CN114818505A - Method for predicting temperature distribution of steel billet in heating furnace based on particle swarm optimization algorithm - Google Patents
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Abstract
The invention provides a method for predicting the temperature distribution of a steel billet in a heating furnace based on a particle swarm optimization algorithm, which comprises the following steps: establishing a one-dimensional unsteady heat conduction differential equation for representing a billet temperature distribution model in the heating furnace, and determining initial conditions and boundary conditions of the equation; replacing the particle values in the particle swarm optimization algorithm with random initial values of boundary conditions, and solving a one-dimensional unsteady heat conduction differential equation to obtain a solved temperature value; taking the mean square error between the solved temperature value and the temperature measurement value as a target function of a heat conduction inverse problem, taking the mean square error as a fitness value, returning the fitness value to the particle swarm optimization algorithm, sequentially inverting the boundary conditions according to the time sequence, and updating the boundary conditions based on the inversion; and calculating the heat conduction positive problem by using the updated boundary conditions, and outputting a temperature value at a specified time and a specified position. The invention can better solve the problems of damping and delay of the unsteady heat conduction differential equation and is more suitable for solving the unsteady heat conduction problem.
Description
Technical Field
The invention relates to the technical field of prediction of temperature distribution of steel billets in a heating furnace, in particular to a method for predicting the temperature distribution of the steel billets in the heating furnace based on a particle swarm optimization algorithm.
Background
The heating furnace is an important process equipment between continuous casting and hot rolling, and is used for heating the steel billet so as to improve the plasticity of the steel billet. The temperature distribution of the steel billet in the heating furnace is one of important bases for measuring the heating quality and realizing the automatic control of the heating furnace, and the quality of the steel billet directly restricts the quality of a finished product of steel.
The heat transfer process of the steel billet in the heating furnace is very complex, because the heating and temperature rising process of the steel billet is a process in which a plurality of heat transfer modes coexist and are mutually coupled, for example, high-temperature furnace gas flows in the heating furnace, and when the furnace gas flows through the surface of a furnace wall and the surface of the steel billet, the phenomenon of heat convection exists; the high-temperature furnace wall can have the heat radiation effect on the steel billet; meanwhile, the heat conduction process can be generated inside the steel billet and the furnace wall. This is only a few major heat transfer processes, and in fact the heating of the billet inside the furnace is more complicated than this.
In practical engineering application, both experimental measurement and theoretical calculation of the temperature distribution of the steel billet have certain difficulties. First, the method is not practical because a large number of thermocouples are provided inside and on the surface of the steel billet to directly measure the temperature of the steel billet, which affects the airflow distribution in the heating furnace and also destroys the structure of the steel billet. Secondly, solving the unsteady heat conduction differential equation by utilizing the traditional heat conduction positive problem is difficult to perform theoretical calculation of the temperature of the steel billet, and because the phenomena of combustion, flow, heat transfer and the like of gas in the heating furnace are very complex, the boundary conditions such as the actual convective heat transfer coefficient or the heat flux density are difficult to determine.
Therefore, the temperature distribution is predicted by using a heat conduction inverse problem, namely, boundary conditions such as heat flux density or convective heat transfer coefficient of the surface of the steel billet are solved by using the known temperature of one or more discrete points in or on the surface of the steel billet in an inversion mode, then, a heat conduction positive problem is solved, and the time-space change condition of the temperature at any position of the steel billet is obtained. To obtain the inversion results, various optimization algorithms are used to solve the inverse problem of thermal conductivity, such as: genetic algorithms, neural network methods, ant colony algorithms, sequential function methods, and particle swarm algorithms. The Particle Swarm Optimization (PSO) has the advantages of simple and easily-realized program, few parameters, easy adjustment, high convergence speed and the like.
According to the physical characteristics of the heat conduction problem, the mathematical form of the unsteady heat conduction differential equation belongs to a diffusion type partial differential equation and has damping property and delay property. The damping property means that the boundary heat flux density has a large influence on the temperature close to the boundary and has a small influence on the temperature far away from the boundary; delayed means that the internal temperature has a delayed effect in time as a function of the surface heat flux density. Thus, an effective method of inverting the boundary heat flow density is to compute it sequentially in time, rather than simultaneously over the entire time domain.
At present, some patents and papers are provided for predicting the temperature distribution of the steel billet and optimizing the algorithm in China. Patent CN105734263A discloses a method for predicting the temperature of the subsequent steel billet in the heating furnace and the temperature of the heating furnace, which obtains the temperature rise coefficient of the steel billet by counting the temperature rise data of the steel billet under different temperature differences of the steel billet and the temperature of the heating furnace. In the aspect of optimization algorithm patents, patent CN111020118A discloses a RH endpoint temperature prediction method based on particle swarm optimization scheme reasoning; the patent CN11125913A discloses an identification method and device for the total heat absorption rate of a heating furnace, which utilizes chaos to generate multi-dimensional particle swarm, and then optimizes the multi-parameter simultaneous solving of the heat conduction inverse problem, but does not consider the damping and delay problems of the unsteady heat conduction differential equation; patent CN113552797A discloses a heating furnace temperature control method and system based on improved particle swarm optimization, which similarly uses chaos to generate multidimensional particle swarm, and then solves multiple parameters simultaneously. In the thesis, "research on source-seeking heat conduction inverse problem based on particle swarm optimization algorithm" (zhang billi, lumei, pottery, libohan, university of Shanghai science and engineering, 2013, (stage 4)), an objective function of a heat conduction inverse problem is established according to a least square principle, and the particle swarm optimization algorithm is adopted to perform inversion solution of a heat source position on the heat conduction inverse problem containing a heat source item, wherein the article is used for calculating steady-state heat conduction.
At present, no patent exists for the aspect of billet temperature in a heating furnace by a particle swarm optimization algorithm aiming at unsteady heat conduction in a time sequence.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for predicting the temperature distribution of steel billets in a heating furnace based on a particle swarm optimization algorithm aiming at the defects of the prior art, and compared with the traditional particle swarm optimization algorithm, the method can better solve the problems of damping and delay of an unsteady heat conduction differential equation and is more suitable for solving the unsteady heat conduction problem.
The technical scheme is as follows: the invention discloses a method for predicting the temperature distribution of a steel billet in a heating furnace based on a particle swarm optimization algorithm, which comprises the following steps of: establishing a one-dimensional unsteady heat conduction differential equation for representing a billet temperature distribution model in a heating furnace, and determining initial conditions and boundary conditions of the equation, wherein the initial conditions comprise a temperature measurement value and a random initial value of the boundary conditions; replacing the particle values in the particle swarm optimization algorithm with random initial values of boundary conditions, and solving a one-dimensional unsteady heat conduction differential equation to obtain a solved temperature value; taking the mean square error between the solved temperature value and the temperature measurement value as a target function of a heat conduction inverse problem, taking the mean square error as a fitness value, returning the fitness value to the particle swarm optimization algorithm, sequentially inverting the boundary conditions according to the time sequence, and updating the boundary conditions based on the inversion; and calculating the heat conduction positive problem by using the updated boundary conditions, and outputting a temperature value at a specified position and at a specified moment.
Further perfecting the technical scheme, the boundary conditions comprise a first class, a second class and a third class; when the boundary condition is of a first type, sequentially inverting the temperature values according to the time sequence by adopting a particle swarm optimization algorithm; when the boundary condition is of a second type, sequentially inverting the heat density values by adopting a particle swarm optimization algorithm according to a time sequence; and when the boundary condition is of a third type, determining the heat density value by using the Newton's cooling law and sequentially inverting the heat density value according to the time sequence by using the particle swarm optimization algorithm according to the rule that the temperature of the surrounding medium changes along with the time and the convection heat exchange coefficient between the surface of the steel billet and the surrounding medium.
Further, the boundary condition is of a second type, the particle swarm optimization algorithm sequentially inverts the heat flow density values according to a time sequence, and the process of updating the boundary condition based on the inversion comprises the following steps:
s1: obtaining a given position x p A temperature measurement and a random initial value of heat flow density;
s2: setting parameters in a particle swarm optimization algorithm;
s3: initializing the random position, random speed, individual optimal value, global optimal value and maximum particle iteration number max _ iter of particles in the particle swarm optimization algorithm;
s4: updating the speed and position of the particles;
s5: replacing the updated particle position with a Kth value in the heat flux density;
s6: dispersing a one-dimensional unsteady heat conduction differential equation and boundary conditions thereof;
s7: setting parameters and initial conditions of a one-dimensional unsteady heat conduction differential equation;
s8: updating boundary conditions and internal node temperature;
s9: if the maximum node number is reached, the next step is carried out, otherwise, the S8 is returned;
s10: solving for position x p The temperature value of (a), calculating x p The solved temperature value of (a) and (x) p Outputting the mean square error between the measured temperature values as a target function of the heat conduction inverse problem, and returning the mean square error as a fitness value to the particle swarm optimization algorithm;
s11: judging whether the fitness value is an individual optimal value, if so, replacing the existing individual optimal value and the corresponding particle position, and if not, directly entering S13;
s12: judging whether the fitness value is the group optimal value, if so, replacing the existing group optimal value and the corresponding particle position, and if not, directly entering S13;
s13: judging whether the convergence condition is met, entering the next step if the convergence condition is met, and returning to the step S4 if the convergence condition is not met;
s14: judging whether the maximum particle iteration times max _ iter is reached, if so, entering the next step, and if not, returning to the step S4;
s15: keeping the Kth value of the obtained heat flow density, judging whether the maximum iteration times is reached, and if the K value of the obtained heat flow density is met, outputting the Kth value of the heat flow density as a final heat flow density value; if the heat flow density does not meet the requirement, returning to S3, and calculating the K +1 th value of the heat flow density until the maximum iteration number N is reached;
s16: and calculating the heat conduction positive problem by using the final heat flow density value, and outputting the temperature value at the specified position and the specified time of the billet.
Step S15 is different from the conventional particle swarm optimization algorithm in that all the quantities to be solved are simultaneously solved as multidimensional parameters, and considering that the influence of the heat flux density has a delay effect in time, the present invention optimizes one heat flux density value each time according to the time sequence, and optimizes the next heat flux density after the current optimization result is obtained.
Further, the setting of the parameters in the particle swarm optimization algorithm in S2 includes: w, c 1 ，c 2 pN, max _ iter, toler, where w is the inertial weight, c 1 、c 2 For the learning factor, pN is the number of particles, max _ iter is the maximum number of particle iterations, and toler is the convergence factor.
Further, the S4 updates the speed and the position of the particle in the particle swarm optimization algorithm;
wherein x is the position of the particle, v is the velocity of the particle, p b For individual optimum, g b For a global optimum, k is the current iteration number, r 1 、r 2 Is [0,1 ]]A random number within the range of the random number,
the influence of the current speed of the particle, the influence of the individual optimum value of the particle itself on the speed, and the influence of the global optimum value of the particle group on the speed are respectively indicated.
Further, in S6, a finite difference method is used to discretize a one-dimensional unsteady thermal conduction differential equation and its boundary conditions
T(x,0)＝T ini ,t＝0,x≥0
Forward difference is adopted for a time term in the one-dimensional unsteady heat conduction differential equation, and central difference is adopted for a space term, so that a discrete equation shown as follows is obtained:
wherein i is the current position, 1 and N are the positions at both ends, N is the current time step, q n The heat flow density at the current time step is shown, and lambda is the heat conductivity coefficient and the unit is W/mK; Δ x is the space step, in m; fo is the grid fourier number:
in the formula, Δ t is a time step and has a unit of s; rho is density in kg/m 3 (ii) a c is the specific heat capacity, and the unit is J/kgK.
Further, in the step S7, parameters in the thermal conductivity differential equation, such as the initial temperature value T, are set ini Thermal conductivity lambda, space step delta x, time step delta t.
Further, the updating the boundary condition in S8 includes
Updating internal node temperature
Further, the objective function of the inverse problem of heat conduction in S10 is
In the formula (I), the compound is shown in the specification,
and
respectively is a solved temperature value and a temperature measured value at the nth moment of the ith position, and N is the total time step number.
Has the advantages that: compared with the prior art, the invention has the advantages that: the method comprises the steps of firstly establishing a one-dimensional unsteady heat conduction differential equation for solving the temperature of the steel billet, secondly obtaining a temperature numerical solution of a solution domain by using a finite difference method, selecting the temperature numerical solution at a position corresponding to a temperature measurement value to carry out mean square error so as to establish a target function of a heat conduction inverse problem, thirdly carrying out space search on the optimal solution of the target function by using a time sequence particle swarm optimization algorithm, finally carrying out inversion to obtain an updated boundary condition, and calculating the temperature value at any position and any time of the steel billet based on the updated boundary condition.
The method adopts the time sequence particle swarm optimization algorithm to invert to obtain the heat flow distribution on the surface of the billet, and compared with the traditional particle swarm optimization algorithm, the method can better solve the problems of damping and delay of the unsteady heat conduction differential equation and is more suitable for solving the unsteady heat conduction problem.
Compared with the traditional particle swarm optimization algorithm, the time-sequential particle swarm optimization algorithm is used for inverting the optimal solution of the heat flux density on one time point by one time point, so that the iteration times can be effectively reduced, and the calculation result can be prevented from falling into the local optimal solution.
Drawings
FIG. 1 is a flow chart of an implementation of particle swarm optimization algorithm for inverting surface heat flux density;
FIG. 2 is a flow chart of an embodiment of temperature calculation for positive thermal conductivity;
FIG. 3 is a schematic diagram of meshing;
FIG. 4 is a comparison of measured temperature at x-0.00528 m with inverted temperature;
fig. 5 shows the measured temperature compared to the inversion temperature at 247 s.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the embodiments.
There are three types of boundary conditions in heat transfer science that are fundamental elements in solving heat transfer problems, with each type of boundary condition having a special case to which it addresses. The first type of boundary condition is a given object surface temperature variation formula; the second type of boundary condition is that a relation between the heat flow density of the surface of the object and time is given; the third type of boundary condition is given by the law of the temperature change of the surrounding medium along with time and the convection heat exchange coefficient of the object surface and the surrounding medium.
In the present invention, the second type of boundary condition and the symmetric boundary condition are used as examples for explanation, and actually, other types of boundary conditions can be used without affecting the whole calculation process. When the selected calculation area is the first type boundary condition, the surface temperature of the steel billet is a known quantity, and the temperature value of the boundary node can be directly taken to be substituted into the calculation for use; when the boundary condition is a third type of condition, the surface temperature of the steel slab is an unknown quantity, and the relationship between the value and the heat flux density can be determined using newton's law of cooling.
As shown in figure 1, the method for predicting the temperature distribution of the billet in the heating furnace based on the particle swarm optimization algorithm selects the billet with the length x of 0.022m, the thermal conductivity lambda of 40W/mK and the density rho of 7500kg/m 3 And the specific heat capacity c is 680J/kgK.
S1: given position x p Temperature measurement T at 0.00528m e (i)＝[20.0,42.63,87.26,153.89,242.52]And a random initial value of heat flow density (q) ini (i) Where i ═ 0,1,2,3,4 denote data at 5 time points;
s2: set the parameters in PSO, w ═ 0.8, c 1 ＝2，c 2 2, pN is 10, max _ iter is 100, toler is 0.01, w is the inertial weight, c 1 ，c 2 The method comprises the following steps of (1) taking a learning factor, pN (maximum number of particles), max _ iter (maximum number of particle iterations) and toler (convergence factor);
s3: initializing random position (x), velocity (v), individual optimum (p) of PSO particles b ) Global optimum value (g) b )；
S4: the velocity and position of the particles in the PSO are updated,
s5: replacing the particle position (x) with the Kth value (q) in the heat flow density ini (K))；
S6: a discrete solution domain, whose meshing is as shown in fig. 3, is set with a space step Δ x of 0.00044m, a grid fourier number Fo of 0.5, and a time step Δ t of 0.0123 s;
s7: setting parameters in the differential equation of thermal conductivity, e.g. initial temperature value T ini ；
S8: updating boundary conditions
(associated with heat flow density), and
updating internal node temperature
S9: judging whether the maximum node number M is reached, if so, entering the next step, and if not, returning to S7;
s10: get the position (x) p ) And (3) solving the temperature value and calculating the mean square error of the temperature value and the measured temperature value:
in the formula (I), the compound is shown in the specification,
and
respectively at the nth time of the ith positionAnd (4) solving the temperature value and the temperature measurement value, wherein N is the total time step number.
Returning the output mean square error sigma as a fitness value to the PSO;
s11: judging whether the fitness value is the individual optimal value (p) b ) If the current individual optimum value and the corresponding particle position are met, replacing the current individual optimum value and the corresponding particle position, and if the current individual optimum value and the corresponding particle position are not met, directly entering S13;
s12: judging whether the fitness value is the group optimal value (g) b ) If the current group optimal value and the corresponding particle position are met, replacing the current group optimal value and the corresponding particle position, and if the current group optimal value and the corresponding particle position are not met, directly entering S13;
s13: judging whether the convergence condition is met, entering the next step if the convergence condition is met, and returning to S4 if the convergence condition is not met;
s14: judging whether the maximum iteration time t is max _ iter, entering the next step if the maximum iteration time t is max _ iter, and returning to the step S4 if the maximum iteration time t is not max _ iter;
s15: keeping the Kth value of the obtained heat flow density, judging whether the maximum iteration number N is equal to N or not, and outputting a final heat flow density value if the maximum iteration number N is equal to N; not satisfied, return to S3, the K +1 th value of the heat flow density is calculated until the maximum number of iterations N is reached.
In this case, the inversion value of the final heat flux density is [0.99876,2.02109,2.99763,4.00587,5.00124], and the corresponding actual values, and the relative error between the two are shown in table 1 below:
s16: the heat conduction positive problem is calculated by using the heat flow density value, and the flow chart is shown in figure 2, so that the temperature value of any position and any time of the billet can be obtained.
For example, the inversion temperature at x 0.00528m is compared to the measured temperature as shown in fig. 4. The inversion temperature at t 247s is compared to the measured temperature as shown in fig. 5. It can be seen that the algorithm has a good inversion effect. In fig. 4, the inversion temperature has a large error at a longer time, and the relative error is 1%, which is mainly caused by the delay effect of unsteady heat conduction.
Compared with the traditional particle swarm optimization algorithm, the method uses the time-sequential particle swarm optimization algorithm to invert the optimal solution of the heat flux density on one time point by one time point, so that the iteration times can be effectively reduced, and the calculation result can be prevented from falling into the local optimal solution.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm is characterized by comprising the following steps of:
establishing a one-dimensional unsteady heat conduction differential equation for representing a billet temperature distribution model in the heating furnace, and determining initial conditions and boundary conditions of the one-dimensional unsteady heat conduction differential equation, wherein the initial conditions comprise temperature measurement values and random initial values of the boundary conditions;
replacing the particle values in the particle swarm optimization algorithm with random initial values of boundary conditions, and solving a one-dimensional unsteady heat conduction differential equation to obtain a solved temperature value;
taking the mean square error between the solved temperature value and the temperature measurement value as a target function of a heat conduction inverse problem, taking the mean square error as a fitness value, returning the fitness value to the particle swarm optimization algorithm, sequentially inverting the boundary conditions according to the time sequence, and updating the boundary conditions based on the inversion;
and calculating the heat conduction positive problem by using the updated boundary conditions, and outputting a temperature value at a specified position and at a specified moment.
2. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 1, wherein the method comprises the following steps of: the boundary conditions comprise a first class, a second class and a third class; when the boundary condition is of a first type, sequentially inverting the temperature values according to the time sequence by adopting a particle swarm optimization algorithm; when the boundary condition is of a second type, sequentially inverting the thermal density values by adopting a particle swarm optimization algorithm according to a time sequence; when the boundary condition is of a third type, the thermal density value is determined by the Newton's cooling law and the particle swarm optimization algorithm according to the time sequence by giving the temperature change rule of the surrounding medium along with the time and the convection heat exchange coefficient between the surface of the billet and the surrounding medium.
3. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 2, wherein the method comprises the following steps of: the boundary conditions are of a second type, the particle swarm optimization algorithm sequentially inverts the heat flow density values according to a time sequence, and the process of updating the boundary conditions based on inversion comprises the following steps:
s1: obtaining a given position x p A temperature measurement and a random initial value of heat flow density;
s2: setting parameters in a particle swarm optimization algorithm;
s3: initializing the random position, random speed, individual optimal value, global optimal value and maximum particle iteration number max _ iter of particles in the particle swarm optimization algorithm;
s4: updating the speed and position of the particles;
s5: replacing the updated particle position with a Kth value in the heat flow density;
s6: dispersing a one-dimensional unsteady heat conduction differential equation and boundary conditions thereof;
s7: setting parameters and initial conditions of a one-dimensional unsteady heat conduction differential equation;
s8: updating boundary conditions and internal node temperature;
s9: if the maximum number of nodes is reached, the next step is carried out, otherwise, the step returns to S8;
s10: solving for position x p The temperature value of (a), calculating x p The solved temperature value of (a) and (x) p Outputting the mean square error between the measured temperature values as a target function of a heat conduction inverse problem, and returning the mean square error serving as a fitness value to the particle swarm optimization algorithm;
s11: judging whether the fitness value is an individual optimal value, if so, replacing the existing individual optimal value and the corresponding particle position, and if not, directly entering S13;
s12: judging whether the fitness value is the group optimal value, if so, replacing the existing group optimal value and the corresponding particle position, and if not, directly entering S13;
s13: judging whether the convergence condition is met, if the convergence condition is met, entering the next step, if not, returning to the step S4;
s14: judging whether the maximum particle iteration times max _ iter is reached, if so, entering the next step, and if not, returning to the step S4;
s15: keeping the Kth value of the obtained heat flow density, judging whether the maximum iteration times is reached, and if the K value of the obtained heat flow density is met, outputting the Kth value of the heat flow density as a final heat flow density value; if the heat flow density does not meet the requirement, returning to S3, and calculating the K +1 th value of the heat flow density until the maximum iteration number is reached;
s16: and calculating the heat conduction positive problem by using the final heat flow density value, and outputting the temperature value at the specified position and the specified time of the billet.
4. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 3, wherein the method comprises the following steps of: setting parameters in the particle swarm optimization algorithm in the step S2 includes: w, c 1 ，c 2 pN, max _ iter, toler, where w is the inertial weight, c 1 、c 2 For the learning factor, pN is the number of particles, max _ iter is the maximum number of particle iterations, and toler is the convergence factor.
5. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 4, wherein the method comprises the following steps of: the S4 updates the speed and the position of the particles in the particle swarm optimization algorithm;
wherein x is the position of the particle, v is the velocity of the particle, p b For individual optimum, g b For a global optimum, k is the current iteration number, r 1 、r 2 Is [0,1 ]]A random number within the range of the random number,
respectively representing the influence of the current speed of the particle, the influence of the individual optimum of the particle itself on the speed and the influence of the global optimum of the particle swarm on the speed.
6. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 5, wherein the method comprises the following steps of: in the step S6, a finite difference method is adopted to disperse the one-dimensional unsteady heat conduction differential equation and the boundary conditions thereof
T(x,0)＝T ini ,t＝0,x≥0
Forward difference is adopted for a time term in the one-dimensional unsteady heat conduction differential equation, and central difference is adopted for a space term, so that a discrete equation shown as follows is obtained:
wherein i is the current position, 1 and N are the positions at both ends, N is the current time step, q n The heat flow density at the current time step is shown, and lambda is the heat conductivity coefficient and the unit is W/mK; Δ x is the space step, in m; fo is the grid fourier number:
in the formula, Δ t is a time step and has a unit of s; rho is density in kg/m 3 (ii) a c is the specific heat capacity, and the unit is J/kgK.
7. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 6, wherein the method comprises the following steps of: in the step S7, parameters in the one-dimensional unsteady thermal conduction differential equation are set, including an initial temperature value T ini Thermal conductivity lambda, space step delta x, time step delta t.
8. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 7, wherein the method comprises the following steps of: the updating of the boundary conditions in S8 includes
Updating internal node temperature
9. The method for predicting the temperature distribution of the steel billet in the heating furnace based on the particle swarm optimization algorithm according to claim 8, wherein the method comprises the following steps: the objective function of the inverse problem of heat conduction in S10 is
In the formula (I), the compound is shown in the specification,
and
respectively is a solved temperature value and a temperature measured value at the nth moment of the ith position, and N is the total time step number.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115950916A (en) * | 2023-03-14 | 2023-04-11 | 中国空气动力研究与发展中心计算空气动力研究所 | A method, device and equipment for detecting heat flux density on the surface of an object |
| CN116817603A (en) * | 2023-06-28 | 2023-09-29 | 北京科技大学 | High-temperature smelting furnace molten pool temperature monitoring and inverting method based on heat conduction inverse problem |
| CN116884520A (en) * | 2023-05-29 | 2023-10-13 | 江南大学 | A method and device for evaluating the change pattern of lipase position selectivity |
| CN118586745A (en) * | 2024-08-06 | 2024-09-03 | 山东太阳耐磨件有限公司 | Steel plate temperature prediction method and system for temperature control system |
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109977559A (en) * | 2019-03-28 | 2019-07-05 | 东北大学 | A kind of Pulverized Fuel Boiler Furnace inverse radiation analysis method for solving based on improved adaptive GA-IAGA |
| CN111125913A (en) * | 2019-12-25 | 2020-05-08 | 东北大学 | Method and device for identifying total heat absorption rate of heating furnace |
| CN113191080A (en) * | 2021-04-26 | 2021-07-30 | 辽宁省交通高等专科学校 | Heating furnace billet temperature field prediction model optimization method based on HMPSO algorithm |
| CN113591242A (en) * | 2021-07-30 | 2021-11-02 | 沈阳航空航天大学 | Dynamic soft measurement method for thickness of continuous casting billet shell |
| CN113849901A (en) * | 2021-07-28 | 2021-12-28 | 上海机电工程研究所 | Improved self-adaptive optimization method and system for contact heat transfer coefficient identification |
-
2022
- 2022-05-10 CN CN202210508593.7A patent/CN114818505B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109977559A (en) * | 2019-03-28 | 2019-07-05 | 东北大学 | A kind of Pulverized Fuel Boiler Furnace inverse radiation analysis method for solving based on improved adaptive GA-IAGA |
| CN111125913A (en) * | 2019-12-25 | 2020-05-08 | 东北大学 | Method and device for identifying total heat absorption rate of heating furnace |
| CN113191080A (en) * | 2021-04-26 | 2021-07-30 | 辽宁省交通高等专科学校 | Heating furnace billet temperature field prediction model optimization method based on HMPSO algorithm |
| CN113849901A (en) * | 2021-07-28 | 2021-12-28 | 上海机电工程研究所 | Improved self-adaptive optimization method and system for contact heat transfer coefficient identification |
| CN113591242A (en) * | 2021-07-30 | 2021-11-02 | 沈阳航空航天大学 | Dynamic soft measurement method for thickness of continuous casting billet shell |
Non-Patent Citations (3)
| Title |
|---|
| YINGXIN LIAO 等: "Integrated Hybrid-PSO and Fuzzy-NN Decoupling Control for Temperature of Reheating Furnace" * |
| 张丽慧;王广军;罗兆明;陈红;: "利用二维导热反问题预测钢坯温度分布" * |
| 王珺琳: "中厚板层流冷却过程温度场模型与实验研究" * |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115950916A (en) * | 2023-03-14 | 2023-04-11 | 中国空气动力研究与发展中心计算空气动力研究所 | A method, device and equipment for detecting heat flux density on the surface of an object |
| CN115950916B (en) * | 2023-03-14 | 2023-05-26 | 中国空气动力研究与发展中心计算空气动力研究所 | Object surface heat flux density detection method, device and equipment |
| CN116884520A (en) * | 2023-05-29 | 2023-10-13 | 江南大学 | A method and device for evaluating the change pattern of lipase position selectivity |
| CN116817603A (en) * | 2023-06-28 | 2023-09-29 | 北京科技大学 | High-temperature smelting furnace molten pool temperature monitoring and inverting method based on heat conduction inverse problem |
| CN116817603B (en) * | 2023-06-28 | 2024-01-02 | 北京科技大学 | Monitoring and inversion method of molten pool temperature in high-temperature smelting furnace based on thermal conduction inverse problem |
| CN118664007A (en) * | 2024-05-29 | 2024-09-20 | 广州大学 | Solder paste temperature soft measurement method and system based on mechanism and support vector regression |
| CN118664007B (en) * | 2024-05-29 | 2026-01-20 | 武汉博联特科技有限公司 | Mechanism and support vector regression-based solder paste temperature soft measurement method, system, electronic equipment and storage medium |
| CN118586745A (en) * | 2024-08-06 | 2024-09-03 | 山东太阳耐磨件有限公司 | Steel plate temperature prediction method and system for temperature control system |
| CN119200503A (en) * | 2024-11-27 | 2024-12-27 | 浙江中威智能家具有限公司 | A temperature compensation control system for laser engraving machine based on multi-source temperature data fusion |
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