A multi-objective parameter optimization method for rotary kiln based on GRNN model

Abstract

A multi-objective parameter optimization method for a rotary kiln based on a GRNN model comprises the following steps: obtaining the process parameters of the rotary kiln to be optimized, and performing numerical simulation by a preset rotary kiln numerical simulation model, and outputting energy efficiency indicators and quality indicators of the process parameters; combining the energy efficiency indicators and quality indicators, taking the coal feed amount, secondary air speed, and secondary air temperature of the rotary kiln as input parameters of the preset GRNN model, and outputting parameters to be optimized of the rotary kiln; establishing a multi-objective optimization function according to the parameters to be optimized, using the parameters to be optimized as the initial population, and using the third generation non-dominated sorting genetic algorithm to optimize the multi-objective optimization function, and outputting the optimal process parameters; optimizing the rotary kiln according to the optimal process parameters. The present invention uses a data model instead of a numerical simulation model as a data support model, and uses NSGA-III to perform multi-objective parameter optimization on a cement rotary kiln, effectively improving energy efficiency.

Description

Technical Field

[0001] The invention belongs to the field of rotary kiln optimization research, and in particular relates to a rotary kiln multi-objective parameter optimization method based on a GRNN model. Background Art

[0002] In the cement production process, preheating, decomposition, and calcination consume the most energy. The combined electricity and coal consumption of the cement rotary kiln can account for over 70% of the total energy consumption. Furthermore, the calcination process, which most significantly impacts product quality, also occurs in the cement rotary kiln. Therefore, the cement rotary kiln is the thermal equipment most relevant to energy consumption and product quality in cement production. Given the high output and energy consumption of the cement industry, with significant potential for improvement, research on energy efficiency optimization of cement rotary kilns is highly necessary.

[0003] Among the related optimization studies, rotary kiln optimization research is a hot topic among scholars in the cement industry. The research methods cover mechanism modeling, data modeling and simulation analysis, and the research directions cover structural optimization, process parameter optimization and other aspects. Zhan Xinjian and others increased the waste heat recovery and enhanced the cooling capacity of the grate cooler by adjusting the fan, coal feed and vibration frequency of the grate cooler, thereby achieving the purpose of energy efficiency optimization and verifying the effectiveness of the research. TAtmaca conducted energy analysis and Analysis revealed that combustion efficiency is the main factor affecting system efficiency, and therefore measures to reduce energy consumption can be implemented through insulation, improved heat transfer efficiency, and effective sealing. Hu Jingyang conducted a heat balance analysis based on data collected from the rotary kiln production site, calculated energy and material income and expenditure, and then carried out preliminary energy reduction optimization. Ditaranto et al. characterized and compared several oxyfuel flames in rotary kilns based on a numerical simulation model and using flames burning in air as a reference. The experimental variables were the oxidant composition and flow rate of the primary and secondary air, but no further optimization was performed.

[0004] In numerical simulation studies of rotary kilns, Boateng et al. established two heat transfer models: one-dimensional axial and two-dimensional cross-sectional models. These models somewhat reproduced the three-dimensional spatial distribution of the temperature field, but the research still had some shortcomings. While the mechanistic modeling of rotary kilns can describe the flow field within the kiln to a certain extent, it is difficult to model and data acquisition is limited. Elattar et al. developed a two-dimensional model of a rotary kiln using Fluent. They studied the effects of various process and geometric parameters on the flame, and thus developed a correlation equation for the confined jet flame length. Che Kai constructed a three-dimensional model of a rotary kiln using Fluent and, based on this, studied the influence of the kiln lining and reaction heat on the flow field within the kiln. Zhao Liangxia et al. used Fluent to study the relationship between the ratio of coal feed rate to primary air volume on NOx concentration and temperature within the kiln, concluding that a ratio of 0.6 is most conducive to achieving higher-quality products. Lu Cong established a numerical simulation model of a rotary kiln using Fluent and, based on this model, constructed a soft-sensing model for maximum temperature. He also optimized the structure of the variable-diameter rotary kiln.

[0005] In industrial multi-objective optimization research, Sohani et al. have made some progress in multi-objective optimization for the toluene production industry. This study took energy consumption, environmental factors, and economic efficiency as optimization objectives. Compared with previous optimization methods, this study considered more comprehensive optimization objectives, and the optimization results achieved were more valuable, as verified by experiments. Chen Qiang et al. conducted comprehensive research on the multi-objective parameter optimization of the performance of the regenerator of a horseshoe flame glass kiln and the firing zone of a ceramic roller kiln. Combining numerical simulation, data modeling, and intelligent optimization algorithms, they achieved better operating results on various thermal equipment. Mohanty et al. conducted research on rotary kilns based on artificial neural networks and GA optimization algorithms. The study demonstrated the effectiveness of multi-objective optimization analysis in evaluating and improving the performance of industrial rotary kiln units. By combining this method with data-driven models, the optimization potential of this research path can be further explored. Hao et al. proposed a multi-objective collaborative optimization method for cement calcination processes. This method takes coal consumption and f-CaO content as optimization targets, proposes the TDRM-Jaya algorithm to optimize the model, and realizes the optimization of the cement calcination process. However, there are problems such as the long sampling time and calcination time interval of f-CaO content on site.

[0006] Based on the above research background, the optimization of cement rotary kiln can be divided into three areas according to different methods: rotary kiln optimization, rotary kiln numerical simulation, and industrial multi-objective optimization, among which:

[0007] Rotary kiln optimization mainly focuses on two aspects: structural optimization and process parameter optimization. The former is more suitable for the early stages of equipment design and development, as structural modification of existing equipment is costly and difficult. The latter, on the other hand, offers low cost, high feasibility, and significant results. However, existing research on rotary kiln process parameters mostly considers a single objective and lacks comprehensive multi-objective optimization research.

[0008] Numerical simulation of rotary kilns has evolved from mechanism modeling to the use of numerical simulation software. The modeling of thermal processes inside rotary kilns has become increasingly complete and reliable, with the characteristics of low cost and comprehensive data, and has become a reliable research tool. However, there is a problem with the lack of appropriate quantitative indicators in subsequent optimization studies of numerical simulations. Most studies simply compare and select experimental groups with relatively good flow field performance as optimization results. On the other hand, numerical simulations are relatively long in calculation time and cannot cover the entire variable space, making it difficult to meet the data requirements of intelligent optimization strategies.

[0009] Industrial multi-objective optimization, a research approach that utilizes numerical simulation models combined with data-driven methods, has proven its feasibility and effectiveness across numerous industries. Cement rotary kilns share significant similarities with these optimization targets, thus leveraging this approach to provide a low-cost, efficient, and effective optimization approach for the cement industry. However, compared to multi-objective optimization research in other industrial sectors, research on cement rotary kilns currently lacks comprehensive, appropriate, and quantitative indicators. Summary of the Invention

[0010] The present invention aims to solve the problems in the prior art that cement rotary kilns require a large amount of experimental group data, the numerical simulation method has a long calculation time and high time cost, and it is difficult to provide a large amount of data support for optimization research, as well as the problems that the optimization research effect of a single objective is limited and multi-objective optimization is difficult to achieve.

[0011] Specifically, the present invention provides a multi-objective parameter optimization method for a rotary kiln based on a GRNN model, comprising the following steps:

[0012] Obtaining the process parameters of the rotary kiln that need to be optimized, and performing numerical simulation using a preset rotary kiln numerical simulation model to output energy efficiency indicators and quality indicators of the process parameters;

[0013] In combination with the energy efficiency index and the quality index, the coal feed rate, secondary air speed, and secondary air temperature of the rotary kiln are used as input parameters of the preset GRNN model, and the parameters to be optimized of the rotary kiln are output;

[0014] Establishing a multi-objective optimization function based on the parameters to be optimized, using the parameters to be optimized as the initial population, and optimizing the multi-objective optimization function using a third-generation non-dominated sorting genetic algorithm to output the optimal process parameters;

[0015] The rotary kiln is optimized according to the optimal process parameters.

[0016] Furthermore, the preset rotary kiln numerical simulation model includes a turbulence model, a particle trajectory model, a pulverized coal combustion model, and a radiation model, wherein the turbulence model satisfies the relationship (1):

[0017]

[0018] Among them, G k is the turbulent kinetic energy, α k is the K-equation turbulent Prandtl number, α ε is the turbulent Prandtl number of the ε equation, C 1ε The value of C is 1.42, 2ε The value of is 1.68;

[0019] The particle trajectory model satisfies the relationship (2):

[0020]

[0021] Among them, F D is the rotational lift, F G is the particle gravity, u p is the particle velocity;

[0022] The pulverized coal combustion model includes a volatile analysis sub-model and a coke combustion sub-model, and the volatile analysis sub-model and the coke combustion sub-model respectively satisfy equations (3) and (4):

[0023]

[0024]

[0025] Among them, m p is the mass of pulverized coal particles, f v,0 is the initial mass fraction of volatile matter, f w,0 is the mass fraction of volatile materials, m p,0 is the initial mass of pulverized coal particles, k is the pulverized coal combustion reaction rate constant, R c is the coke combustion rate, p is the oxygen partial pressure, K c is the diffusion coefficient, K d is the dynamic coefficient;

[0026] The radiation model satisfies the relationship (5):

[0027]

[0028] Where α is the absorption coefficient, σ s is the scattering coefficient, C is the phase function coefficient, and G is the incident amplitude.

[0029] Furthermore, the parameters to be optimized include maximum firing temperature, firing zone length, and thermal efficiency.

[0030] Furthermore, in the preset GRNN model, the input parameter in the i-th group of working conditions is defined as x i , the output parameter to be optimized is y i , then the parameters to be optimized satisfy the following relation (6):

[0031] y i =f(x i )(i=1,2,…,n) (6);

[0032] Among them, x i Specifically expressed as x i =[m i ,v i ,t i ],m i 、v i , t i are the specific values of the three variables, namely, the coal feed rate, the secondary air speed, and the secondary air temperature in the i-th group of working conditions, and y i Specifically expressed as y i =[T i ,L i ,η i ], where T i 、L i ,η i are the specific values of the three indicators of the maximum firing temperature, the firing zone length, and the thermal efficiency in the i-th group of working conditions;

[0033] The predicted value of the parameter to be optimized at x is defined as f(x), and the predicted value f(x) satisfies the relationship (7):

[0034]

[0035] Furthermore, the preset GRNN model includes an input layer, a pattern layer, a summation layer, and an output layer. In the i-th group of working conditions, the input variable dimension M is 3, the output variable dimension K is 3, there are N training data groups, the number of neurons in the input layer is the same as the input variable dimension M, the number of neurons in the pattern layer is the same as the training group N, the summation layer includes two types of neurons: numerator units and denominator units. The number of numerator units is the same as the output variable dimension K, the denominator unit is 1, and the number of neurons in the output layer is the same as the output variable dimension K.

[0036] Furthermore, the activation function of the pattern layer satisfies the relation (8):

[0037]

[0038] Among them, X is the input variable, X i is the center of the i-th neuron, and σ is the smoothing factor.

[0039] Furthermore, the weight of the molecular unit is defined as y i,j , the output of the molecular unit in the j-th dimension satisfies the relationship (9):

[0040]

[0041] The output of the denominator unit satisfies the relationship (10):

[0042]

[0043] Furthermore, the neuron output of the output layer satisfies the relation (11):

[0044]

[0045] Furthermore, the multi-objective optimization function satisfies the relationship (12):

[0046]

[0047] Among them, f1=-T=k(m,v,t), f2=-L=g(m,v,t), and f3=-η=h(m,v,t) are the three objective functions of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively; k(m,v,t), g(m,v,t), and h(m,v,t) are the data models of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively.

[0048] The beneficial effects achieved by the present invention are:

[0049] First, using a data model instead of a numerical simulation model can effectively serve as a data support model for optimization research, with the advantages of short calculation time and low time cost. Compared with other data modeling methods, the GRNN model has better prediction capabilities even with less training data;

[0050] 2. The third-generation non-dominated sorting genetic algorithm (NSGA-III) was used to perform multi-objective parameter optimization on the cement rotary kiln, and the process parameter combination for the optimal operating conditions of the cement rotary kiln was obtained, effectively improving the energy efficiency of the cement rotary kiln.

[0051] Attached photos

[0052] Figure 1 1 is a flowchart of the steps of a multi-objective parameter optimization method for a rotary kiln based on a GRNN model provided by an embodiment of the present invention;

[0053] Figure 2 Schematic diagram of the structure of the preset GRNN model provided by an embodiment of the present invention;

[0054] Figure 3 Schematic diagram of reference points of the NSGA-III algorithm provided in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram of the basic flow of the NSGA-III algorithm provided by an embodiment of the present invention;

[0056] Figure 5 Schematic diagram of the distribution of the temperature field inside the rotary kiln provided by an embodiment of the present invention;

[0057] Figure 6 Schematic diagram of the distribution of the temperature field inside another rotary kiln provided by an embodiment of the present invention;

[0058] Figure 7 is a schematic diagram of flue gas temperature provided by an embodiment of the present invention;

[0059] Figure 8 Schematic diagram of the velocity flow field at the outlet of a four-channel burner of a rotary kiln provided by an embodiment of the present invention;

[0060] Figure 9 Schematic diagram of O2 component distribution in a rotary kiln provided by an embodiment of the present invention;

[0061] Figure 10 2 is a schematic diagram comparing the maximum firing temperatures provided by an embodiment of the present invention;

[0062] Figure 11 1 is a schematic diagram of the comparison of the lengths of the fired zones provided in an embodiment of the present invention;

[0063] Figure 12 1 is a schematic diagram of thermal efficiency comparison provided by an embodiment of the present invention;

[0064] Figure 13 Schematic diagram of a solution set for a multi-objective optimization problem provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0066] Please refer to Figure 1 , Figure 1 1 is a flowchart of a multi-objective parameter optimization method for a rotary kiln based on a GRNN model provided by an embodiment of the present invention, which specifically includes the following steps:

[0067] S1. Obtain process parameters of a rotary kiln that need to be optimized, perform numerical simulation using a preset rotary kiln numerical simulation model, and output energy efficiency indicators and quality indicators of the process parameters.

[0068] Specifically, in the embodiment of the present invention, the basic equations involved in the numerical simulation of the rotary kiln are conservation of mass, conservation of energy, conservation of momentum and conservation of components, because the thermal process in the kiln conforms to the most basic physical process and also includes the process of chemical reaction between different components such as coal powder combustion.

[0069] The basic equations in the embodiments of the present invention are as follows:

[0070] The mass conservation equation:

[0071]

[0072] Among them, ρ is density, t is time, x, y, z are coordinates, and u, v, w are velocity components corresponding to the coordinates.

[0073] Energy conservation equation:

[0074]

[0075] Where T is temperature, λ is thermal conductivity, S T represents the viscous dissipation term.

[0076] Momentum conservation equation:

[0077]

[0078] in, μ is the dynamic viscosity, p is the air flow pressure, S u 、S v 、S w is the generalized source term.

[0079] Component conservation equation:

[0080]

[0081] Among them, c m is the volume concentration, D m is the diffusion coefficient of m, S m is the production capacity of component m.

[0082] The preset rotary kiln numerical simulation model includes a turbulence model, a particle trajectory model, a pulverized coal combustion model, and a radiation model.

[0083] In the numerical simulation process, the main basis for selecting the turbulence model is the characteristics of the flow field, whether the fluid is compressible, the accuracy of the calculation, and the computing power of the computer. Through the analysis of the rotary kiln process, after the primary air is blown out from the burner, there will be a very high flow rate and accompanied by strong swirling wind. The air flow velocity along the axis of the rotary kiln will decrease rapidly. The embodiment of the present invention selects the RNG k-ε model as the turbulence equation. Its advantage is that the calculation convergence effect is good in the simulation example of strong swirling flow and large velocity gradient, which can improve the calculation accuracy to a certain extent and reduce the calculation amount to a certain extent. The turbulence model satisfies the relationship (1):

[0084]

[0085] Among them, G k is the turbulent kinetic energy, α k is the K-equation turbulent Prandtl number, α ε is the turbulent Prandtl number of the ε equation, C 1ε The value of C is 1.42, 2ε The value of is 1.68;

[0086] The simulation of the pulverized coal combustion process in a rotary kiln is the key to the numerical simulation model. The movement of pulverized coal particles in a rotary kiln is very complex. The pulverized coal particles interact with the fluid and with the wall, causing the movement to change. In the embodiment of the present invention, the discrete phase model of the Fluent software can better restore the movement path of the pulverized coal particles in the kiln, thereby improving the accuracy of the numerical simulation model. The discrete phase model is a tracking particle algorithm defined based on the Lagrangian method. The fluid in the simulation can be regarded as a continuous phase and the solid particles as a discrete phase. The model first calculates the flow field of the continuous medium and then calculates the movement trajectory of the particles in this flow field on this basis. In this calculation process, the collision between particles and the heat, mass and momentum between the discrete phase and the continuous phase are ignored after the particle trajectory calculation. In the embodiment of the invention, it is assumed in the discrete phase model that the diameter, initial velocity direction and size of the pulverized coal particles are consistent, and the pulverized coal particles are uniformly ejected from the coal air outlet surface of the burner. The discrete phase model calculation is performed every 40 steps during the numerical simulation calculation process. The particle trajectory model satisfies the relationship (2):

[0087]

[0088] Among them, F D is the rotational lift, F G is the particle gravity, u p is the particle velocity;

[0089] In the rotary kiln, pulverized coal particles are ejected from the air outlet of the four-channel burner and mixed with high-temperature air to cause combustion. In Fluent, the combustion of pulverized coal particles is usually simulated using the Eddy Dissipation combustion model in the component transport model. The pulverized coal combustion model includes a volatile analysis sub-model and a coke combustion sub-model. The volatile analysis sub-model and the coke combustion sub-model respectively satisfy the following equations (3) and (4):

[0090]

[0091]

[0092] Among them, m p is the mass of pulverized coal particles, f v,0 is the initial mass fraction of volatile matter, f w,0 is the mass fraction of volatile materials, m p,0 is the initial mass of pulverized coal particles, k is the pulverized coal combustion reaction rate constant, R c is the coke combustion rate, p is the oxygen partial pressure, K c is the diffusion coefficient, K d is the dynamic coefficient;

[0093] In summary, the embodiment of the present invention concludes that the cement rotary kiln uses radiation heat transfer as the main heat transfer mode. Therefore, the radiation model needs to be considered in the model setting. In view of the characteristics of the rotary kiln's long cylinder length and large length-to-diameter ratio, the embodiment of the present invention chooses to use the P1 radiation model as the radiation model of this numerical simulation. The P1 radiation model is more general and takes radiation scattering into consideration. It is suitable for research objects with more complex structures and involving combustion processes. It has the characteristics of fast calculation speed and high efficiency. The radiation model satisfies the relationship (5):

[0094]

[0095] Where α is the absorption coefficient, σ s is the scattering coefficient, C is the phase function coefficient, and G is the incident amplitude.

[0096] Preferably, the embodiment of the present invention also sets boundary conditions to simulate real-life scenarios. Some boundary conditions of the inlet and outlet are set as shown in Table 1, wherein the secondary air duct and each air duct of the burner are set as velocity inlet, the kiln outlet is set as pressure outlet, and the wall surface is set as a no-slip wall surface.

[0097] Table 1 Table of some boundary conditions of rotary kiln

[0098]

[0099] S2. Combining the energy efficiency index and the quality index, taking the coal feed rate, secondary air speed, and secondary air temperature of the rotary kiln as input parameters of a preset GRNN model, and outputting the parameters to be optimized of the rotary kiln.

[0100] GRNN was first proposed by Specht in 1991. It is an improved form of radial basis network. Compared with other models, it has better nonlinear regression capabilities, high fault tolerance and robustness. It is an effective method for solving nonlinear regression problems. Since the data in the embodiment of the present invention is obtained through numerical simulation experiments, the amount of data is relatively small compared to the experimental group and some unstable data exists. Therefore, GRNN is the data model construction method selected by the embodiment of the present invention. It conforms to the data characteristics, has good prediction capabilities even when there is less training data, and can handle some unstable data.

[0101] The parameters to be optimized include maximum firing temperature, firing zone length, and thermal efficiency.

[0102] Furthermore, in the preset GRNN model, the input parameter in the i-th group of working conditions is defined as x i , the output parameter to be optimized is y i , then the parameters to be optimized satisfy the following relation (6):

[0103] y i =f(x i )(i=1,2,…,n) (6);

[0104] Among them, x i Specifically expressed as x i =[m i ,v i ,t i ],m i 、v i , t i are the specific values of the three variables, namely, the coal feed rate, the secondary air speed, and the secondary air temperature in the i-th group of working conditions, and y i Specifically expressed as y i =[T i ,L i ,η i ], where T i 、L i ,η i are the specific values of the three indicators of the maximum firing temperature, the firing zone length, and the thermal efficiency in the i-th group of working conditions;

[0105] The GRNN regression method is implemented based on kernel regression of the density estimation concept. To obtain the observation value f(x) of a certain point x, we first calculate the conditional probability density of Y under the condition of x, and then solve the expectation of the continuous variable to finally obtain the model prediction value under the condition of x.

[0106] The predicted value of the parameter to be optimized at x is defined as f(x), and the predicted value f(x) satisfies the relationship (7):

[0107]

[0108] In equation (7), the conditional probability density f Y (y|x) can be obtained by dividing the joint probability density of X and Y by the marginal probability density with respect to X, that is:

[0109]

[0110] Combining the above equation with equation (7), we can obtain the regression function of f(x):

[0111]

[0112] The joint probability density of X and Y and the marginal probability density of X can be obtained by training the data set And the Parzen-Rosenblatt density estimator is used to estimate, that is:

[0113]

[0114] Where K(x) is the kernel function of the density estimator; h is the smoothness, which controls the width of the kernel. Based on Equation (14), it can be simplified by using the Nadaraya-Watson regression estimator. After normalizing the training set data, the weighting function can be defined as:

[0115]

[0116] Among them, for any x Combining the above relationships, we can get the regression formula of f(x):

[0117]

[0118] The kernel function of GRNN adopts the Gaussian distribution function, namely:

[0119]

[0120] Where m0 is the dimension of x, here it is 3. Assume that the same width σ is used, σ and the smoothness h have the same mapping on the kernel function, and x i is the center of the kernel function, that is:

[0121]

[0122] Substituting the above formula into the regression estimator, we get:

[0123]

[0124] If expressed in matrix form, the final regression function of the preset GRNN model is obtained;

[0125]

[0126] Furthermore, the preset GRNN model includes an input layer, a pattern layer, a summation layer, and an output layer. For details, please refer to Figure 2 , Figure 2 : is a schematic diagram of the structure of the preset GRNN model provided by an embodiment of the present invention. In the i-th group of working conditions, the input variable dimension M is 3, the output variable dimension K is 3, and there are N training data groups in total;

[0127] The input layer of the network is responsible for receiving the input variable set. The number of neurons in the input layer is the same as the dimension M of the input variable. In this model, the input layer has 3 neurons.

[0128] The pattern layer of the network is responsible for activating the data information based on the Gaussian function, and the number of neurons in the pattern layer is the same as that in the training group N;

[0129] The summation layer of the network is responsible for performing weighted summation and arithmetic summation on the neurons of the pattern layer respectively. The summation layer includes two types of neurons: numerator units and denominator units. The number of numerator units is the same as the dimension K of the output variable, and the number of denominator units is 1;

[0130] The output layer of the network is responsible for calculating the two types of neurons in the summation layer, and the number of neurons in the output layer is the same as the dimension K of the output variable.

[0131] Furthermore, the activation function of the pattern layer satisfies the relation (8):

[0132]

[0133] Among them, X is the input variable, X i is the center of the i-th neuron, and σ is the smoothing factor.

[0134] Furthermore, the weight of the molecular unit is defined as y i,j , the output of the molecular unit in the j-th dimension satisfies the relationship (9):

[0135]

[0136] The output of the denominator unit satisfies the relationship (10):

[0137]

[0138] Furthermore, the neuron output of the output layer satisfies the relation (11):

[0139]

[0140] S3. Establish a multi-objective optimization function based on the parameters to be optimized, use the parameters to be optimized as the initial population, and use the third-generation non-dominated sorting genetic algorithm to optimize the multi-objective optimization function, and output the optimal process parameters.

[0141] In the cement production process, energy efficiency and quality are both very important criteria. It is necessary to ensure product quality while maximizing energy efficiency during production, thereby ensuring the highest possible production economy while ensuring product quality. In other words, in the optimization of rotary kiln parameters, it is necessary to find an optimal combination of process parameters that not only appropriately increases the maximum firing temperature and the firing zone length, but also maximizes thermal efficiency. However, energy efficiency and quality are strongly coupled, and it is impossible to achieve the optimal value at the same time. Among them, the thermal efficiency of the rotary kiln is evaluated by its energy utilization capacity, while the maximum firing temperature and firing zone length are evaluated by whether the operating temperature field meets the standards.

[0142] Furthermore, the multi-objective optimization function satisfies the relationship (12):

[0143]

[0144] Among them, f1=-T=k(m,v,t), f2=-L=g(m,v,t), and f3=-η=h(m,v,t) are the three objective functions of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively; k(m,v,t), g(m,v,t), and h(m,v,t) are the data models of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively.

[0145] The embodiment of the present invention uses the third generation non-dominated sorting genetic algorithm to optimize the multi-objective optimization function. The third generation non-dominated sorting genetic algorithm (NSGA-III) is an optimization algorithm based on reference point selection. Figure 3 and Figure 4 , Figure 3 Schematic diagram of reference points of the NSGA-III algorithm provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of the basic flow of the NSGA-III algorithm provided by an embodiment of the present invention.

[0146] Specifically, the basic process of the NSGA-III algorithm is as follows: First, a reference point needs to be constructed, and then an initial population P with N individuals is randomly generated. t , and generate Q by cross mutation t The offspring population, P t and Q t Merge into a new population R with 2N individuals t , then R t The 2N individuals in the population are sorted non-dominatedly, and the individuals that can be selected based on the non-dominated level are directly selected into the next generation parent population P t+1 , discard the dominated individuals selected based on the non-dominated level, and then select the individuals that cannot be selected based on the non-dominated level based on the reference point mechanism to make the individual space sparsely distributed until the number of individuals meets N-(x+y); finally, merge the two groups of individuals selected by the two different selection mechanisms into P t+1 The parent population repeats the above process until the end condition is reached.

[0147] S4. Optimizing the rotary kiln according to the optimal process parameters.

[0148] For example, in an embodiment of the present invention, based on the Ansys Fluent 2020R1 numerical solution software, the basic equations, RNG k-ε turbulence model, discrete phase model, Eddy Dissipation combustion model, and P1 radiation model are solved using the SIMPLEC algorithm, and the boundary conditions used are shown in Table 1 above.

[0149] The specific solution process is as follows: Because the numerical simulation of the rotary kiln is relatively complex, it is difficult to open multiple models at the same time, and the calculation results are slow to converge and prone to errors. Therefore, a cold numerical simulation should be performed first. In this step, only the basic equations and the RNG k-ε turbulence model are enabled. After 400 iterations, it can be found that the simulated flow field has stabilized. Then, after the simulation is smooth and stable, the discrete phase model, Eddy Dissipation combustion model, and P1 radiation model are enabled. Ignition is achieved by setting a small high-temperature area at the burner outlet. The model solution calculation is continued, and the hot numerical simulation stage is entered.

[0150] Since the discrete phase model of the embodiment of the present invention is set to perform a particle motion trajectory calculation every 40 steps, the residual curve of this numerical simulation will fluctuate once every 40 steps, which is a normal phenomenon. In addition, since the coal powder combustion process in the cement rotary kiln is very complex, the calculation convergence residual of this numerical simulation is larger than that of the usual research case. Therefore, the numerical changes of several key position points such as the kiln tail temperature and the burning zone area temperature are monitored to determine whether the calculation has converged. After about 1600 steps of calculation, the numerical values and residual curves of each monitoring point tend to be stable. At this point, it can be considered that the numerical simulation calculation has converged iteratively, and subsequent data post-processing can be performed.

[0151] In the embodiment of the present invention, after solving the preset rotary kiln numerical simulation model, the distribution of the temperature field inside the rotary kiln can be obtained, such as Figure 5 and Figure 6 shown.

[0152] The temperature distribution inside the rotary kiln reveals that the temperature initially increases and then decreases along the kiln's length. Pulverized coal, ejected at high speed by the primary air, ignites approximately 10 meters from the kiln head. The heat released by the combustion is transferred to the flue gas, forming a high-temperature zone. Following this high-temperature zone, the flue gas temperature gradually decreases along the kiln's length to the kiln outlet due to heat dissipation through the kiln walls and consumption during cement combustion. The cross-sectional temperature cloud diagram shows that the overall temperature distribution across the cross section is uniform, contributing to improved firing quality. The temperature decreases along the radius, consistent with the actual kiln lining heat dissipation and firing heat consumption.

[0153] Through the temperature data analysis of the temperature field, it can be seen that the highest firing temperature in the kiln is 1855K, which is relatively low. This situation may lead to low cement firing quality and low product quality, indicating that there is still a lot of room for optimization.

[0154] like Figure 7 As shown, the flue gas enters the rotary kiln from the kiln head with an initial temperature of 300K, and begins to heat up rapidly about 10m away from the kiln head, breaking through 1773K at 15m away from the kiln head, and reaching a maximum temperature of 1855K at about 16m away from the kiln head. After 16m, the flue gas temperature decreases in a step-by-step manner, falling below 1773K at about 22m away, and finally discharged from the kiln tail at 1534K. Combined with the explanation of the method for dividing the various areas of the cement rotary kiln above, the area from 0m to 15.1m from the kiln head can be divided into the cooling zone, the area from 15.1m to 22.2m from the kiln head can be divided into the firing zone, and the area from 22.2m from the kiln head to the kiln tail outlet can be divided into the cooling zone. Therefore, the firing zone length of this rotary kiln under the basic working conditions is about 7.1m, which is a value on the lower side of the qualified length range.

[0155] After solving the preset rotary kiln numerical simulation model, the velocity flow field at the outlet of the four-channel burner of the rotary kiln can be obtained, such as Figure 8 shown.

[0156] The flow vector diagram shows that the primary air velocity is significantly higher than the secondary air velocity, particularly the swirl and axial wind within the primary air. The swirl outlet is located between the secondary and central air. This creates a significant velocity gradient between the swirl, the secondary air, and the central air, leading to the formation of several recirculation zones. These recirculation zones facilitate the adsorption and aggregation of pulverized coal, allowing for full combustion and faster and more efficient heat release. Therefore, the velocity flow field distribution of this numerical simulation model aligns with theoretical results, and it is also apparent that the velocity gradient may be closely linked to pulverized coal combustion. The primary and secondary air speeds should be considered as parameters to be optimized.

[0157] After the rotary kiln numerical simulation model is preset, the distribution of O2 components in the rotary kiln can be obtained, such as Figure 9 shown.

[0158] The O2 component distribution contour shows that the O2 mass fraction is relatively stable and close to the initial content between 0 and 5 meters from the kiln head, indicating that in this range, O2 has not yet been consumed by the pulverized coal combustion as a combustion aid. However, the O2 mass fraction decreases rapidly between 5 and 15 meters, concentrating near the axis, indicating that the pulverized coal is fully combusted in this range. From 15 meters to the kiln tail, the O2 mass fraction remains essentially constant, exiting the kiln tail at a mass fraction of 6.6%, indicating that the pulverized coal has been completely burned and no longer consumes O2. Compared to the temperature contour, the O2 mass fraction contour shows a somewhat similar distribution shape, but its change trend is more forward, which is consistent with the phenomenon that pulverized coal burns first and then releases heat. Furthermore, the flame shape is more distinct in the O2 mass fraction contour, appearing hammer-shaped, which is consistent with theoretical practice.

[0159] The preset rotary kiln numerical simulation model used in the embodiment of the present invention is verified as follows:

[0160] By comparing the flow field variation trends of the measured parameter data obtained from actual measurements with the numerical simulation results, we compared and analyzed the overall situation of the actual and simulated conditions to verify the reliability of the numerical simulation model. The comparison between the numerical simulation model provided by the embodiment of the present invention and the actual data is shown in Table 2 below.

[0161] Table 2 Model validation table

[0162]

[0163] As can be seen from Table 2, the simulated values for the maximum temperature, kiln tail temperature, kiln head temperature, and kiln tail O2 mass fraction all exhibit slight deviations from the actual values, but the maximum relative error is only 8.9%, and the relative errors do not exceed 10%. Combined with the relative errors and the fact that the temperature, velocity, and O2 cloud maps analyzed above are consistent with the actual distribution inside the rotary kiln, this demonstrates the high reliability of the numerical simulation model constructed in this embodiment of the present invention.

[0164] At the same time, combining energy efficiency and quality indicators, we calculate the rotary kiln's thermal efficiency, maximum firing temperature, and firing zone length. This provides quantitative energy efficiency and quality values for the initial operating conditions. Subsequent optimization studies can use this as a benchmark to determine the effectiveness of the optimization. The specific values of each indicator for the initial operating conditions are shown in Table 3 below.

[0165] Table 3 Numerical table of various indicators under initial working conditions

[0166] Evaluation indicators Initial operating condition values Thermal efficiency 53.08％ Maximum firing temperature 1855.0K Length of fired belt 7.1m

[0167] The preset GRNN model used in the embodiment of the present invention is verified as follows:

[0168] With the secondary air speed, secondary air temperature and coal feed rate as input variables, and the maximum firing temperature, firing zone length and thermal efficiency as output variables, a data model of the rotary kiln is constructed to replace the numerical simulation model with low computational efficiency. First, based on the orthogonal experimental table of three factors and nine levels and using the numerical simulation model, 108 sets of experimental data are obtained, and the values of each indicator are calculated. The parameter levels are shown in Table 4 below. Since the purpose of the embodiment of the present invention is to find the optimal working conditions, eliminating some extreme working conditions does not affect the optimization results, and can improve the modeling and prediction rates. Finally, 72 groups are determined as training groups and 10 groups are determined as test groups.

[0169] Table 4 Parameter level table

[0170]

[0171] For GRNN, when given a set of training variables, its network structure and weight value y i,j The smoothing factor σ plays a deterministic role in the accuracy of the GRNN model. If the smoothing factor σ approaches infinity, the prediction result will approach the average value of the output variable in the training set. If the smoothing factor σ approaches infinitesimal, the prediction result will approach the output variable value closest to that point, which is overfitting. The embodiment of the present invention determines that the optimal value of the smoothing factor σ is 0.1 through cross-validation.

[0172] After completing the data modeling, it is very necessary to check the accuracy of the established rotary kiln data model to see whether it can replace the numerical simulation model. The embodiment of the present invention compares the data model prediction values of the highest firing temperature, firing zone length and thermal efficiency in 10 test groups with the numerical simulation experimental values, calculates the relative error of the predicted values relative to the experimental values, and thus determines whether the established GRNN data model is accurate and reliable. The comparison results are as follows: Figure 10 、 Figure 11 、 Figure 12 shown.

[0173] Depend on Figure 10 、 Figure 11 、 Figure 12 The comparison results show that the relative errors between the predicted and experimental values for the three output dimensions are all within 10%. Therefore, it can be inferred that the error of the preset GRNN model constructed in this embodiment of the present invention is within an acceptable range and can replace the numerical simulation model for subsequent optimization.

[0174] In order to illustrate the accuracy of the preset GRNN model in more detail, Table 5 lists the experimental values, predicted values and relative errors of the 10 test groups in detail.

[0175] Table 5 Relative error between experimental value and predicted value

[0176]

[0177] Table 5 shows that across the 10 test groups, the maximum relative errors for the maximum firing temperature, firing zone length, and thermal efficiency were 3.43%, 9.73%, and 7.24%, respectively. The minimum relative errors were 0.19%, 5.73%, and 0.02%, respectively. The average relative errors were 1.87%, 7.68%, and 3.20%, respectively. This conclusion further validates the accuracy and reliability of the pre-configured GRNN model.

[0178] After verifying the accuracy of the GRNN data model, the embodiment of the present invention is also compared with common data modeling methods to further verify the advantages of the modeling method of the preset GRNN model in small sample data modeling, as shown in Table 6 below.

[0179] Table 6 Comparison of GRNN and BPNN regression effects

[0180]

[0181] In an embodiment of the present invention, an example of solving the multi-objective optimization function is as follows:

[0182] The calculation software used is Matlab R2020b. Based on the PlatEMO multi-objective optimization platform, the population size is set to 30, the crossover coefficient is 0.5, the coefficient of variation is 0.5, and the number of iterative calculations is 3000. The multi-objective optimization problem is solved by the NSGA-III algorithm, and the Pareto front solution set is obtained as follows: Figure 13 shown.

[0183] Depend on Figure 13 It can be seen that the Pareto solutions solved by NSGA-III are relatively evenly distributed. The 30 Pareto front solutions in the figure can be further selected based on the different emphasis on energy efficiency and quality in practice and the different process requirements of different products. Combined with the actual demand range for the firing zone temperature and firing zone length, the embodiment of the present invention selects the Pareto front solution with a maximum firing temperature of 2038.1K, a firing zone length of 17.9m, and a thermal efficiency of 66.21% as the optimal solution. The corresponding process parameter combination is a coal feed rate of 1.09kg / s, a secondary air speed of 2.77m / s, and a secondary air temperature of 1162K. Under this process parameter combination, the thermal efficiency is relatively high, and the maximum firing temperature and firing zone length are appropriate.

[0184] After selecting the optimal process parameter combination from the Pareto solution set, in order to intuitively reflect the optimization effect, the energy efficiency and quality index values corresponding to the optimal process parameter combination are compared with the energy efficiency and quality index values of the initial working conditions. The optimization effect is shown in Table 7 below.

[0185] Table 7 Comparison between initial solution and optimal solution

[0186]

[0187] As shown in the table above, the optimized operating conditions increased the maximum firing temperature by 183.1K, the firing zone length by 10.8m, and the thermal efficiency by 13.13% compared to the pre-optimization conditions. These results fully demonstrate the effectiveness of the optimization strategy proposed in this paper for optimizing cement production process parameters. While significantly improving the energy efficiency of the rotary kiln, the firing quality was also improved compared to the original level. This not only effectively improves the energy efficiency of the rotary kiln, but also ensures a high temperature and a reasonable distribution of the temperature field.

[0188] The beneficial effects achieved by the present invention are:

[0189] First, using a data model instead of a numerical simulation model can effectively serve as a data support model for optimization research, with the advantages of short calculation time and low time cost. Compared with other data modeling methods, the GRNN model has better prediction capabilities even with less training data;

[0190] 2. The third-generation non-dominated sorting genetic algorithm (NSGA-III) was used to perform multi-objective parameter optimization on the cement rotary kiln, and the process parameter combination for the optimal operating conditions of the cement rotary kiln was obtained, effectively improving the energy efficiency of the cement rotary kiln.

[0191] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM). For example, in one possible embodiment, a computer program is stored on the computer-readable storage medium, and when the computer program is executed by the processor, it implements the various processes and steps in the multi-objective parameter optimization method of the rotary kiln based on the GRNN model provided in the embodiment of the present invention, and can achieve the same technical effect. To avoid repetition, it will not be described here.

[0192] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0193] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better embodiment. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present invention.

[0194] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only a preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, which are all within the protection of the present invention.

Claims

1. A multi-objective parameter optimization method for a rotary kiln based on a GRNN model, characterized in that: The following steps are involved: Obtaining the process parameters of the rotary kiln that need to be optimized, and performing numerical simulation using a preset rotary kiln numerical simulation model to output energy efficiency indicators and quality indicators of the process parameters; In combination with the energy efficiency index and the quality index, the coal feed rate, secondary air speed, and secondary air temperature of the rotary kiln are used as input parameters of the preset GRNN model, and the parameters to be optimized of the rotary kiln are output; Establishing a multi-objective optimization function based on the parameters to be optimized, using the parameters to be optimized as the initial population, and optimizing the multi-objective optimization function using a third-generation non-dominated sorting genetic algorithm to output the optimal process parameters; Optimizing the rotary kiln according to the optimal process parameters; The preset rotary kiln numerical simulation model includes a turbulence model, a particle trajectory model, a pulverized coal combustion model, and a radiation model, wherein the turbulence model satisfies the relationship (1): Among them, G k is the turbulent kinetic energy, α k is the K-equation turbulent Prandtl number, α ε is the turbulent Prandtl number of the ε equation, C 1ε The value of C is 1.42, 2ε The value of is 1.68; The particle trajectory model satisfies the relationship (2): Among them, F D is the rotational lift, F G is the particle gravity, u p is the particle velocity; The pulverized coal combustion model includes a volatile analysis sub-model and a coke combustion sub-model, and the volatile analysis sub-model and the coke combustion sub-model respectively satisfy equations (3) and (4): Among them, m p is the mass of pulverized coal particles, f v,0 is the initial mass fraction of volatile matter, f w,0 is the mass fraction of volatile materials, m p,0 is the initial mass of pulverized coal particles, k is the pulverized coal combustion reaction rate constant, R c is the coke combustion rate, p is the oxygen partial pressure, K c is the diffusion coefficient, K d is the dynamic coefficient; The radiation model satisfies the relationship (5): Where α is the absorption coefficient, σ s is the scattering coefficient, C is the phase function coefficient, and G is the incident amplitude; The parameters to be optimized include maximum firing temperature, firing zone length, and thermal efficiency.

2. The multi-objective parameter optimization method for rotary kiln based on GRNN model according to claim 1, characterized in that: In the preset GRNN model, the input parameter is defined as x in the i-th group of working conditions. i , the output parameter to be optimized is y i , then the parameters to be optimized satisfy the following relation (6): y i =f(x i )(i=1,2,…,n) (6); Among them, x i Specifically expressed as x i =[m i ,v i ,t i ],m i 、v i , t i are the specific values of the three variables, namely, the coal feed rate, the secondary air speed, and the secondary air temperature in the i-th group of working conditions, and y i Specifically expressed as y i =[T i ,L i ,η i ], where T i 、L i ,η i are the specific values of the three indicators of the maximum firing temperature, the firing zone length, and the thermal efficiency in the i-th group of working conditions; The predicted value of the parameter to be optimized at x is defined as f(x), and the predicted value f(x) satisfies the relationship (7):

3. The multi-objective parameter optimization method for rotary kiln based on GRNN model according to claim 2, characterized in that: The preset GRNN model includes an input layer, a pattern layer, a summation layer, and an output layer. In the i-th group of working conditions, the input variable dimension M is 3, the output variable dimension K is 3, and there are N training data groups. The number of neurons in the input layer is the same as the input variable dimension M, the number of neurons in the pattern layer is the same as the training data group N, the summation layer includes two types of neurons: numerator units and denominator units. The number of numerator units is the same as the output variable dimension K, the denominator unit is 1, and the number of neurons in the output layer is the same as the output variable dimension K.

4. The multi-objective parameter optimization method for rotary kiln based on GRNN model according to claim 3, characterized in that: The activation function of the pattern layer satisfies the relation (8): Among them, X is the input variable, X i is the center of the i-th neuron, and σ is the smoothing factor.

5. The multi-objective parameter optimization method of rotary kiln based on GRNN model according to claim 4, characterized in that: The weight of the molecular unit is y i,j , the output of the molecular unit in the j-th dimension satisfies the relationship (9): The output of the denominator unit satisfies the relationship (10):

6. The multi-objective parameter optimization method for rotary kiln based on GRNN model according to claim 5, characterized in that: The neuron output of the output layer satisfies the relationship (11):

7. The multi-objective parameter optimization method for rotary kiln based on GRNN model according to claim 1, characterized in that: The multi-objective optimization function satisfies the relation (12): Among them, x1=-T=k(m,v,t), f2=-L=g(m,v,t), and f3=-η=h(m,v,t) are the three objective functions of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively; k(m,v,t), g(m,v,t), and h(m,v,t) are the data models of the maximum firing temperature, the firing zone length, and the thermal efficiency, respectively.

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