Fuzzy modeling and prediction of combustion layers ′ temperature for power plant

Abstract

This paper develops a fuzzy modeling strategy to study the temperature of different combustion layers in a power plant. First, a new infrared temperature measurement system is developed to measure three layers (bottom, middle and upper) temperature on both sides of the boiler. Then, a fuzzy clustering modeling algorithm is designed based on entropy to determine the structure of the fuzzy model and the corresponding fuzzy memberships of local models. The effect of modeling mismatches are overcome by the use of online identification of parameters. Simulation results show that the effectiveness of the proposed method can be achieved for a 660 MW power plant.

Keywords

Data-driven modeling combustion layer temperature multi-model fuzzy subtractive clustering

1 Introduction

Coal is still the main power generation energy in modern society due to its cheap price and abundant reserves, and more than 40%of the world’s electricity production comes from coal [1]. However, the Chinese government has put forward strong requirements for coal-fired power plants and required them to improve boiler efficiency and reduce emissions of pollutants. This has prompted operators to find new solutions for combustion optimization [2]. Combustion optimization has become increasingly popular in power plants over the past few years. One of them is to obtain the effective parameters of the boiler through a new measurement method and establish an effective boiler combustion system model.

Common boiler models include mechanism models [3, 4] and computational fluid dynamics (CFD) models [5, 6]. The former mainly studies boiler models based on basic physical laws and field data, especially for dynamics of the steam generating systems. While CFD models have been extensively applied in predicting the erodynamic fields, temperature distributions and combustion products of utility boilers, especially in analyzing the pulverized coal combus-tion, the composition and flow of flue gas [6]. In addition, the data-driven model [7 –13] is attracting more and more attention. Usually, a boiler combustion characteristic model is established firstly, and then the operation parameters are optimized with boiler efficiency and NOx emission as performance indexes. In [7], the feed forward neural network is used to build a combustion model, and information analysis based on random search, fuzzy C-mean clustering and minimization of information free energy is performed iteratively in the process to optimize the model. [8-12] adopted support vector machine (SVM) for modeling and artificial intelligence algorithms such as genetic algorithm (GA) [8 –12] for optimization, among which [12] also compared the optimization effect of GA with ant colony optimization algorithm (ACO) and particle swarm optimization (PSO). This method is mainly used for steady-state optimization, and the results can be used as a reference for guiding operation under the same condition. However, due to the lack of equipment in the actual operation process, it is difficult to accurately and real-time measure the combustion information in the furnace [14]. This leads to the absence of identifica-tion data that can be used for dynamic modeling.

Furnace temperature is one of the important parameters for boiler combustion optimization, and it is the most direct reflection of the stability of the furnace combustion state. In many projects, the authors have demonstrated the importance of boiler temperature in combustion process [15, 16]. The relations among the predicted temperature, O2 and CO2 mass fractions are discussed [16], and it is proved that the NOx formation is closely related to the combustion process and temperature. In recent years, the contactless temperature measurement technologies have become more popular in power plant for monitoring boiler, which include acoustic technology [17, 18], laser absorption spectroscopy technology [19] and optical radiation technology [20 –22]. As a fast developing optical radiation technology, infrared temperature measurement can collect the temperature information of furnace in real time and realize on-line monitoring [22]. However, most of the above methods measure the temperature information of the whole furnace, and there are few measuring devices that specifically in studying the temperature information of the main combustion zone of furnace (the maximum heat releasing zone, including all the burners).

The boiler model is essentially a nonlinear controlled object, and Hammerstein model, or gravitational search algorithm (GSA) of the system are commonly established by using nonlinear system identification methods [23]. However, the above model structure is often difficult to characterize the global performance of complex systems. In order to establish a system model of large-scale or full-scale conditions, the application of multi-model modeling method based on decomposition-synthesis in nonlinear systems has attracted more and more attention [24 –27], especially in modeling the nonlinear process of unit in thermal power plant [28 –32].Compared with the traditional modeling methods, the modeling based on fuzzy rules is a multi-model method. Each rule of fuzzy model can be regarded as a local model, that is, fuzzy modeling describes the process of the whole system through the local model [33, 34].

Most of the pulverized coal is burned in the main combustion zone. The temperature of the zone where the burner is located and different layers in the main combustion zone were measured. The temperature distribution in this area is greatly affected by the operating conditions of the burners, which motivated authors of this paper to carry on a research on modeling the combustion process based on the temperature distribution in the furnace. Based on the energy balance principle, the factors affecting the temperature of different layers in the main combustion zone are analyzed and selected to build the combustion process model. The modeling approach in this paper relies on the data-driven fuzzy modeling strategy. The fuzzy subtractive clustering based on entropy is used to provide an appropriate division of the operation condition by input-output data of the plant. It determine the structure of the fuzzy model and the corresponding fuzzy memberships of local models. To eliminate the effect of modeling mismatch, the algorithm realizes on-line identification of parameters, and the model will be updated when new data coming to the system. The model obtained can be directly used for the synthesis of model-based control algorithms, which will positively influence the combustion process control.

2 Measurement and analysis

2.1 The infrared temperature measuring system

The power plant under consideration is a 660 MW ultra-supercritical opposed-wall-fired boiler, as shown in Fig. 1. The furnace is 73200.0 mm in height and has a cross section of 22162.4 mm × 15456.8 mm. The low NOx swirling burners of three layers (bottom, middle and upper) have been arranged at the front and back walls of the furnace. The front wall is layer A, B and C from bottom to top, while the back wall is layer D, E and F, and there is a total of 36 burners. Sixteen SOFA (separated over-fired air) ports, which are divided into four groups (two groups on the front wall and two groups on the back wall) are equipped above the highest burner elevation to achieve air-staging combustion. The infrared temperature measuring devices are located at the fixed and extended side in the furnace. There are three layers infrared measuring devices (bottom, middle, upper) respectively and they are installed at 400 mm above burner horizontal line considering the environment of boiler [35]. The distribution of infrared temperature measuring devices and burners in the furnace is shown in Fig. 1.

Fig. 1

The distribution diagram of infra-red temperature measuring devices and burners.

The temperature measurement system is mainly composed of infra-red detector, signal processor, heat insulation protection structure, cooling structure and filter, among which the cooling and filtering parts can also play a role of preventing the infra-red detector from dust pollution. The temperature measurement range is from 400°C to 1650°C. In order to ensure the real-time and accuracy of temperature measurement in boiler, the device is directly installed in the water wall fin of the boiler in this system.

2.2 The temperature of different combustion layers

The data used in this study was collected from the studied subject from one power plant in China. The operation data in all 5760 samples is taken every 30 seconds in 2 days. Fig. 2 shows the temperatures at different combustion layers. In main combustion zone, the temperature is gradually increasing from the bottom layer to the upper layer. During the operation, the burners of A, B and D are put into operation all the time, then the burners of E and F will be put into operation when the load increases. When the upper burners(C and F) are out of operation, the temperature of upper layer is also higher than the middle layer, this may be due to thermal inertia and over fire air of furnace. Frequent switching of burners of E and F leading to the complex changes of the temperature. This is very obvious in the middle layer.

Fig. 2

The temperature curves of different layers.

The temperature change is consistent with the load in generally. As the height rises, the consistency between temperature and load increases. Since the burners in bottom are always running, the temperature of the bottom layer does not change much. It may be used a parameter to judge combustion stability, especially in low load. The consistency between the upper layer temperature and load is very well. Here, using the Pearson correlation coefficient to illustrate this consistency between temperature and load, it is calculated by $ρ_{load, T} = \frac{cov (load, T)}{σ_{load} σ_{T}}$ (1) where load is the load of boiler, T is the temperature of layer, cov (load, T), σ_load and σ_T represent covariance and standard deviation respectively.

The upper temperature has a good correlation with the load, the correlation coefficient is 0.8963, mainly due to the upper in the main combustion zone is relatively stable, which can well reflect the change of the boiler load. The temperature of layer can reflect the real-time burning status of the furnace, and it can provide a key reference for boiler control and shorten the control time delay. The correlation coefficient is shown in Table 1.

Table 1

The correlation coefficient between temperature and load

Temperature	Correlation coefficient
Upper	0.8963
Middle	0.6271
Bottom	0.7261

3 The one-dimensional combustion model of main combustion zone

Pulverized coal is burned in the furnace, and the heat is mainly transmitted through radiation. Due to the interaction of physical and chemical processes such as flow, combustion and heat transfer in the furnace, the combustion is very complicated and many factors need to be considered [36]. Usually, the zone where the burners are located (i.e. the maximum heat release zone) is called the main combustion zone, including all burners. Most of the fuel heat sent to the boiler is released in this main zone. In traditional heat transfer calculation, the main combustion zone is usually regarded as an in-dependent section, and the coupling of combustion process and radiation heat transfer in this zone is rarely studied. In this paper, the main combustion zone is divided according to the burner arrangement, which can reflect the actual working condition of fuel staging of the burner more reasonably. Each combustion layer contains a layer of burner and a temperature measuring device.

The one-dimensional model in main combustion zone describes both the burning and burnout process of the furnace. The model is developed based on the zone method, and the main combustion zone is divided into three layers (bottom, middle and upper). Each layer contains 12 burners, and the bottom contains A and D, the middle contains B and E, the upper contains C and F. The combustion model is established in each layer according to the mass and energy balance [37, 38]. The flue gas temperature of combustion layer can be determined by $I_{in} + Q_{fuel} + Q_{rad, in} - Q_{rad, out} - I_{out} = 0$ (2) Where Q_fuel is fuel combustion releasing heat, Q_rad,out is the radiant leasing heat of the flue gas flow in this layer, Q_rad,in is the radiant leasing heat of the flue gas flow in other layer, I_in and I_out is the inlet and outlet physical enthalpy of the flue gas flow in this layer. In addition, the above terms can be calculated through Equations (2), (3) and (4): $Q_{fuel} = P_{i} (\frac{100}{100 - q_{4}} β_{cr} Q_{ar, net} + Q_{air} + Q_{hs} - Q_{slag})$ (3) $Q_{rad} = σ {aT}^{4} φ S$ (4) $I = P_{i} V_{cp} (T - 273.15)$ (5)

The above equations contain the radiant leasing heat of the flue gas flow in other layer Q_rad, the physical enthalpy of the flue gas flow I, the fuel put into the furnace P_i, mechanical incomplete combustion heat loss q₄, the fuel heat as received Q_ar,net, the burnout rate β_cr, the heat taken in by air Q_air, the heat taken in by external heat source Q_hs, the heat of slag taking out Q_slag, the furnace blackness a, the product of the thermal effective coefficient φ and the total area of this layer S, the temperature of combustion layer T, the average specific heat capacity of 1 kg fuel combustion products V_cp and σ = 5.67 × 10^-8.

Therefore, according to the characteristics of burning, heat release and heat transfer in different layers, the temperature of each layer can be determined as follows. The subscripts 1, 2, 3 of the terms represent the bottom, middle and upper layers. The bottom layer: $\begin{matrix} P_{1} V_{cp 1} (T_{1} - 273.15) + σ {aT}_{1}^{4} φ S \\ = P_{1} (\frac{100}{100 - q_{4}} β_{cr 1} Q_{ar, net} + Q_{air} + Q_{hs} - Q_{slag}) \end{matrix}$ (6)

The middle layer: $\begin{matrix} (P_{1} + P_{2}) V_{cp 2} (T_{2} - 273.15) - P_{1} V_{cp 1} (T_{1} - 273.15) + \\ σ {aT}_{2}^{4} φ S - σ {aT}_{1}^{4} φ S = P_{1} β_{cr 21} Q_{ar, net} + \\ P_{2} (\frac{100}{100 - q_{4}} β_{cr 2} Q_{ar, net} + Q_{air} + Q_{hs} - Q_{slag}) \end{matrix}$ (7)

The upper layer: $\begin{matrix} (P_{1} + P_{2} + P_{3}) V_{cp 3} (T_{3} - 273.15) - \\ (P_{1} + P_{2}) V_{cp 2} (T_{2} - 273.15) + σ {aT}_{3}^{4} φ S - \\ σ {aT}_{2}^{4} φ S = P_{1} β_{cr 31} Q_{ar, net} + P_{2} β_{cr 32} Q_{ar, net} + \\ P_{3} (\frac{100}{100 - q_{4}} β_{cr 3} Q_{ar, net} + Q_{air} + Q_{hs} - Q_{slag}) \end{matrix}$ (8)

Obviously, the temperature of each layer has the characteristics of strong coupling, and which is closely related to the fuel quantity, excess air coefficient, burnout rate and the stain coefficient of the wall. For the purpose of closed-loop control of the combustion process, the coal feeders and secondary air dampers are often taken as input signals in standard combustion optimization empirical models. The innovation of this paper is to choose the parameters of each layer to model the temperature of each layer in the furnace, which allows a better analysis of each level of input on the combustion process. Thus, the coal feeders and secondary air dampers are selected as the manipulated variable to build the model in Section 4.

4 Data-driven fuzzy modeling

According to the analysis of the previous sections, the temperature model of different combustion layers has the characteristics of multivariable, nonlinear and strong coupling. Therefore, the data-driven fuzzy model is proposed for the temperature of combustion layer. The fuzzy subtractive clustering based on entropy is proposed for the designing of the fuzzy model, which is used to determine the number of local models and their corresponding membership. The algorithm realizes online identification and the resulting model can be applied directly to combustion optimization control.

4.1 Model description

The following discrete fuzzy model can be used to present the temperature of furnace with both fuzzy inference rules and local models [39]: $\begin{matrix} R_{i} : if & y_{i} (k - 1) is A_{i 1}, \dots, y_{i} (k - n_{y}) is A_{in}, \\ u_{i 1} (k - t_{d}) is A_{in + 1}, \dots, \\ u_{i 1} (k - t_{d} - m) is A_{in + m + 1}, \\ u_{ir} (k - t_{d}) is A_{in + rm + 1}, \dots, \\ u_{ir} (k - t_{d} - m) is A_{in + rm + 1} \\ then \\ y_{i} (k) & = a_{i 1} y_{i} (k - 1) + a_{i 2} y_{i} (k - 2) + \dots \\ + a_{in} y_{i} (k - m + 1) + a_{in + 1} u_{i} (k - t_{d}) + \dots \\ + a_{in + m + 1} u_{i} (k - t_{d} - m) + \dots \\ + a_{in + rm + 1} u_{ir} (k - t_{d}) + \dots \\ + a_{in + rm + 1} u_{ir} (k - t_{d} - m) \end{matrix}$ (9) Where R_i (i = 1, 2, ⋯ , n) denotes the i-th fuzzy inference rule, n is the number of fuzzy rules, A_j (j = i1, i2, ⋯ , (in + rm + 1)) is the fuzzy sets, u = (u₁, ⋯ , u_m) is the control input vector with time delay t_d), y_i (k) is the output vector, a_in is the consequent parameter.

Let ${\tilde{μ}}_{i}$ be the normalized membership function of the fuzzy set A_j, φ (k) is the antecedent vector of the fuzzy model, which is also the clustering input, composed by current and past measurable variables of the plant, then the fuzzy model can be expressed in the global form. $\hat{y} (k) = \frac{\sum_{n = 1}^{n} {\tilde{μ}}_{i} y_{i} (k)}{\sum_{n = 1}^{n} {\tilde{μ}}_{i}}$ (10)

Use the following equation to calculate μ_i corresponding to i-th rule [40]. ${\tilde{μ}}_{i} (φ (k)) = \exp [- \frac{(φ (k) - c_{i})^{T} (φ (k) - c_{i})}{σ_{i}^{2}}]$ (11) where c_i is the cluster center, c_ij is the j-th neighbor center of c_i, $σ_{i} = k_{s} \frac{1}{n} \sum_{j = 1}^{n} | c_{i} - c_{ij} |$ and k_s is a constant.

4.2 Fuzzy clustering modeling algorithm

Clustering analysis is a multivariate statistical analysis method, and also being called the unsupervised classification, which is a branch of unsupervised pattern recognition. Fuzzy subtractive clustering, fuzzy C-mean and G-K (Gustanfson-Kessel) clustering are the most used clustering methods. Fuzzy subtractive clustering method is adopted in this paper. It defined the potential of clustering center fixed by the data sample as density, which can be calculated by the distance between data points and other data samples as following: $P (φ (i)) = \frac{1}{1 + \frac{1}{N - 1} \sum_{j = 1, j \neq i}^{N} (φ (i) - φ (j))^{T} (φ (i) - φ (j))}$ (12) Where φ (i) ∈ Φ = [φ (1) , φ (2) , ⋯ , φ (N)] , i = 1, 2, ⋯ , N. φ (i) is the sample of the data and N is the number of the data set Φ.

The recurrence form can be written as: $\begin{matrix} P_{k} (c_{i}) & = \frac{1}{1 + \frac{1}{k - 1} \sum_{j = 1, j \neq i}^{k} (c_{i} - φ (j))^{T} (c_{i} - φ (j))} \\ = \frac{(k - 1) P_{k - 1} (c_{i})}{k - 2 + P_{k - 1} (c_{i}) + γ (k) P_{k - 1} (c_{i})} \end{matrix}$ (13) Where γ (k) = (c_i - φ (k)) ^T (c_i - φ (k)).

The density of data can achieve the purpose of clustering. However, in the actual clustering process, due to the uncertain disturbances, it is difficult to ensure the accuracy of clustering results. So entropy is introduced to take the degree of the orderly into account during the clustering process. The smaller the entropy value is, the more regular the data set is, that is, it is more suitable for clustering center. The formula of binary entropy can be expressed as following: $E = - P \log_{2} (P) - (1 - P) \log_{2} (1 - P)$ (14)

In the process of clustering, all data samples are taken as possible clustering center, and the data density is calculated, then the entropy is calculated according to the data density. The expression of system entropy as following: $E_{k} = - P_{k} \log_{2} (P_{k}) - (1 - P_{k}) \log_{2} (1 - P_{k})$ (15)

Each data in the dataset will have an impact on other data in the process of online clustering. When the new data comes, the density of the data sample E_k (φ (k)) is recalculated and compared with the density of the original cluster center E_k (c_i). Thus, a more reasonable fuzzy set and rule number are determined. r_s is the set value of the maximum distance between the new data and its nearest cluster center and E_s is the set value of the density which defined by the density of the corresponding cluster center. The Fig. 3 shows the flow of clustering algorithm.

Fig. 3

The flow of clustering algorithm.

4.3 The identification of local model

As mentioned in [41], the Takagi-Sugeno (T-S) model composed of rules ${\tilde{μ}}_{i}$ of Equation (11) can be represented by a linear discrete-time controlled auto regression integrated moving average (CARIMA) structure with the form $A (z^{- 1}) y (k) = z_{- d} B (z^{- 1}) u (k) + ξ (k) / Δ$ (16) Where △=1 - z^-1 is difference operator, ξ (k) is a zero mean white noise, y (k) and u (k) are output and control sequence of system, $A (z^{- 1}) = 1 + \sum_{i = 1}^{n_{a}} a_{i} z^{- i}$ and $B (z^{- 1}) = \sum_{i = 0}^{n_{b}} b_{i} z^{- i}$ are polynomials of z^-1, n_a and n_b are the system input and output order respectively.

Let $μ_{i} = {\tilde{μ}}_{i} / \sum_{i = 1}^{n} {\tilde{μ}}_{i}$ , there is the global form is derived from Equation (11). $\hat{y} (k) = \sum_{i = 1}^{n} μ_{i} y_{i} (k)$ (17) $\hat{y} (k) = \sum_{i = 1}^{n} μ_{i} φ (k) θ_{i} + ξ (k)$ (18) where ${\begin{matrix} φ (k) = [- y & (k - 1), \dots, - y (k - n_{A}), \\ u & (k - d), \dots, u (k - d - n_{B})]^{T} \\ θ_{i} = [a_{1}, & \dots, a_{n_{A}}, b_{0}, \dots, b_{n_{B}}]^{T} \end{matrix}$

For the boiler operation data, different clustering centers correspond to different operating conditions. The number of submodels covering the large-scale dynamic characteristics of the system can be obtained during the clustering process. The model of different working conditions can be obtained by identifying of different working conditions. From Equation (18), the parameters of submodel can be fitted by recursive least square (RLS). In the process of model parameter extraction, the global optimization index or local optimization index shall be defined to determine the final value. In contrast, the local optimal strategy is superior in most cases because of its small calculation amount, fast calculation speed and strong robustness. The cost function of local optimization can be write as following: $\begin{matrix} Q_{L} = & \sum_{i = 1}^{n} μ_{i} (y (k) - \hat{y} (k, θ_{i}))^{2} \\ = & (Y_{L} - Ψ_{L} θ)^{T} Λ_{i} (Y_{L} - Ψ_{L} θ) \end{matrix}$ (19) Where n is the number of cluster center, $θ = [θ_{1}^{T} θ_{2}^{T} \dots θ_{n}^{T}]^{T}$ belongs to R^{[n×(n_a+n_b+1)]×1} and θ_i (i = 1, 2, ⋯ , n) is the i-th vector of θ, Y_L = [y_L (1) y_L (2) ⋯ y_L (n)] ^T is the output of the system and y_L (1) = y_L (2) = ⋯ = y_L (n) = y (k), $Ψ_{L} = [φ_{L}^{T} (1) φ_{L}^{T} (2) \dots φ_{L}^{T} (n)]^{T}$ belongs to R^{n×[N×(n_a+n_b+1)]} and $φ_{L}^{T} (1) = φ_{L}^{T} (2) = \dots = φ_{L}^{T} (n) = φ^{T} (k)$ , Λ_i = dig belongs to R^n×n.

Then, the parameters of the submodel can be obtained by the following recursive formula. $\begin{matrix} \hat{θ} (k) = & \hat{θ} (k - 1) + K_{L} (k) λ_{i} (y_{L} (k) - φ_{L}^{T} (k) \hat{θ} (k - 1)) \\ K_{L} (k) = & P_{L} (k - 1) φ_{L} (k) (φ_{L}^{T} (k) P_{L} (k - 1) φ_{L} (k) + 1)^{- 1} \\ P_{L} (k) = & (I - K_{L} (k) λ_{i} φ_{L}^{T} (k)) P_{L} (k - 1) \end{matrix}$ (20)

In addition, the identification accuracy of multiple models can be evaluated by the nondimensional error index (NDEI) [42] described as following: $I_{NDEI} = [\sum_{k = 1}^{N} (y (k) - \hat{y} (k))^{2} / \sum_{k = 1}^{N} (y (k) - \bar{y})^{2}]^{\frac{1}{2}}$ (21)

4.4 Simulation of the model

Based on the operation data of power plant boiler, the temperature model of different layers is identified. Using 1000 data samples, they were divided into two groups. As training data, the first 500 data are used to train the identification model. Another 500 data, as the checking data, are used to check the generalization ability of the model.

The simulation results are shown in Figs. 6 . Although there is a certain error at beginning of the identification process, the prediction results obtained by the algorithm as a whole can reflect the actual output of the temperature of different layers very well. The error curves of Figs. 7 indicate that the identification results are continuously recursively corrected and the accuracy is effectively improved during the operation of the algorithm.

Fig. 4

Comparison of the training data identification result with actual output.

Fig. 6

Comparison of the checking data identification result with actual output.

Fig. 5

Tracking error of the identification model in training data.

Fig. 7

Tracking error of the identification model.

The index of the identification process is shown in Table 2. The table also shows the reliability of the identification result, that is, the system can still ensure stable output in the case of possible large error due to external interference.

Table 2

The index of the identification process in checking data

Process	Layer	The maximum error	NDEI
	Bottom	24.0425	7.9905
Training	Middle	14.5416	0.6498
	Upper	33.3793	1.1881
	Bottom	5.2187	2.3295
Checking	Middle	13.0167	1.1038
	Upper	13.7347	1.6189

In order to further confirm the above analysis results, recursive least squares (RLS) and entropy clustering multi model identification method without initial adjustment (ECMM) were used for comparison, and the results are shown in Table 3.

Table 3

Comparison between different identification methods

		NDEI
Layer	RLS	ECMM	Ours
Bottom	7.2961	4.0453	2.3295
Middle	4.8275	2.0914	1.1038
Upper	4.9559	2.1840	1.6189

5 Conclusion

The infrared temperature measurement system is applied in a 660MW power plant boiler to measure the temperature of different combustion layers. The experimental results show that the combustion tem-perature is closely related to the combustion process. The temperature of different combustion layers can reflect the change of the combustion in the furnace. In the main combustion zone, the temperature in-creases gradually from the bottom layer to the upper layer. And the temperature of combustion layer is consistent with the load.

The principle of heat and mass transfer during the furnace combustion is analyzed in detail, and the main manipulated variables of the temperature model are determined. On this basis, a data-driven model of combustion process based on fuzzy T-S multi model is established. The simulation results show that the identified output can track the output smoothly in the case of external interference, which proves the effectiveness of the method. The model can be directly used in the synthesis of model-based control algorithm, which is interpretable and easy to implement in industry. It is beneficial for operators to understand the vertical temperature distribution of the furnace, monitor the combustion state, and realize the refined combustion control of the furnace.

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