Coal mill parameter identification method based on improved grey wolf algorithm

Abstract

The invention belongs to the technical field of boiler coal pulverizing system simulation models, and relates to a coal mill parameter identification method based on an improved grey wolf algorithm, which comprises the following steps of: (1) establishing a nonlinear dynamic numerical pattern of a coal pulverizing system and determining parameters to be identified; (2) acquiring data required by parameter identification; (3) initializing a population by using Tent chaotic mapping and setting initial parameters; (4) constructing a fitness function and calculating fitness; (5) introducing a nonlinear convergence factor and a Levy flight disturbance strategy to update individual positions; and (6) judging a termination condition. The method is based on a coal pulverizing system operation mechanism, utilizes power plant DCS historical data, reduces the influence of data errors on identification through a 3 sigma criterion and a maximum information coefficient algorithm, and improves a traditional grey wolf algorithm through a Tent chaotic mapping initialization population, a nonlinear convergence factor dynamic adjustment search step size and a Levy flight disturbance strategy. And through layer-by-layer optimization of a staged strategy, accurate identification of the coal mill model is realized.

Description

Technical Field

[0001] This invention relates to a method for identifying coal mill parameters based on an improved gray wolf algorithm, belonging to the technical field of boiler pulverizing system simulation model. Background Technology

[0002] With the development of my country's power industry, the proportion of MPS-type medium-speed coal mills used in power plant pulverizing systems is constantly increasing. The main function of a coal mill is to grind raw coal into pulverized coal that meets certain requirements and then dry the pulverized coal. The grinding process of raw coal includes coal crushing, gas-solid two-phase flow, and heat transfer, making it an object with highly nonlinear characteristics. The MPS-type medium-speed coal mill adopts automated control, offering good safety, rapid response to boiler load changes, and numerous advantages such as good output stability, low pulverizing power consumption, minimal wear on grinding components, and minimal impact of wear on output. It is widely used in the pulverizing systems of large-scale power units in China. Therefore, the operating status of the coal mill directly affects whether the boiler can operate stably. To study the operating characteristics of this system, it is necessary to establish an accurate nonlinear model of the coal mill. Therefore, parameter identification of the coal mill simulation model is of great significance.

[0003] Currently, commonly used parameter identification algorithms include least squares, Kalman filtering, and Bayesian analysis. Least squares is a classic method for estimating parameters by minimizing the sum of squared residuals between predicted and observed values. It is widely used in various regression problems, but its parameter estimation capability for strongly nonlinear models is insufficient, requiring linearization approximation. Kalman filtering is suitable for joint state and parameter estimation of linear Gaussian systems, but it also has limitations in identifying nonlinear systems, requiring extended Kalman filtering for nonlinear problems. However, linearization of the Jacobian matrix may introduce bias. Bayesian analysis derives the posterior distribution of parameters from the prior distribution and likelihood function, achieving uncertainty quantification. However, Bayesian analysis also faces challenges such as excessively long Markov chains in large state spaces, slow chain mixing speeds, and susceptibility to local low-probability regions, leading to excessively long convergence times. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide a method for identifying coal mill parameters based on an improved Grey Wolf algorithm. This method achieves accurate identification of coal mill parameters. First, by analyzing the operating mechanism of a power plant boiler pulverizing system, a nonlinear dynamic model of the primary air duct and the coal mill is established. Then, historical power plant data combined with the improved Grey Wolf algorithm are used to identify the unknown parameters in the model.

[0005] To achieve the aforementioned objectives and address the problems existing in the prior art, the technical solution adopted by this invention is: a method for identifying coal mill parameters based on an improved gray wolf algorithm, comprising the following steps: Step 1: Establish a nonlinear dynamic model of the pulverizing system and determine the parameters to be identified, including the primary air duct model, the coal storage capacity model in the pulverizer, and the pulverizer outlet temperature model. The specific implementation includes the following sub-steps: (a) Establish a primary air duct model. The function of the primary air duct is to send cold primary air and hot primary air into the cold and hot primary air ducts of each coal mill through their respective air headers, and control their flow rate by the opening of the damper. Then, they are mixed and sent into the coal mill. A four-input two-output model is established by analyzing the heat balance and material balance in the primary air duct. The inputs include cold primary air temperature, cold air valve opening, hot primary air temperature and hot air valve opening. The outputs include primary air flow rate and primary air temperature. The nonlinear dynamic equations established are described by formulas (1) to (2).

[0006]

[0007] in, The time inertia constant of the primary airflow rate. The time inertial constant of the primary wind temperature. To adjust the opening of the primary air regulating valve, To adjust the opening of the primary hot air regulating valve, This refers to the flow rate of the primary air duct when the regulating valve is fully open. This refers to the flow rate of the primary hot air duct when the regulating valve is fully open. This refers to the primary airflow rate after mixing. The rate of change of primary airflow after mixing. The temperature of the primary air cooling system. The temperature of the primary hot air. This refers to the temperature of the hot primary air before it enters the coal mill after mixing. This represents the rate of change in the temperature of the hot primary air before it enters the coal mill after mixing. The specific heat capacity of the primary air is [not specified]. The specific heat capacity of the primary air is... The specific heat capacity of the primary air after mixing is given; the parameter to be identified is... , , , ; (b) Establish a model of the amount of coal stored in the coal mill. Since the amount of raw coal and pulverized coal inside the coal mill cannot be directly measured, the mill current is used to characterize the measurable state of the amount of coal stored in the mill. The models of the amount of raw coal and pulverized coal inside the coal mill are established by using the conservation of heat and the conservation of materials, respectively. The inputs include the speed of the coal feeder, the primary air flow rate and the primary air temperature, and the output is the coal mill current. The nonlinear dynamic equations established are described by formulas (3) to (7).

[0008]

[0009]

[0010]

[0011]

[0012] in, The amount of raw coal on the grinding bowl. The rate of change of the amount of raw coal on the grinding bowl. This refers to the coal feed rate of the coal feeder. For the coal feeder speed, For the quality of pulverized coal inside the coal mill, The rate of change in the mass of pulverized coal inside the coal mill. This refers to the pulverized coal flow rate at the coal mill outlet. The primary air differential pressure at the inlet and outlet of the coal mill. The conversion coefficient from raw coal to pulverized coal per unit time. This is the pulverized coal flow rate ratio coefficient. , , These are all proportionality coefficients used to characterize the current of the coal mill; the parameters to be identified are... , , , , ; (c) Establish a coal mill outlet temperature model. Based on the energy conservation of coal mill input and output, the input includes cold primary air temperature, hot primary air temperature, primary air temperature, sealing air temperature, primary air flow rate, coal mill current, and coal feed rate. The output is the mill outlet temperature. The nonlinear dynamic equations established are described by formulas (8) to (18).

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] in, The temperature of the powder mixture at the mill outlet. The rate of change of temperature of the air-powder mixture at the mill outlet. To input the total heat of the coal mill, To output the total heat of the coal mill, This refers to the amount of metal involved in heat exchange within the coal mill. For primary wind physical heat, The physical heat of raw coal To generate heat for coal mill grinding, For the physical heat of the sealed air, The primary air and the sealed air carry away physical heat. The heat consumed to evaporate the moisture from the raw coal. The heat consumed to heat the fuel To dissipate heat from the equipment, This is the air leakage coefficient for sealing. The specific heat capacity of the primary air at the mill outlet. The specific heat capacity of the primary air at the grinding inlet, The specific heat capacity of raw coal, The temperature of the raw coal. The heat generation coefficient of the mill, This represents the amount of moisture evaporated from the raw coal. The average isobaric specific heat capacity of water vapor. The specific heat capacity of water, The moisture content of raw coal, The specific heat capacity of water-containing fuels, The heat dissipation coefficient is the parameter to be identified. ; Step 2: Obtain the data required for parameter identification. Collect the data required in Step 1 from the historical database of the power plant's DCS system. To ensure the validity of the data, outliers in the raw data are identified and processed, and the time delay between data points is considered to reduce the impact of data errors on parameter identification and improve the accuracy of parameter identification. The specific implementation includes the following sub-steps: (a) Adopt The criteria handle outliers in the data, assuming the mean of a set of data is... The variance is The data is distributed in The probability is 99.73%. Outlier data outside this range is removed, and the mean of adjacent values ​​is used to fill the gap. (b) The maximum information coefficient (MIC) is used to estimate the time delay of the variables. The time series is reconstructed based on the delay between the input and output feature variables. The original dataset is... , where n is the dimension of the input variable. For the target variable, within the maximum delay time range, the variable... Different delay times are embedded sequentially according to the data sampling interval for the variables. Perform time series reconstruction to obtain variables embedded with different delay times. ,set up The range is Calculate the input variables respectively Under different delay times and target variables The MIC value is used to select the target variable. The time series with the largest MIC value , to make him , The delay time at the corresponding moment is the variable. The corresponding delay time, the ordered corrected dataset is ; Step 3: Initialize the population using the Tent chaotic map and set initial parameters, including the population size. and maximum number of iterations The range of parameters to be identified, and the Tent chaotic mapping initialization population, can make the population distribution more uniform and the ergodicity stronger, effectively enhance the diversity and global search capability of the population, and ensure that the initial population is more uniformly distributed in the search space, which is described by formula (19).

[0024] in, Indicates the first in the population i The state of an individual; Step 4: Construct fitness functions and calculate fitness. Construct fitness functions for the primary air model, mill internal coal quantity model, and mill outlet temperature model parameters respectively, and select the individual with the best current fitness as the model. , , The wolf, specifically includes the following sub-steps: (a) For the primary air model, the root mean square error between the actual output and the model output of the primary air flow rate and the primary air temperature at the mill inlet is used as the individual fitness function, which is described by formula (20).

[0025] in, For individual fitness function, The number of sampling points. and These are the weighting coefficients. For the first The actual value of a single airflow at a given moment. For the first The predicted value of wind flow at a given moment. For the first The actual value of the grinding inlet temperature at a given moment. For the first Predicted grinding inlet temperature at a given moment; (b) For the mill coal quantity model, the root mean square error between the actual output of the mill current and the model output error is used as the individual objective function, which is described by formula (21).

[0026] in, For the first The actual current value at each moment. For the first The predicted current value at each moment; (c) For the mill outlet temperature model, the root mean square error of the error between the actual output of the mill outlet temperature and the model output is used as the individual fitness function, which is described by formula (22).

[0027] in, For the first The actual value of the mill outlet temperature at a given moment. For the first Predicted mill outlet temperature at a given moment; Step 5: Introduce a nonlinear convergence factor and a Lévy flight perturbation strategy to update the individual position. The convergence factor is updated through a nonlinear mechanism to balance global exploration and local exploitation. The Lévy flight perturbation is introduced to apply random transitions to the neighborhood of the optimal solution, thereby improving the ability to escape local optima. The specific implementation includes the following sub-steps: (a) The nonlinear convergence factor based on the tangent function is obtained through parameters. The decay rate is dynamically adjusted. In the early stage, the algorithm maintains stability with a low decay rate and tends to perform a global search. In the middle stage, the algorithm is guided to shift from global exploration to local development by rapidly reducing the search step size. In the later stage, the decay rate slows down to maintain a refined search. The update of the nonlinear convergence factor is described by formula (23).

[0028] in, Represents the convergence factor vector. Let be the initial value of the convergence factor. This represents the final value of the convergence factor. To adjust the parameters, This represents the current iteration number. This represents the maximum number of iterations. (b) Lévy flight is a random search mechanism that follows the Lévy distribution. The movement pattern of frequent short-distance jumps and occasional long-distance jumps can expand the search range of the population and reduce the risk of getting trapped in local optima. The Lévy flight strategy is simulated by the Mantegna algorithm and described by formula (24).

[0029] in, For the flight path, , For random numbers that follow a normal distribution, if Let gamma function be the standard deviation, which is described by formula (25).

[0030] Among them, parameters The range of values ​​is ,now The value is 1.5. While generating new positions based on the Lévy flight perturbation can be done, it cannot be guaranteed that the fitness of the new solution will always be better than that of the original solution. Therefore, a greedy strategy is introduced: if the updated fitness is better, the new position replaces the original position; otherwise, the original position is retained. Step 6: Determine the termination condition. If the maximum number of iterations or the convergence accuracy is met, output the optimal solution; otherwise, return to step 4.

[0031] The beneficial effects of this invention are as follows: A method for identifying parameters of a coal mill based on an improved gray wolf algorithm includes the following steps: (1) establishing a nonlinear dynamic model of the pulverizing system and determining the parameters to be identified; (2) obtaining the data required for parameter identification; (3) initializing the population using the Tent chaotic mapping and setting initial parameters; (4) constructing a fitness function and calculating the fitness; (5) introducing a nonlinear convergence factor and a Lévy flight perturbation strategy to update the individual position; and (6) determining the termination condition. Compared with existing technologies, this invention has the following advantages: First, by using the maximum information coefficient algorithm to analyze the time delay factor of data variables, it can effectively reduce the impact of the time delay difference between features on the accuracy of system parameter identification and improve the reliability of the identification results. Second, by introducing the Tent chaotic mapping, the nonlinear convergence factor, and the Lévy flight perturbation strategy to improve the traditional gray wolf algorithm, the optimized algorithm achieves a balance between global search capability and local exploitation capability, which can effectively improve the accuracy of model parameter identification. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method steps of the present invention.

[0033] Figure 2 This invention establishes a nonlinear dynamic model structure diagram of the powder-making system.

[0034] Figure 3 This is a flowchart of the improved Grey Wolf algorithm of this invention. Detailed Implementation

[0035] The invention will now be further described with reference to the accompanying drawings.

[0036] like Figure 1 As shown, a method for identifying coal mill parameters based on an improved gray wolf algorithm includes the following steps: Step 1: Establish a nonlinear dynamic model of the pulverizing system and determine the parameters to be identified, including the primary air duct model, the coal storage capacity model in the pulverizer, and the pulverizer outlet temperature model. The model structure is as follows: Figure 2 As shown, the specific implementation includes the following sub-steps: (a) Establish a primary air duct model. The function of the primary air duct is to send cold primary air and hot primary air into the cold and hot primary air ducts of each coal mill through their respective air headers, and control their flow rate by the opening of the damper. Then, they are mixed and sent into the coal mill. A four-input two-output model is established by analyzing the heat balance and material balance in the primary air duct. The inputs include cold primary air temperature, cold air valve opening, hot primary air temperature and hot air valve opening. The outputs include primary air flow rate and primary air temperature. The nonlinear dynamic equations established are described by formulas (1) to (2).

[0037]

[0038] in, The time inertia constant of the primary airflow rate. The time inertial constant of the primary wind temperature. To adjust the opening of the primary air regulating valve, To adjust the opening of the primary hot air regulating valve, This refers to the flow rate of the primary air duct when the regulating valve is fully open. This refers to the flow rate of the primary hot air duct when the regulating valve is fully open. This refers to the primary airflow rate after mixing. The rate of change of primary airflow after mixing. The temperature of the primary air cooling system. The temperature of the primary hot air. This refers to the temperature of the hot primary air before it enters the coal mill after mixing. This represents the rate of change in the temperature of the hot primary air before it enters the coal mill after mixing. The specific heat capacity of the primary air is [not specified]. The specific heat capacity of the primary air is... The specific heat capacity of the primary air after mixing is given; the parameter to be identified is... , , , ; (b) Establish a model of the amount of coal stored in the coal mill. Since the amount of raw coal and pulverized coal inside the coal mill cannot be directly measured, the mill current is used to characterize the measurable state of the amount of coal stored in the mill. The models of the amount of raw coal and pulverized coal inside the coal mill are established by using the conservation of heat and the conservation of materials, respectively. The inputs include the speed of the coal feeder, the primary air flow rate and the primary air temperature, and the output is the coal mill current. The nonlinear dynamic equations established are described by formulas (3) to (7).

[0039]

[0040]

[0041]

[0042]

[0043] in, The amount of raw coal on the grinding bowl. The rate of change of the amount of raw coal on the grinding bowl. This refers to the coal feed rate of the coal feeder. For the coal feeder speed, For the quality of pulverized coal inside the coal mill, The rate of change in the mass of pulverized coal inside the coal mill. This refers to the pulverized coal flow rate at the coal mill outlet. The primary air differential pressure at the inlet and outlet of the coal mill. The conversion coefficient from raw coal to pulverized coal per unit time. This is the pulverized coal flow rate ratio coefficient. , , These are all proportionality coefficients used to characterize the current of the coal mill; the parameters to be identified are... , , , , ; (c) Establish a coal mill outlet temperature model. Based on the energy conservation of coal mill input and output, the input includes cold primary air temperature, hot primary air temperature, primary air temperature, sealing air temperature, primary air flow rate, coal mill current, and coal feed rate. The output is the mill outlet temperature. The nonlinear dynamic equations established are described by formulas (8) to (18).

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] in, The temperature of the powder mixture at the mill outlet. The rate of change of temperature of the air-powder mixture at the mill outlet. To input the total heat of the coal mill, To output the total heat of the coal mill, This refers to the amount of metal involved in heat exchange within the coal mill. For primary wind physical heat, The physical heat of raw coal To generate heat for coal mill grinding, For the physical heat of the sealed air, The primary air and the sealed air carry away physical heat. The heat consumed to evaporate the moisture from the raw coal. The heat consumed to heat the fuel To dissipate heat from the equipment, This is the air leakage coefficient for sealing. The specific heat capacity of the primary air at the mill outlet. The specific heat capacity of the primary air at the grinding inlet, The specific heat capacity of raw coal, The temperature of the raw coal. The heat generation coefficient of the mill, This represents the amount of moisture evaporated from the raw coal. The average isobaric specific heat capacity of water vapor. The specific heat capacity of water, The moisture content of raw coal, The specific heat capacity of water-containing fuels, The heat dissipation coefficient is the parameter to be identified. ; Step 2: Obtain the data required for parameter identification. Collect the data required in Step 1 from the historical database of the power plant's DCS system. To ensure the validity of the data, outliers in the raw data are identified and processed, and the time delay between data points is considered to reduce the impact of data errors on parameter identification and improve the accuracy of parameter identification. The specific implementation includes the following sub-steps: (a) Adopt The criteria handle outliers in the data, assuming the mean of a set of data is... The variance is The data is distributed in The probability is 99.73%. Outlier data outside this range is removed, and the mean of adjacent values ​​is used to fill the gap. (b) The maximum information coefficient (MIC) is used to estimate the time delay of the variables. The time series is reconstructed based on the delay between the input and output feature variables. The original dataset is... , where n is the dimension of the input variable. For the target variable, within the maximum delay time range, the variable... Different delay times are embedded sequentially according to the data sampling interval for the variables. Perform time series reconstruction to obtain variables embedded with different delay times. ,set up The range is Calculate the input variables respectively Under different delay times and target variables The MIC value is used to select the target variable. The time series with the largest MIC value , to make him , The delay time at the corresponding moment is the variable. The corresponding delay time, the ordered corrected dataset is ; Step 3: Initialize the population using the Tent chaotic map and set initial parameters, including the population size. and maximum number of iterations The range of parameters to be identified, and the Tent chaotic mapping initialization population, can make the population distribution more uniform and the ergodicity stronger, effectively enhance the diversity and global search capability of the population, and ensure that the initial population is more uniformly distributed in the search space, which is described by formula (19).

[0055] in, Indicates the first in the population i The state of an individual; Step 4: Construct fitness functions and calculate fitness. Construct fitness functions for the primary air model, mill internal coal quantity model, and mill outlet temperature model parameters respectively, and select the individual with the best current fitness as the model. , , The wolf, specifically includes the following sub-steps: (a) For the primary air model, the root mean square error between the actual output and the model output of the primary air flow rate and the primary air temperature at the mill inlet is used as the individual fitness function, which is described by formula (20).

[0056] in, For individual fitness function, The number of sampling points. and These are the weighting coefficients. For the first The actual value of a single airflow at a given moment. For the first The predicted value of wind flow at a given moment. For the first The actual value of the grinding inlet temperature at a given moment. For the first Predicted grinding inlet temperature at a given moment; (b) For the mill coal quantity model, the root mean square error between the actual output of the mill current and the model output error is used as the individual objective function, which is described by formula (21).

[0057] in, For the first The actual current value at each moment. For the first The predicted current value at each moment; (c) For the mill outlet temperature model, the root mean square error of the error between the actual output of the mill outlet temperature and the model output is used as the individual fitness function, which is described by formula (22).

[0058] in, For the first The actual value of the mill outlet temperature at a given moment. For the first Predicted mill outlet temperature at a given moment; Step 5: Introduce a nonlinear convergence factor and a Lévy flight perturbation strategy to update the individual position. The convergence factor is updated through a nonlinear mechanism to balance global exploration and local exploitation. The Lévy flight perturbation is introduced to apply random transitions to the neighborhood of the optimal solution, thereby improving the ability to escape local optima. The specific implementation includes the following sub-steps: (a) The nonlinear convergence factor based on the tangent function dynamically adjusts the decay rate through parameters. In the early stage, the algorithm maintains stability with a low decay rate and tends to perform a global search. In the middle stage, the algorithm is guided to shift from global exploration to local development by rapidly reducing the search step size. In the later stage, the decay rate slows down, maintaining a refined search. The update of the nonlinear convergence factor is described by formula (23).

[0059] in, Represents the convergence factor vector. Let be the initial value of the convergence factor. This represents the final value of the convergence factor. To adjust the parameters, This represents the current iteration number. This represents the maximum number of iterations. (b) Lévy flight is a random search mechanism that follows the Lévy distribution. The movement pattern of frequent short-distance jumps and occasional long-distance jumps can expand the search range of the population and reduce the risk of getting trapped in local optima. The Lévy flight strategy is simulated by the Mantegna algorithm and described by formula (24).

[0060] Where s is the flight path, , For random numbers that follow a normal distribution, if Let gamma function be the standard deviation, which is described by formula (25).

[0061] Among them, parameters The range of values ​​is ,now The value is 1.5. While generating new positions based on the Lévy flight perturbation can be done, it cannot be guaranteed that the fitness of the new solution will always be better than that of the original solution. Therefore, a greedy strategy is introduced: if the updated fitness is better, the new position replaces the original position; otherwise, the original position is retained. Step 6: Termination condition check. If the maximum number of iterations or convergence accuracy is met, output the optimal solution; otherwise, return to step 4. The improved Grey Wolf algorithm flow is as follows: Figure 3 As shown.

[0062] The advantages of this invention are as follows: Based on the operating mechanism of the pulverizing system, it utilizes historical data from the power plant's DCS, reduces the impact of data errors on identification through the 3σ criterion and the maximum information coefficient algorithm, and improves the traditional gray wolf algorithm by initializing the population using Tent chaotic mapping, dynamically adjusting the search step size using nonlinear convergence factors, and employing the Lévy flight perturbation strategy to enhance its local optimal escape capability. Through a phased strategy and layer-by-layer optimization, it achieves accurate identification of the coal mill model.

Claims

1. A method for identifying coal mill parameters based on an improved gray wolf algorithm, characterized in that, Includes the following steps: Step 1: Establish a nonlinear dynamic model of the pulverizing system and determine the parameters to be identified, including the primary air duct model, the coal storage capacity model in the pulverizer, and the pulverizer outlet temperature model. The specific implementation includes the following sub-steps: (a) Establish a primary air duct model. The function of the primary air duct is to send cold primary air and hot primary air into the cold and hot primary air ducts of each coal mill through their respective air headers, and control their flow rate by the opening of the damper. Then, they are mixed and sent into the coal mill. A four-input two-output model is established by analyzing the heat balance and material balance in the primary air duct. The inputs include cold primary air temperature, cold air valve opening, hot primary air temperature and hot air valve opening. The outputs include primary air flow rate and primary air temperature. The nonlinear dynamic equations established are described by formulas (1) to (2). ； ； in, The time inertia constant of the primary airflow rate. The time inertial constant of the primary wind temperature. To adjust the opening of the primary air regulating valve, To adjust the opening of the primary hot air regulating valve, This refers to the flow rate of the primary air duct when the regulating valve is fully open. This refers to the flow rate of the primary hot air duct when the regulating valve is fully open. This refers to the primary airflow rate after mixing. The rate of change of primary airflow after mixing. The temperature of the primary air cooling system. The temperature of the primary hot air. This refers to the temperature of the hot primary air before it enters the coal mill after mixing. This represents the rate of change in the temperature of the hot primary air before it enters the coal mill after mixing. The specific heat capacity of the primary air is [not specified]. For the specific heat capacity of the primary air, The specific heat capacity of the primary air after mixing is given; the parameter to be identified is... , , , ; (b) Establish a model of the amount of coal stored in the coal mill. Since the amount of raw coal and pulverized coal inside the coal mill cannot be directly measured, the mill current is used to characterize the measurable state of the amount of coal stored in the mill. The models of the amount of raw coal and pulverized coal inside the coal mill are established by using the conservation of heat and the conservation of materials, respectively. The inputs include the speed of the coal feeder, the primary air flow rate and the primary air temperature, and the output is the coal mill current. The nonlinear dynamic equations established are described by formulas (3) to (7). ； ； ； ； ； in, The amount of raw coal on the grinding bowl. The rate of change of the amount of raw coal on the grinding bowl. This refers to the coal feed rate of the coal feeder. For the coal feeder speed, For the quality of pulverized coal inside the coal mill, The rate of change in the mass of pulverized coal inside the coal mill. This refers to the pulverized coal flow rate at the coal mill outlet. The primary air differential pressure at the inlet and outlet of the coal mill. The conversion coefficient from raw coal to pulverized coal per unit time. This is the pulverized coal flow rate ratio coefficient. , , These are all proportionality coefficients used to characterize the current of the coal mill; the parameters to be identified are... , , , , ; (c) Establish a coal mill outlet temperature model. Based on the energy conservation of coal mill input and output, the input includes cold primary air temperature, hot primary air temperature, primary air temperature, sealing air temperature, primary air flow rate, coal mill current, and coal feed rate. The output is the mill outlet temperature. The nonlinear dynamic equations established are described by formulas (8) to (18). ； ； ； ； ； ； ； ； ； ； ； in, The temperature of the powder mixture at the mill outlet. The rate of change of temperature of the air-powder mixture at the mill outlet. To input the total heat of the coal mill, To output the total heat of the coal mill, This refers to the amount of metal involved in heat exchange within the coal mill. For primary wind physical heat, The physical heat of raw coal, To generate heat for coal mill grinding, For the physical heat of the sealed air, The primary air and the sealed air carry away physical heat. The heat consumed to evaporate the moisture from the raw coal. The heat consumed to heat the fuel To dissipate heat from the equipment, This is the air leakage coefficient for sealing. The specific heat capacity of the primary air at the mill outlet. The specific heat capacity of the primary air at the grinding inlet, The specific heat capacity of raw coal, The temperature of the raw coal. The heat generation coefficient of the mill, This represents the amount of moisture evaporated from the raw coal. The average isobaric specific heat capacity of water vapor. The specific heat capacity of water, The moisture content of raw coal, The specific heat capacity of water-containing fuels, The heat dissipation coefficient is the parameter to be identified. ; Step 2: Obtain the data required for parameter identification. Collect the data required in Step 1 from the historical database of the power plant's DCS system. To ensure the validity of the data, outliers in the raw data are identified and processed, and the time delay between data points is considered to reduce the impact of data errors on parameter identification and improve the accuracy of parameter identification. The specific implementation includes the following sub-steps: (a) Adopt The criteria handle outliers in the data, assuming the mean of a set of data is... The variance is The data is distributed in The probability is 99.73%. Outlier data outside this range is removed, and the mean of adjacent values ​​is used to fill the gap. (b) The maximum information coefficient (MIC) is used to estimate the time delay of the variables. The time series is reconstructed based on the delay between the input and output feature variables. The original dataset is... , where n is the dimension of the input variable. For the target variable, within the maximum delay time range, the variable... Different delay times are embedded sequentially according to the data sampling interval for the variables. Perform time series reconstruction to obtain variables embedded with different delay times. ,set up The range is Calculate the input variables respectively Under different delay times and target variables The MIC value is used to select the target variable. The time series with the largest MIC value , to make him , The delay time at the corresponding moment is the variable. The corresponding delay time, the ordered corrected dataset is ; Step 3: Initialize the population using the Tent chaotic map and set initial parameters, including the population size. and maximum number of iterations The range of parameters to be identified, and the Tent chaotic mapping initialization population, can make the population distribution more uniform and the ergodicity stronger, effectively enhance the diversity and global search capability of the population, and ensure that the initial population is more uniformly distributed in the search space, which is described by formula (19). ； in, Indicates the first in the population i The state of an individual; Step 4: Construct fitness functions and calculate fitness. Construct fitness functions for the primary air model, mill internal coal quantity model, and mill outlet temperature model parameters respectively, and select the individual with the best current fitness as the model. , , The wolf, specifically includes the following sub-steps: (a) For the primary air model, the root mean square error between the actual output and the model output of the primary air flow rate and the primary air temperature at the mill inlet is used as the individual fitness function, which is described by formula (20). ； in, For individual fitness function, The number of sampling points. and These are the weighting coefficients. For the first The actual value of a single airflow at a given moment. For the first The predicted value of wind flow at a given moment. For the first The actual value of the grinding inlet temperature at a given moment. For the first Predicted grinding inlet temperature at a given moment; (b) For the mill coal quantity model, the root mean square error between the actual output of the mill current and the model output error is used as the individual objective function, which is described by formula (21). ； in, For the first The actual current value at each moment. For the first The predicted current value at each moment; (c) For the mill outlet temperature model, the root mean square error of the error between the actual output of the mill outlet temperature and the model output is used as the individual fitness function, which is described by formula (22). ； in, For the first The actual value of the mill outlet temperature at a given moment. For the first Predicted mill outlet temperature at a given moment; Step 5: Introduce a nonlinear convergence factor and a Lévy flight perturbation strategy to update the individual position. The convergence factor is updated through a nonlinear mechanism to balance global exploration and local exploitation. The Lévy flight perturbation is introduced to apply random transitions to the neighborhood of the optimal solution, thereby improving the ability to escape local optima. The specific implementation includes the following sub-steps: (a) The nonlinear convergence factor based on the tangent function is obtained through parameters. The decay rate is dynamically adjusted. In the early stage, the algorithm maintains stability with a low decay rate and tends to perform a global search. In the middle stage, the algorithm is guided to shift from global exploration to local development by rapidly reducing the search step size. In the later stage, the decay rate slows down to maintain a refined search. The update of the nonlinear convergence factor is described by formula (23). ； in, Represents the convergence factor vector. Let be the initial value of the convergence factor. This represents the final value of the convergence factor. To adjust the parameters, This represents the current iteration number. This represents the maximum number of iterations. (b) Lévy flight is a random search mechanism that follows the Lévy distribution. The movement pattern of frequent short-distance jumps and occasional long-distance jumps can expand the search range of the population and reduce the risk of getting trapped in local optima. The Lévy flight strategy is simulated by the Mantegna algorithm and described by formula (24). ； in, For the flight path, , For random numbers that follow a normal distribution, if Let gamma function be the standard deviation, which is described by formula (25). ； Among them, parameters The range of values ​​is ,now The value is 1.

5. While generating new positions based on the Lévy flight perturbation can be done, it cannot be guaranteed that the fitness of the new solution will always be better than that of the original solution. Therefore, a greedy strategy is introduced: if the updated fitness is better, the new position replaces the original position; otherwise, the original position is retained. Step 6: Determine the termination condition. If the maximum number of iterations or the convergence accuracy is met, output the optimal solution; otherwise, return to step 4.

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