Management of the Torch Structure with the New Methodological Approaches to Regulation Based on Neural Network Algorithms

Abstract

A method for evaluating the thermophysical characteristics of the torch is developed. Mathematically the temperature at the end of the zone of active combustion based on continuous distribution functions of particles of solid fuels, in particular coal dust. The particles have different average sizes, which are usually grouped and expressed as a fraction of the total mass of the fuel. The authors suggest taking into account the sequential nature of the entry into the chemical reactions of combustion of particles of different masses. In addition, for the application of the developed methodology, it is necessary to divide the furnace volume into zones and sections. In particular, the initial section of the torch, the zone of intense burning and the zone of afterburning. In this case, taking into account all the thermophysical characteristics of the torch, it is possible to make a thermal balance of the zone of intense burning. Then determines the rate of expiration of the fuel-air mixture, the time of combustion of particles of different masses and the temperature at the end of the zone of intensive combustion. The temperature of the torch, the speed of flame propagation, and the degree of particle burnout must be controlled. The authors propose an algorithm for controlling the thermophysical properties of the torch based on neural network algorithms. The system collects data for a certain time, transmits the information to the server. The data is processed and a forecast is made using neural network algorithms regarding the combustion modes. This allows to increase the reliability and efficiency of the combustion process. The authors present experimental data and compare them with the data of the analytical calculation. In addition, data for certain modes are given, taking into account the system’s operation based on neural network algorithms.

1. Introduction

1.1. Operation of Solid Fuel Steam Generators with Different Characteristics

To ensure uninterrupted generation of heat and electricity, coal of various grades and different thermal characteristics can be used at thermal power plants. In addition, even the characteristics of coal produced in a single field will vary depending on the specific coal seam. It should also be noted that the thermal properties of coal vary depending on the conditions of transportation and storage.

Thus, the properties of the fuel agent entering the boiler units of the thermal power plant (TPP) are constantly changing, which often leads to different burning conditions. In the most general case, the burn-up time of fuel particles varies, which leads to an increase or decrease in the length of the flare, physical underburning, slagging of the heating surfaces, and heat losses with flue gases.

Thus, for reliable and efficient operation of solid fuel steam generators with different characteristics, it is necessary to develop a method for controlling the structure of the flare with the possibility of conducting modes using predictive control.

1.2. Review of the Works of the Authors of the Research Topic

The processes of solid fuel combustion are studied by scientists all over the world [1]. The most comprehensive data on the preparation of coal dust at thermal power plants can be found in [1]. One of the most difficult obstacles for high-quality combustion of solid fuel is its polyfractional composition, this is confirmed by the mathematical models of the authors [2]. The most important condition for complete combustion is the presence of the necessary amount of air as an oxidizer and the fineness of the grinding of coal dust, which the authors note [3]. In the work [1], various mathematical models of the combustion process are presented. In the study [3], the authors consider mathematical models of vibro treatment of solid fuel. The burning theory and mathematical modeling of the combustion process were founded by Spalding, Zeldovich and Pomerantsev. In the book [4], Spalding presents modern methods of mathematical modeling, which are basic for computer modeling programs. Zeldovich and Pomerantsev in [5] presented chemical formulas for the formation of combustion products in the process of burning organic fuel. Spalding provided the fundamental basis of chemical reactions of combustion, physical and mathematical burning, torch development in a furnace of the boiler, predict the behavior of various torch configurations and different fuel. Pomerantsev subsequently [5] developed the basics of practical use of the accumulated knowledge on specific high-temperature objects in his works, while he uses the data of world scientists, including the American professor F. A. Williams [6]. In the conditions of natural gas shortage in some Central Asian states, scientists supported the main ideas of world scientists and in 2000–2010 began to develop new methodological approaches to solving the problems of burning lignite, one of the main works is [7]. Finally, in this work [7], the topic of dust sieving was raised for the first time, which was later reflected in the already mentioned work [3].

Rosendahl’s research supports the idea of insufficient methodological support for heat transfer processes in high-temperature units. Co-authored with Mando, a manuscript with his own mathematical model was published [8]. In the article [9], Asotani and co-authors pay attention to the model of the behavior of coal particles together with air, while the proposed mathematical model is in good agreement with [8] and some scientific assumptions of the authors [5]. All models proposed in the review do not contradict each other, as well as the fundamental laws of physics and heat transfer [8,9].

Nowadays, computer mathematical modeling programs for the combustion of coal dust take into account the thermophysical characteristics of the fuel, the average determining (equivalent) particle size. Note that modern software packages provide an idea of the distribution of temperature, velocity, and concentration fields, which are related by known dependencies [4,6], but the accuracy and reliability of the data obtained does not always meet the criteria necessary to start designing a boiler unit or changing dust preparation systems. It is required to conduct experimental studies and compare them with the results of computer modeling. The authors of the work [10] note the impossibility of applying standard methods to micro-mill coal particles, which is confirmed by the results of experiments [11].

The developments of scientists in the field of neural network algorithms and automated control systems are worth noting. Current research on the application of neural network technologies in the energy sector is focused on the field of weather regulation. [12]. The project proposes to take into account the world experience based on the obtained experimental data, combine the calculation methods and introduce adaptive weight coefficients for them. The author has been studying the burning of coal dust for a long time and has experience that allows us to evaluate the reliability of the results of neural network forecasting in this area [13].

Currently, the topic raised by the authors of the article is relevant. Researchers from various countries and scientific laboratories are developing mathematical models of combustion processes and ways to control thermophysical parameters.

In the work [14], the authors consider the flare technology of organic fuel combustion, by analogy with the one that is the basis of this article. Researchers in the article [15] deal with the topic of fuel combustion as part of an improved thermal power plant. In the same article [15], the issues of automatic control of the torch structure are discussed. Scientific developments in the article [16] show the need to use predictive systems for regulating the thermophysical properties of the torch. The authors of the article [17], as well as the researchers in the article [18], on the basis of predictive modules and models of furnace devices of steam generators, suggest the need to introduce neural network algorithms in industry, in particular for regulating the composition of combustion products. Similar studies were conducted in laboratories around the world. In addition, the article [19] considers the simulation of the operation of a steam generator in terms of the concentrations of combustion products and fuel composition. In [20], the analysis of experimental data and modeling data using statistical methods is carried out. The scientific work [21] concerns the model of the movement of combustion products. The article [22] uses a mathematical model of a similar type. In addition, in the works [21,22], as well as in the work [17], the issues of control using neural network algorithms are touched upon.

Based on the results of research in the world, as well as mathematical methods developed by the authors themselves, a number of works related to the introduction of neural network algorithms in the industry were compiled. For example, in [23], the process of burning in a flare of coal particles is considered with a basic method for estimating the size of coal particles. In the study [24], an algorithm for data transmission and processing using piecewise linear functions was developed. In [25,26], the authors developed the methods used in the studies [23,24]. In particular, methods of mathematical analysis of combustion processes have been developed on the basis of control systems and particle size estimation technology.

1.3. Purpose and Objectives of the Study

The purpose of this work is to ensure efficient fuel combustion under conditions of regularly changing properties of the fuel agent.

To achieve the goal, the following tasks are set:

(1)

Development of a calculation method that allows determining the required particle burn-up time based on the properties of the fuel-air mixture to ensure the required length of the flare, limited by the geometry of the boiler unit.

(2)

Adapting the methodology to the capabilities of modern technologies, taking readings from instruments and sensors, affecting the fuel-air flow and regulating the thermal characteristics of the flow and the quality of fuel supplied to the furnace in particular.

(3)

Creating a software algorithm that allows you to calculate the necessary impact and perform regulation, as well as collecting and systematizing data on the expected (calculated) and produced (real) effect with the construction of predictive characteristics.

(4)

Development of a neural network control algorithm that can be able to learn from the information collected in point 3 and be configured for a given type of boiler unit.

2. Research Contribution to Science

2.1. Fuel under Study

The research is carried out on boiler units of the Barnaul Boiler Plant (BBP) type with a frontal arrangement of burners, as fuel, the boiler house uses coals of the Shoptykol and Sarykol deposits of the Maikuben coal basin in Kazakhstan of the B3 brand. The properties of coals are similar, but there are also differences. Data on the composition of the coals of the Maikuben basin of the heat engineering laboratory are known [27].

We present the average characteristics of the three groups of coals studied: lowest heat of combustion of fuel per working mass Q^c_l = 15,755–19,570 kJ/kg, ash content A^d = 13–28, humidity W^d = 18, yield of volatile combustibles V^daf = 41–43%, carbon content C^daf = 72–74%, calcium oxide CaO = 3–6% from Kazakhstan and Russia.

In addition, the authors of the article note that the object of research regularly conducts pilot burning of coal batches from various fields, including the Kansko-Achinsk and Kuznetsk basins from Russia, which differ sharply in properties from the project Chelyabinsk coal and the coals of the Maikuben basin from Kazakhstan that are burned on a permanent basis.

Rational use of fuel resources is an important issue of the modern economy, which exists in conditions of limited supply of the fuel and energy market. Moreover, the decision to increase coal production until 2035 was supported at the government and ministerial levels. In addition, with the correct organization of the burning process, the development of methods for controlling the flare, and even more so the introduction of neural network algorithms, in addition to reducing fuel consumption per boiler, the rationalization of fuel combustion leads to a reduction in emissions and has a beneficial effect on the environment.

2.2. The Scientific Novelty of the Work

The scientific novelty of the work contains words that improved theoretical and methodological framework for the study of heat transfer during the combustion of pulverized coal in the combustion chamber and energy of steam generators. Specifically, that framework based on the concept of the flare continuum and created by the authors of the methodology for the assessment of flame length and time of burning. In process of burning time the fuel particles change their properties under conditions of regularly heat transfer. The parameters of the combustion process, based on Equation (13), are adapted to the capabilities of modern technologies, taking readings from instruments and sensors, affecting the fuel-air flow. Furthermore, regulating the thermal characteristics of the flow and the quality of the fuel supplied to the furnace impact on heat transfer. It should be noted that the authors have developed an algorithm for determining the temperature at the end of the intense burning zone. Based on this algorithm, a program was created to predict this temperature.

2.3. The Practical Significance of the Work

The practical significance is to increase the efficiency of the designed boiler units, as well as extend the life and increase the efficiency of already used. This fact will allow the boiler unit to adapt quickly to fluctuations in the properties of the mixture of fuel and oxidant. One variant of adaptation is quickly change the temperature field when changing fuel. That leads to prevent excessive slagging surfaces and underburning of fuel to increase the thermal efficiency of the boiler unit by adjusting the length of the torch at the depth of the combustion space.

The applied part of the work from the point of view of economic prospects for science is that the developed software product does not use complex and expensive computer systems for modeling, such as ANSYS 19.0 [28], Comsol 5.5 [29], MathCad 15.0 [30], SolidWorks 2019 [31], because the algorithms of this product are based on the use of empirical data measured during the operation of the boiler unit, organized in database tables. For the possibility of implementing the tasks set, a BKZ-210-140F boiler was selected as a test unit.

3. Applied Developed Schemes and Methods

3.1. Data Transfer Scheme

The implementation of the set goals is impossible without a data transmission structure. This structure was built on the basis of available resources, it is relatively simple and meets the following requirements:

• automated data collection capability;
• the ability to save the history of education;
• the possibility of limiting the impact on the combustion process;
• the ability to verify the calculated data by the manager.

The data is processed as follows (Figure 1).

A thermal picture of the furnace is built on the basis of the data measured by optical pyrometers and thermal probes. Such indicators as the speed of the air jet and the fuel-air mixture, the temperature and concentration of reagents in the exhaust gases behind the furnace, the fractional and chemical composition of the source fuel are also measured.

The recorded readings are transmitted to the SCADA server, which acts as a local computer of the enterprise with the installed SCADA system. Through the program interface of the SCADA administrator application, data is transmitted to the Scada Sql Service, from where it is exported to the Microsoft SQL database via a communication channel, after which it can be used by third-party programs.

The application developed by the authors, at certain intervals, accesses the database for information. Based on the difference between this information about the current heat pattern and previous calculations suggesting its future state, as well as on the difference between the input data of the calculation and the current input data, the calculation algorithms are adjusted. The process of adjusting the calculation algorithms and its general principles are described in detail in the relevant sections of the article.

Upon completion of the training, which involves adapting the calculation algorithms to obtain accurate results, the program makes a new calculation and sends a signal to the regulatory authorities: dampers, blow fans, valves, and so on. However, before the command is executed, it must pass an adequacy check. This is a necessary step for the first time, because mistakes are inevitable in the course of training. For some coefficients, the function can turn into a divergent series and give significant deviations. When the position of the regulating body changes, the thermal picture of the furnace chamber also changes, followed by a new measurement.

3.2. The Method of Calculation of the Combustion Process of Various Types of Solid Fuel in a Flare

This technique allows you to calculate the required coal grinding fineness and the fuel feed rate on the burner section in order to ensure a certain time of particle burnout and adjust the length of the torch.

The authors also introduce the following concepts, definitions and limitations for the methodology, which is part of the developed methodological concept. It is proposed to introduce into the theory of heat transfer the influence factor of the mathematical description of the fractional composition of coal dust. For the first time, the authors introduce the concept of a flare continuum as a continuous medium in which the processes of burning and heat transfer are studied. Distinctive feature of the proposed solutions is that when moving in the flare continuum, the fuel dust enters the process of heating, separation and combustion of volatiles, combustion of coke in a diffraction mixture, starting with small fractions with the size of δmin and ending with large fractions with the size of particles δmax. Therefore, for the analysis of thermal and temperature processes in the flare continuum, it is necessary to associate the analysis of the total residue with the local value of the fraction in the ensemble of fuel particles F(δi). This theory was previously verified in detail by the authors [13] and it was proved that the Rosin-Rammler distribution can be replaced by a normal distribution along the Gauss curve. In solving these problems, we use the methods of dividing the furnace chamber into zones, which were also previously used by the authors [7], the equations of stationary and non-stationary thermal conductivity, radiation and convective heat transfer.

Figure 2 shows the combustion chamber. The calculation is based on the following model. In the zone of active combustion (1–3) occurs the ignition and burnout of the main mass of fuel. It is divided into a flare ignition section (1–2) and a balanced heat sink combustion section (2–3). In the fuel reburning zone (3–4), the fuel residue is burned out and the combustion products are cooled.

In this article, we consider a solution for the following initial conditions: replacing the fuel with another fuel with known properties. In this case it is necessary to adjust the length of the torch by changing the grain size of the coal and the feed rate of the fuel air mixture.

(1)

By converting the basic heat balance equation for the flame ignition area, we obtain [13]:

$$l_f=\frac{{\lambda }_f·\left({\mathrm{T}}_{f0}-{\mathrm{T}}_0\right)·{\mathrm{F}}_f}{a_f·{\mathrm{Q}}_l^c·{\mathrm{B}}_c+{\mathrm{Q}}_l^{c.ad}·{\mathrm{B}}_c^{ad}-{\mathsf{\sigma }}_0·a_{fl}·{\mathrm{T}}_{f0}{}^4·{\sum }_{\mathrm{i}=1}^{\mathrm{i}=\mathrm{n}}{\left({\mathsf{\Psi }}_{\mathrm{i}}·{\mathrm{F}}_{\mathrm{i}}\right)}_{a.b}-\left({\mathrm{I}}_{f0}-{\mathrm{I}}_0\right)·\mathrm{r}·{\mathrm{B}}_c}$$

(1)

where $l_f$—the length of the torch at the ignition site, m; ${\lambda }_f$—conditional coefficient of thermal conductivity of the gas medium(flue gases), kW/(m $·$ K); ${\mathrm{T}}_{f0}$—flame temperature at the end of the ignition zone, K; ${\mathrm{T}}_0$—initial temperature, averaged for the embrasures and the surface of the screens, K; ${\mathrm{F}}_f$—cross-sectional area of the torch in the active combustion zone, m²; $a_f$—integral degree of fuel burn-up at the end of the ignition phase; ${\mathrm{Q}}_l^c$—lowest heat of combustion of fuel per working mass, kJ/kg; ${\mathrm{B}}_c$—fuel consumption per working weight, kg/s; ${\mathrm{Q}}_l^{c.ad}$—the lowest calorific value of the illuminating fuel per working mass, kJ/m³; ${\mathrm{B}}_c^{ad}$—illumination fuel consumption per working weight, m³/s; ${\sigma }_0$—universal Stefan-Boltzmann constant, kW/(m²·K⁴); $a_{fl}$—degree of blackness of the torch; $\sum _{\mathrm{i}=1}^{\mathrm{i}=\mathrm{n}}{\left({\mathsf{\Psi }}_{\mathrm{i}}·{\mathrm{F}}_{\mathrm{i}}\right)}_{a.b}$—complex of effective heat perception surface of the active combustion zone, m2; ${\mathrm{I}}_{f0}$—the enthalpy of the combustion products related to 1 kg of fuel at a temperature of ${\mathrm{T}}_{f0}$, kJ/kg; ${\mathrm{I}}_0$—the enthalpy of the combustion products related to 1 kg of fuel at a temperature of ${\mathrm{T}}_0$, kJ/kg; $\mathrm{r}$—mass fraction of recirculation gases introduced through the burners.

Additional restrictions must be introduced to start the calculation. Based on the experimental data, one can take: ${\lambda }_f\approx 1$ kW/(m $·$ K); ${\mathrm{T}}_0\approx$ 900 K; ${\mathsf{\sigma }}_0$ = 5.67·10⁻¹¹ kW /(m²·K⁴); $a_f\approx$0.9. Values ${\mathrm{B}}_c$, ${\mathrm{B}}_c^{ad}$, $\mathrm{r}$ accepted based on the data on the operation of the boiler. Values ${\mathrm{Q}}_l^c$, ${\mathrm{Q}}_l^{c.ad}$, are based on data about fuel. Values ${\mathrm{I}}_{f0}$, ${\mathrm{I}}_0$ are taken according to the graphs of the dependence of the enthalpy of the combustion products on their temperature for different types of fuel. Value ${\mathrm{T}}_{f0}$ it depends on the properties of the fuel and is taken before starting the boiler according to the fuel composition analysis or test combustion, and during the operation of the boiler is specified by monitoring. Value $a_{fl}$ accepted 0.9 according to the standard. Complex $\sum _{\mathrm{i}=1}^{\mathrm{i}=\mathrm{n}}{\left({\mathsf{\Psi }}_{\mathrm{i}}·{\mathrm{F}}_{\mathrm{i}}\right)}_{a.b}$ it is calculated according to the standard method of thermal calculation [32], and the cross-sectional area of the torch in the active combustion zone ${\mathrm{F}}_f$ it is calculated by formulas (2) and (3). For a furnace chamber with a front burner layout [32]:

$${\mathrm{F}}_f{ = \mathrm{H}}_{a.b}·{\mathrm{A}}_f$$

(2)

For a combustion chamber with a counter arrangement of burners [32]:

$${\mathrm{F}}_f{ = \mathrm{H}}_{a.b}·{\mathrm{C}}_f$$

(3)

where ${\mathrm{H}}_{a.b}$—height of the active combustion zone, m; ${\mathrm{A}}_f$—width of the combustion chamber, m; ${\mathrm{C}}_f$—depth of the combustion chamber, m. Values ${\mathrm{H}}_{a.b}$, ${\mathrm{A}}_f$, ${\mathrm{C}}_f$ depend on the geometry of the combustion chamber.

(2)

From the dependences relating the length of the flare and the fuel flow rate [13], we can obtain [13]:

$${\mathsf{\omega }}_0=\frac{\left(l_f{}^3+19.0476·l_f{}^2+11.337875·d_0{}^3·l_f\right)·\mathsf{\alpha }}{56.44·d_0{}^2}$$

(4)

${\mathsf{\omega }}_0$—the speed of movement of particles on the burner section, m/s; $l_f$—the length of the torch at the ignition site, m; $d_0$—diameter of the burner mouth (or equivalent diameter), m; $\mathsf{\alpha }$—the heat transfer coefficient on the surface of the particles, W/(m²·K).

From the experimental data it can be taken that $\mathsf{\alpha }$ = 100 W/(m²·K).

(3)

The velocity of the particles in the flare will vary according to the dependence [4]:

$${\mathsf{\omega }}_f{=\mathsf{\omega }}_0·k_{\mathrm{F}}·k_{\mathrm{V}}·k_{\mathrm{T}}$$

(5)

${\mathsf{\omega }}_{\mathrm{f}}$—the velocity of the particles in the flare, m/s; ${\mathsf{\omega }}_0$—the speed of movement of particles on the burner section, m/s; $k_{\mathrm{F}}$—the factor of influence of the change in the torch cross-section on the particle velocity; $k_{\mathrm{V}}$—the factor of influence of the change in the volume flow rate of the medium in the flare on the particle velocity; $k_{\mathrm{T}}$—the factor of influence of the change in the flame temperature on the particle velocity.

The factor of influence of the change in the torch cross section on the particle velocity can be determined by Equation [4]:

$$k_{\mathrm{F}} = \frac{1}{1 + 0.21·\frac{l_f}{d_0}}$$

(6)

Under the influence of factors $k_{\mathrm{V}}$ and $k_{\mathrm{T}}$ there will be little impact on the speed of fuel particles in the considered ignition area due to the peculiarities of the nature of the flame development.

Thus, for the ignition site, Equation (5) can be written as [4]:

$${\mathsf{\omega }}_f = \frac{{\mathsf{\omega }}_0·d_0}{d_0 + 0.21·l_f}$$

(7)

(4)

Time of burning particles polyfractional torch at the site of inflammation [13]:

$$\mathsf{\tau }=\frac{l_f}{{\mathsf{\omega }}_f}$$

(8)

where $\mathsf{\tau }$—time of burning of the particles of the poly-fraction torch in the ignition area, s; $l_f$—the length of the torch at the ignition site, m; ${\mathsf{\omega }}_f$—the velocity of the particles in the torch, m/s.

(5)

The relationship of the burn-up time with the particle size, and the influence of the fractional composition on the combustion process [13]:

$${\mathsf{\tau }}_{bur}=\frac{\mathsf{\delta }·\mathsf{\rho }·\mathrm{c}·\mathrm{m}}{2·\mathsf{\alpha }·\mathsf{\varsigma }}·\ln \left(\frac{{\mathrm{t}}_{f }{- \mathrm{t}}_0}{{\mathrm{t}}_{f }{– \mathrm{t}}_{bur}}\right)$$

(9)

where ${\mathsf{\tau }}_{bur}$—the burning time of the fuel particle averaged by the properties, s;$\mathsf{\delta }$—particle size (diameter), m; $\mathsf{\rho }$—particle density, kg/m³; $\mathrm{c}$—mass heat capacity of the particle material, kJ/(kg·°C); $\mathrm{m}$—coefficient of thermal massiveness of the fuel particle; $\mathsf{\alpha }$—coefficient of heat transfer to the particle surface, W/(m²·K); $\mathsf{\varsigma }$—the shape factor of the particles; ${\mathrm{t}}_f$—the temperature of the flue gases, °C; ${\mathrm{t}}_0$—the initial temperature of the particle, °C; ${\mathrm{t}}_{bur}$—temperature of intensive release of volatile substances, °C.

In the first approximation, we can consider ${\mathrm{t}}_{bur}$ the ignition temperature of the combustible mixture (this assumption is necessary to start the calculation). With a raise ${\mathrm{t}}_{bur}$ the temperature difference decreases and the particle burning ${\mathsf{\tau }}_{bur}$ increases.

The coefficient of thermal massiveness of the fuel particle takes into account the influence of the thermal massiveness of the particles on the temperature field [33]:

$$\mathrm{m} = 1 + \frac{\mathsf{\alpha }·\mathsf{\delta }}{2·{\mathsf{\lambda }}_{con.f}·\left(\mathsf{\varsigma } + 2\right)}$$

(10)

where $\mathrm{m}$—coefficient of thermal massiveness of the fuel particle; $\mathsf{\alpha }$—coefficient of heat transfer to the particle surface, W/(m²·K); $\mathsf{\delta }$—particle size (diameter), m; ${\mathsf{\lambda }}_{con.f}$—conditional coefficient of thermal conductivity of the gas medium (flue gases), kW/(m·K); $\mathsf{\varsigma }$—the shape factor of the particles.

From the experimental data: $\mathsf{\alpha }$ = 100 W/(m²·K); ${\mathsf{\lambda }}_{con.f}$ = 0.15 kW/(m·K).

Value $\mathsf{\varsigma }$ it is a mathematical abstraction [33] and when the particle shape is approximated to a sphere $\mathsf{\varsigma }$ = 3.

Then Equation (9) can be transformed to search for ${\mathrm{t}}_{\mathrm{int}}$ [4,13]:

$${\mathrm{t}}_{bur}{ = \mathrm{t}}_f - \frac{{\mathrm{t}}_f{ - \mathrm{t}}_0}{\exp \left(\frac{4·\mathsf{\alpha }·\mathsf{\varsigma }·{\mathsf{\tau }}_{bur}·{\mathsf{\lambda }}_{con.\mathrm{f}}·\left(\mathsf{\varsigma } + 2\right)}{\mathsf{\delta }·\mathsf{\rho }·\mathrm{c}·\left(2·{\mathsf{\lambda }}_{con.f}·\mathsf{\varsigma } + 4·{\mathsf{\lambda }}_{con.f} + \mathsf{\alpha }·\mathsf{\delta }\right)}\right)}$$

(11)

4. Forecasting

Forecasting characterizes the future development of the heat map (a set of thermal fields that change over time) of the furnace chamber of a boiler unit, based on the hypothesis of preserving the impact of the main factors of the past period on the forecast period or the possibility to justify and take into account the direction of their changes in the considered perspective. Here, the prospects of forecasts are related to the inertia of thermal systems.

Fuel combustion processes are non-stationary. The time series is affected at different times by different factors. Their influence of some of them, for one reason or another, is weakened while others act more actively. Thus, the real process proceeds in the changing conditions that make up its external environment, to which it adapts, and the model, in turn, adapts to the series representing this process.

The longer the forecast period (pre-emption), the more the factors that affect the course of the process, both directly and indirectly, vary. In addition, unforeseen factors that significantly deform the process under study may indicate their influence. These include factors that do not have the necessary data to predict their impact at the time of making the forecast, as well as those whose nature is uncertain.

The difficulty of constructing a mathematical model is to approximate the indefinite quantities in terms of deterministic and random ones. Random variables, unlike undefined ones, have a distribution curve and a certain probability of falling into a given interval.

The goal of adaptive methods is to build self-adjusting thermal and chemical fuel-oxidative models that can reflect time-varying conditions, take into account the information value of different members of the time sequence, and give fairly accurate estimates of future members of the series. That is why such models are intended primarily for short-term forecasting, and in this case can be used to adjust the length of the flare and the time of particle burn-up depending on the continuously changing composition of the fuel mixture and oxidizer in a limited range.

It is important to note that for the successful adaptation of the model, the greatest approximation of the number of measurements in relation to the prediction interval is necessary. And the prediction interval should be determined by the dynamics of the process. Combustion processes are not time-consuming, relatively quick, but taking into account the reduction in the heterogeneity of fuel with a high degree of quality grinding and mixing, as well as a low rate of daily fluctuations in temperature (ambient) air supplied to oxidize, it can be assumed that the number of measurements performed once a minute will be enough to capture the direct impact of regulation on the combustion process.

The prediction is made based on a variety of recorded readings, such as the feed rate and temperature of the fuel, air, fuel-air mixture and flue gases, the average specific heat of combustion of the fuel, the release of volatiles, the fractional composition, the excess air coefficient, the carbon monoxide content in the flue gases. The database that contains the necessary information is shown in

Table 1. Database appearance (Part 1).

Date Time	Hot Air: Speed, m/s	Hot Air: Temperature, °C	Fuel-Air Mixture: Speed, m/s	Fuel-Air Mixture: Temperature, °C	Fuel: Net Calorific Value, kJ/kg
11.10.2019 13.00.00	8	350	8.46	340	22961
11.10.2019 13.01.00	8	350	8.46	340	22961
11.10.2019 13.02.00	8.1	349	8.57	338	22961
11.10.2019 13.03.00	8.1	349	8.58	337	22961
11.10.2019 13.04.00	8	350	8.46	340	22961
11.10.2019 13.05.00	8	350	8.46	340	22961
11.10.2019 13.06.00	8	350	8.46	340	22961
11.10.2019 13.07.00	8	350	8.46	340	22961
11.10.2019 13.08.00	8.05	349	8.54	336	22961
11.10.2019 13.09.00	8.05	349	8.52	337	22961

and

Table 2. Database appearance (Part 2).

Date Time	Fuel: Output of Flammable Volatile Substances, %	Fuel: Fractional Composition, Mode 1, R35, %	Fuel: Fractional Composition, Mode 2, R40, %	Fuel: Fractional Composition, Mode 1, R45, %	Exhaust Gases: Concentration of CO behind the Furnace (Irregulary), %	Exhaust Gases: Concentration of CO (Regulary on the Device), %
11.10.2019 13.00.00	32	35	40	45	0.02	0.022
11.10.2019 13.01.00	32	35	40	45	0.02	0.022
11.10.2019 13.02.00	32	35	40	45	0.02	0.021
11.10.2019 13.03.00	32	35	40	45	0.02	0.021
11.10.2019 13.04.00	32	35	40	45	0.02	0.022
11.10.2019 13.05.00	32	35	40	45	0.02	0.022
11.10.2019 13.06.00	32	35	40	45	0.02	0.022
11.10.2019 13.07.00	32	35	40	45	0.02	0.022
11.10.2019 13.08.00	32	35	40	45	0.02	0.021
11.10.2019 13.09.00	32	35	40	45	0.02	0.02
11.10.2019 13.10.00	32	35	40	45	0.02	0.022

. The authors develop the possibility of taking into account the slagging of the furnace walls on the basis of the temperature difference on the heating surface, the temperature of the fuel slag formation and the chemical composition of the slag-removing water.

The Matlab programming environment was chosen to create the software product. As a result, the software product receives parameter values for input through text windows, which include non-calculated values of the method, and characterize the composition and properties of the fuel, the properties of the torch, data on flue gases and the geometry of the boiler unit. One variable is selected from the parameters, and the limits of its change in percent are set.

An example of how the program works is shown in Figure 3. The function of the torch length as a function of the flame temperature at the ignition site is constructed.

The advantage of forecasting in the long run is to reduce the computational error. Thus, the books [32,33], from which a significant part of the formulas and average values for this method are derived or taken, estimates an engineering error of 10–15%. At the same time, the measurement error of the sensors used (optical pyrometers, water-cooled thermosondes, gas analyzer) does not exceed 4–5%. Therefore, when adapting the methodology, we can expect a reduction in the estimated prediction error from 15% to 5%.

5. Adaptation of Control Methods Using Neural Network Algorithms

The adaptation procedure is based on the trial and error method, which is a universal tool for developing behavioral algorithms [34]. The sequence of the adaptation process is as follows. Let the model be in the initial state, that is, the current values of the weight coefficients for key values are determined, which determine the significance of certain data and the strength of their influence on the result. In the proposed method, these are two dozen values reflected in the “Argument” column of the calculation program, as well as the fuel composition, but the fuel composition cannot be analyzed with the frequency of the simulation step, so it is averaged.

According to the model, a forecast is made: a calculation is made showing the expected thermal state of the furnace of the boiler unit after the simulation step has expired. Then an analysis is performed showing how far from the actual value the result obtained from the model is. The error, which is the difference between the steady-state length of the torch and the predicted one, is fed to the system input via feedback and is used by the model in accordance with its logic to recalculate the weight coefficients for key variables in order to better match the behavior of the function with the real combustion processes. Then a forecast is made for the next point in time, and the whole process is repeated. Thus, the adaptation is carried out iteratively.

The parameter characterizes the model’s reaction speed to changes in the combustion process dynamics. The process of training the model consists in selecting the best adaptation parameter based on samples based on retrospective material.

Mathematical models are used to describe time series [34]. When implementing the theory and methods of controlling neural networks in application to heat engineering equipment, practical and scientific problems arise. Existing energy technology complexes, including equipment that generates heat and electricity, require the improvement and development of the theory, methods and algorithms of automatic control, including neural control based on the collection of data on system parameters using controllers and processing by software with the ability to train a neural network. The collection of data on the system parameters is possible with the help of controllers and processing by means of software with the possibility of training a neural network, which differs from existing approaches in that for the first time it is proposed to use the principles of building neural networks, in the special case of the Kosko two-layer neural network model [34]. In addition, when adapting neural network algorithms, models of unconditional optimization, steepest descent, and algorithms for minimizing the root-mean-square error (LMS) are used [35].

Let’s assume that the time series $x_{\mathsf{\tau }}$, created by some model can be represented as two constituents [35]:

$$x_{\mathsf{\tau }}{ = \mathsf{\xi }}_{\mathsf{\tau }}{ + \mathsf{\epsilon }}_{\mathsf{\tau }}$$

(12)

where ${\mathsf{\epsilon }}_{\mathsf{\tau }}$—a component of a time series created by a random, non-autocorrelated process with zero mathematical expectation and finite variance that affects only the value of the synchronous term of the series; ${\mathsf{\xi }}_{\mathsf{\tau }}$—a component of a time series created by a deterministic function or random process that determines the value of several or all subsequent members of the series.

The problem of training an artificial network is to use the apparatus of the theory, which allows for various cases to determine the optimal coefficients of the neural theory of solving problems by programming methods. At the same time, the influence of the delay in signal transmission is important in the algorithm. The interaction is described by weight coefficients [34]:

$$S_{\mathsf{\tau }} = \mathsf{\gamma }·x_{\mathsf{\tau }} + \mathsf{\beta }·S_{\mathsf{\tau }-1}$$

(13)

${\mathrm{S}}_{\mathsf{\tau }}$—the value of the exponential average at the moment $\mathsf{\tau }$; $\mathsf{\gamma }$—the smoothing parameter, and $\mathsf{\gamma }$ = const and 0 < $\mathsf{\gamma }$ < 1; $\mathsf{\beta }$ = 1 − $\mathsf{\gamma }$.

Transforming Equation (13) we get [34]:

$$S_{\mathsf{\tau }}{ = S}_{\mathsf{\tau }-1} + \mathsf{\gamma }·\left(x_{\mathsf{\tau }}{ - S}_{\mathsf{\tau }-1}\right)$$

(14)

Figure 4 illustrates the selection of weight coefficients and the adaptation of the neural network. Figure 5 shows a graph of a predictive model based on a neural network algorithm with different weight coefficients ${\gamma }_1$.

6. Uncertainty and Validation

The obtained research results should be checked for the correctness of the data obtained, namely, to calculate the uncertainty. In addition, it is necessary to validate the measurement methodology.

The authors emphasized in their work that such curves can be constructed in the operation of industrial steam generators.

Calculate the arithmetic mean of the temperature of the flame from all measurements at a given point [36]:

$$T=\frac{1}{\mathrm{n}}{\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{T}}_{\mathrm{i}}$$

(15)

After calculating Equation (17), we get the value T = 817 K.

For sources of random uncertainty, we calculate the uncertainty by type A [34]:

$${\mathrm{u}}_{\mathrm{A}}\left(\mathrm{T}\right)=\sqrt{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{T}}_{\mathrm{i}}-\mathrm{T})}{\mathrm{n}\left(\mathrm{n}-1\right)}}$$

(16)

Calculations using Equation (18) gave the result ${\mathrm{u}}_{\mathrm{A}}\left(\mathrm{w}\right)=0.8\%$.

For sources of systematic uncertainty (instrument error) calculating the uncertainty by type B [34]:

$${\mathrm{u}}_{\mathrm{B}}\left(\mathrm{T}\right)=\frac{\Delta \mathrm{T}}{\sqrt{3}}$$

(17)

Calculations using Equation (19) give the value of ${\mathrm{u}}_{\mathrm{B}}\left(\mathrm{T}\right)=1.58\%.$

Calculate the total standard uncertainty [34]:

$${\mathrm{u}}_{\mathrm{C}}\left(\mathrm{T}\right)=\sqrt{{\mathrm{u}}_{\mathrm{A}}{\left(\mathrm{T}\right)}^2 +{ \mathrm{u}}_{\mathrm{B}}{\left(\mathrm{T}\right)}^2}$$

(18)

Using Equation (18), we can get the value ${\mathrm{u}}_{\mathrm{C}}\left(\mathrm{T}\right)=\sqrt{0.64 + 2.4964}=1.771\%.$

For the confidence probability (coverage probability) p = 0.95 (recommended in the Manual calculation of uncertainty) specify the coverage factor k = 2 and calculate the extended measurement uncertainty [34]:

$$\mathrm{u}={\mathrm{ku}}_{\mathrm{C}}\left(\mathrm{T}\right)$$

(19)

We get that the uncertainty is equal to 3.542 %. According to the norms of the Customs Agreement of the countries of the Eurasian Economic Union [36] the uncertainty limit when working with high-pressure units is 5 %.

Validation of the methodology was carried out in the software package Matlab. Validation is shown on Figure 5 and Figure 6, with Error = 895.5186 (Normal), Error = 177.7951 (Lognormal). The graphs are made in Matlab.

7. Results and Discussion

The authors conducted a number of experiments on power steam generators. Burning torch temperature, reagent flow rate, combustion volume, concentration of combustion products, and a number of other equally important parameters of the combustion process were measured.

These experimental results were compared with the analytical calculation and with the data of predictive regulation through the use of neural network algorithms. As mentioned earlier, in the previous chapter, all experimental data underwent the procedure of finding the range of uncertainty and validation of the applied methodology.

The following is an example of experimental studies. At the length of the torch l = 5.1 m the flame temperature was reached T = 1786 K. The steam generator operated under steam production mode D = 60 kg of steam per second. At the same time, the fuel burned had a calorific value of 26.780 kJ/kg (Figure 7).

We present experimental data on the operation of BKZ boilers (Boiler unit type BKZ). For the boiler, the data are given at the rated load of the boiler D = 53 kg of steam per second, in addition, when burning coal with a calorific value of 24.560 kJ/kg. Parameters measured in the experiment: speed w₀ = 8 m/s, T₀ = 1371 K, d₀ = 0.9 m, T = 1721 K, l = 5.33 m. For a boiler with a nominal boiler load of D = 44 kg of steam per second, in addition, when burning coal with a calorific value of 22.450 kJ/kg, the parameters measured in the experiment are: speed w₀ = 9.2 m/s, T₀ = 1389 K, d₀ = 0.86 m, T = 1685 K, l = 4.75 m.

The obtained experimental data show the dependence of temperature and speed on the type of fuel and the operating mode of the boiler.

We present the forecast data for the methodology developed by the authors, which were compared with the experimental data. For a boiler with a rated boiler load of D = 53 kg of steam per second, in addition, when burning coal with a calorific value of 24.560 kJ/kg. Forecast data: speed w₀ = 7.89 m/s, T₀ = 1366 K, T = 1712 K, l = 5.21 m. For a boiler with a rated boiler load of D = 44 kg of steam per second when burning coal with a calorific value of 22.450 kJ/kg forecast parameters: speed w₀ = 9.12 m/s, T₀ = 1381 K, T = 1678 K, l = 4.69 m.

We present analytical calculated data, which were compared with experimental data. For a boiler with a rated boiler load of D = 53 kg of steam per second, in addition, when burning coal with a calorific value of 24.560 kJ/kg. Forecast data: speed w₀ = 7.85 m/s, T₀ = 1363 K, T = 1709 K, l = 5.16 m. For a boiler with a rated boiler load of D = 44 kg of steam per second when burning coal with a calorific value of 22.450 kJ/kg forecast parameters: speed w₀ = 9.1 m/s, T₀ = 1377 K, T = 1672 K, l = 4.63 m.

Thus, the data obtained by the predictive method is the closest to the experimental data. For the temperature correlation coefficient c for neural network algorithms, the comparison of the normal probability density distribution will be as follows (Figure 8).

The data according to the Figure 8 results meet the conditions of the experiment according to the developed method. Similar models and calculations were previously obtained by Ş. Ţălu in the work [37]. Modern technological and heat exchange processes are characterized by a wide variety of control operations and experiments. The obtained statistical data passed the uncertainty calculation and validation of the experimental methodology. Figure 8 confirms that when calculating the uncertainty, its range was from 1.024 to 1.034.

The authors would like to note that during the experiment, the values for the temperature correlation coefficient were studied from the obtained data, based on the sample. The values obtained include the effects of influence from external factors, the overall standard deviation was estimated, and a sensitivity analysis was performed.

8. Conclusions

(1)

A method for evaluating the thermophysical characteristics of the torch is developed. The temperature at the end of the intense combustion zone is mathematically determined based on the continuous distribution function of solid fuel particles, in particular, coal dust.

(2)

A calculation method has been developed to determine the required particle burn-up time based on the properties of the fuel-air mixture to ensure the required flare length, limited by the geometry of the boiler unit, and this method has been adapted to the capabilities of modern technologies, taking readings from instruments and sensors, affecting the fuel-air flow and regulating thermal characteristics.

(3)

The length of the initial section of the torch is determined lf, where the fuel has not yet ignited, which depends on the intensity of the heat supply to the initial site α, adopted temperature of intensive release of volatile substances t_bur, the flow velocity at the exit of the burner ω₀ and its changes with an increase in temperature and the opening of the torch. In addition, it is determined that the burn-up time of particles with the size of δi the polyfraction flow depends on the fuel characteristics and the kinetic parameter of the combustion process ω when taking into account the influence of the temperature of the flare continuum T_f0.

(4)

A software algorithm has been created that allows calculating the necessary impact and regulating it, as well as collecting and systematizing data on the calculated and real effect with the construction of predictive characteristics. An algorithm for controlling the thermophysical properties of the torch based on neural network algorithms is proposed. The developed system collects data over time, transmits the information to the server. The data is processed and a forecast is made using neural network algorithms regarding the burning modes. It is shown that this allows to increase the reliability and efficiency of the combustion process.

(5)

The experimental data underwent sensitivity analysis, including an uncertainty band, and the methodology was validated. Experimental data are presented, which are compared with the data of the analytical calculation. In addition, data for certain combustion modes are provided, taking into account the operation of the system based on neural network algorithms.