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Flame Images for Oxygen Content Prediction of Combustion Systems Using DBN Yi Liu, Yu Fan, and Junghui Chen Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b00576 • Publication Date (Web): 18 Jul 2017 Downloaded from http://pubs.acs.org on July 18, 2017

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Energy & Fuels

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Flame Images for Oxygen Content Prediction of Combustion

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Systems Using DBN

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Yi Liu1, Yu Fan1, Junghui Chen2*

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1. Institute of Process Equipment and Control Engineering, Zhejiang University of

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Technology, Hangzhou, 310014, People’s Republic of China

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2. Department of Chemical Engineering, Chung-Yuan Christian University, Chung-Li,

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Taiwan, 320, Republic of China

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Revision Submitted to Energy & Fuels

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May, 2017

25 26 ∗ Corresponding author. Tel.: +886-3-2654107; Fax: +886-3-2654199 E-mail: [email protected](J. Chen). 1

ACS Paragon Plus Environment

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Abstract: As an increasingly popular method in the machine learning field, deep learning is applied to

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industrial combustion processes in this work. Using easily available color flame images obtained by the

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charge-coupled device (CCD), a soft sensor system based on deep learning is proposed to predict the

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outlet oxygen content online. Unlike the traditional principal component analysis which only extracts

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linear features, a multi-layer deep belief network (DBN) is designed to extract the nonlinear features

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for better description of the important trends in a combustion process. With the DBN-based multi-level

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representation of the CCD flame images, more useful information about the physical properties of a

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flame can be characterized. Sequentially, in a supervised fine-tuning stage, two DBN-based regression

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models are simply constructed to obtain the nonlinear relationship between the flame images and the

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outlet oxygen content. The advantages of the proposed deep learning-based analyzing and modeling

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method are demonstrated via on-site tests in a real combustion system.

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Key words: combustion system; deep belief network; deep learning; feature extraction; oxygen content;

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flame images

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1. Introduction

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In many industrial processes, the furnace is essential fuel-fired equipment converting the chemical

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energy into the thermal energy by combustion. A mixture of fuel and air is often required for

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combustion. However, it would cause the fuel-inefficient or pollution problems when the air content in

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the furnace is not at its optimal condition. Additionally, the use of fuel blends and low-quality fuels

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may exacerbate the severity of the pollution emissions and flame instability. In recent years, extensive

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kinetics and experimental research has been conducted [1-4]. Nevertheless, the key quality variables

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(e.g., the outlet O2 content) in combustion are difficult to measure online. Although hardware analyzers

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are often used in industrial processes, they have some disadvantages. For example, both the purchase

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and maintenance costs of the extractive oxygen gas analyzers are relatively high. Additionally, the right

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time to maintain those analyzers is not exactly known. Furthermore, the measurement delay is not

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conducive to online monitoring and control of combustion processes. To achieve better performance in

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the combustor, it is important to construct an accurate model with the capability of providing reliable

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quality prediction (e.g., the outlet O2 content) in combustion.

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Conventionally, the process performance of a combustion system is monitored by experienced

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operators. However, the poor working environment makes the operators difficult to accurately quantify

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the combustion performance [5]. The main index for measuring and monitoring combustion is the

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temperature [6]. One main shortcoming of the conventional temperature measurement equipment (e.g.,

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thermocouples) is that the flame measurement area is limited. Only the temperature at one point rather

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than the temperature distribution of the flame is provided. To prevent accidents, several flame detectors

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have been applied to combustion systems [7]. Nevertheless, there are some problems in those flame

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detectors. It is not easy to configure the flame detector for accurate detection when it is installed. For

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example, infrared or ultraviolet detectors do not provide enough measurements of the flame mainly

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because only single-point measurements are available. In such a situation, the temperature distributions

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of the flame may not be provided accurately [7, 8]. On the other hand, laser and optical-fiber based

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detectors, despite of their advantages in quantitative measurements, are too expensive and complicated

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to be deployed in industrial furnaces [9-11].

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With the advancement of digital image processing, the online continuous observation of the flame

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has become cost-effective [11]. Only using traditional CCD (charge-coupled device) cameras and

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flame-grabbers, flame images can be directly obtained. That is, the flame images are received by a

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color CCD camera and digitized using the frame grabber. The temperature distribution visualization of

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the flame in a gasifier was proposed by Yan et al. [12]. Draper et al. proposed an image-based method

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to obtain the total emissivity and the coal flame temperature [13]. Gonzalez-Cencerrado et al. utilized

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the flame visualization and image processing to characterize a combustion state [14, 15].

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Nowadays, with lots of image data, research on the image analysis for various process applications is

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increasingly important [16-27]. The characteristics of flames provide important information of its

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measurement quality in the combustion performance [8]. The flames in different burning conditions

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can be characterized by color models [25]. Because of low costs and simplicity, more CCD-based

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approaches rather than laser-based methods have been used to describe the flame temperature

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distribution. As a classical multivariate statistical method, principal component analysis (PCA) can

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extract a set of principal components to capture the main variations of the multivariate process data

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[18]. With the images analyzed by the PCA method in the normal operating process, online monitoring 3


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and control strategies are designed to improve the performance of combustion processes [10, 26, 27].

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However, PCA and most of the image analysis methods can process multivariate process data only in

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their raw forms [28]. That is to say, a representation at a more abstract level is necessary for better

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image analysis.

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One of the novel deep learning techniques can construct a data-driven model with a multi-layer

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architecture to represent the input data with multiple levels of abstraction [28-30]. With its remarkable

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representation ability, deep learning has obtained increasing attention in speech recognition, drug

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discovery, and many other applications [28-34]. A recent review of deep learning can be found in [27].

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More recently, deep learning was applied to data-driven chemical process modeling fields [35, 36].

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However, to our best knowledge, deep learning has rarely been applied to combustion processes. This

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paper is the first-ever attempt to develop a deep learning-based soft sensor system for online quality

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prediction of the combustion process. Unlike the traditional PCA only extracting linear features, the

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nonlinear features can be extracted by a multi-layer deep belief network (DBN) [28-30]. A large

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volume of data is embedded in each digital flame image in the form of pixel values. The key and

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interesting aspect of deep learning is that the important features can be extracted from the data through

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a general learning procedure [28]. Sequentially, using a supervised fine-tuning stage, a DBN-based

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regression model can be simply constructed to obtain the nonlinear relationship between the extracted

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features and the oxygen content.

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The remainder of this work is organized into the following 4 sections. The combustion system is first

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described in Section 2. In Section 3, the deep learning method for analyzing and modeling of flame

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images is presented. Additionally, detailed implementations of the multi-layer DBN-based soft sensors

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are made in this section. The proposed method is evaluated using a real combustion system in Section 4.

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The comparison study between traditional soft sensor approaches and the proposed method is also

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investigated. Finally, a brief conclusion and the future research direction are included in Section 5.

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2. Description of Combustion Systems

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In industrial combustion systems, the combustion efficiency can be found by measuring the

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conversion effectiveness of fuel to heat. To reduce the operating cost and satisfy the requirements of 4


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environmental regulations, the combustion efficiency and emission content should be controlled at a

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suitable level. Measuring the oxygen and NOx contents in the exhaust gas by gas analyzers can be

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delayed, though. In such a situation, the oxygen content-based feedback controller tends to

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overcompensate [26, 27]. As an alternative, the online-measured flame images can provide sufficient

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information to reflect the current burning status. Therefore, monitoring and control strategies using

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flame images have attracted more attention recently [8, 10, 11, 26, 27]. In this study, real data from the

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pilot-scale combustion furnace are used to demonstrate the advantages of the proposed deep

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learning-based analyzing and modeling method.

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The experimental combustion system (2.58 × 2.47 × 1.5 m) is shown in Fig. 1. The furnace wall was

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covered by ceramic fiber cotton for the purpose of fire resistance. The industrial heavy oil is used as

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fuel to heat up the combustion system (North American, Type: 5514-6, with the maximum heat of

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451,000 kcal/h). The fuel flow can be tuned. The combustion air is fed using the fan with direct-drive

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variable frequency. And the maximum load of the air flow is 990 m3/h. The O2, CO, and NOx contents

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of emission gases are recorded by a gas analyzer. All the process variables, including the furnace

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temperature, the furnace pressure, the fuel flow rate, the air flow rate, and the flue gas information, are

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measured by a SCADA system automatically.

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(Fig. 1 goes here.)

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The flame images in the furnace are obtained using a digital color camera. To maintain the image

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quality, the CCD camera with cooling equipment can be protected against damage caused by the high

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temperature. Additionally, the front of the camera is linked with a set of optical filters to prevent color

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saturation in the camera. The collected signals are sent to a computer via an IEEE-1394a interface. In

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the experiments, each flame image has 658 × 492 pixels and a resolution of 24 bits per pixel. The

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images are collected at one frame per 5s.

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3. Deep Learning for Analyzing and Modeling Flame Images

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3.1. Description of deep learning-based modeling framework

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Deep learning methods have been applied to explore and analyze intricate structures in 5


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high-dimensional data (e.g., image and natural language). Interestingly, unlike traditional machine

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learning methods, unsupervised and supervised learning are properly integrated into a framework,

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yielding a semi-supervised model [28-30]. When deep learning is applied to regression problems, using

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the extracted features in the unsupervised learning stage, a regression model is established in the

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supervised learning stage.

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As illustrated cases, five flame images of the combustion with different oxygen contents are shown

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in Fig. 2. The flame images have some inherent relationships with oxygen contents. For example, a

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general decreasing trend can be obtained by manually observing the flame images. Additionally, several

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areas in the flame images contain only useless information or noise, such as the black background of

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the furnace and the gas pipeline. However, just through human experience, getting the quantitative

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relationship between the oxygen contents and the observed flame images is difficult. In practice,

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important features are more attractive to be learnt from images automatically rather than being

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designed by engineers in a cumbersome manner.

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(Fig. 2 goes here.)

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Therefore, for the online prediction of the oxygen content, the deep learning method is used to

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directly construct a soft sensor system upon the flame images. The main modeling framework is shown

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in Fig. 3. There are two main learning stages with their detailed algorithms formulated in Section 2.2

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and Section 2.3, respectively. In the first unsupervised learning stage, the characteristics of the flame

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images X can be extracted through a DBN-based multi-level network. That is to say, flame images can

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be represented using the extracted features Φ. Sequentially, the DBN-based regression model can be

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constructed in the second supervised learning stage. The extracted features Φ are the input vectors and

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the oxygen contents Y are the output vectors.

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(Fig. 3 goes here.)

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3.2. Stage 1: Training restricted Boltzmann machine structure 6


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In this sub-section, the DBN structure and its advantages are described. DBN is a multi-layer

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structure built up by a series of individual restricted Boltzmann machine (RBM) [29, 30]. The RBM

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can be viewed as a nonlinear feature extraction that can be used to reduce the data dimensions. The

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main modeling procedures of a DBN hierarchically constructed with L RBM layers are shown in Fig. 4.

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The number of hidden layers of DBN is usually defined as L. And the input layer is defined as 0. The

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first RBM structure RBM1 initialized by the stochastic parameters θ1 = {W1, b1, c1} is composed of the

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visible layer v1 and the hidden layer h1 . It should be noticed that the flame images X are the visible

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layer v1 . After RBM1 has been trained, let v 2 = h1 and the second RBM layer RBM2 can be trained in

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the same manner. For training the layer RBMl+1, the visual layer of RBMl+1 (i.e., vl +1 ) can be initially

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defined as the output variables of the hidden layer of RBMl (i.e., hl ), i.e., vl +1 = hl [30].

11

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(Fig. 4 goes here.)

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There are two layers in an RBM structure, namely the visible layer v corresponding to the

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components of the observations and the hidden variables h representing the outputs of RBM,

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respectively. The energy function of RBM is established, indicating the energy level of the structure in

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the current condition.

18 Energy ( v, h ) = −b T v − cT h − h T Wv

(1)

19 20

where v ∈ R n×1 and h ∈ R m×1 are both the vectors of the binary values (0 or 1), and θ = {W , b , c}

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denote the parameters of the energy function. The probability distribution of the visual layer P ( v ) is

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formulated as follows [32]:

23 P (v) = =

∑ h exp  − Energy ( v, h )  Z ∑ h exp  − Energy ( v , h ) 

∑ v ∑ h exp  − Energy ( v , h ) 

24 7


(2)

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where Z denotes the partition function given by summing over all the possible pairs of visible and

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hidden vectors [32]. The nodes (i.e., neural units) are independent of others on the same layer. And

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each node is connected to other layers fully.

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For determination of an RBM structure, only the visible layer v is at hand and the hidden layer h to

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be estimated. Therefore, it is reasonable to set the training objective of RBM as the maximized P ( v ) ,

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which is the probability model of the input data. Maximize the likelihood by minimizing the distance

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between the distribution of the input variables and the distribution of the visible variables. Using Eq.

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(2), the log-likelihood function of the total visible variables log L ( θ ) is established as:

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{

log L ( θ ) = ∑ v log P ( v ) = ∑ v log ∑ h exp  − Energy ( v, h )  − log Z

}

(3)

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Optimization is typically performed by the gradient descent method. As an effective solution to

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computing the gradient, the contrastive divergence algorithm is adopted [30-34]. The parameters of

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RBM are continuously updated by the gradient descent method until the convergence is reached. The

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detailed algorithmic implementations for obtaining the RBM structure with its parameters

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θ = {W , b , c} can be found in [31, 32].

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After this training stage, the weights in DBN can be obtained by sequential construction of several

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RBMs. The DBN training process is totally unsupervised as no target variable is involved. Through the

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way of feature extraction layer by layer, the flame images are mapped onto different dimensions.

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Consequently, with the DBN-based multi-level representation of the CCD flame images, useful

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information related to the physical properties of a flame can be characterized.

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To handle RGB (red, green and blue channels) color flame images, the main DBN-based feature

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extraction procedure is proposed and shown in Fig. 5. There are K color flame images, each with a size

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of N1×N2. They are arranged into three dimensional arrays with the size (K, N1 ×N2, 3) according to

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their colors (red, green, and blue). Accordingly, the flame images X can be denoted as XR, XG, and XB,

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respectively. For each color channel, a sub-DBN structure is first established. They are denoted as 8


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DBNR, DBNG, DBNB, respectively. On top of them, a whole DBN feature representation based on the

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features from three bottom sub-DBNs are stacked.

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When the three-channel data directly converted into a big vector are applied to DBN, there are two

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disadvantages compared with DBN trained with the three color channels separately. First, training a

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DBN-based feature extraction model for a color channel is more efficient mainly because the network

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weights are greatly reduced. Second, directly using a big vector of three-channel data may lead to an

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over-fitting problem because different color channels of data are mixing. Consequently, the proposed

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modeling structure in Fig. 5 can absorb the information in the color images efficiently.

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(Fig. 5 goes here.)

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3.3. Stage 2: Fine-tuning a regression model

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As aforementioned, a multi-layer DBN structure has been constructed by a series of RBMs. Every

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hidden layer in the unsupervised DBN model describes the underlying characteristics of the flame

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images. However, the oxygen content is still not utilized, so it is irrelevant to the DBN model so far. In

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this sub-section, supervised learning methods are adopted to adjust the weights of the whole deep

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learning network. As a result, the DBN-based extracted features can be connected to the oxygen

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contents in an interpretable way.

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In a supervised learning manner, using the flame images and corresponding oxygen contents, two

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DBN-based regression models are constructed. One regression model connected to the DBN structure

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is the traditional neural network trained by the well-known back-propagation (BP) algorithm [37]. This

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soft sensor model is simply denoted as DBN-BP. The other regression model connected to the DBN

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structure is the popular support vector regression(SVR) in the past few years [38, 39]. Similarly, the

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soft sensor model is simply denoted as DBN-SVR. Generally, current regression models can be simply

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connected to DBN to form a deep learning network-based prediction model.

27 28 29

In summary, for both of the proposed DBN-BP and DBN-SVR methods, there are two main analyzing and modeling stages for the flame images in a combustion process.

30 9


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Stage 1: Pre-train the DBN structure to extract the features of the flame images by stacking a series of RBMs in a successive manner. Stage2: Train the deep learning network-based soft sensor models with flame images and corresponding oxygen contents in a supervised fine-tuning stage.

5 6

The entire training procedure can be implemented in a straightforward way. Moreover, with a

7

semi-supervised learning method, the oxygen contents can be predicted by the extracted features in the

8

DBN structure. This property makes the proposed DBN-BP and DBN-SVR soft sensors more suitable

9

to combustion processes.

10 11

4. Application Results and Discussion

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A set of 9,000 data points are collected from the experiments in the Industrial Technology Research

13

Institute of Taiwan. This data set includes both of the flame images (X) and the measured oxygen

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contents (Y) collected from the furnace. With a simple random sampling method, the whole data set is

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separated into two parts, including a training set with 6,500 samples, and a testing set with 2,500

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samples. As aforementioned, the proposed modeling method includes two main stages of the feature

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extraction stage in Section 4.1 and the quality prediction stage in Section 4.2, respectively.

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4.1. Feature extraction results and discussion

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Using the data of the flame images, the DBN model can be trained to make its random weight

21

convergence. Then, the features of the flame images in the training set can be extracted by the trained

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DBN model. These extracted features can be considered as the low dimensional expression of flame

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images. They cover important information of the image while eliminating some troublesome outliers

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and noise. As a result, the flame images can be reconstructed using the extracted features.

25 26

As an evaluation index for different feature extraction methods, the error between the reconstructed

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images and the original images, namely the reconstruction error for every pixel, can be defined as

28

follows [34].

29 ei ,rec = xi − xi ,rec 10


(4)

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where xi and xi ,rec are the ith pixel of the original flame images and the reconstruction images using

3

the DBN method, respectively. A probabilistic interpretation of the reconstruction error is simply as a

4

particular form of the energy function. Generally, this means that examples with low reconstruction

5

errors have higher probability according to the model [34].

6 7 8

Additionally, the following reconstruction rate (RR) in Eq.(5) can describe how much information in an original color image is still contained in the reconstructed color image.

9  3 N1 N2 xi ,rec ∑ 1−  i =1 xi RR =  1 −  3 N1 N 2   

   × 100%    

(5)

10 11

where 3N1 N2 denotes the number of pixels of a color flame image (as shown in Fig. 5).

12 13

The detailed frequency histograms of the information in the reconstructed images using DBN for

14

both of the training and the testing sets are shown in Fig. 6. Most of the RR values of the images are in

15

the range of [0.97, 0.99]. For the testing set, an average of RR = 98.25% of the original image

16

information is restored using the DBN model. These results indicate that the good reconstruction

17

performance can be obtained using the DBN-based feature extraction method.

18

19

(Fig. 6 goes here.)

20 21

In additional to the general results abovementioned, the reconstruction effects using the DBN

22

method are illustrated in Fig. 7. In this figure, the original image, the reconstructed image, and the

23

reconstruction error for both the training sample and the testing sample are shown. It can be indicated

24

that the reconstructed image is smoother than its original one for both the training and testing samples.

25

In a typical combustion process, the flame is produced from the mixture of fuel and air. It has three

26

main regions, including the inner regions, the outer regions, and the middle regions. As shown in Figs. 11


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7(b) and 7(e), the outer region of the flame is difficult to characterize because of their violent and

2

unstable states. By removing the irregular features, the outer regions in the reconstructed images are

3

relatively smooth as shown in Figs. 7(a) and 7(d). The middle regions of the flame can be distinguished

4

from another part of the flame in a relatively simple way mainly because of their consistency in the

5

combustion process. Figs. 7(c) and 7(f) represent the reconstruction error of the corresponding flame

6

images, and the lighter color areas mean the smaller reconstruction error. It is shown that the light blue

7

regions of the outer flame denoting the reconstruction errors are a little large. Additionally, there is a

8

little large reconstruction error in the innermost regions. In summary, the DBN method can extract

9

main characteristics of the flame images in the combustion process.

10

11

(Fig. 7 goes here.)

12 13

4.2. Oxygen content prediction results and discussion

14

As aforementioned, two regression models for the oxygen content prediction in the combustion

15

systems are built directly using the features extracted by the DBN model. They are denoted as DBN-BP

16

and DBN-SVR, respectively. For comparison, two traditional regression models named PCA-SVR and

17

PCA-SVR are used for the oxygen content prediction. These regression models can be trained using the

18

common cross-validation method. Three evaluated indices for the prediction performance, including

19

the root mean square error (RMSE), relative RMSE (denoted as RE simply), and the maximal absolute

20

error (MAE), are given below respectively.

21 Ntst

∑ ( yˆ − y )

RMSE =

i

i

2

N tst

(6)

i =1

RE =

 yˆ i − yi   yi  i =1 

N tst

∑

2

N tst

MAE = max yˆi − yi , for i = 1,L, N tst

(7)

(8)

22

where yˆi is the prediction value of yi, i.e., the oxygen content in the combustion systems. And N tst

23

denotes the number of testing samples.

24 12


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Energy & Fuels

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To illustrate the nonlinear feature extraction results of DBN in a clear way, the two-dimensional

2

codes are shown in Fig. 8(a). Their connections with the oxygen contents, distinguished by different

3

colors, are also plotted in Fig. 8. For comparison, the PCA-based linear feature extraction results with

4

two main important components are shown in Fig. 8(b). The reconstructed information seems almost

5

the same as DBN according to the RR index in Eq. (5). Actually, it clearly indicates that the codes from

6

DBN can produce better visualization for the oxygen content prediction than the scores using the two

7

main components of PCA. Especially for most of the oxygen contents in the range of [4.5, 6.5], the

8

traditional two-dimensional features using PCA may not be easily identified and distinguished.

9

Interestingly, the DBN-based feature extraction can generate a distinct distribution to better capture the

10

main characteristics of the oxygen content prediction in the combustion systems.

11

12

(Fig. 8 goes here.)

13 14

The overall comparison results among DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for

15

the prediction of the oxygen content are shown in Fig. 9. Both DBN-BP and DBN-SVR methods

16

exhibit a better prediction performance than the conventional PCA-based regression models. Especially,

17

the prediction results of the oxygen contents in the range of [4.5, 6.5] are clearly shown in Fig. 10. The

18

PCA-BP and PCA-SVR methods cannot achieve good prediction for these contents mainly because the

19

features are not suitably extracted (Fig. 8(b)). Additionally, as shown in Fig. 11, the frequency

20

histograms of the prediction errors show that the DBN-based methods are superior to the PCA-based

21

methods. Moreover, the online prediction results of these four methods are compared and listed in

22

Table1. All the evaluation indices in Table 1 show that DBN-based soft sensors are more accurate than

23

the other two approaches. The RE index of DBN-BP is only 5.543 %, which is much smaller than

24

9.907 % of PCA-BP. The main reason is that the prediction results of the oxygen contents in the range

25

of [1, 2] using DBN-BP are more accurate than using PCA-BP. Therefore, from all the obtained results,

26

the proposed DBN-based analyzing and modeling methods exhibit more accurate prediction results

27

than the traditional PCA-based methods in terms of the online prediction of the oxygen content in an

28

industrial combustion system.

29

30

(Fig. 9 is about here.) 13


Energy & Fuels

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

(Fig. 10 is about here.)

2

(Fig. 11 is about here.)

3

(Table 1 is about here.)

4 5

5. Conclusion

6

This work addresses the development of accurate quality prediction models for complicated

7

combustion systems. Using flame images directly, a deep learning method is used to extract the

8

important features and then construct a regression model to predict the oxygen content online. The

9

proposed method has two main advantages. First, compared with the traditional linear feature

10

extraction approaches (e.g., PCA), the DBN method can extract the nonlinear features of flame images.

11

Second, with a deep network structure, the information from images can be better acquired in the DBN

12

model. Consequently, more informative features can be dugout in an efficient way. These two

13

properties make the proposed DBN method more suitable for the description of nonlinear processes.

14

Moreover, a regression model can be directly jointed with the features for online prediction of the

15

oxygen content. Through the experimental results, the proposed method is shown to be superior to the

16

traditional methods in terms of image analysis and quality prediction of combustion processes.

17 18

In the current work, the data of 2D flame images are collected. In such a situation, new models need

19

to be developed with the position change between the camera and the flame. The extension work with

20

three-dimensional (3D) spatial image data will be further discussed in the future. Additionally, it would

21

be also interesting to develop advanced monitoring and control strategies using deep learning for

22

combustion processes.

23 24

Acknowledgment

25

The authors would like to gratefully acknowledge Ministry of Science and Technology, R.O.C. (MOST

26

103-2221-E-033-068-MY3) and National Natural Science Foundation of China (Grant No. 61640312)

27

for the financial support. Also, they would like to thank Industrial Technology Research Institute of

28

Taiwan for providing the industrial data.

29 14


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1

Abbreviations

2

BP = back propagation

3

DBN = deep belief network

4

DBN-BP = deep belief network-back propagation

5

DBN-SVR = deep belief network-support vector regression

6

MAE = maximal absolute error

7

PCA = principal component analysis

8

PCA-BP = principal component analysis-back propagation

9

PCA-SVR = principal component analysis-support vector regression

10

RE = relative root-mean-square error

11

RMSE = root-mean-square error

12

RR = reconstruction rate

13

SVR = support vector regression

14 15

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1

Figure Captions

2

Fig. 1. Scheme of the experimental combustion system

3

Fig. 2. Original flame images with their corresponding oxygen contents in a descending order

4

Fig. 3. The main deep learning-based analyzing and modeling framework for online prediction of the

5

oxygen content directly using the flame images in combustion systems

6

Fig. 4. The main training procedures of a multi-level DBN structure by stacking a series of RBMs

7

successively

8

Fig. 5. The DBN-based analyzing the flowchart for the three channels of the color flame images

9

Fig. 6. The frequency histogram of the information in the reconstructed images using DBN for the

10

training and testing sets

11

Fig. 7. In the training set: (a) a reconstructed image using DBN, (b) the original image, and (c) the

12

reconstruction error. In the testing set: (d) a reconstructed image using DBN, (e) the original image, and

13

(f) the reconstruction error.

14

Fig. 8. Comparisons between DBN and PCA-based feature extraction methods: (a) The two codes

15

generated by a DBN model. (b) The scores produced by PCA using the first two important components

16

Fig. 9. Comparison of DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for prediction of the

17

oxygen content in an industrial furnace

18

Fig. 10. Comparison among DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for the prediction

19

of the oxygen contents (in the range of 4.5 ~ 6.5) in an industrial furnace

20

Fig. 11. The frequency histogram of the prediction errors of the oxygen content in an industrial furnace

21

using DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods

22 23

Table Captions

24

Table 1 Comparisons of DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for the prediction of

25

the oxygen content for the testing set.

26

19


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1 2

Fig. 1. Scheme of the experimental combustion system

3 4

20


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7.18 %

1 2 3

6.30 %

5.28 %

4.02 %

1.93 %

Fig. 2. Original flame images with their corresponding oxygen contents in a descending order

4 5

21


Energy & Fuels

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1 2 3

Φ

4 5

Fig. 3. The main deep learning-based analyzing and modeling framework for online prediction of the

6

oxygen content directly using the flame images in combustion systems

7 8

22


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Energy & Fuels

1 2 3

4 5

Fig. 4. The main training procedures of a multi-level DBN structure by stacking a series of RBMs

6

successively

7 8

23


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1 2 3

DBN-based feature representation

hRGB vRGB DBNR

Image K

Image 2

hR

hG

hB

vR

vG

vB

B G R

R

G

B

K

B G R

R

G

B

2

B G R

Image 1 N1

X

XG

XR

R 1

N2

G N1N2

1

XB

B N1N2

1

1 N1N2

Images unfolded to three channels N1 & N2: Size of images K: Number of images

4 5

DBNB

DBNG

Fig. 5. The DBN-based analyzing the flowchart for the three channels of the color flame images

6 7

24


Page 25 of 31

1 2

0.40 0.35

Train Set Test Set

0.30

Relative Frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.25 0.20 0.15 0.10 0.05 0.00 0.965

0.970

0.975

0.980

0.985

0.990

0.995

Information of Reconstruction Image

3 4

Fig. 6. The frequency histogram of the information in the reconstructed images using DBN for the

5

training and testing sets

6 7

25


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1 0. 8 0. 6 0. 4 0. 2

1 2

0

(a)

(b)

(c) 1 0. 8 0. 6 0. 4 0. 2

3 4

0

(d)

(e)

(f)

5

Fig. 7. In the training set: (a) a reconstructed image using DBN, (b) the original image, and (c) the

6

reconstruction error. In the testing set: (d) a reconstructed image using DBN, (e) the original image, and

7

(f) the reconstruction error.

8 9

26


Page 27 of 31

1 2

1.5

3 7

7

2

6.5

6

5

Score 2

5.5 0

6

1 Oxygen Content

0.5

6.5

5.5 0 5

-0.5

-1 4.5

-1

4.5

-2

4

4

3.5 -1.5 -2.5

Oxygen Content

1

Code 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

-2

-1.5

-1

-0.5 Code 1

0

0.5

1

3.5 -3 -3

1.5

-2

-1

0 Score 1

1

2

3

3 4

Fig. 8. Comparisons between DBN and PCA-based feature extraction methods: (a) the two codes

5

generated by a DBN model; (b) the scores produced by PCA using the first two important components

6 7

27


Energy & Fuels

1 2

8 PCA-SVR PCA-BP DBN-SVR DBN-BP real data

7

6

5 Oxygen Content

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

3

2

1

0

0

500

1000

1500

2000

2500

Sample Number

3 4

Fig. 9. Comparison of DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for the prediction of the

5

oxygen content in an industrial furnace

6 7

28


Page 29 of 31

1 2

PCA-SVR PCA-BP DBN-SVR DBN-BP real data

6.5

6

Oxygen Content

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

5.5

5

4.5

4

3.5

700

800

900

1000 Sample Number

1100

1200

3 4

Fig. 10. Comparison of DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for the prediction of

5

the oxygen contents (in the range of 4.5 ~ 6.5) in an industrial furnace

6 7

29


Energy & Fuels

1 2

0.5

Frequency Counts of DBN-BP Frequency Counts of DBN-SVR Frequency Counts of PCA-BP Frequency Counts of PCA-SVR

0.4

Relative Frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 31

0.3

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Error

3 4

Fig. 11. The frequency histogram of the prediction absolute errors of the oxygen content in an

5

industrial furnace using DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods

6 7

30


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Energy & Fuels

1 2 3

Table 1 Comparisons of DBN-BP, DBN-SVR, PCA-BP and PCA-SVR methods for the prediction of

4

the oxygen content for the testing set. Method

RMSE

RE (%)

MAE

DBN-BP (proposed)

0.139

5.543

0.606

PCA-BP

0.246

9.907

1.094

DBN-SVR (proposed)

0.157

6.655

0.703

PCA-SVR

0.267

11.50

1.319

5 6 7 8 9 10

31


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