Combustion stability monitoring through flame imaging and stacked sparse autoencoder based deep neural network

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Combustion stability monitoring through flame imaging and stacked sparse autoencoder based deep neural network Zhezhe Hana, Md. Moinul Hossainb, Yuwei Wangc, Jian Lia, Chuanlong Xua,

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a

Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China School of Engineering and Digital Arts, University of Kent, Canterbury, Kent CT2 7NT, UK c China Energy Jianbi Power Plant, Zhenjiang 212006, China b

H I GH L IG H T S

novel deep learning model is established for predicting combustion stability. • AAutomatic of combustion stability label is achieved. • Quantitativegeneration evaluation of combustion stability are presented. • Generalizationandandqualitative robustness of the model are verified. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Combustion stability Flame imaging Stacked sparse autoencoder Innovative loss function Gaussian mixture model

Combustion instability is a well-known problem in the combustion processes and closely linked to lower combustion efficiency and higher pollutant emissions. Therefore, it is important to monitor combustion stability for optimizing efficiency and maintaining furnace safety. However, it is difficult to establish a robust monitoring model with high precision through traditional data-driven methods, where prior knowledge of labeled data is required. This study proposes a novel approach for combustion stability monitoring through stacked sparse autoencoder based deep neural network. The proposed stacked sparse autoencoder is firstly utilized to extract flame representative features from the unlabeled images, and an improved loss function is used to enhance the training efficiency. The extracted features are then used to identify the classification label and stability index through clustering and statistical analysis. Classification and regression models incorporating the stacked sparse autoencoder are established for the qualitative and quantitative characterization of combustion stability. Experiments were carried out on a gas combustor to establish and evaluate the proposed models. It has been found that the classification model provides an F1-score of 0.99, whilst the R-squared of 0.98 is achieved through the regression model. Results obtained from the experiments demonstrated that the stacked sparse autoencoder model is capable of extracting flame representative features automatically without having manual interference. The results also show that the proposed model provides a higher prediction accuracy in comparison to the traditional data-driven methods and also demonstrates as a promising tool for monitoring the combustion stability accurately.

1. Introduction The phenomenon of combustion instability has been encountered in many combustion processes such as power plants [1], gas turbines [2], rocket motors [3] and other industrial areas (steel, cement and food production). Unstable combustion conditions can result in issues such as furnace vibration, high pollutant emission, lower efficiency, and nonuniform thermal distribution, etc. [4]. Furthermore, the operation of

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power plants must be flexible in order to accommodate the intermittency of increasing levels of renewable generation and fluctuating demand. Also, variability in fuels, including a wide range of biomass, biofuels and even low ranking coals creates frequent transients that impose risks and challenges for emission control in the power generation sector. For modern power generation, it is crucial to improve energy conversion efficiency as well as to reduce pollutant emissions such as NOx and SO2 [5]. The problem of combustion instability becomes

Corresponding author. E-mail address: [email protected] (C. Xu).

https://doi.org/10.1016/j.apenergy.2019.114159 Received 5 August 2019; Received in revised form 18 October 2019; Accepted 12 November 2019 0306-2619/ © 2019 Published by Elsevier Ltd.

Please cite this article as: Zhezhe Han, et al., Applied Energy, https://doi.org/10.1016/j.apenergy.2019.114159

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Nomenclature

h3 h6 Ci c×c s r×r t pj Ppenalty LSparse Lt p wi Y

Abbreviations AE autoencoder BN batch normalization BP back-propagation CNN convolutional neural network DBN deep belief network DNN deep neural network EM expectation-maximization GMM Gaussian mixture model ML maximum-likelihood MSE mean square error MSSIM mean structural similarity PCA principal component analysis PCA-BP principal component analysis-back-propagation PCA-SVM principal component analysis-support vector machine PCA-SVR principal component analysis-support vector regression PSNR peak signal-to-noise ratio ReLU rectified linear unit SPE squared prediction error SVM support vector machine SVR support vector regression SSAE stacked sparse autoencoder SSAE-BP stacked sparse autoencoder-back-propagation SSAE-SVM stacked sparse autoencoder-support vector machine SSAE-SVRstacked sparse autoencoder-support vector regression KL Kullback–Leibler

Greek letters

Symbols

X Xrec Xn

lower-level hidden features higher-level hidden features the i th convolution layer size of convolution filter the stride of convolution filter size of pooling kernel the stride of pooling kernel the j th activation of hidden neuron penalty term sparse penalty term loss function the traditional loss function of the first-level network probability, mixture density the i th Gaussian weighting value random D-dimensional vector

the input layer of the original image the reconstructed layer of the reconstructed image noisy image

φ ς γ γik, j

corruption ratio normal distribution random variable hidden neuron the location (i, j ) value in the k th feature map of inputs

δik, j η ξ μ θ ψ αih ̂ θML ψ S (·) ϖi Φ(·) σ

the location (i, j ) value in the k th feature map of outputs sparse rate maximum number of grayscale values in the image expectation Gaussian mixture models number of mixture components mixture weights maximum likelihood estimation combustion stability index the activation function in the back-propagation network weight values in the back-propagation network mapping function in the support vector machine width parameter of the Gaussian kernel

Various models have been developed for monitoring the combustion stability, and flame imaging and soft-computing techniques are considered to be a promising technical approach. Lu et al. [13] developed an imaging-based multifunctional system that is capable of providing an instantaneous and quantitative measurement of the combustion process. It has been suggested that a range of flame parameters such as geometric (size, shape, and location), luminous (brightness and nonuniformity) and thermodynamic (flicker and temperature) can be derived from flame images. Bai et al. [14] developed a multi-mode technique based on flame features (i.e., texture and color) for monitoring the combustion conditions. Chen et al. [15] applied principal component analysis (PCA) method to discover principal components or combinational variables of flame images that can be used to describe critical trends and variations in the combustion process. Although these works demonstrated the feasibility of flame imaging techniques for combustion process monitoring, the robustness of these methods is weak and unable to extract representative flame features from noisy images. As a result, the prediction reliability of these models is severely reduced. As a breakthrough in artificial intelligence (AI), deep learning-based techniques have attracted significant attention in the field of combustion monitoring [16,17]. Because deep learning-based techniques are able to extract discriminative features from raw data through multiple layers of nonlinear transformation automatically, they not only overcome the deficiency of inferior representational ability of the traditional shallow models (PCA and linear discriminant analysis) but also revokes the tedious feature extraction and selection process. Wang et al. [18] established a multi-layer convolutional neural network (CNN) to

severe due to the recent trend of using a wide range of biomass, biofuels and even low ranking coals. Therefore, the combustion process should be controlled to maintain the combustion states efficiently. Various techniques were developed and applied for monitoring the combustion states such as oxy-fuel combustion [6], partially premixed compression [7]. Significant studies were also carried out to investigate the behavior of combustion stability. For instance, Fichera et al. [8] studied the dynamic behavior of thermal-acoustic combustion instabilities through traditional linear and non-linear approaches in a methane-fuelled laboratory combustor. Li et al. [9] investigated the stability of a 1D thermos-acoustic system theoretically and numerically for predicting stability behaviors of a non-linear standing wave and characterized the dynamic interaction between a premixed flame and acoustic disturbances by using interaction index-delay H-τ model. Schuller et al. [10] proposed a mechanism of instability by measuring and analyzing the velocity fluctuations at the burner outlet, the pressure fluctuations inside the burner and the variations of the spontaneous light emission. However, the combustion stability is difficult to determine, as it is a broad perception largely related to the fuel-to-air ratio, ignition stability of fuel, and thermal-acoustic stability between heat release and acoustic oscillations [11]. Moreover, a better understanding of combustion instability is essential for the formulation of effective combustion control strategies. The effectiveness of these control strategies may be limited due to the delayed combustion stability monitoring results [12]. Therefore, the development of an accurate and intelligent monitoring model for combustion stability is desirable for an in-depth understanding of combustion processes and effective control strategies of the combustion process. 2

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operating conditions to establish and evaluate the model. A comparative study is further carried out between the proposed model and the traditional data-driven methods.

identify the combustion state and measure the heat release rate. This study demonstrated that the representative features are the proved key factor for obtaining satisfactory monitoring performance in terms of prediction accuracy in comparison to the basic deep neural network (DNN) with multiple fully connected layers. However, an obvious problem with the deep learning network is that a large number of labeled data are needed. In addition, the performance of the monitoring model mainly depends on the scale and quality of the labeled data [19]. In practice, it is difficult to obtain such a large amount of labeled data, which requires precise experimental settings and prior knowledge. An appropriate solution is to consider unsupervised learning models, such as the deep belief network (DBN) and autoencoder (AE) [20]. For instance, Akintayo et al. [21] employed an end-to-end convolutional selective autoencoder framework to detect the instability of a swirl-stabilized combustor through flame images. Qin et al. [22] proposed an unsupervised framework, which combines convolutional auto-encoder, PCA, and hidden Markov model to monitor the combustion condition by the uniformly spaced flame images. Although the unsupervised network can extract representative features from unlabeled images, a certain amount of labeled data is still needed to establish and validate the model. It can be seen that the requirement of a certain amount of labeled data is inevitable and needs to be prepared in advance to establish the model. A thorough review of the literature revealed that the quantitative monitoring of combustion stability has rarely been considered. The quantitative prediction is also an essential step in the combustion processes to improve the operation quality, and it can be used to make critical decisions for operational adjustment [23,24]. In this study, a novel stacked sparse autoencoder (SSAE) based deep neural model is proposed for qualitative and quantitative monitoring of combustion stability. The SSAE model is established to extract representative features of flame images. To improve the robustness of the feature extraction, a denoising coding technique is incorporated into the SSAE model. An improved loss function is also proposed to strengthen the training efficiency of the SSAE model. The classification label of the flame is generated through the combination of clustering (K-means and Gaussian mixture model) and statistical (Hotelling’s T 2 and squared prediction error) analysis. Furthermore, an approach is proposed based on clustering and image features to identify the combustion stability index, and their results are analyzed. Finally, classification and regression models are established based on the extracted flame features to determine the flame stability label. Experiments were carried out on an ethylene fired gas combustor under different

2. Methodology 2.1. Overall strategy Fig. 1 shows the technical strategy of the stacked sparse autoencoder based deep neural network for combustion stability monitoring. It mainly consists of two stages, i.e., stage 1: feature extraction and label generation, and stage 2: stability monitoring. The specific steps are as follows: Stage 1: Step 1: A high-speed camera (Phantom Miro M310) is used to acquire flame images under different combustion conditions. All acquired images are then resized to 256 (H) × 256 (V) and normalized by their maximum grayscale value. Step 2: A feature learning network (i.e., SSAE) is established with parameters initialization and trained. The trained SSAE is then used for image feature extraction and image reconstruction. Step 3: After that, all images are classified into two clusters based on clustering analysis through K-means and Gaussian mixture model (GMM) algorithms. It is noteworthy that the same cluster images belong to the same category of combustion stability. Step 4: Two classification labels (i.e., stable and unstable) are achieved according to T 2 and squared prediction error (SPE) statistical and clustering analysis. In this way, the classification label of each image is obtained. Step 5: The stability index of each image is calculated based on the clustering analysis and the image features. Stage 2: Step 1: Two classification models are established through backpropagation (BP) and support vector machine (SVM), denoted as SSAEBP and SSAE-SVM using the image features and statistical information obtained in Stage 1. The qualitative combustion stability label is then determined through these models. Step 2: In order to identify the quantitative stability index, two

Fig. 1. The technical strategy of the stacked sparse autoencoder based deep neural network for combustion stability monitoring. 3

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hidden feature vector h3 is transformed into the input variable to acquire h6 (higher-level hidden features). In the SSAE, the feature learning process follows a series of operations, such as denoising, convolution, batch normalization, activation, and pooling. An overview of these operations is described as follows: Denoising: In order to obtain the robust and representative learned features of the flame images, a denoising autoencoder learning algorithm is used by adding different noises with the input signals [25]. However, different types of corruption processes can be considered, such as Gaussian, salt-and-pepper, and mask noises. In this study, the white Gaussian noise is considered, for example, the corrupted version Xn is obtained with a fixed corruption ratio to the input X , as shown below:

regression models are further established through BP and support vector regression (SVR), denoted as SSAE-BP and SSAE-SVR using the image features and clustering information obtained in Stage 1. 2.2. Stage 1: Feature extraction and label generation A. Stacked sparse autoencoder (SSAE) The autoencoder (AE) is a symmetrical neural network that extracts the feature with a minimum reconstruction error. However, the AE is prone to gradient disappearance or gradient explosion during the training process due to its multiple hidden layer structure. To solve this issue, Hinton et al. [20] proposed a viewpoint, called ’pre-train’, which splits a complicated network into stacked sub-networks. The training failure can be avoided because the network parameters of each layer can be assigned specific values, rather than random initialization. Nonetheless, the stacked sub-networks provide lower training efficiency and generalization ability due to the simplicity of the single-hidden layer structure and the difficulty in parameter selection. It is difficult to deal diverse, massive and complex flame images collected under different combustion conditions for the single-hidden layer structure. In order to overcome the aforementioned limitations, the SSAE model is proposed based on two-level networks with five hidden layers in each network. The general architecture of the SSAE model is illustrated in Fig. 2. In the first-level network, the input layer X is mapped into a hidden layer h3 (called lower-level hidden features). Then, h3 is mapped back into the reconstructed layer, Xrec . In the second-level network, the

I Xn = IX + φς

(1)

where IX and I Xn denote the pixel intensity of the original image and noisy image, respectively; φ is the corruption ratio; ς is a normal distribution random variable within a range of −2.576 to 2.576 with the probability of 99%. Convolution: Convolution operation is a practical solution for feature extraction. Through a convolution layer, feature maps can be generated by sliding multiple filters over the complete input sequence. Each filter scans the input neurons with a fixed size and stride and produces a feature map that can be regarded as the input of the next convolutional layer. As shown in Fig. 2, Ci (R@c × c + s ) presents the i th convolution layer and it has R filters. Each filter scans the input neurons with a fixed size of c × c and a stride of s .

Fig. 2. The architecture of the proposed SSAE model. E: encoder; D: Decoder; C: Convolution; BN: batch normalization; ReLU: activation function; P: pooling; U: Upsampling. 4

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Batch normalization: The DNN training is complicated by the fact that the input distribution of each layer changes with the parameters of the previous layers. As a result, the training process can be slow due to a lower learning rate and careful consideration is required for parameter initialization. To address this problem, the output of each convolution layer is processed by a batch normalization (BN) technique. BN can effectively reduce the feature correlation and allow DNN to use a higher learning rate. It also provides a flexible option to initialize the parameters. In some cases, it also acts as regularize to eliminates dropout [26]. Activation function: A rectified linear unit (ReLU) is used as an activation function of the hidden neuronγ , which is defined as [27]:

KL (ptarget pj ) = ptarget log

ptarget pj

+ (1 − ptarget ) log

1 − ptarget 1 − pj

if ptarget = pj , KL (ptarget pj ) = 0 . Otherwise, the KL (ptarget pj ) increases monotonically as pj deviates from ptarget . B. Loss function The sparse penalty term is used as the loss function, which is expressed as: F

LSparse = ηPpenalty = η ∑ KL (ptarget pj )

(8)

j=1

y (γ ) = max (0, γ )

(2)

where η is the sparse rate. In addition, mean square error (MSE) and peak signal-to-noise ratio (PSNR) [31] are used as loss functions, where LMSE is expressed as:

The ReLU is an unsaturated piecewise linear function, which is faster than the saturated nonlinear function, such as Sigmoid and TanH. Notably, the Sigmoid function is used in the third decoder to ensure that the intensity range of the reconstructed layer Xrec is consistent with the input layer X , which is defined as:

1 y (γ ) = 1 + e−γ

LMSE =

Pooling and upsampling: The pooling operation is carried out to reduce the parameters of the network. In this study, P (r × r + t ) is the pooling layer that condenses the feature map by selecting a maximum value with a r × r transformation kernel and a step of t . The pooling operation is useful to improve the translation invariance, which is expressed as:

γik, j

LPSNR =

(4)

1 E

1 1 = 1 + PSNR 1 + 10log10

ξ2 LMSE

( )

LMSSIM = 1 − MSSIM (X , Xrec ) = 1 −

(10)

(11)

1 M

M

∑ SSIM (xj , xrec,j) j=1

(12)

where X and Xrec are the original and reconstructed images; x j and x rec, j are the image contents at the j th local window; M is the number of a local window in the image. The MSSIM ranges from 0 to 1 (0 means entirely dissimilar and 1 means precisely similar). Finally, the innovative loss function of the first-level network L1 is defined as:

(5)

i=1

(9)

i=1 j=1

Though MSE can quantify the absolute error between the result and the reference image, it cannot quantify the structural similarity completely. Structural similarity (SSIM) [32] is used to explore changes in image structure, including pixel inter-dependency as well as masking of contrast and pixel intensity. However, the SSIM is an overall similarity of paired images, and it cannot pay attention to their local content differences. Therefore, an extension of SSIM called mean SSIM (MSSIM) [33] is used to overcome this deficiency. The MSSIM is a rolling average of the SSIM, estimated from two images within a local window. In order to avoid undesirable “blocking” artefacts, a symmetric Gaussian weighting window [11 × 11] is used with a standard deviation of 1.5 and the function is defined as W = {wi i = 1, 2, ⋯M } , normalized to M unit sum (∑i = 1 wi = 1). The LMSSIM is defined as:

E

∑ sij

Z

Lt = LSparse + LMSE + LPSNR

where and represent the value of location (i, j ) in the k feature map of inputs and outputs. In the upsampling layer, a bilinear interpolation method [28] is used to achieve the expansion of the feature dimension, which can be regarded as the reversal of the pooling operation. Sparse penalty term: Although the reconstructed layer of the basic AE is able to restore the input layer correctly, it is possible that the network simply copies information from the input layer to the hidden layer. In this way, the extracted features may be redundant and insufficient for further utilization. To avoid this, the sparse penalty term is added in the SSAE model, which actually works on the hidden layer (h3 and h6 ) to control the number of “active” neurons. While the output of a neuron is close to 1, the neuron is considered as “active”, otherwise, it is “inactive”. In most cases, it is better to keep the neurons of the hidden layer “inactive” so that the learned features are of the constraint rather than simply repeating the input [26]. Assume sij (i ∈ (1, E ), j ∈ (1, F )) represents the activation of the hidden neuron j , where E represents the number of images in the training dataset and F represents the number of neurons in the hidden layer. Then the average activation of each hidden neuron j can be calculated by:

pj =

A

∑ ∑ (xrec,ij − xij )2

where ξ represents the maximum number of greyscales of the image (255 for an 8-bit monochrome image). Then, the traditional loss function of the first-level network Lt is defined as:

th

δik, j

1 AZ

where x ij and x rec, ij represent the location (i, j ) of the pixel intensity of the original and reconstructed image; A and Z are the image height and width. The loss function LPSNR is defined as:

(3)

δik, j = max 0 ≤ n ≤ p {γik∙ r + t, j ∙ r + t }

(7)

L1 = Lt + LMSSIM

where pj is expected to be close to zero, meaning that the neurons of the hidden layer are mostly “inactive”. A penalty term Ppenalty is supplemented to the loss function, which penalizes pj if it deviates significantly from the sparse target ptarget . The penalty term Ppenalty is defined as [29]:

(13)

Since the input of the second-level network is not real images, the image quality assessment metrics are not used in the loss function L2 . Then, L2 is defined as:

L2 = LSparse + LMSE

(14)

F

Ppenalty =

∑ KL (ptarget j=1

pj )

C. Clustering method

(6)

Two clustering methods, K-means and GMM, are used to classify the image features, respectively. The principle of the K-means is considered according to the distance from each point to the centroids. The

where KL (ptarget pj ) is the Kullback–Leibler divergence (KL divergence) [30], which acts as a sparsity constraint and can be calculated by: 5

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stability index ψ is derived based on the D -dimensional feature vector G = {gi i = 1, 2, ⋯D} and center vector of two clusters. The stability index ψ is defined as:

Euclidean distance [34] is used to calculate the distance and can be represented as: D

∑ (Θi − Γ)i 2

d (Θ, Γ) =

d=D

(15)

i=1

ψ=

where Θi and Γi are the i th value of two different D-dimensional vectors. Fig. 3 presents the detailed procedure of the K-means algorithm, whose iterations can be completed until the centroids unchanged. The GMM has an ability to smooth approximation for general probability density function by the weighted sum of multiple Gaussian functions. If a random vector v obeys Gaussian distribution, the probability p (v μ, ∑ ) can be calculated as:

p (v μ,

∑

)=

−1 1 exp ⎛− (v − μ)T ∑ (v − μ) ⎞ 2 ⎠ ⎝ 2π ∑

ψ

(16)

i=1

(Y μ , ∑ ) h i

(17)

where ψ is the number of mixture components; αih (i = 1, 2, ⋯, ψ , h = 1, 2, ⋯, H ) is the mixture weights, which satisfies the constraints of ψ ∑i = 1 αih = 1 and αih ≥ 0 . The mixture density is a weighted linear combination of ψ component uni-modal Gaussian density functions, h pih (Y μih , ∑i ) [35]. The log-likelihood function corresponding to the mixture density is: D d=1

D

ψ

∑ log ∑ αih ∙pih ⎛yd ⎜

d=1

i=1

⎝

μih ,

h

∑i

⎞ ⎟ ⎠

(18)

Then, the Maximum Likelihood (ML) estimation is also used:

̂ = argmax {logp (Y θh)} θML θ

(20)

As can be seen from Stage 1, the proposed SSAE model is established and trained by using a large number of unlabeled flame images. The trained SSAE model is then used to extract deep features of flame images. Subsequently, these extracted features are further analyzed by the clustering method to obtain the classification label and stability index of each image. However, feature analysis is a complicated and time-consuming process without generalizing ability. In view of this, an effective and simple process is required to solve this crucial issue. In Stage 2, a direct non-linear mapping between the image feature and the label is established to solve the above issue. Actually, it is essentially a classification and regression prediction problem in machine learning. In this stage, different classification and regression models are separately established based on the known label of flame images (results of feature analysis in Stage 1) to predict the combustion stability of unknown images and also to investigate the optimal model in terms of prediction accuracy. In order to achieve a more accurate prediction model, the labeled images are examined carefully to remove the mislabeled images. Two SSAE-based classification models are developed based on BP and SVM methods, denoted as SSAE-BP and SSAE-SVM. It is worth noting that BP and SVM are widely applied to perform classification and regression tasks of complicated non-linear systems [38]. In this study, the classification models are developed to evaluate the flame states such as stable or unstable, qualitatively. The output value of the model is either 0 or 1, where 0 indicates an unstable state and 1

h

i

logp (Y θh) = log ∏ p (yd θh) =

d=D

2.3. Stage 2: Models establishment for combustion stability monitoring

1

∑ αih ∙pih

d=D

∑d = 1 (gd − gdstable )2 + ∑d = 1 (gd − gdunstable )2

where gdstable represents the d th value in the center vector of the stable cluster, gdunstable represents the d th value in the center vector of the unstable cluster. The stability index can evaluate the stability of each image in a range of from 0 to 1, where 0 means extremely unstable and 1 means completely stable.

where μ is the expectation, ∑ is variance. The Gaussian mixture model is the weighted sum of K-component probability. For an H-class problem, there can be a set of GMMs {θ1, θ2⋯,θH } associated with H classes. For a D -dimensional vector Y = {yi i = 1, 2, ⋯D} , the mixture density for the h th model is defined as:

p (Y θh) =

∑d = 1 (gd − gdunstable )2

(19)

With the help of the Expectation-Maximization (EM) algorithm [36], the optimum parameters are obtained by iterations until the likelihood estimation converges. The detailed procedure of the GMM algorithm is shown in Fig. 4. D. T 2 and SPE statistics Although the image features are classified into two clusters by the clustering methods, it is still impossible to identify which cluster is stable and unstable. Also, different clustering methods provide different clustering results. Therefore, it is necessary to consider a multivariate statistical method to provide indicative information and recognition of clustering results. In this way, the accuracy of different clustering methods can be compared. The physical parameters such as geometric parameters (ignition point and ignition area) and luminous parameters (luminous region, brightness, non-uniformity, mean intensity, and flame area) are calculated from the reconstructed flame images. The detailed definition and determination of these parameters can be found in [13,23]. The Hotelling’s T 2 and SPE [37] values are calculated to identify the variations of the process data and above 95% confidence limit indicates that the combustion is regarded at an unstable state. Remarkably, the deep features generate the reconstructed image, so removing the noise from the original image is conducive to improve the accuracy of statistical analysis. E. Combustion stability index

Fig. 3. The procedure of the K-means algorithm.

In order to evaluate the combustion stability quantitatively, a 6

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established independently, the number of output neurons is set to 1 (k = 1). The classification label is used as the output target when creating the classification model. The stability index is used as the output target for the regression model. The error gradient descent algorithm is used to adjust appropriate weights between neurons, to minimize the mean square error between the network output value and the actual one, thus completing the BP network training. The trained BP can be directly used to predict the combustion state by feeding new image features. B. SVM and SVR The SVM is originated from a binary classification problem, which separates the classes with the largest gap (i.e., Maximum margin) between the borderline instances (called support vectors) [39]. Fig. 7 presents a geometrical view of the SVM. The training samples, such as the 16-dimensional SSAE features, are distributed into two classes, i.e., stable and unstable. Note that, the space formulated by SSAE features is a two-dimensional space to facilitate the visualization. SVM seeks an optimal hyperplane to separate the two classes, which is the maximum distance from the nearest training samples. The training samples that lie on the margin are called support vectors. Since samples are not entirely separable, so SVM allows some misclassifications to find the appropriate hyperplane. In the performance phase, test samples can be identified as one of the known classes by using trained SVM. For example, Fig. 7 presents an example of test samples that are classified into a stable state. For non-linearly separable data problems, SVM used kernels to transform the data from known space to a feature space where the data can be separated with a decision surface (known as hyperplane). Fig. 8 presents the geometrical view of kernels. It can be seen that the initial data is inseparable in input space (represented by 2-D space). The kernels transformed the data to feature space (represented by 3-D space) and separated by a hyperplane. Mathematically, the kernel is a function that accepts two arguments and applies a mapping to the arguments, and then returns the value of their dot product. Assuming that Oi and Oj are two data points, Φ(·) is a mapping function, L represents the kernel function and is given by:

Fig. 4. The procedure of the GMM algorithm.

indicates a stable state. Two SSAE-based regression models are also established based on the BP and SVR methods, named as SSAE-BP and SSAE-SVR. The regression models are used in this study to evaluate combustion stability quantitatively in a range of 0 to 1. When the output value is close to 1, the combustion state is extremely stable. A brief overview of the BP, SVM and SVR methods can be found below. A. BP neural network

L (Oi, Oj ) = Φ(Oi )T Φ(Oj )

The BP neural network is a feed-forward network, which consists of an input layer, one or more hidden layers and an output layer. Each layer comprises several nodes called neurons. Neurons of one layer are directly connected to the next layer by their weights. For example, inputs {x i i = 1, 2, ⋯, m} are fed to the network; the output y is a weighted sum of its inputs transformed by an activation function S (·) . The process can be formulated as follows;

In this study, the Gaussian radial basis functions (RBF) [40] is chosen as the kernel function, which is expressed:

Lrbf (Oi, Oj ) = exp ⎛⎜− ⎝

2σ 2

2

⎞⎟ ⎠

(23)

where σ is the width parameter of the Gaussian kernel. The SVM can be used for regression tasks, called SVR. In contrast to the SVM classification model, SVR seeks an optimal hyperplane for fitting all training samples, which is the minimum distance from the farthest training samples. Fig. 9 illustrates the schematic of the SVR. For non-linearly fitting data problems, kernel functions are used to map the feature space similar to the SVM, and then the regression is performed. Once the new images are obtained, their input features through the

i=m

⎛ ⎞ y = S ⎜ ∑ ϖi x i + b⎟ ⎝ i=1 ⎠

Oi − Oj

(22)

(21)

where {ϖi i = 1, ⋯, m} the weight is the values of a network connection; b is the bias. This procedure can be understood by the schematic presented in Fig. 5. In this study, a single hidden layer based BP neural network is used to retrieve image labels (classification label or stability index) from image features, as shown in Fig. 6. The input layer consists of a set of neurons representing the image features X = {x i i = 1, 2, ⋯, m} . The 16dimensional image features extracted by SSAE are used as inputs, so the number of input neurons is set to 16 (m = 16). In the hidden layers, each neuron transforms the values from the previous layer with a weighted linear summation followed by a non-linear activation function (i.e., Sigmoid function). The number of hidden neurons is set to 10 (n = 10 ), which is determined by cross-validation. The output layer receives the values from the hidden layer and transforms them into output values. Since the classification and regression models are

Fig. 5. The procedure of BP within one neuron. 7

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Fig. 6. The BP network architecture for monitoring combustion stability.

Fig. 7. A geometrical view of the SVM.

Fig. 9. Schematic diagram of SVR.

trained SVM and SVR can identify the corresponding qualitative and quantitative combustion states. The details of SVM can be found in [41].

found elsewhere in [42,43]. The fuel flow (FF) and airflow (AF) rates were measured by flow meters. A monochromatic high-speed camera with a resolution of 260 (H) × 384 (V) pixels at 1000 frames/second (f/s) is used to capture flame images under different operating conditions. To prevent the images from being too dark and saturated, the exposure time is set to 3 μs. Eight different conditions are considered, and their equivalent ratios (ERs) are calculated as listed in Table 1. For each ER, 5000 flame images were recorded and denoted as dataset A. For the ERs = 0.19, 0.34 and 0.69, 1000 images were recorded and denoted as dataset B. In order to eliminate the influence of image size and accelerate the convergence speed of the neural network, each image is resized to 256 (H) × 256 (V) and normalized by its maximum value. An example of flame images under five different ERs (dataset A) is shown in Fig. 11. Even though the flame appearance, such as size, brightness, and structure, varies with the ERs, it is difficult to identify the stable and unstable conditions from the flame physical appearances. Hence, the

3. Experimental results and discussion 3.1. Data collection To verify the effectiveness of the proposed model, experiments were carried out on a co-flow diffusion flame burner. The schematic diagram of the system setup is illustrated in Fig. 10. In the co-flow burner, fuel is supplied to the combustor through an internal tube with a maximum flow rate of 600 ml/min. Air is supplied through an external tube with a maximum flow rate of 3 m3/h. The internal and external diameters of the tubes are 10 mm and 50 mm, respectively. The space between the two tubes is filled with 3 mm diameter glass beads and a mesh to reduce the non-uniformity of the flow. The details of the co-flow burner can be

Fig. 8. Schematic diagram of the kernel. 8

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Fig. 10. Schematic diagram of the experimental setup.

(dataset A1) from dataset A is corrupted by white Gaussian noise and then trained the unsupervised SSAE model. As a Gaussian noise, the corruption ratio is set to 0.3 via cross-validation by comparison with other ratios such as 0.1, 0.2, 0.4 and 0.5. Secondly, the remaining 20% of the data (dataset A2) is used to test the SSAE performance and identify the flame features. A total of 4975 images are accurately labeled from dataset A2 through clustering and statistical analysis to form dataset A3. In the final step, 80% of data from A3 is used to train the classification and regression models. The remaining 20% of data is used to testing the performance of the classification and regression models. Once the classification and regression models are established and tested, these two models are further tested using the dataset B. Note that the dataset B contained in total 3000 images and they are acquired under three different operating conditions.

Table 1 Overview of experimental conditions used in the dataset. Dataset

Dataset A

Dataset B

ER

FF (ml/min)

AF (m3/h)

Total number of images

0.86 0.43 0.29 0.21 0.17 0.69 0.34 0.19

500 500 500 500 500 400 400 400

0.5 1.0 1.5 2.0 2.5 0.5 1.0 1.8

5000 5000 5000 5000 5000 1000 1000 1000

proposed model is established based on the flame images for monitoring combustion stability. In this study, Anaconda with Python is used as the programming language, and tensorflow1.8.0 is used for the programming framework of deep neural network algorithm. An Intel i7-8700 K CPU, 32 GB RAM, and GeForce GTX 1080 Ti GPU are used to train and evaluate the model.

3.3. Training process The hyper-parameters used in the proposed SSAE model are illustrated in Table 2. The parameters of the SSAE are updated via backpropagation using the stochastic gradient descent method [44]. To identify the quality of correlation for the different feature extraction methods, the reconstructed error between the original image and the reconstructed image is calculated. In this study, it is named as reconstruction quality Q [45] and defined as:

3.2. Data sorting An overview of the dataset that used to establish and validate the models is depicted in Fig. 12. The entire dataset is divided into two parts: dataset A (five conditions) and dataset B (three conditions). The dataset A contained 5000 images for each condition and used to establish and validate the SSAE-based models. Firstly, 80% of data

(a) ER = 0.86

(b) ER = 0.43

A

Q=

Z

∑i = 1 ∑ j = 1 x ij x rec, ij A

Z

A

Z

∑i = 1 ∑ j = 1 (x ij )2 ∑i = 1 ∑ j = 1 (x rec, ij )2

(c) ER = 0.29

(d) ER = 0.21

Fig. 11. Example of flame images for five different ERs. 9

(24)

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Fig. 12. Overview of the dataset.

data representation. This technique can convert 16-dimensional representation to a two-dimensional (2-D) map, and the resulting 2D maps (scatterplot) are illustrated in Fig. 15 (a)-(b), respectively. It can be seen that the learned features are clearly separated in the feature space for five different ERs. Although noticeable misclassification points (red scatterplots) can be found in both the clustering results, the clustering accuracy of GMM is obviously outperformed that of Kmeans. Generally, when the combustion conditions (such as ERs) are constant, the acquired images should have the same characteristics such as stability. Although the flame shape may fluctuate under the same conditions, the flame characteristics can be unchanged. Therefore, these misclassification points are attributed to the fact that the images acquired under the same condition should assign into the same cluster but misclassified into another cluster. These misclassification points can be considered as outliers, and they can be deleted. Based on the results of Fig. 15, a total of 189 misclassification points are found for the Kmeans while only 25 misclassification points for the GMM. To sum up, the GMM performs better with 99.5% clustering accuracy and the discrepancy between the extracted features can be identified accurately.

Table 2 Parameters setting up of the SSAE. First-level network

ε1 η1 1 ptarget

0.01 0.4 0.08

Second-level network Learning rate Sparse rate Sparse target

ε2 η2 2 ptarget

0.001 0.3 0.1

Learning rate Sparse rate Sparse target

The Q value varies from 0 to 1, where 0 for uncorrelated image and 1 for the correlated image. For the first-level SSAE network, the optimum iteration is selected based on the minimum reconstruction quality Q for the dataset A2. The minimum Q value for the traditional and proposed loss functions against different iterations is shown in Fig. 13. It can be seen that the minimum Q value increases before 60 iterations and then decreases gradually for the proposed loss function due to the declining ability of generalization caused by over-fitting. It can also be seen that the minimum Q value reaches a maximum of 0.95 at 60th iteration under the effect of the proposed loss function. Whereas, a maximum value of 0.93 at 100th iteration is observed for the effect of the traditional loss function. Thus, the results indicate that the proposed loss function effectively improved the training accuracy of the first-level SSAE network. It means that high-quality reconstruction can be achieved with fewer iterations, and thus an accurate reconstruction can be obtained by the proposed SSAE method. Fig. 14 depicts the training and testing progress of the second-level SSAE network. As presented in the loss curves of datasets A1 (training loss) and A2 (testing loss), it can be seen that the network loss converges at the 50th iteration. Therefore, in this study, the number of iterations for the second-level network is set to 50 to restrain over-fitting.

Traditional loss function Proposed loss function

0.96

Minimum Q

0.94

3.4. Features extraction and cluster classification Once the SSAE is trained, the learned features of the flames are extracted for the dataset A2 using the SSAE encoder. The K-means and GMM algorithm are then separately utilized to separate the learned features into two different clusters (first and second) and to identify misclassification points. The clustering results are visualized by the tSNE technique [46] to demonstrate the proposed SSAE model is capable of learning discriminative features from flame images. Note that the tSNE is an effective data visualization technique for high-dimensional

0.92 0.90 0.88 0.86 20

40

60

80

100

120

Iterations Fig. 13. The minimum Q value against different iterations. 10

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3.5. T 2 and SPE analysis

Training loss Testing loss

1.0

In order to obtain the combustion stability category (i.e., stable and unstable) of each cluster, the statistical analysis (described in section D) is carried out based on the reconstructed image. Note that, the images of dataset A2 are reconstructed through the first-level SSAE network, named as a reconstructed layer Xrec . To reduce the randomness of a single image, each sample is created as an average of four successive images. In this way, the reconstructed 5000 images are formed into 1250 samples. Seven physical parameters (such as ignition point, ignition area, luminous region, brightness, non-uniformity, mean intensity, and flame area) of the flame derived from each sample are used to calculate the T 2 and SPE and the results are obtained from the analysis are shown in Fig. 16. In the figure, the red line represents the 95% confidence limit. It can be seen that there are some false warnings in the first 1200 samples, but they present a stable state with a 95% confidence limit. Whereas, the remainder samples show a very unstable state. The false warning occurs because the statistical analysis is based on the linear transformation of the shallow flame parameters, which may not predict the label accurately.

Loss

0.8 0.6 0.4 0.2 0.0

0

10

20

30

40

Iterations

50

60

70

80

Fig. 14. Training and testing progress of the second-level SSAE network with different iterations.

100

ER = 0.86 ER = 0.43 ER = 0.29

Dimension 2

50

ER = 0.21 ER = 0.17

3.6. Label generation Based on the statistical information, the first three conditions (ERs = 0.8, 0.43 and 0.29) are stable, while the last two (ERs = 0.21 and 0.17) are unstable. It can be determined that the first cluster and the second cluster [refer to Fig. 15] belong to the stable and unstable categories, respectively. Then, each image of dataset A2 is given a classification label. In order to achieve a more accurate monitoring model, the 25 misclassification points [refer to Section 3.4] are deleted from the dataset A2, resulting in a total of 4975 images with the precise classification labels. The stability index of each image is also achieved by using Eq. (20). Finally, a total of 4975 images is formed in the dataset A3 with the precise classification label and stability index. Then, 80% of the dataset A3 is randomly chosen to form the dataset A4 to establish the classification and regression models, and the remaining 20% to form the dataset A5 for testing models [refer to Fig. 12].

0

-50

Misclassification points -100

First cluster -100

-50

Second cluster 0

Dimension 1

50

100

(a) The clustering results from K-means. 100

ER = 0.86 ER = 0.43 ER = 0.29

Dimension 2

50

3.7. Combustion stability monitoring

ER = 0.21 ER = 0.17

A. Classification models The classification models (SSAE-BP and SSAE-SVM) are established through the SSAE features and statistical analysis obtained in Stage 1. Two typical models such as PCA-BP and PCA-SVM with 16 principal components are also established, and a comparative study is carried out. F1-score [47] is used to evaluate the performance of classification models in a range of values 0 to 1. When the F1-score is closed to 1 indicates that the model has a strong classification ability. The F1-score is a harmonic mean of precision and recall, defined as:

0

-50

Misclassification points -100

Second cluster

First cluster -100

-50

precision (p) =

0

Dimension 1

50

recall (r ) =

100

TP TP + FP

TP TP + FN

F1 − score = 2 ×

(b) The clustering results from GMM.

p×r p+r

(25) (26) (27)

where TP is truly positive; FP is false positive; FN is a false negative. For each classification model, 10 trials were performed on the dataset A5, and the averaged result is listed in Table 3. It is evident that both SSAE-based models exhibit a better prediction performance than the PCA-based model. In particular, the F1-score of the SSAE-SVM model reaches 0.99 with an accuracy of 99.43%. Therefore, the SSAE-SVM model is recommended as an optimum classification model for the

Fig. 15. Visualization of extracted features through K-means and GMM clustering techniques.

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Fig. 16. Combustion states identification through T 2 and SPE analysis under different ERs.

T2 value T2 confidence limit (95%)

100

T2

80 60

False warning

40 20 0

Unstable state

Stable state 0

250

12

500

Samples

750

1000

1250

SPE value SPE confidence limit (95%)

10

SPE

8 False warning

6 4 2 0

Unstable state

Stable state 0

250 ER=0.86

500 ER=0.43

Samples

750

ER=0.29

1000 ER=0.21

F1-score

Accuracy (%)

PCA-BP PCA-SVM SSAE-BP SSAE-SVM

0.63 0.67 0.90 0.99

64.64 73.78 89.92 99.43

3.8. Comprehensive analysis and discussion A. Analysis of denoising coding Since the level of corruption noise is a vital hyper-parameter in the SSAE, it is important to investigate the effect of corruption noise on SSAE performance. Different ratios from 0 to 0.5 with a step size of 0.1 are added to the training dataset A1. Fig. 17 shows the clustering accuracy of the testing data (dataset A2) under different corruption ratios. It can be seen that in all cases, the clustering accuracy of GMM is higher than that of K-means, and GMM reaches its maximum at the ratio of 0.3. This result not only demonstrates that GMM is more suitable for clustering the flame features but also provides an appropriate corruption

qualitative monitoring of combustion stability. B. Regression models The regression models (SSAE-BP and SSAE-SVR) are established based on the SSAE features and clustering method obtained in Stage 1. The root mean square error (RMSE) and the coefficient of determination (R2 ) [48] are used to evaluate the performance of the regression models. When R2 is close to 1 indicates that the model has a strong recognition ability. The evaluation indices R2 is given as:

R2 = 1 −

S ∑i = 1 S ∑i = 1

Table 4 Comparison of regression accuracy obtained by the proposed and traditional data-driven models.

(Pi − Pi )2 (Pi − P¯i )2

ER=0.17

performance in comparison to the PCA-BP and PCA-SVR models. Particularly, the SSAE-BP model is recommended with the R2 of 0.98 and the RMSE of 0.03, which demonstrates a better performance for the quantitative assessment of combustion stability.

Table 3 Overview of classification accuracy achieved by the proposed and traditional data-driven models. Model

1250

(28)

where S represents the number of images in the dataset A5, Pi is the prediction value of Pi , and P¯i is the average of the measured value P . A comprehensive comparison of the regression models is listed in Table 4. It can be seen that the SSAE-based models provide better prediction 12

Model

R2

RMSE

PCA-BP PCA-SVR SSAE-BP SSAE-SVR

0.83 0.79 0.98 0.95

0.12 0.14 0.03 0.07

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Accuracy (%)

98 96 94 92 90 GMM K-means

88 86

0

0.1

0.2

0.3

0.4

(a) Original images

0.5

Corruption ratio Fig. 17. Effect of denoising coding on clustering accuracy.

level of 0.3. The GMM method also shows that the accuracy is decreased for the ratios = 0.4 and 0.5. This verifies that a proper denoising coding can improve SSAE performance, but too noisy degrade the quality of input data and thus lead to a lower clustering performance. B. Robustness analysis of monitoring models

ER = 0.69

Further, to investigate the robustness of the SSAE-based models, the testing dataset A5 is corrupted by ratio values of 0 to 0.5 and a step size of 0.1. For each noise, the test trial is repeated 10 times to guarantee the reliability of the result. Fig. 18(a) shows the F1-score of the SSAE-SVM model and Fig. 18(b) shows the R2 of the SSAE-BP regression model under different corrupted ratios. It can be seen that the testing accuracy with the ratio of 0.1 and 0.2 is almost the same as the without noise for the SSAE-SVM. While the ratio is 0.3, the accuracy decreased obviously, but the prediction accuracy is still above 0.9. Even if the ratio is 0.4, the SSAE-SVM classification model still achieved the F1-score of 0.86, and the SSAE-BP regression model reached the R2 of 0.91. With the further increase of noise level, the performance of the classification and regression models severely degraded. Overall, it can be concluded that the proposed SSAE-based models can perform accurately for combustion stability monitoring even with the noisy data, which is significantly important for a practical and complex environment.

ER = 0.34

ER = 0.19

(b) Corrupted images Fig. 19. Example of flame images under three operating conditions.

images were recorded under three completely new operation conditions (i.e., ER = 0.69, 0.34 and 0.19) [refer to Fig. 12, and dataset B]. Dataset B is corrupted with ratio = 0.3, and example images of the three conditions are shown in Fig. 19. To verify that the proposed approach is able to learn discriminative features from the noisy images, the t-SNE technique is used to visualize the learned features. As shown in Fig. 20, the features of the three conditions are accurately separated, despite a few misclassification points (red scatterplots) in the ER = 0.19. It can be seen that the first two conditions (ERs = 0.69 and 0.34) are stable, and the rest of the condition is unstable. It suggests that the combustion state changes from stable to unstable when the ER is less than 0.21, as seen in Fig. 16. Fig. 21 illustrates the qualitative identification results achieved by the proposed SSAE-SVM classification model. It can also be seen that the trend of combustion stability is

4. Evaluation of the proposed models In order to evaluate the performance of the proposed models, flame

1.0

1.0

0.9

R2

F1-scores

0.9 0.8

0.8 0.7 SSAE-SVM 0.6

0

0.1

0.2

SSAE-BP 0.3

Corruption ratio

0.4

0.7

0.5

(a) SSAE-SVM

0

0.1

0.2

0.3

Corruption ratio (b) SSAE-BP

Fig. 18. Performance analysis of the proposed models under different corruption ratios. 13

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suggested that the SSAE model not only predicts the combustion stability from the known dataset but also be applied to complete an unknown dataset, which is essential for the so-called intelligent monitoring model. The results obtained from the different experimental conditions demonstrated that the proposed model is feasible with excellent adaptability, which lays a foundation to use in various combustion processes such as coal combustion, biomass co-firing combustion and even in the combustion engine without significant changes. Although the proposed model used in this study is for monitoring the combustion stability, it can be further tuned to study the different combustion phenomena such as condition monitoring, NOx prediction, slagging and fouling prediction without retraining the complete model. It has been realized that a high-quality and a vast number of images are required to establish an accurate and robust monitoring model. In industrial applications, it is difficult to obtain such high-quality images due to the harsh environment and limited access for system installation. The model proposed in this study has the ability to perform well in corrupted data, and it is verified through the different levels of corrupted ratios incorporating in the flame images. It can be concluded that the SSAE model is feasible and effective for monitoring the stability of combustion processes under different operating conditions.

ER = 0.69 ER = 0.34 ER = 0.19

Misclassification points

Dimension 2

50

0

-50

First cluster

-100 -100

Second cluster

-50

0

Dimension 1

50

100

Fig. 20. Feature visualization for different ERs through the t-SNE technique.

consistent with the results obtained by the clustering method. Although there are some false recognitions, most samples can be identified accurately with an F1-score of 0.93 and a classification accuracy of 93.47%. The false recognitions are mainly concentrated in the third ER = 0.19, and the other two conditions can be identified correctly, which explains the combustion state is more prone to remain unchanged under stable conditions. The quantitative assessment of combustion stability is achieved by the SSAE-BP regression model and illustrated in Fig. 22, where the red line is the average value. A higher deviation can be seen for the ER = 0.19 in comparison to the ERs = 0.69 and 0.34. The qualitative and quantitative predicted results presented in Figs. 21 and 22 show a similar trend of identification of combustion states for the different ERs, and it demonstrates the reliability of the classification and regression models. The prediction result can further be employed to investigate the fluctuation of each flame image. Table 5 shows the average stability index of each condition with their standard deviations. A stable state can be seen for the ER = 0.69 with an average value of 0.87 and an extremely unstable state for the ER = 0.19. It can also be seen that the standard deviation of stability index increases with the decrease of stability index, exhibiting a sharp fluctuation of the combustion state. Overall, it has been observed that the SSAE-SVM model provides the higher prediction accuracy (i.e., F1-score of 0.99, and accuracy of 99.43%) whereas a better performance (R2 = 0.98 and RMSE = 0.03) is achieved through the SSAE-BP regression model. These high prediction accuracies further prove the robustness of the SSAE model. It is also

5. Conclusions It is crucial to develop an intelligent monitoring model to identify the combustion stability as well as for an in-depth understanding of combustion processes and optimize the operating conditions. In this study, a novel approach was proposed for the combustion stability monitoring through a stacked sparse autoencoder based deep neural network. The proposed method is able to overcome the shortcomings of the traditional techniques, such as poor robustness, unlabeled images and inability to quantitative assessment. A modified loss function is defined to improve the training efficiency of the deep autoencoder. Classification and regression models were established for qualitative and quantitative prediction of the combustion stability, respectively. Experiments were carried out on the co-flow diffusion flame burner. The main outcomes drawn from this study are summarized as follows: (a) The stacked sparse autoencoder is able to extract the characteristic features from the unlabeled flame images automatically with improved anti-noise ability and training efficiency. The flame images under different operation conditions can be accurately separated into two clusters through clustering analysis, and the stability of each cluster can be identified by statistical analysis. Further, the

Predicted label

1

False recognitions ER = 0.69 ER = 0.34 ER = 0.19

0

Stable state 0

1000

Unstable state

Samples

2000

Fig. 21. Predication of combustion stability for different ERs. 14

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1.00

Stability index

0.75

0.50 ER = 0.69 ER = 0.34 ER = 0.19 Average line

0.25

0.00

Stable state 0

1000

Unstable state

Samples

2000

3000

Fig. 22. Identification of the combustion stability index for different ERs.

References

Table 5 Comparison of combustion stability index for different ERs. ER

Average

STD (%)

0.69 0.34 0.19

0.87 0.79 0.32

2.0 4.0 13.0

[1] Ti S, Chen Z, Li Z, Kuang M, Xu G, Lai J. Wang Z. Influence of primary air cone length on combustion characteristics and NOx emissions of a swirl burner from a 0.5 MW pulverized coal-fired furnace with air staging. Appl Energy 2018;211:1179–89. https://doi.org/10.1016/j.apenergy.2017.12.014. [2] Zhang R, Hao F, Fan W. Combustion and stability characteristics of ultra-compact combustor using cavity for gas turbines. Appl Energy 2018;225:940–54. https://doi. org/10.1016/j.apenergy.2018.05.084. [3] Park K, Lee C. Low frequency instability in laboratory-scale hybrid rocket motors. Aerosp Sci Technol 2015;42:148–57. https://doi.org/10.1016/j.ast.2015.01.013. [4] Krzywanski J, Nowak W. Neurocomputing approach for the prediction of NOx emissions from CFBC in air-fired and oxygen-enriched atmospheres. J Power Technol 2017;97(2):75–84http://www.papers.itc.pw.edu.pl/index.php/JPT/ article/view/646. [5] Krzywanski J, Czakiert T, Blaszczuk A, Rajczyk R, Muskala W, Nowak W. A generalized model of SO2 emissions from large- and small-scale CFB boilers by artificial neural network approach Part 2. SO2 emissions from large- and pilot-scale CFB boilers in O2/N2, O2/CO2 and O2/RFG combustion atmospheres. Fuel Process Technol 2015;139:73–85. https://doi.org/10.1016/j.fuproc.2015.08.009. [6] Habib M, Rashwan S, Nemitallah M, Abdelhafez A. Stability maps of non-premixed methane flames in different oxidizing environments of a gas turbine model combustor. Appl Energy 2017;189:177–86. https://doi.org/10.1016/j.apenergy.2016. 12.067. [7] An Y, Tang Q, Vallinayagam R, Shi H, Sim J, Chang J, et al. Combustion stability study of partially premixed combustion by high-pressure multiple injections with low-octane fuel. Appl Energy 2019;248:626–39. https://doi.org/10.1016/j. apenergy.2019.04.048. [8] Fichera A, Losenno C, Pagano A. Experimental analysis of thermo-acoustic combustion instability. Appl Energy 2001;70(2):179–91. https://doi.org/10.1016/ S0306-2619(01)00020-4. [9] Li X, Huang Y, Zhao D, Yang W, Yang X, Wen H. Stability study of a nonlinear thermoacoustic combustor: Effects of time delay, acoustic loss and combustion-flow interaction index. Appl Energy 2017;199:217–24. https://doi.org/10.1016/j. apenergy.2017.04.074. [10] Schuller T, Durox D, Candel S. Self-induced combustion oscillations of laminar premixed flames stabilized on annular burners. Combust Flame 2003;135(4):525–37. https://doi.org/10.1016/j.combustflame.2003.08.007. [11] Su S, Pohl JH, Holcombe D, Hart JA. Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers. Prog Energy Combust Sci 2001;27(1):75–98. https://doi.org/10.1016/S0360-1285(00)00006-X. [12] Cammarata L, Fichera A, Pagano A. Neural prediction of combustion instability. Appl Energy 2002;72(2):513–28. https://doi.org/10.1016/S0306-2619(02) 00024-7. [13] Lu G, Yan Y, Colechin M. A digital imaging based multifunctional flame monitoring system. IEEE Trans Instrum Meas 2004;53(4):1152–8. https://doi.org/10.1109/ tim.2004.830571. [14] Bai X, Lu G, Hossain M, Yan Y, Liu S. Multimode monitoring of oxy-gas combustion through flame imaging, principal component analysis, and kernel support vector machine. Combust Sci Technol 2016;189(5):776–92. https://doi.org/10.1080/ 00102202.2016.1250749. [15] Chen J, Chan L, Cheng Y. Gaussian process regression based optimal design of combustion systems using flame images. Appl Energy 2013;111:153–60. https:// doi.org/10.1016/j.apenergy.2013.04.036. [16] Chen J, Hsu T, Chen C, Cheng Y. Monitoring combustion systems using HMM probabilistic reasoning in dynamic flame images. Appl Energy 2010;87(7):2169–79. https://doi.org/10.1016/j.apenergy.2009.11.008. [17] Liu Y, Fan Y, Chen J. Flame images for oxygen content prediction of combustion systems using DBN. Energy Fuels 2017;31(8):8776–83. https://doi.org/10.1021/ acs.energyfuels.7b00576.

classification label of each image can be achieved. Generally, the proposed model capable of solving the problem of requiring quantitative label images through the combustion stability index. (b) Classification and regression models that established can provide qualitative and quantitative predictions of flame stability, respectively. Their prediction performances are verified through the experimental study. The results show that the F1-score of the stacked sparse autoencoder based support vector machine and the Rsquared of the stacked sparse autoencoder based backpropagation models provide 0.99 and 0.98, respectively, demonstrating that the proposed models are feasible for combustion stability monitoring. (c) The proposed stacked sparse autoencoder based model can easily be tuned to monitor the combustion conditions without retraining the model. As a consequence, a complete unsupervised model will be developed for combustion process monitoring. Overall, the proposed model shows a promising tool for combustion stability monitoring, and it can be suitable for other combustion processes such as coal combustion, biomass co-firing combustion and even in the combustion engine without significant changes. The future work will be focused on tailoring the proposed model for monitoring combustion conditions and predicting the NOx emission.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements This work was supported by the National Natural Science Foundation of China [No. 51676044]; the Social Development Project of Jiangsu Province [No. BE20187053]; the Fundamental Research Funds for the Central Universities [No. 2242019k1G018].

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