Predictions of the Key Operating Parameters in Waste Incineration Using Big Data and a Multiverse Optimizer Deep Learning Model

Abstract

In order to accurately predict the key operating parameters of waste incinerators, this paper proposes a prediction method based on big data and a Multi-Verse Optimizer deep learning model, thus providing a powerful reference for controlling the optimization of the incinerator combustion process. The key operating parameters that were predicted, according to the control objectives, were determined to be the steam flow, gas oxygen, and flue temperature. Firstly, a large amount of measurement data were collected, and 27 relevant control system parameters with a high correlation with the predicted variables were obtained via a mechanism analysis. The input variables of the prediction model were further determined using the improved WesselN symbolic transfer entropy algorithm. The delay time between the variables was found using a gray correlation coefficient, the prediction time was determined to be 6 min according to the delay time distribution of the flame feature, and the time delay compensation was applied to each parameter. Finally, the support vector machine was optimized using a Multi-Verse Optimization algorithm to complete the prediction of the key operating parameters. Experiments showed that the root mean square error of the proposed model for the three output variables—the steam flow, gas oxygen, and flue temperature—were 0.3035, 0.2477, and 1.6773, respectively, which provides a high accuracy compared to other models.

1. Introduction

Currently, as the global economy is booming, people’s living standards are improving and the amount of municipal waste being generated is increasing day by day. According to the relevant data, China’s domestic waste generation increased to 271.19 million tons in 2021, up 6.39% from 2020 [1]. The high growth rate of domestic waste generation also makes the task of domestic waste removal more difficult. At present, the main methods of domestic waste disposal include incineration, landfill, and composting [2,3]. Among them, compared to the other two methods, waste incineration has the great advantage of “harmless, reduction and resource utilization” [4,5]. Especially when combined with the power generation industry, it can share the huge pressure of urban electricity production, so it has been widely adopted by a large number of countries and regions [6,7].

At present, as the composition and incineration characteristics of domestic waste vary greatly from region to region, and the type of incinerator being used also varies. Among them, common waste incinerators include grate-type, rotary-type, and fluidized bed furnaces, etc. [8,9,10]. Chinese waste has a high water content, low average calorific value, and large lumps, so grate-type waste incinerators are often used. However, due to the waste calorific value fluctuating and being difficult to measure, the impact on the environment can not be ignored [11,12].

In order to effectively analyze the complex heat transfer, mass transfer, and physicochemical reaction processes that exist inside the bed during the combustion process of grate furnace waste incinerators, Wang et al. [13] combined the combustion characteristics of waste to establish a model of water evaporation, as well as an analysis of volatile combustion and coke combustion in the incinerator. Zhang [14] proposed the idea of phased modeling, establishing a mathematical model of the mechanism. However, the mechanism-modeling method can only construct quantitative transfer relationships between specific chemical elements or substances, which cannot be used for real-time control calculations and dynamic simulation predictions, and thus cannot help to control optimization.

To provide assistance with control decisions, some scholars have proposed neural-network-based parameter prediction or modeling methods. You et al. [15] proposed four different nonlinear models to predict the waste heat value in real time and provide reliable heat value data for the control system. A support-vector-machine-based prediction model for the operating parameters of a large domestic waste incinerator grate has been proposed in the literature [16]. Yang et al. [17] proposed a model based on a long short-term memory network to predict the main steam parameters of a waste incinerator. A neural network model based on a time domain input framework was developed in the literature [18] to predict the trends of the main steam parameters of waste incinerators in the following five minutes. The above study showed that the neural-network-based modeling method has a high fitting accuracy and generalization ability, but the selection of the model input data and hyper-parameters is crucial to the fitting accuracy, and the adoption of effective input data and hyper-parameter selection methods can lead to a significant improvement in the model’s accuracy. The Multi-Verse Optimization (MVO) algorithm is a novel parameter search method, which has been widely used by scholars in industrial process parameter optimization in recent years. Mekalathur et al. [19] used MVO for estimating Weibull parameters and proved that the best results were obtained by using the MVO algorithm, with an error of less than one. Two modifications have been employed to the conventional Multi-Verse Optimizer in the literature [20], and the proposed method also achieved a better performance in modeling the twin-rotor system, as well as the flexible manipulator system. To solve the overfitting and underfitting that result from the improper parameters of a SVM, one example from the literature [21] used MVO to optimize the parameters of the SVM.

Flame combustion images can reflect many key conditions, such as the degree of combustion, heat generation, and the thickness of the material layer during waste incineration. Operators often judge the combustion status and give control commands based on the combustion images. In order to effectively utilize and analyze flame combustion monitoring images, Huang et al. [22] characterized and evaluated the combustion status by extracting the image features, predicted the main steam temperature at future moments based on artificial neural networks, and realized a diagnosis of bias combustion problems. Wang et al. [23] used DCS feature variables and image features as input variables to the neural network to build a long short-term memory network model and predict the main steam temperature data in the following 6 min.

In summary, this paper proposes a method for predicting the key operating parameters of waste incinerators based on big data and a Multi-Verse Optimizer deep learning model. In total, 4 image features and 31 process variables were extracted as input variables, and the improved WesselN symbolic transfer entropy method was used to screen the relevant control variables in the furnace as model inputs, thus effectively providing guidance data for optimized control parameters. Finally, an effective MVO-SVM prediction model was established.

2. Methods and Principles

2.1. Structure of Grate-Type Waste Incinerator

Municipal waste is generally transported to waste-to-energy plants by special transport vehicles, and after entering these plants, it has to go through a fermentation process for 5–7 days first [8]. The purpose of this process is to exude the water in the waste to improve the calorific value of the waste. The higher the calorific value of the waste after fermentation, the higher the average temperature in the furnace, and the greater the average values of the corresponding main steam flow and main steam pressure parameters [24]. However, the unstable composition content of waste leads to large fluctuations in the calorific value of the waste. Thus, the significance of the impact on the stability of the incineration in the furnace cannot be ignored [25].

After fermentation is complete, the waste is sent by a crane to the feed hopper and transported through the feed grate to the incinerator. The feed grate is a multi-stage reciprocating grate with a particular inclination divided into five sections [26]. Among them, Section 1 and Section 2 are the drying sections, where the waste exudes water. In the drying section, the thickness of the waste layer is high and the overall temperature is low, so it will not be burned in a large area. Section 3 and Section 4 are combustion grates. When passing through them, the waste starts to burn vigorously, the thickness of the layer is reduced, and the combustion temperature is generally above 700 °C [27]. The fifth section is a cooling section; the combustible part of the garbage in this section has been basically burned. The remaining ashes are taken out of the furnace from the slag discharge port under the grate. Each section of the grate comprises three sets of reciprocating grates, including sliding, rotating, and fixed grates. A sliding grate with an adjustable sliding speed and number of slides per unit time is responsible for pushing the waste forward, while a rotating grate rotates up and down at a fixed speed to ensure that the primary air is thoroughly mixed with the waste so that the waste can be entirely burned [28].

The waste entering the furnace tends to have large lumps and tiny pores, requiring a lot of air to fuel its combustion. Therefore, in addition to the ash hopper underneath the grate for the collection of the combustion fallout, there are also ventilation ducts feeding a large amount of air. This air is called “primary air”, which is pumped from the top of the waste fermenter and blown into the furnace chamber after passing through the air preheater. The air fed into the drying unit is called “drying air”, which is mainly used to help the waste in the drying unit to fully precipitate water; the air fed into the combustion unit is called “gasification air”, which is mainly used to provide a large amount of oxygen for combustion; and the air fed into the cooling unit is called “cooling air”. The air preheater does not preheat it and it is mainly used to help the unburned waste burn as soon as possible. Among them, the gasification air and drying air critically influence the waste combustion state. Therefore, they also closely affect the stability of the main steam parameters and the release of dioxins and other harmful substances produced by incomplete waste combustion [29].

After the complete combustion of the waste above the grate, a large amount of water, carbon, and volatiles are analyzed, resulting in a high combustion temperature. In order to ensure the complete combustion of the unburned waste in the vertical flue, secondary air is arranged below the vertical flue to strengthen the oxygen in the furnace, thus ensuring the secondary combustion of the incomplete combustion products and reducing the chemical incomplete combustion loss and excess air coefficient in the furnace [30].

The flue gas is exchanged with water vapor in the superheater piping to produce high-temperature, high-pressure superheated steam, which further drives the turbine to rotate, converting thermal energy into kinetic energy again. The higher the amount of heat exchange per unit of time, the higher the flow of superheated steam, and, correspondingly, the higher the kinetic energy generated. Therefore, to ensure the unit’s stable operation, it is necessary first to ensure the stability of the superheated steam parameters. After the heat exchange, the combustion flue gas is discharged from the furnace through the flue gas duct, and the oxygen content in the flue gas is an essential basis for the adequacy of the reaction incineration. The overall structure of the incinerator is shown in Figure 1.

2.2. Selection of Input and Output Variables for Predictive Model

The incinerator’s safety, stability, and efficiency are ensured mainly by maintaining the steam flow and gas oxygen stability. At the same time, to ensure that the combustion process is environmentally friendly and that the generation of dioxins is effectively suppressed, it is necessary to ensure that the temperature of the vertical flue is maintained within a reasonable range. Therefore, for the control objectives, the output variables of the predictive model were determined to be the steam flow, gas oxygen, and vertical flue temperature.

According to the basic structure of the incinerator and the combustion mechanism, the primary airflow, primary damper opening, secondary airflow, operating speed of the feeding grate, and operating speed of the sliding and turning grate are necessary combustion-regulating parameters, which have a decisive influence on the steam flow and gas oxygen, so they are chosen as the initial alternative variables of the input variables. In addition, the process parameters, such as the image characteristic parameters, the layer thickness, which can better reflect the combustion condition of the waste layer, and the calorific value of the waste, which can characterize the heat content per unit of waste, are also used as the key input variables of the predictive model.

2.3. Flame Image Characteristic Calculation

Waste incineration plants generally install two or more webcams at the center of the wall above the cooling section of the incinerator, and the captured flame-monitoring images are connected through a network cable and eventually transmitted to the central control room. The flame-monitoring screen can help the operator to visually determine the material layer’s thickness, the flame burning situation, and the waste distribution to accurately give control instructions, ensure a sufficient fuel supply, and maximize the waste-burning level.

In this paper, we use image processing to obtain four characteristics of flame images to digitize the flame features judged by operators with the naked eye and facilitate dynamic modeling and direct adoption by automatic control systems.

Feature 1: The effective flame area rate [31]. Its meaning is the ratio of the effective gray area of the flame to the overall screen area. It is obtained using Equation (1).

$$S_v=\frac{1}{n}{\displaystyle \sum _{i=1}^X{\displaystyle \sum _{j=1}^{Y}G[f(x_i,y_j)-g_{th}]}}$$

(1)

where $X$ and $Y$ are the number of pixels in the flame image along the x-axis and y-axis directions, $f(x_i,y_j)$ is the gray value of the pixel point at the ith row and jth column in the image, $g_{th}$ is the effective area gray threshold, and $G$ is a step function defined as:

$$G(x)=\left\{\begin{array}{ll}1& x\ge 0\\ 0& x<0\end{array}\right.$$

(2)

Features 2 and 3: The flame’s horizontal center is divided into the left-side center and the right-side center. They characterize the center of the flame on the left and right sides in the horizontal direction, respectively, so that they can reflect the burning height and deflection of the material layer. The formula is:

$$G_l=\frac{{\displaystyle \sum _{(x,y\in S_l)}[f(x_i,y_j)\cdot y_j]}}{{\displaystyle \sum _{(x,y\in S_l)}f(x_i,y_j)}}; G_r=\frac{{\displaystyle \sum _{(x,y\in S_r)}[f(x_i,y_j)\cdot y_j]}}{{\displaystyle \sum _{(x,y\in S_r)}f(x_i,y_j)}}$$

(3)

where $S_l$ is the set of pixel points in the effective region of the flame in the left half of the image, $S_r$ is the set of pixel points in the effective region of the flame in the right half of the image, and $y_j$ is the y-axis coordinate of the pixel point.

Feature 4: The vertical center of the flame. This characterizes the center of the overall flame in the vertical direction and can be effective if there is a bias burn. The formula is as follows.

$$G_h=\frac{{\displaystyle \sum _{(x,y\in S)}[f(x_i,y_j)\cdot x_i]}}{{\displaystyle \sum _{(x,y\in S)}f(x_i,x_i)}}$$

(4)

where $S$ is the set of valid pixel points of the whole image and $x_i$ is the x-axis coordinate of the pixel point.

An actual flame combustion image taken from a waste incineration plant is shown in Figure 2, where the effective flame outline is circled in white; the horizontal centers of the flame on the left and right sides are marked with red dots; and the vertical center of the flame is marked with a green dot.

After a large number of comparisons of calculation results, it is found that these four characteristic parameters respond accurately to the flame characteristics and have a higher correlation with key operating parameters such as the steam flow, so these four image characteristic parameters are included as the initial input parameters for the prediction model.

2.4. Improved WesselN Symbolic Transfer Entropy

A waste incinerator is a complex multivariate coupled system. To obtain the appropriate input variables and delay times for dynamic modeling, it is necessary to eliminate the redundant variables by observing the correlations among the multivariate variables to determine the factors that play a significant influence. At present, the commonly used means of correlation analyses mainly focus on statistical standards, such as the Pearson correlation coefficient [32], a typical correlation analysis [33], and gray correlation [34]. However, these methods can often only obtain the correlation characteristics between variables, and not the causal link between two time series, and it is often impossible to infer the actual key control variables that affect the output parameters.

In 1969, Granger first proposed a causal analysis method for evaluating the existence of interactions between bivariate time series, called the “Granger causality test” [35]. However, this method can only be applied to linear systems and is prone to spurious causality for high-dimensional time series. In 2000, Schreiber proposed the concept of transfer entropy [36], which effectively solves the problem of capturing the asymmetric driving response relationship between two systems and can calculate the coupling strength between two variables more accurately. This approach starts from the concept of “entropy” in information theory and portrays the degree of change in the amount of information contained in variable B when variable A changes, from the perspective of probability density.

Considering two time series, $X$ and $Y$, the transfer entropy is defined as:

$$T{E}_{X\to Y}={\displaystyle \sum _{y_{t+1},x_t,y_t}p(y_{t+1},x_t,y_t)}\log \frac{p(y_{t+1}|x_t,y_t)}{p(y_{t+1}|y_t)}$$

(5)

where $x_t$ and $y_t$ are the historical observations of the time series $X$ and $Y$, respectively, $p(y_{t+1},x_t,y_t)$ is the joint probability density function, and $p(y_{t+1}|x_t,y_t)$ and $p(y_{t+1}|y_t)$ are the conditional probability density functions, respectively.

When $T{E}_{X\to Y}>0$, a causal relationship exists from the time series $X$ to $Y$, and the larger the value, the stronger the causal relationship.

There are many noise oscillations of time series in waste incineration plants, and the transfer entropy will be easily disturbed by high-frequency fluctuations of the series, thus misjudging the causality. “Symbolic transfer entropy’’ [37] is proposed for the noise oscillation characteristic of the series. Firstly, the input time series is transformed into a rank vector using the symbolic method, and then the transfer entropy is obtained from the transformed rank vector according to Formula (5).

In a symbolic analysis of heart rate signals, Wessel et al. [38] proposed a four-symbol static time series transformation method, which was derived as follows.

$$s_i=\left\{\begin{array}{ll}\begin{array}{l}0,\\ 1,\\ 2,\\ 3,\end{array}& \begin{array}{c}{u}_1<x_i<(1+\beta )u_1,or(1+\beta )u_2<x_i<u_2\\ (1+\beta )u_1<x_i,or{x}_i<(1+\beta )u_2\\ (1-\beta )u_1<x_i<u_1,or{u}_2<x_i<(1-\beta )u_2\\ (1-\beta )u_2<x_i<(1-\beta )u_1\end{array}\end{array}\right.$$

(6)

where $x_i$ is the ith parameter in the continuous time series, $u_1$ is the mean of all the elements larger than 0 in series $x_i$, $u_2$ is the mean of all the elements less than 0 in series $x_i$, and $\beta$ is the offset coefficient.

To improve the numerical complexity and introduce temporal memory information, the symbolized sequence $s_i$ is further encoded, as in Equation (7). The encoded data range from 0 to 255.

$$w_i=64\cdot s_i+16\cdot s_{i+1}+4\cdot s_{i+2}+s_{i+3}$$

(7)

However, in the above WesselN symbolization, a mean value of less than 0 elements is obtained as a threshold for classifying the symbolic rank. The problem is that the operational data in industrial sites are distributed in the positive interval range with no negative elements. In addition, the threshold interval of the above method is set singularly, and when the data have an uneven probability distribution density in the distribution domain, they cannot be divided effectively. For this reason, this paper proposes an improved WesselN symbolization method, calculated as follows.

$$s_i=\left\{\begin{array}{cc}\begin{array}{c}0,\\ 1,\\ 2,\\ 3,\end{array}& \begin{array}{c}\min (x)\le x_i<v_2\\ v_2\le x_i<\overline{x}\\ \overline{x}\le x_i<v_1\\ v_1\le x_i<\max (x)\end{array}\end{array}\right.$$

(8)

$$v_1=\overline{x}+\alpha [\max (x)-\overline{x}]$$

(9)

$$v_2=\overline{x}-\alpha [\overline{x}-\min (x)]$$

(10)

where $\max (x)$ is the maximum value of the time series $x$, $\min (x)$ is the minimum value of the time series $x$, and $\overline{x}$ is the mean value of the time series $x$.

As an example, the steam flow data compare the sequence before and after symbolization, as shown in Figure 3.

To compare the effectiveness of the proposed method for causality mining between two time series, two sets of series in the power plant with a known causality according to operational experience and mechanisms are used as test data.

Test 1: Drying air flow–Steam flow. These two data sets have a strong causal linkage. When the drying air volume increases, the steam flow rate will significantly increase.

Test 2: Cooling water flow–Steam flow. These two data sets are typical of a false cause-and-effect relationship; the trend is always the same, but the cooling water flow rate does not cause changes in the steam flow rate.

For these two sets of data, the Improved WesselN (EN), Transfer entropy (E1), Difference symbolized transfer entropy (E2), WesselN (E3), Mutual information (E4), Grey relational analysis (E5), and Pearson coefficient (E6) are calculated between them, respectively.

The comparison results are obtained as shown in Figure 4 and

Table 1. Results of the improved WesselN causality test.

Method	Drying Air-Steam Flow	Cooling Water Flow-Steam Flow
EN	1.2	0.3
E1	0.2	0.15
E2	0.05	0.02
E3	0.55	0.2
E4	1	0.35
E5	0.7958	0.6173
E6	0.77	0.7712

.

For all the tested algorithms, the larger the calculated result, the stronger the causality, otherwise, the weaker it is. For test 1, since the two sequences have a strong causal relationship, the larger the computed result, the more accurate the causality capture. Conversely, for test 2, since the two tested sequences are spuriously causal, the smaller the calculated result, the more precise the causality capture between the two sequences.

According to the test results, compared to other methods, the proposed method in this paper yields the largest value in test 1 and a relatively small value in test 2, indicating a good causality calculation ability.

2.5. Multi-Verse Optimization and Support Vector Machine

Multi-Verse Optimization (MVO) is a new intelligent optimization algorithm that Seyedali Mirjalili et al. proposed in 2016 [39]. The algorithm is based on the multiverse theory, which believes that there are black and white holes in the universe. Black holes attract cosmic space–time through wormholes, and white holes are the matter that black holes spit out after absorbing too much matter. The algorithm uses the expansion mechanism of the universe in a random creation process to gradually converge the search space to the optimal position. The algorithm contains fewer hyper-parameters and has a better parameter search ability for models with more parameters to be optimized. Many related experiments have shown that the algorithm can exhibit an ultra-high speed search capability and a high search accuracy for high-dimensional search problems.

The traversal process of the algorithm is mainly divided into the exploration process and the mining process, which are performed as follows.

Assuming that the search space contains $m$ universes:

$$U=[u_1;u_2;\cdots ;u_m]$$

(11)

$$u_i=[{\chi }_i{}^1,{\chi }_i{}^2,\cdots {\chi }_i{}^k]$$

(12)

$${\chi }_i^j=\left\{\begin{array}{cc}\begin{array}{l}{\chi }^{\ast }\\ {\chi }_i^j\end{array}& \begin{array}{l}{r}_1<NI(u_i)\\ r_1\ge NI(u_i)\end{array}\end{array}\right.$$

(13)

where $u_i$ is the ith universe, $k$ is the number of optimized variables, $NI(u_i)$ is the standard expansion rate of the ith universe $u_i$, $r_1$ is a random number between 0 and 1, and ${\chi }^{\ast }$ is the variable in the ith universe that is selected according to the roulette mechanism.

To iterate to obtain the optimal universe, it is necessary to find the optimal universe with the help of wormholes. The wormhole existence possibility (WEP) and traveling distance rate (TDR) are set, which are calculated as follows.

$$WEP=\min (WEP)+\frac{l}{L}[\max (WEP)-\min (WEP)]$$

(14)

$$TDR=1-\frac{l^{(1/\gamma )}}{L^{(1/\gamma )}}$$

(15)

where $\max (WEP)$ is the maximum value of $WEP$ (set to 1 in this paper), $\min (WEP)$ is the minimum value of $WEP$, set to 0.2 in this paper, $l$ is the current number of iterations, $L$ is the maximum number of iterations, $\gamma$ defines the number of detections that change with the number of iterations, and the higher the value of $\gamma$, the faster the local detection speed.

Assuming that wormhole tunneling is permanently established between the current universe and the optimal universe, this optimization mechanism can be expressed as:

$${\chi }_j^i=\left\{\begin{array}{cc}\begin{array}{c}\left\{\begin{array}{c}{\mathsf{{\rm X}}}_j+TDR\cdot [r_4\cdot (u{b}_j-l{b}_j)+l{b}_j]\\ {\mathsf{{\rm X}}}_j-TDR\cdot [r_4\cdot (u{b}_j-l{b}_j)+l{b}_j]\end{array}\right.\\ {\chi }_j^i\end{array}& \begin{array}{c}\begin{array}{c}{r}_3<0.5\\ r_3\ge 0.5\end{array}\\ r_2\ge WEP\end{array}\end{array}\right.$$

(16)

where ${\mathsf{{\rm X}}}_j$ is the jth variable in the current optimal universe, $u{b}_j$ is the highest value of the jth variable in all the traversed universes of history, $l{b}_j$ is the lowest value of the jth variable in all the traversed universes of history, and $r_2$, $r_3$, and $r_4$ are random numbers between 0 and 1. The search concept diagram of the algorithm is shown in Figure 5.

The Goldstein–Price function is used to test the MVO’s search capability. The formula of the function is shown in Equation (17).

$$\begin{array}{l}f(x)=[1+{(x_1+x_2+1)}^2(19-14x_1+3x_1^2-14x_2)]\\ \begin{array}{lll}& & +6\end{array}{x}_1{x}_2+3x_2^2)][30+{(2x_1-3x_2)}^2(18-32x_1\\ \begin{array}{lll}& & +12x_1^2+48\end{array}{x}_2-36x_1{x}_2+27x_2^2)]\end{array}$$

(17)

where the input domain is usually on the square:

$$\left\{x\right|x_i\in (-5,5),i=1,2\}$$

(18)

It can be easily obtained from the surface of the function’s distribution properties that the function’s maximum value in the definition domain approaches infinity and the minimum value approaches 0. According to the iterative curve, the MVO algorithm quickly reaches the minimum value in the 2nd round and finds the minimum value in the 30th round. The overall running time of the program is 1.5 s, which is faster than that of other optimization algorithms, indicating that the MVO algorithm can find the optimal value for multi-dimensional optimization problems.

The search flow chart of the algorithm is shown in Figure 6. The distribution characteristic surface of the function is shown in Figure 7a, and the iteration curve of the search process is shown in Figure 7b.

A support vector machine (SVM) is used to build the prediction model of this paper, and its basic principle is as follows.

For linear regression problems, the objective of the SVM is to solve for the following regression function.

$$y=w\cdot x+b$$

(19)

where $x$ is the input sample of the model, $w$ is the weight coefficient, and $b$ is the bias coefficient.

By introducing the slack variables ${\sigma }_i$, ${\sigma }^{*}$, the optimization objective can be transformed into:

$$\left\{\begin{array}{l}\min \frac{1}{2}||\omega |{|}^2+C{\displaystyle \sum _{i=1}^h({\sigma }_i+{\sigma }^{*})}\\ \begin{array}{ll}s.t.& \left\{\begin{array}{c}{y}_i-\omega x_i-b\le \epsilon +{\sigma }_i\\ \omega x_i+b-y_i\le \epsilon +{\sigma }^{*}\end{array}\right.\end{array}\end{array}\right.$$

(20)

where $\epsilon$ is the error coefficient, $h$ is the number of training samples, and $C$ is the penalty factor, which controls the degree of penalty of the model for the sample exceeding the error, and the larger the $C$ is, the better the model fits the training sample.

The above equation is a typical optimization problem with constraints. To solve such a problem, the Lagrange multiplier method is used to construct the dyadic problem. The Lagrange function adds the constraint function to the objective function by multiplying it by a factor called the Lagrange multiplier. By taking the derivatives of each variable through the Lagrange function to zero, the set of candidate values can be found and then verified to find the optimal value. A description of the dyadic problem is obtained in the following form:

$$\left\{\begin{array}{l}\begin{array}{ll}\max & \begin{array}{l}-\frac{1}{2}{\displaystyle \sum _{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })({\alpha }_j-{\alpha }_j^{\ast })(x_i-x_j)-}\\ {\displaystyle \sum _{i=1}^n{\alpha }_i({\epsilon }_i-y_j)-}{\displaystyle \sum _{i=1}^n{\alpha }_i^{\ast }({\epsilon }_i+y_j)}\end{array}\end{array}\\ \begin{array}{ll}s.t.& \left\{\begin{array}{c}{\displaystyle \sum _{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })=0}\\ 0\le {\alpha }_i,{\alpha }_i^{\ast }\le C(i=1,2,\cdots ,n)\end{array}\right.\end{array}\end{array}\right.$$

(21)

where $y_j$ is the training target and ${\alpha }_i$ and ${\alpha }_i{}^{\ast }$ are the Lagrange multipliers.

The objective regression-considering function can be obtained using the optimality sufficient condition (KKT condition).

$$y={\displaystyle \sum _{i=1}^n({\alpha }_i-{\alpha }_i^{\ast })(x_i\cdot x)}+b$$

(22)

Since only the inner product operation between training samples is involved in the above problem, the algorithm can effectively emerge from a high-level crisis.

The SVM can only model a single output. Thus, the three predicted parameters are modeled separately, and the weighted average of the root-mean-square-error (RMSE) of the three models is used as the optimization objective function of the MVO, which is expressed as follows.

$$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{n}};F={\delta }_{y_1}\cdot RMS{E}_{y_1}+{\delta }_{y_2}\cdot RMS{E}_{y_2}+{\delta }_{y_3}\cdot RMS{E}_{y_3}$$

(23)

where $y_i$ is the actual sample value, ${\widehat{y}}_i$ is the model prediction value, $n$ is the amount of data, and the weighting coefficients: ${\delta }_{y_1}$, ${\delta }_{y_2}$, and ${\delta }_{y_2}$ are determined by the relative magnitude of the corresponding $RMSE$ and are taken as: 3.3/2.8/17.5, respectively.

For the SVM, two hyper-parameters must be optimized simultaneously: the penalty coefficient $C$ and the kernel parameter $\sigma$. Therefore, there are two variables “${\chi }_i$” within each universe. By setting the number of iteration rounds and the number of universes, the model’s iterative search for optimization can be performed.

3. Predictive Modeling Steps

To establish an accurate prediction model for the key parameters of waste incinerators, the processes of variable selection, time delay estimation, data pre-processing, and model training are required. The specific modeling process is as follows.

• According to the combustion stability, economy, and environmental protection targets required in the control objectives, the predicted output variables of the model are determined to be the steam flow, flue gas oxygen, and vertical flue temperature.
• A total of 4 flame image characteristics and 27 control-system-related parameters are used as the initial model input variables, then the improved WesselN symbolic transfer entropy algorithm is used to find the causality between all 31 initial variables and the 3 model output parameters. Finally, 14 parameters are selected as the model input data.
• To complete the delay compensation, the gray correlation coefficient is used to find the delay time between the 14 input variables and the 3 output variables.
• The training and test data are selected and the data pre-processing is completed using outlier rejection, filtering, and normalization algorithms.
• The number of iteration rounds and the number of universes are set, and the MVO is used to optimize the key parameters $C$ and $\sigma$ of the SVM, thus completing the model training for the SVM using the training data.
• The SVM is trained once using the output as three output parameters, i.e., three prediction models exist. The prediction effect of the trained models is tested using the test data, and finally, the final prediction results can be obtained.

The flow chart of the modeling process is shown in Figure 8.

4. Model Prediction Results and Analysis

4.1. Results of Variable Selection Based on Improved WesselN

The measurement data and image features of a waste-to-energy plant from 1 February to 7 February 2022 are used for a causality test analysis.

After the improved WesselN symbolization, the transfer entropy of the 31 initial variables and the 3 output parameters are obtained separately, and the results show that, for the 3 output parameters, there are 14 parameters, including the 4 image feature parameters with larger transfer entropy values, so these 14 variables with a greater transfer entropy are selected as the model input variables.

The transfer entropy values of the selected 14 variables are shown in

Table 2. Improved WesselN symbolic transfer entropy of 14 selected input variables.

Variable Number	Variable Name	Transfer Entropy
		Steam Flow	Gas Oxygen	Flue Temperature
Var1	Effective flame area rate	2.49	3	0.26
Var2	Left horizontal center of the flame	2.5	2.95	0.26
Var3	Right horizontal center of the flame	2.51	2.85	0.24
Var4	Vertical center of the flame	2.43	2.72	0.26
Var5	Thickness of dry section layer	2.43	2.49	0.3
Var6	Thickness of gasification section layer	2.43	2.55	0.3
Var7	Dry air flow	2.14	2.22	0.32
Var8	Gasification air flow	2.36	2.43	0.44
Var9	Secondary air flow	0.77	0.8	0.2
Var10	Calorific value of waste	2.33	2.41	0.28
Var11	The third-section grate turnover times	2.31	2.45	0.29
Var12	Sliding speed of the first grate	0.54	1.21	0.28
Var13	Sliding speed of second grate	0.6	0.68	0.18
Var14	Sliding speed of third grate	0.64	0.5	0.45

, and a comparison of the transfer entropies of the overall 31 variables is shown in Figure 9. In the figure, Var15–Var31 indicate the remaining 17 variables that are not selected, which include the control system regulation parameters such as the damper opening, grate turning times, and cooling air flow, etc.

4.2. Time Delay Estimation Results Based on Gray Correlation Coefficient

The data from 1 February to 7 February 2022 are used as a sample to calculate the gray correlation coefficients between each input parameter and output parameter for different delay times, which are calculated as follows.

$${\xi }_i(k)=\frac{\underset{s}{\min } \underset{t}{\min } | x_0(t)-x_s(t)| +\rho \underset{s}{\max } \underset{t}{\max } |x_0(t)-x_s(t) |}{| x_0(k)-x_i(k) |+\rho \underset{s}{\max } \underset{t}{\max } | x_0(t)-x_s(t)|}$$

(24)

$$\varpi =\frac{1}{n}{\displaystyle \sum _{k=1}^n{\xi }_i}(k)$$

(25)

where $x_0(t)$ is the reference series, $x_s(t)$ is the comparison series, $\rho \in [0,1]$ is the resolution factor, ${\xi }_i(k)$ is the correlation coefficient at the kth moment, and $n$ is the length of the time series.

The gray correlation coefficients between each input parameter and the 3 output parameters are calculated separately, and the highest coefficient values and their delays with the 14 input parameters and the steam flow are shown in

Table 3. Highest coefficient values and their delays between the 14 input parameters and steam flow.

Variable	Var1	Var2	Var3	Var4	Var5	Var6	Var7	Var8	Var9	Var10	Var11	Var12	Var13	Var14
Delay time (s)	387	388	344	370	255	305	548	551	401	-	708	648	553	438
Coefficient	0.5261	0.5058	0.5354	0.5642	0.6588	0.5816	0.6016	0.5499	0.4054	0.6761	0.338	0.4452	0.4727	0.5068

; the highest coefficient values and their delays with the gas oxygen are shown in

Table 4. Highest coefficient values and their delays between the 14 input parameters and gas oxygen.

Variable Number	Var1	Var2	Var3	Var4	Var5	Var6	Var7	Var8	Var9	Var10	Var11	Var12	Var13	Var14
Delay time (s)	346	368	399	315	208	367	562	526	345	-	675	548	503	458
Coefficient	0.5917	0.6084	0.5594	0.5368	0.6427	0.7097	0.6306	0.7028	0.3808	0.7332	0.4876	0.5677	0.3425	0.6708

; and the highest coefficient values and their delays with the flue temperature are shown in

Table 5. Highest coefficient values and their delays between the 14 input parameters and flue temperature.

Variable	Var1	Var2	Var3	Var4	Var5	Var6	Var7	Var8	Var9	Var10	Var11	Var12	Var13	Var14
Delay time (s)	324	331	314	297	216	316	473	581	189	-	578	406	326	289
Coefficient	0.5777	0.5767	0.6438	0.6628	0.6788	0.5948	0.6346	0.5589	0.2129	0.7078	0.4147	0.4137	0.4148	0.5147

.

According to the calculation results of the delay time, the delay times of the flame image features for the key operational parameters are about 5–6 min, and, since the flame feature image parameters play a key role in the prediction, the prediction duration is set to 6 min. Thus, the data at the current moment are used as the model inputs for the variables with a delay time of less than 360 s. For the variables with a delay time larger than 360 s, the time delay compensation is adopted, i.e., the data before (the delay time) seconds are used as the model inputs.

Among them, since the measurement of the calorific value of the waste itself has a certain lag, it is impossible to estimate the time delay based on the data, so no time delay compensation is performed.

4.3. Model Test Results

The actual production data of a waste-to-energy plant are used as training and test samples, and the interval of the samples is set to 10 s. A total of 10 h of data from 8:00 to 18:00 on 1 February 2022 are used as the test sample to test the prediction effect of the model proposed in this paper.

To compare the effectiveness and prediction accuracy of the method proposed in this paper, two sets of tests are used for a comparison and validation.

Experiment 1: To verify the help of the image characteristic parameters and latency compensation in the model prediction. Firstly, the training data, iteration period, and MVO parameters are kept unchanged, and the model training is completed by removing the image feature parameters with a delay compensation to form model A. Secondly, the model training is completed by removing the delay compensation with the image feature parameters as inputs to form model B. Model A and model B are put together with model C of this paper, which has both image feature parameters and a delay compensation, and the same set of prediction effects is observed using the same set of test data.

The final comparison data are shown in

Table 6. RMSE comparison data of Experiment 1.

Model	RMSE
	Steam Flow	Gas Oxygen	Flue Temperature
A	0.5964	0.4706	4.074
B	0.4734	0.3559	2.598
C	0.3035	0.2477	1.6773

and the test results’ comparison curve is shown in Figure 10.

In experiment 1, for the three output variables, the RMSEs of the test data of both model A and model B are larger than that of model C, and the fluctuations in the prediction curves are more dramatic, which fully illustrates that the addition of the image feature parameters and a delay compensation provides a better enhancement of the model prediction effect, which can reduce the prediction error and improve the prediction accuracy.

Experiment 2: To verify the effectiveness of the MVO algorithm in finding the optimal parameters of the SVM. The training data and the iteration period are also guaranteed to be constant. The Particle Swarm Optimization algorithm (PSO) [40], Beetle Antennae Search algorithm (BAS) [41], Sparrow Search algorithm (SSA) [42], and MVO-optimized SVM are used with the same image feature parameters and time delay compensation, respectively, and the prediction effect is finally observed using the same set of test data. Since optimization algorithms are generally strongly stochastic, ten sets of tests are performed for each algorithm, and the Wilcoxon sign rank test [43] is performed between the RMSEs of the prediction results of the three comparison algorithms and the RMSEs of the MVO, respectively, to prove the optimization effectiveness of the MVO algorithm.

The $RMSE$ comparison data are shown in

Table 7. RMSE comparison data of Experiment 2.

Round	RMSE of Steam Flow				RMSE of Gas Oxygen				RMSE of Flue Temperature
	PSO	BAS	SSA	MVO	PSO	BAS	SSA	MVO	PSO	BAS	SSA	MVO
1	0.4395	0.4963	0.4937	0.3258	0.2694	0.5112	0.3462	0.1572	1.9513	2.1972	2.6683	1.7406
2	0.3334	0.4892	0.4628	0.2591	0.3487	0.5328	0.3352	0.2532	2.9153	2.1257	2.4171	1.5581
3	0.3835	0.4880	0.3779	0.3136	0.2535	0.4777	0.3496	0.2121	2.4812	2.0026	2.8824	1.6271
4	0.3275	0.4833	0.5164	0.2745	0.4010	0.4580	0.3596	0.2665	2.6347	1.7103	2.4218	1.8147
5	0.4166	0.5013	0.4715	0.2899	0.3930	0.4692	0.3674	0.2770	2.3910	2.1548	2.5818	1.7598
6	0.4196	0.5028	0.4595	0.3166	0.3501	0.4628	0.3457	0.2843	2.1938	2.2565	2.2715	1.4797
7	0.4226	0.5454	0.4860	0.3311	0.3465	0.4106	0.3337	0.2223	1.5781	1.9306	2.3750	1.6342
8	0.3935	0.5839	0.4683	0.2664	0.2257	0.4375	0.3516	0.2679	2.6879	2.0551	2.2662	1.6429
9	0.4092	0.5256	0.3841	0.3378	0.3791	0.4867	0.3538	0.2541	2.4139	2.0916	2.5785	1.7214
10	0.3762	0.4885	0.4386	0.3198	0.2404	0.4487	0.3477	0.2830	2.4408	1.8741	2.7603	1.7942
Mean	0.3821	0.5104	0.4559	0.3035	0.3206	0.4629	0.3490	0.2477	2.3688	2.0398	2.5223	1.6773

. The Wilcoxon signed-rank test results are given in

Table 8. The results of the Wilcoxon signed-rank test.

Output	$\mathit{p}$
	Test between MVO and PSO	Test between MVO and BAS	Test between MVO and SSA
Steam flow	0.0039	0.002	0.002
Gas oxygen	0.0195	0.002	0.002
Flue temperature	0.0039	0.0059	0.002

and the test result comparison curve is shown in Figure 11.

Based on the above tables and figures, we can analyze that:

• In Experiment 2, firstly, for the three lots of output data, the mean $RMSE$ of the MVO is smaller than that of the other optimization algorithms for all ten sets. Secondly, all the $p$ values are less than 0.05 in the Wilcoxon signed-rank test. These results indicate that the MVO has a significant parameter-seeking optimization ability compared to the other algorithms, and that the MVO-SVM algorithm can also achieve the relatively highest prediction accuracy.
• Comparing Experiment 1 and Experiment 2, when there are no image feature parameters as inputs or no delay compensation, the RMSEs of the prediction results are higher than the model prediction results obtained using either optimization algorithm, indicating that the image feature parameters and delay compensation are crucial for the establishment of the prediction model.
• For all the comparison cases in the experiments, the curve trajectories of the prediction results are synchronized with the fluctuations in the actual values, only with larger errors, which indicates that the support vector machine has a good regression-fitting effect for building a prediction model for the key operating parameters of waste incinerators.

5. Conclusions

To improve the stability, economy, and environmental protection of waste incinerator control systems, reduce the pollutant emission index, and provide a practical reference for optimizing the control system, a prediction model for the key operating parameters of incinerators based on measurement data and flame image features was proposed.

Firstly, according to the control system’s environmental protection, stability, and economic indexes, the steam flow, gas oxygen, and flue temperature were determined as the model’s prediction output parameters. Then, flame images were processed, and four image parameters that effectively reflected the flame characteristics were extracted as the model’s input parameters. With them, 31 pieces of initial input data were chosen according to the control logic, and the improved WesselN symbolic transfer entropy was used to find the causality with the output data. Finally, 14 variables with the highest causalities were selected as the model’s inputs, the delay compensation was completed, and the MVO-SVM-based prediction model was established after iterative loops.

Conclusions were obtained as follows:

• The images of the flame-monitoring screen were obtained through the webcam, four image parameters that could better reflect the flame characteristics were extracted through image processing, they were added to the input parameters of the prediction model, and the comparison experiments showed that the addition of the image feature parameters significantly improved the prediction accuracy of the model.
• This paper proposed a causality analysis algorithm among a time series based on improved WesselN symbolic transfer entropy. The improved algorithm could effectively overcome the high-frequency noise of the time series, extract the fluctuation characteristics of the series, and divide the rank interval. Compared to other causalities, the improved algorithm had a more accurate ability to capture the causality of the time series.
• This paper proposed a prediction method based on the Multi-Verse Algorithm to optimize support vector machines. Compared to other two optimization algorithms, the MVO had a stronger global optimal point search capability and effectively reduced the model’s testing error.