Heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm

Abstract

The application provides a heating furnace temperature optimization method based on hybrid modeling and an improved sand dune cat swarm algorithm, and comprises the following steps: step 1, collecting billet parameters, heating furnace structure parameters and production conditions and operation parameters; step 2, establishing a billet temperature distribution hybrid prediction model, and predicting the billet temperature distribution at the current moment according to the predicted billet temperature distribution at the previous moment, the heating furnace structure parameters, the furnace temperature at the current moment and the production conditions and operation parameters; step 3, constructing a heating furnace temperature optimization objective function, and constructing constraint conditions based on the billet temperature distribution predicted by the above hybrid prediction model and the billet-in and billet-out temperatures; and step 4, optimizing the multiple section furnace temperature optimal set values set according to the furnace length by using the improved SCSO algorithm according to the rolling rhythm, and outputting the section furnace temperature optimal set values.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of furnace temperature optimization of a steel rolling heating furnace, and relates to a heating furnace temperature optimization method based on hybrid modeling and an improved sand dune cat swarm algorithm. BACKGROUND

[0002] The hot rolling process is an important process in steel production, and its energy consumption accounts for about 10% of the entire steel production process. The heating furnace is the most important energy-consuming equipment in the hot rolling production, and its energy consumption accounts for 60%-70% of the total energy consumption of the hot rolling process, and it bears the primary task of energy saving and emission reduction in the hot rolling process. The main function of the heating furnace is to heat the billet to the temperature specified by the hot rolling process. However, the temperature of the billet cannot be measured continuously online during the heating process, so it is difficult to use traditional loop control strategies for direct control of the billet temperature. At present, the method of changing the furnace temperature setting is commonly used to indirectly control the billet temperature in production, and the furnace temperature setting is mostly given by the operator according to experience. The furnace temperature set by artificial experience often has a large margin, which can easily cause the billet to overheat or even burn, directly resulting in increased energy consumption and carbon emissions, increased oxidation and burning loss of the billet, and also affecting the service life of the heating furnace. Analyzing the heat transfer mechanism inside the heating furnace and clarifying the relationship between the furnace temperature and the billet temperature distribution are effective ways to change the above situation, and the goal is to improve the heating quality of the billet, reduce energy consumption and carbon emissions, and reduce oxidation and burning loss.

[0003] The goal of heating furnace temperature optimization is to determine the optimal heating furnace temperature setting value for each section according to the rolling rhythm of the rolling mill, while meeting the constraints of the required billet heating quality and production safety, etc. Optimization algorithm is the key to heating furnace temperature optimization, and its ability determines whether the optimal temperature setting value for each section can be obtained in the constraint space. Intelligent optimization algorithms such as immune algorithm, genetic algorithm, particle swarm optimization and differential evolution are superior to traditional nonlinear optimization algorithms in initial value sensitivity, convergence and global search, and have been widely used in heating furnace temperature optimization. However, the heating furnace temperature optimization problem has the characteristics of complexity, constraint, nonlinearity and multiple local minima, and the calculation precision of some commonly used algorithms for furnace temperature optimization is low, it is difficult to quickly and stably find the optimal temperature setting value for each section suitable for production conditions, and the optimization effect is not ideal.

[0004] The high-precision billet temperature distribution prediction model is another key to solve the heating furnace temperature optimization problem, which is the basis and premise of the furnace temperature optimization. Most of the existing furnace temperature optimization researches adopt mechanism prediction model, and considering the real-time requirement, the billet temperature distribution mechanism prediction model based on the total heat absorption rate is generally adopted. In actual application, the value of the total heat absorption rate is regarded as a fixed curve distributed along the furnace length direction. However, researches show that the distribution curve of the total heat absorption rate along the furnace length direction is not fixed, and it is affected by the heating furnace productivity and the operation parameters. That is to say, the total heat absorption rate will change with the change of the production conditions and the operation parameters. Therefore, the existing method of regarding the value of the total heat absorption rate as a fixed curve distributed along the furnace length direction is simple, but it cannot adapt to the actual situation of complex and changeable production conditions and operation parameters, which will lead to low precision of the built billet temperature distribution prediction model, and further greatly affect the actual effect of the furnace temperature optimization. SUMMARY

[0005] The application provides a heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm, which optimizes the heating furnace temperature, obtains the optimal setting of the temperature of each section suitable for the production conditions, and can practically improve the feasibility and effectiveness of the optimization results, so as to achieve the purposes of improving the billet heating quality, reducing energy consumption and carbon emission, and reducing oxidation loss.

[0006] The application provides a heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm, which includes the following steps:

[0007] Step 1: collecting the billet parameters, the heating furnace structure parameters, and the production conditions and operation parameters;

[0008] Step 2: establishing a billet temperature distribution hybrid prediction model, predicting the billet temperature distribution at the current time according to the predicted billet temperature distribution at the previous time, the heating furnace structure parameters, the furnace temperature at the current time, and the production conditions and operation parameters;

[0009] Step 3: constructing a heating furnace temperature optimization objective function, and constructing a constraint condition based on the billet temperature distribution predicted by the hybrid prediction model and the entering and exiting furnace temperatures;

[0010] Step 4: according to the rolling rhythm, adopting the improved SCSO algorithm to optimize the optimal setting values of the temperatures of multiple sections set according to the furnace length, and outputting the optimal setting values of the temperatures of each section.

[0011] In the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application, the billet parameters in step 1 include: billet size, density, thermal conductivity and specific heat capacity; the heating furnace structure parameters include: furnace length and furnace structure; the production conditions and operation parameters include: entry temperature, exit temperature, rolling rhythm, heating time, output, furnace pressure, heating system, exit rhythm and combustion product composition.

[0012] In the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application, step 2 is specifically:

[0013] Step 2.1: The billet temperature distribution hybrid prediction model adopts a two-dimensional unsteady mathematical model, and the following assumptions are made for the model to simplify the model:

[0014] a) The furnace temperature is only a function of the distribution along the furnace length direction;

[0015] b) The influence of the billet scale during heat exchange is ignored;

[0016] c) The convection heat transfer and radiation heat transfer between the furnace gas and the billet are comprehensive heat flux boundary conditions;

[0017] d) The billet moves at a uniform speed during heating;

[0018] Step 2.2: A two-dimensional unsteady heat conduction equation is established according to the billet cross section, and the specific mathematical description is as follows:

[0019]

[0020] In the formula, x∈[0,L x ], y∈[0,L y ], L x is the billet cross section width, L y is the billet cross section height; T is the billet temperature distribution, represented as T(x,y,τ), which is a function of coordinates (x,y) and heating time τ; ρ(T) is the density of the billet when the temperature is T; C p (T) is the specific heat capacity of the billet when the temperature is T; λ(T) is the thermal conductivity of the billet when the temperature is T;

[0021] Step 2.3: The boundary conditions are established, and the data description is as follows:

[0022]

[0023]

[0024] Where q U and q L are the heat flux density of the upper surface of the billet and the heat flux density of the lower surface of the billet, respectively; σ is the Boltzmann constant; with respectively total heat absorption rate of upper hearth and total heat absorption rate of lower hearth; T f is furnace temperature, T s is predicted billet surface temperature at previous time; billet two sides adopt insulation thermal boundary condition;

[0025] Step 2.4: billet section is discretized into multiple unit cells, difference equation of each node is established according to two-dimensional unsteady heat conduction equation, and difference iteration method is used to solve temperature of each node, and then billet temperature distribution is obtained.

[0026] In the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application, the total heat absorption rate of the upper hearth in the step 2.3 is identified according to the BP neural network and the total heat absorption rate of the lower hearth Specifically:

[0027] 1) taking production conditions and operation parameters as input, and taking total heat absorption rate of upper hearth and total heat absorption rate of lower hearth as output;

[0028] 2) establishing BP neural network and initializing weight and bias value;

[0029] 3) calculating output of each node of hidden layer and output layer;

[0030] 4) calculating reverse error;

[0031] 5) weight learning;

[0032] 6) judging whether error meets standard, if yes, obtaining representation relationship between production conditions and operation parameters and total heat absorption rate of upper hearth and total heat absorption rate of lower hearth; otherwise, executing 7);

[0033] 7) judging whether iteration number is reached, if yes, obtaining representation relationship between production conditions and operation parameters and total heat absorption rate of upper hearth and total heat absorption rate of lower hearth; otherwise, returning to step 2).

[0034] In the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application, the step 3 is specifically:

[0035] Step 3.1: target function of heating furnace temperature optimization is integral minimum of heating furnace temperature to furnace length, and mathematical expression is as follows:

[0036]

[0037] In the formula, J represents target function; L represents heating furnace length; T f (l) represents furnace temperature of billet at heating furnace l;

[0038] Step 3.2: Constructing constraint conditions, the specific mathematical description is as follows:

[0039] T s (τ)-T c (τ)≤ΔT1

[0040]

[0041] T s (τ end )-T c (τ end )≤ΔT2

[0042] T s (τ end )-T a ≤ΔT3

[0043] T fmin (l)≤T f (l)≤T fmax (l)

[0044] In the formula: T c (τ) represents the billet center temperature at τ moment predicted by the mixed prediction model of billet temperature distribution; T s (τ) represents the billet surface temperature at τ moment predicted by the mixed prediction model of billet temperature distribution; ΔT1 represents the maximum cross-section temperature difference in the billet heating process, which is related to the steel grade, upper and lower surface heat flux density, and heating system according to the rolling process requirements; represents the maximum temperature rise rate, which is related to the structure parameters and operation parameters; ΔT2 represents the maximum cross-section temperature difference of the billet at the discharging moment, which is related to the steel grade, upper and lower surface heat flux density at the discharging moment, and heating system according to the rolling process requirements; ΔT3 represents the maximum difference between the surface temperature of the billet at the discharging moment and the target discharging temperature, which is set according to the rolling process requirements; T s (τ end ) represents the surface temperature of the billet at the discharging moment; T c (τ end ) represents the center temperature of the billet at the discharging moment; T a represents the target discharging temperature, which is set according to the rolling process requirements; T fmin (l) and T fmax (l) respectively represent the lower limit and upper limit of the furnace temperature at the heating furnace l.

[0045] In the heating furnace temperature optimization method based on mixed modeling and improved sand dune cat swarm algorithm in the application, the step 4 is specifically:

[0046] Step 4.1: Randomly initialize an initial population of N individual sand cats within the search range. Use the billet temperature distribution mixed prediction model to predict the billet temperature at this moment. Then calculate the fitness value of the objective function, record the initial optimal solution, and begin iteration. The position of each sand cat is considered a potential solution vector. The solution vector of individual sand cat i consists of the furnace temperatures of j segments, expressed as:

[0047] Pos i =[T f,1 ,T f,2 ,...,T f,j i = 1, 2, ..., N

[0048] Step 4.2: In the t-th iteration, calculate the general sensitivity r corresponding to the population according to the following formula. G r G The value of t decreases linearly from 2 to 0 according to t;

[0049]

[0050] In the formula: s M The maximum general sensitivity is represented by a value of 2; t represents the current iteration number.

[0051] Step 4.3: In the t-th iteration, calculate the sensitivity r corresponding to each individual sand cat i according to the following formula. i ;

[0052] r i =r G ×rand(0,1)

[0053] In the formula: rand(0,1) represents a random number between 0 and 1;

[0054] Step 4.4: Determine if t ≤ 0.5 × t max , t max The maximum number of iterations is given. If the condition is met, the current search is in the early stage, and step 4.5 is executed; otherwise, the current search is in the later stage, and step 4.8 is executed.

[0055] Step 4.5: In the t-th iteration, calculate the process parameter R corresponding to each individual sand cat i according to the following formula. i ;

[0056] R i =2×r G ×rand(0,1)-r G

[0057] Step 4.6: In the t-th iteration, the process parameters R for each individual sand cat i are determined according to the following formula. idetermine to execute exploration or exploitation task, generate a new position Pos of dune cat individual i i (t+1) to complete dune cat individual update:

[0058]

[0059] wherein: Pos b represents the current global optimal position; Pos c (t) represents the current position of the t th generation dune cat individual i; Pos rnd represents a random position, Pos rnd = |rand(0,1) x Pos b - Pos c (t) |; θ represents a random angle on a circle between 0 and 360; Pos bc (t) represents the t th generation best candidate position;

[0060] Step 4.7: At the t th iteration, according to the updated position Pos i (t+1) of each dune cat individual i, call the billet temperature distribution hybrid prediction model to predict the billet temperature distribution, calculate the fitness value of the objective function after constraint processing, update the current global optimal position by using greedy selection, and finally return to step 4.2;

[0061] Step 4.8: When currently located in the later search stage, judge mod(t,2) = 0, if the condition is met, enter the evaluation stage; otherwise, enter the adjustment stage and execute step 4.9;

[0062] In the evaluation stage, randomly select N / 2 dune cat individuals in the population to execute exploration task, and the remaining dune cat individuals execute exploitation task, then complete dune cat individual update according to the method of step 4.6, calculate the fitness value of the objective function according to the method of step 4.7 after constraint processing, update the current global optimal position; and calculate the decision index according to the number of successful individuals of exploration task and exploitation task;

[0063] Step 4.9: In the adjustment stage, according to the decision index generated in the last iteration, determine whether the population executes exploration task or exploitation task, then complete dune cat individual update according to the method of step 4.6, calculate the fitness value of the objective function according to the method of step 4.7 after constraint processing, and update the current global optimal position;

[0064] Step 4.10: Determine whether the maximum number of iterations is reached, if the maximum number of iterations is reached, output the optimal setting value of each section furnace temperature; if the maximum number of iterations is not reached, return to step 4.2.

[0065] In the heating furnace temperature optimization method based on hybrid modeling and improved sand cat swarm algorithm of the application, the decision index is calculated according to the number of individuals successful in exploration tasks and development tasks in step 4.8, specifically:

[0066] If the fitness value of the objective function of the sand cat individual is less than the fitness value of the objective function of the current global optimal position, the current global optimal position is updated according to greedy selection, the sand cat individual is considered to be updated successfully, the number of individuals successful in exploration tasks and the number of individuals successful in development tasks are recorded, and the decision index is calculated according to the following formula:

[0067]

[0068] Wherein, δ is the decision index, S R is the number of individuals successful in exploration tasks, S I is the number of individuals successful in exploration tasks.

[0069] In the heating furnace temperature optimization method based on hybrid modeling and improved sand cat swarm algorithm of the application, the decision index δ generated in the last iteration is used to determine whether the population performs exploration tasks or development tasks in step 4.9, specifically:

[0070] If δ> δ2, all individuals perform exploration tasks; if δ< δ1, all individuals perform development tasks; if δ1< δ< δ2, all individuals are randomly and evenly distributed to perform exploration tasks and development tasks, and 0< δ1< δ2< 1.

[0071] The heating furnace temperature optimization method based on hybrid modeling and improved sand cat swarm algorithm of the application has at least the following beneficial effects:

[0072] 1、The application takes minimizing the integral of the heating furnace temperature with respect to the furnace length as the objective function, uses the cross-section temperature difference constraint in the billet heating process, the billet temperature rise rate constraint, the process requirement billet discharge cross-section temperature difference constraint, the billet discharge temperature and target discharge temperature difference constraint, and the upper and lower limit constraints of the furnace temperature as constraint conditions, uses the proposed adaptive SCSO algorithm (ASCSO) for optimization, makes up for the defects of the standard SCSO algorithm in the evolution mode, improves the calculation accuracy and convergence speed of the algorithm, and further improves the performance of the algorithm in solving the furnace temperature optimization problem, so that the optimal furnace temperature setting value suitable for the production condition can be quickly and stably found, the feasibility and effectiveness of the optimization result can be improved, and the purposes of improving the billet heating quality, reducing energy consumption and carbon emissions, and reducing oxidation loss can be achieved.

[0073] 2、The steel billet temperature distribution hybrid prediction model with the core of total heat absorption in the application can accurately identify the total heat absorption rate on line according to the production conditions and operation parameters through the BP neural network, and a high-precision steel billet temperature distribution hybrid prediction model is obtained, so that the steel billet temperature distribution in the heating furnace can be more accurately predicted, and the calculated steel billet temperature rise curve is closer to the measured value, thereby laying a good model foundation for the rolling heating furnace temperature optimization. BRIEF DESCRIPTION OF DRAWINGS

[0074] Figure 1 The flow chart of the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm is a flow chart of the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application.

[0075] Figure 2 The flow chart of constructing the steel billet temperature distribution hybrid prediction model is a flow chart of constructing the steel billet temperature distribution hybrid prediction model.

[0076] Figure 3 The flow chart of identifying the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace based on the BP neural network is a flow chart of identifying the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace based on the BP neural network.

[0077] Figure 4 The schematic diagram of discretizing the steel billet section into mxn unit cells is a schematic diagram of discretizing the steel billet section into mxn unit cells.

[0078] Figure 5 The flow chart of optimizing and calculating the optimal set value of the furnace temperature of each section by using the improved SCSO algorithm is a flow chart of optimizing and calculating the optimal set value of the furnace temperature of each section by using the improved SCSO algorithm. DETAILED DESCRIPTION

[0079] As Figure 1 The flow chart of the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm is a flow chart of the heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm of the application, taking a steel rolling production line of a certain steel plant as an example, and including the following steps:

[0080] Step 1: Collect the steel billet parameters, heating furnace structure parameters and production conditions and operation parameters. The steel billet parameters include: steel billet size, density, thermal conductivity, specific heat capacity and thermal diffusivity; the heating furnace structure parameters include: furnace length and furnace structure; and the production conditions and operation parameters include: entry temperature, exit temperature, rolling rhythm, heating time, output, furnace pressure, heating system, exit rhythm and composition of combustion products.

[0081] In the implementation, the steel billet size is 200mmx200mmx5000mm, the rolling rhythm is 75t / h, the steel billet entry temperature is room temperature 20℃, the rolling process requires that the surface temperature of the steel billet when exiting the furnace is not lower than 1160℃, the cross-section temperature difference is less than 35℃, the heating furnace length is 24m, and the algorithm termination condition is to reach the maximum iteration number.

[0082] Step 2: Establishing a mixed prediction model of billet temperature distribution, predicting the billet temperature distribution at the current time according to the predicted billet temperature distribution at the previous time, the heating furnace structure parameters, the furnace temperature at the current time, and the production conditions and operation parameters, as shown in Figure 2 Step 2: Establishing a mixed prediction model of billet temperature distribution, predicting the billet temperature distribution at the current time according to the predicted billet temperature distribution at the previous time, the heating furnace structure parameters, the furnace temperature at the current time, and the production conditions and operation parameters, as shown in

[0083] Step 2.1: The mixed prediction model of billet temperature distribution adopts a two-dimensional non-steady-state mathematical model. First, the following assumptions are made to simplify the model:

[0084] a) The furnace temperature is only a function of the furnace length direction distribution;

[0085] b) The influence of the billet scale during heat exchange is ignored;

[0086] c) The convection and radiation heat transfer between the furnace gas and the billet is a comprehensive heat flux boundary condition;

[0087] d) The billet moves at a uniform speed during heating;

[0088] Step 2.2: A two-dimensional non-steady-state heat conduction equation is established according to the billet cross section, and the specific mathematical description is as follows:

[0089]

[0090] In the formula, x∈[0,L x ], y∈[0,L y ], L x is the billet cross section width, L y is the billet cross section height; T is the billet temperature distribution, represented as T(x,y,τ), which is a function of coordinates (x,y) and heating time τ; ρ(T) is the density of the billet when the temperature is T; C p (T) is the specific heat capacity of the billet when the temperature is T; λ(T) is the thermal conductivity of the billet when the temperature is T;

[0091] Step 2.3: Establishing boundary conditions, the data description is as follows:

[0092]

[0093]

[0094] Where q U and q L are the heat flux density of the upper surface of the billet and the heat flux density of the lower surface of the billet, respectively; σ is the Boltzmann constant; and are the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace, respectively; T f is the furnace temperature, T s is the predicted billet surface temperature at the previous time; The billet sides adopt an insulating thermal boundary condition;

[0095] As Figure 3 shown, in particular implementation, according to BP neural network identification in the step 2.3 in the upper hearth total heat absorption rate And the lower hearth total heat absorption rate Specifically:

[0096] 1) take production conditions and operating parameters as input, and take the upper hearth total heat absorption rate and the lower hearth total heat absorption rate as output;

[0097] 2) establish BP neural network and initialize weight and bias value;

[0098] 3) calculate the output of each node in the hidden layer and the output layer;

[0099] 4) calculate the reverse error;

[0100] 5) weight learning;

[0101] 6) judge whether the error meets the standard, if it meets the standard, the representation relationship between production conditions and operating parameters and the upper hearth total heat absorption rate and the lower hearth total heat absorption rate is obtained; otherwise, 7) is executed;

[0102] 7) judge whether the iteration number is reached, if it is reached, the representation relationship between production conditions and operating parameters and the upper hearth total heat absorption rate and the lower hearth total heat absorption rate is obtained; otherwise, return to step 2).

[0103] Step 2.4: discretize the billet section into multiple unit cells, establish the difference equation of each node according to the two-dimensional unsteady heat conduction equation, and solve the temperature of each node by using the difference iteration method to obtain the billet temperature distribution.

[0104] As Figure 4 shown, discretize the billet section into m x n unit cells, and the area of each unit cell is Δx x Δy. According to the two-dimensional unsteady heat conduction equation, it is changed into a difference equation (a total of (m+1) x (n+1) equations) by finite difference. There are three forms, which correspond to the difference equation of each node on the surface, the difference equation of four end points and the difference equation of internal points respectively. Specifically, they are:

[0105] Taking the point T m / 2,n on the surface as an example, the difference equation is:

[0106]

[0107] Taking the point T 0,n / 2 on the left surface as an example, the difference equation is:

[0108]

[0109] End point at point T 0,0 The difference equation is:

[0110]

[0111] Internal point at center point T m / 2,n / 2 The difference equation is:

[0112]

[0113] From the above formula, according to the node temperature of the billet at the previous time and the furnace temperature at this time, the temperature of the node of the billet at this time can be calculated. The equation is solved by using the difference iteration method, and the temperature of the billet at this time can be obtained.

[0114] Step 3: Construct the heating furnace temperature optimization objective function, and construct the constraint condition based on the steel billet temperature distribution predicted by the above hybrid prediction model and the entering and exiting furnace temperature, and the step 3 is specifically:

[0115] Step 3.1: The objective function of the heating furnace temperature optimization is the integral minimum of the heating furnace temperature to the furnace length, which is mathematically expressed as follows:

[0116]

[0117] In the formula, J represents the objective function; L represents the heating furnace length; T f (l) represents the furnace temperature of the billet at the heating furnace l;

[0118] Step 3.2: Construct the constraint condition, and the specific mathematical description is as follows:

[0119] T s (τ)-T c (τ)≤ΔT1

[0120]

[0121] T s (τ end )-T c (τ end )≤ΔT2

[0122] T s (τ end )-T a ≤ΔT3

[0123] T fmin (l)≤T f (l)≤T fmax (l)

[0124] In the formula: T c (τ) represents the center temperature of the steel billet at τ time predicted by the steel billet temperature distribution hybrid prediction model; Ts (T) represents the billet surface temperature at time τ predicted by the mixed prediction model of billet temperature distribution; ΔT1 represents the maximum cross-section temperature difference in the billet heating process, which is related to the steel grade, the upper and lower surface heat flux density, and the heating system according to the rolling process requirements; represents the maximum temperature rise rate, which is related to the structural parameters and the operating parameters; ΔT2 represents the maximum cross-section temperature difference at the billet discharge time required by the process, which is related to the steel grade, the upper and lower surface heat flux density at the discharge time, and the heating system according to the rolling process requirements; ΔT3 represents the maximum difference between the surface temperature of the billet at the discharge time and the target discharge temperature, which is set according to the rolling process requirements; T s (T end ) represents the surface temperature of the billet at the discharge time; T c (T end ) represents the center temperature of the billet at the discharge time; T a represents the target discharge temperature, which is set according to the rolling process requirements; T fmin (l) and T fmax (l) represent the lower and upper limits of the furnace temperature at the heating furnace l, respectively.

[0125] Step 4: according to the rolling rhythm, the improved SCSO algorithm is used to optimize the optimal set value of the furnace temperature of the multiple sections set according to the furnace length, and the optimal set value of the furnace temperature of each section is output, as shown in Figure 5 , the step 4 is specifically:

[0126] Step 4.1: randomly initialize the initial population composed of N dune cats in the search range, call the mixed prediction model of billet temperature distribution to predict the billet temperature at this time, then calculate the fitness value of the objective function, record the initial optimal solution, and start iteration; the position of each dune cat is regarded as a potential solution vector, and the solution vector of the dune cat individual i is composed of the furnace temperature of j sections, which is represented as:

[0127] Pos i = [T f,1 , T f,2 , …, T f,j ] i = 1, 2, …, N

[0128] Step 4.2: at the tth iteration, the general sensitivity r G of the population is calculated according to the following formula: G , the value of r M is linearly decreased from 2 to 0 according to t;

[0129]

[0130] In the formula: s M represents the maximum general sensitivity, which is 2; t represents the current iteration number;

[0131] Step 4.3: In the t-th iteration, calculate the sensitivity r corresponding to each individual sand cat i according to the following formula. i ;

[0132] r i =r G ×rand(0,1)

[0133] In the formula: rand(0,1) represents a random number between 0 and 1;

[0134] Step 4.4: Determine if t ≤ 0.5 × t max , t max The maximum number of iterations is given. If the condition is met, the current search is in the early stage, and step 4.5 is executed; otherwise, the current search is in the later stage, and step 4.8 is executed.

[0135] Step 4.5: In the t-th iteration, calculate the process parameter R corresponding to each individual sand cat i according to the following formula. i ;

[0136] R i =2×r G ×rand(0,1)-r G

[0137] Step 4.6: In the t-th iteration, the process parameters R for each individual sand cat i are determined according to the following formula. i Make a judgment to determine whether to perform an exploration or development task, and generate a new position Pos for the sand cat individual i. i (t+1) to complete the individual update of the Sand Cat:

[0138]

[0139] In the formula: Pos b Pos represents the current globally optimal position. c (t) represents the current position of individual i in generation t of the sand cat; Pos rnd Pos represents a random position. rnd =|rand(0,1)×Pos b -Pos c (t)|;θ represents a random angle on a circle between 0 and 360; Pos bc (t) represents the best candidate position in generation t;

[0140] Step 4.7: In the t-th iteration, based on the updated position Pos of each individual Sand Cat i... i(t+1), the mixed prediction model of billet temperature distribution is called to predict the billet temperature distribution, the fitness value of the objective function is calculated after constraint processing, the current global optimal position is updated by using greedy selection, and step 4.2 is returned finally;

[0141] Step 4.8: When currently located in the later search stage, it is judged that mod(t, 2) = 0, if the condition is met, the evaluation stage is entered; otherwise, the adjustment stage is entered, and step 4.9 is executed.

[0142] In the evaluation stage, N / 2 dune cats are randomly selected from the population to perform the exploration task, and the remaining dune cats perform the development task, then the dune cat individual is updated according to the method of step 4.6, and the fitness value of the objective function is calculated according to the method of step 4.7, and the current global optimal position is updated; and the decision index is calculated according to the number of individuals successful in the exploration task and the development task;

[0143] In specific implementation, the decision index is calculated according to the number of individuals successful in the exploration task and the development task, specifically:

[0144] If the fitness value of the objective function of the dune cat individual is less than the fitness value of the objective function of the current global optimal position, the current global optimal position is updated according to the greedy selection, the dune cat individual is considered to be updated successfully, the number of individuals successful in the exploration task and the number of individuals successful in the development task are recorded, and the decision index is calculated according to the following formula:

[0145]

[0146] Wherein, δ is the decision index S R is the number of individuals successful in the exploration task, S I is the number of individuals successful in the exploration task.

[0147] Step 4.9: In the adjustment stage, it is judged whether the population performs the exploration task or the development task according to the decision index generated in the last iteration, then the dune cat individual is updated according to the method of step 4.6, and the fitness value of the objective function is calculated according to the method of step 4.7, and the current global optimal position is updated;

[0148] In specific implementation, it is judged whether the population performs the exploration task or the development task according to the decision index δ generated in the last iteration, specifically:

[0149] If δ> δ2, all individuals perform the exploration task; if δ< δ1, all individuals perform the development task; if δ1< δ< δ2, all individuals are randomly and evenly distributed to perform the exploration task and the development task, 0< δ1< δ2< 1.

[0150] Step 4.10: judging whether the maximum iteration number is reached, if the maximum iteration number is reached, outputting the optimal set value of the furnace temperature of each section; if the maximum iteration number is not reached, returning to step 4.2.

[0151] The application combines the heating furnace temperature optimization characteristics, fully analyzes the process, and provides a rolling steel heating furnace temperature optimization method based on hybrid modeling and improved sand dune cat algorithm, intelligently optimizes the heating furnace temperature, practically improves the feasibility and effectiveness of the optimization result, so as to achieve the purposes of improving the heating quality of the billet, reducing energy consumption and carbon emission, reducing oxidation loss and the like. An adaptive SCSO (Adaptive SCSO, ASCSO) algorithm is developed for accurate and rapid solution of the heating furnace temperature optimization problem. In the algorithm, a new adaptive evolution mode is proposed to make up for the deficiency of the basic SCSO in the evolution mode, to improve the calculation accuracy and convergence speed, so as to further improve the performance of the algorithm in solving the furnace temperature optimization problem, and to quickly and accurately find the optimal set value of the furnace temperature of each section. For the construction of the billet temperature distribution prediction model, a data-driven method is proposed to establish the relationship between the operating parameters and production conditions and the total heat absorption rate, to identify the total heat absorption rate online, and to obtain a billet temperature distribution hybrid prediction model. Specifically, the process mechanism is deeply studied, and a two-dimensional non-steady-state mathematical model and boundary conditions are constructed. Considering the time-varying nature of the total heat absorption rate in the boundary conditions, based on the BP neural network, a data-driven method is used to establish the functional relationship between the operating parameters and production conditions and the total heat absorption rate, to accurately identify the total heat absorption rate online, and to obtain a high-precision billet temperature distribution hybrid prediction model, laying a good model foundation for furnace temperature optimization.

[0152] The above only describes the preferred embodiments of the present application and is not intended to limit the idea of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A heating furnace temperature optimization method based on hybrid modeling and improved dune cat swarm algorithm, characterized in that, The application comprises the following steps: Step 1: collecting the billet parameters, the heating furnace structure parameters, and the production conditions and operation parameters; Step 2: establishing a mixed prediction model of the billet temperature distribution, predicting the billet temperature distribution at the current time according to the predicted billet temperature distribution at the previous time, the heating furnace structure parameters, the furnace temperature at the current time, and the production conditions and operation parameters; Step 3: constructing a heating furnace temperature optimization objective function, and constructing constraint conditions based on the predicted billet temperature distribution by the mixed prediction model and the entering and exiting furnace temperatures; Step 4: according to the rolling rhythm, the improved dune cat swarm algorithm is used to optimize the optimal setting values of the furnace temperature in multiple sections set according to the furnace length, and the optimal setting values of the furnace temperature in each section are output, specifically as follows: Step 4.1: randomly initializing an initial population consisting of N dune cats in the search range, calling the mixed prediction model of the billet temperature distribution to predict the billet temperature at this time, then calculating the fitness value of the objective function, recording the initial optimal solution, and starting iteration; the position of each dune cat is regarded as a potential solution vector, and the solution vector of the dune cat individual i is composed of the furnace temperatures of j sections and is represented as: Step 4.2: At the tth iteration, the general sensitivity corresponding to the population is calculated according to the following formula , is valued according to a linear decrease from 2 to 0 as a function of t; In the formula: represents the maximum general sensitivity, and takes a value of 2; t represents the current iteration number; Step 4.3: At the tth iteration, the sensitivity r corresponding to each dune cat individual i is calculated according to the following formula i ; In the formula: rand(0, 1) represents a random number between 0 and 1; Step 4.4: Judgment , is the maximum iteration number. If the condition is satisfied, the current is in the early search stage, and step 4.5 is executed. Otherwise, the current is in the late search stage, and step 4.8 is executed. Step 4.5: At the tth iteration, calculate the process parameter R for each dune cat individual i according to the following formula i ; Step 4.6: At the tth iteration, the process parameter R for each dune cat individual i is updated according to the following formula i A decision is made to perform an exploration or exploitation task, generating a new position for the dune cat individual i to complete the dune cat individual update: wherein: represents the current global optimum position; represents the current position of dune cat individual i in generation t; represents a random position, ; represents a random angle on a circle between 0 and 360; represents the best candidate position in generation t; Step 4.7: At the t-th iteration, according to the updated position of each dune cat individual i , the billet temperature distribution hybrid prediction model is called to predict the billet temperature distribution, after constraint processing, the fitness value of the objective function is calculated, the current global optimal position is updated using greedy selection, and finally step 4.2 is returned. Step 4.8: when currently located in the later search stage, it is judged whether mod(t, 2) = 0, if the condition is met, the evaluation stage is entered; otherwise, the adjustment stage is entered, and step 4.9 is executed; In the evaluation stage, N / 2 dune cats are randomly selected from the population to perform the exploration task, and the remaining dune cats perform the development task, then the dune cat individual is updated according to the method of step 4.6, after constraint processing, the fitness value of the objective function is calculated according to the method of step 4.7, and the current global optimal position is updated; and the decision index is calculated according to the number of successful individuals of the exploration task and the development task; Step 4.9: in the adjustment stage, it is judged whether the population performs the exploration task or the development task according to the decision index generated in the last iteration, then the dune cat individual is updated according to the method of step 4.6, after constraint processing, the fitness value of the objective function is calculated according to the method of step 4.7, and the current global optimal position is updated; Step 4.10: it is judged whether the maximum number of iterations is reached, if the maximum number of iterations is reached, the optimal setting values of the furnace temperature in each section are output; if the maximum number of iterations is not reached, step 4.2 is returned.

2. The furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm according to claim 1, wherein, The billet parameters in the step 1 include the billet size, density, thermal conductivity, and specific heat capacity; the heating furnace structure parameters include the furnace length and furnace structure; and the production conditions and operation parameters include the entering and exiting furnace temperatures, rolling rhythm, heating time, output, furnace pressure, heating system, tapping rhythm, and composition of combustion products.

3. The hybrid modeling and improved sand dune cat swarm algorithm based furnace temperature optimization method according to claim 1, wherein, The step 2 specifically comprises the following steps: Step 2.1: the mixed prediction model of the billet temperature distribution adopts a two-dimensional unsteady mathematical model, and the following assumptions are made to simplify the model: a) the furnace temperature is only a function of the furnace length direction; b) the influence of the steel billet scale in the heat exchange process is ignored; c) the convection and radiation heat transfer between the furnace gas and the steel billet is a comprehensive heat flux boundary condition; d) the steel billet moves at a constant speed during the heating process; Step 2.2: A two-dimensional unsteady heat conduction equation is established according to the billet section, and the specific mathematical description is as follows: wherein , is the billet cross-section width, is the billet cross-section height; T is the billet temperature profile expressed as is a function of the coordinates and the heating time ; is the billet density at temperature T; is the billet specific heat capacity at temperature T; is the billet thermal conductivity at temperature T; Step 2.3: The boundary conditions are established, and the data description is as follows: wherein, and are the heat flux density on the upper surface of the billet and the heat flux density on the lower surface of the billet, respectively; is the Boltzmann constant; and are the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace, respectively; T f is the furnace temperature, T s is the predicted billet surface temperature at the previous time; an insulating thermal boundary condition is used on both sides of the billet; Step 2.4: The billet section is discretized into multiple cells, and the difference equation of each node is established according to the two-dimensional unsteady heat conduction equation, and the temperature of each node is solved by using the difference iteration method, and then the temperature distribution of the billet is obtained.

4. The furnace temperature optimization method based on hybrid modeling and improved sand dune cat swarm algorithm according to claim 3, wherein, According to the BP neural network identification, the total heat absorption rate of the upper hearth in step 2.3 and the total heat absorption rate of the lower hearth , specifically: 1) Taking the production conditions and operation parameters as inputs, and taking the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace as outputs; 2) Establish a BP neural network and initialize the weight and bias values; 3) Calculate the output of each node in the hidden layer and output layer; 4) Calculate the reverse error; 5) Weight learning; 6) Determine whether the error meets the standard, if it does, the relationship between the production conditions and operation parameters and the total heat absorption rate of the upper furnace and the total heat absorption rate of the lower furnace is obtained; otherwise, step 7) is performed; 7) Determine whether the number of iterations has been reached, if it has, the relationship between the production conditions and operation parameters and the total heat absorption rate of the upper and lower furnaces is obtained; otherwise, return to step 2).

5. The hybrid modeling and improved sand dune cat swarm algorithm based furnace temperature optimization method according to claim 1, wherein, The step 3 is specifically: Step 3.1: The objective function of the heating furnace temperature optimization is the integral minimum of the heating furnace temperature to the furnace length, which is mathematically expressed as follows: In the formula, J represents an objective function; L represents a heating furnace length; represents a furnace temperature of the billet at the heating furnace l; Step 3.2: Build the constraint condition, and the specific mathematical description is as follows: In the formula: This indicates the prediction made by the mixed prediction model of billet temperature distribution. The center temperature of the steel billet at that moment; This indicates the prediction made by the mixed prediction model of billet temperature distribution. The surface temperature of the steel billet at any given time; This indicates the maximum cross-sectional temperature difference during the billet heating process. According to the rolling process requirements, it is related to the steel grade, the heat flux density of the upper and lower surfaces, and the heating system. This indicates the maximum rate of temperature rise, which is related to structural and operating parameters. The maximum cross-sectional temperature difference of the billet when it exits the furnace, as required by the process, is related to the steel grade, the heat flux density of the upper and lower surfaces at the time of exiting the furnace, and the heating system, according to the rolling process requirements. This represents the maximum difference between the surface temperature of the billet when it exits the furnace and the target exit temperature, and is set according to the rolling process requirements; This indicates the surface temperature of the steel billet when it exits the furnace; This indicates the center temperature of the steel billet when it exits the furnace; This indicates the target exit temperature, which is set according to the rolling process requirements; and These represent the lower and upper limits of the furnace temperature at point l in the heating furnace, respectively.

6. The hybrid modeling and improved sand dune cat swarm algorithm based furnace temperature optimization method according to claim 1, wherein, The decision index in step 4.8 is calculated according to the number of successful individuals of the exploration task and the development task, which is specifically: If the fitness value of the objective function of the dune cat individual is less than the fitness value of the objective function of the current global optimal position, the current global optimal position is updated according to the greedy selection, and the dune cat individual is considered to be updated successfully, the number of individuals successful in exploration and development tasks is recorded, and the decision index is calculated according to the following formula: wherein S is a decision metric, R S is the number of individuals that successfully completed the exploration task. I S is the number of individuals that successfully completed the exploration task.

7. The hybrid modeling and improved sand dune cat swarm algorithm based furnace temperature optimization method according to claim 1, wherein, the decision metric produced in step 4.9 according to the last iteration determining whether the population is performing an exploration task or an exploitation task is specifically If δ>δ2, all individuals perform exploration task; if δ<δ1, all individuals perform development task; if δ1<δ<δ2, all individuals are randomly and evenly distributed to perform exploration task and development task, 0<δ1<δ2<1.

Images