone: +86-13933628751. E-mail: zhihuiyuang@163. com. ORCID

Guo-Qiang Li: 0000-0002-7117-2710 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant 61403331), the Program for the Top Young Talents of Higher Learning Institutions of Hebei (Grant BJ2017033), the Natural Science Foundation of Hebei Province (Grant F2016203427), the China Postdoctoral Science Foundation (Grant 2015M571280), and the Doctorial Foundation of Yanshan University (Grant B847).

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5. CONCLUSION In this study, the models of NOx emissions and boiler efficiency from a 300 MW CFBB were established by the proposed DBLM. To train and test the proposed DBLM model, a large amount of real data (28 801 cases with 28 attribute parameters) were collected from the SIS of a 300 MW coal-fired power plant, in which 26 operational parameters are taken as the inputs of the models and the other 2 attribute parameters NOx emissions and boiler efficiency are taken as outputs. Experimental results reveal that the proposed DBLM model with high repeatability could achieve high predictive accuracy and good generalization performance. In comparison to the other three state-of-the-art methods (TELM, PELM, and LSFLN), the DBLM could outperform in terms of the performance evaluation criteria (RMSE and R2). Therefore, the DBLM model could be an alternative learning machine tool for predicting NOx emissions and boiler efficiency and be the basis of combustion optimization of a coal-fired boiler in power plants to improve the boiler efficiency and reduce NOx emissions. In addition, as a result of the better performance, the DBLM could also be an alternative learning machine tool in other fields, such as image recognition, drug−target interaction perdition, cancer screening, etc. However, there still exists big room for us to explore the DBLM in our future work. One challenging topic is how to make full use of the sparse representation in the DBLM, and another challenging topic is how to make the DBLM own online learning ability. I


Article

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Deep Bidirectional Learning Machine for Predicting NOx Emissions

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