A finite element method for calculating the erosion boundary of the longitudinal section of the furnace hearth

Abstract

The present invention discloses a finite element method for calculating the erosion boundary of a hearth longitudinal section, belonging to the technical field of blast furnace hearth erosion detection. The method calculates the position of the hearth erosion boundary by obtaining temperature values ​​detected by a thermocouple array arranged in the hearth carbon bricks. During the calculation process, the erosion boundary calculation problem is transformed into a function optimization problem, which is solved using a particle swarm algorithm. When designing the objective function, the curvature constraint of the erosion boundary is considered to obtain a smoother erosion boundary. During the optimization process, the finite element method is used for heat conduction analysis, improving the accuracy of temperature calculation and making the calculated blast furnace hearth erosion boundary closer to the actual erosion boundary.

Description

Technical Field

[0001] The invention relates to a finite element method for calculating the erosion boundary of a hearth longitudinal section, and belongs to the technical field of blast furnace hearth erosion detection. Background Art

[0002] The steel industry is a vital sector in my country, with steel production ranking first in the world for over a decade. Blast furnaces are key pieces of equipment in steelmaking and serve as the primary equipment in the ironmaking process. Due to their high construction and maintenance costs, the economic efficiency of blast furnace ironmaking depends on their service life. Blast furnace smelting takes place in a sealed vertical furnace. Solid charge materials such as coke, iron ore, and solvent are charged from the upper chamber, while molten iron and slag are periodically or continuously discharged from the taphole at the lower chamber. Based on the charge's temperature, chemical composition, and physical form, the blast furnace is divided into five major sections from top to bottom: the block zone, the remelting zone, the dripping zone, the tuyere combustion zone, and the hearth. The hearth is a crucial area of ​​the blast furnace, where iron atoms exist in the form of liquid molten iron. Therefore, the hearth's lining is highly susceptible to corrosion, significantly impacting the life of the blast furnace. A major challenge in predicting corrosion is that molten iron can cover the eroded areas of the hearth lining, making it difficult to directly observe the erosion status.

[0003] To prevent burnout of the blast furnace hearth, a mathematical model describing heat conduction within the hearth is required to analyze and calculate erosion of the hearth lining. During the middle and later stages of a blast furnace's service life, the erosion morphology and thickness of the hearth lining can be assessed to rationally schedule furnace maintenance and overhaul periods, ensuring the safety of the hearth structure. This also requires fully utilizing existing thermal measurement parameters to closely approximate actual conditions and accurately reflect the working conditions of the hearth lining.

[0004] Generally speaking, mathematical models for blast furnace hearth lining erosion are based on heat transfer theory. Different mathematical models are developed based on thermal parameters such as temperature and heat flux, and these models are continuously evolving. Research on blast furnace hearth erosion has been conducted by combining forward and inverse models. Forward models often predict the location of erosion based on erosion excitation. However, due to the complex mechanisms of the hearth lining, involving oxidation, thermal stress, mechanical erosion, and other factors, as well as the complex production volume and media, predicting the location of the erosion line from a forward perspective is extremely difficult. Inverse models, on the other hand, directly utilize existing measurable thermal parameters such as temperature and heat flux of the blast furnace hearth in service to determine the lining erosion state. This involves solving for the unknown geometric boundaries given known parameters such as the partial geometric boundaries, thermal conductivity, temperature, and heat flux. Therefore, inverse models are more practical than forward models and are currently the primary method for analyzing blast furnace hearth erosion.

[0005] In order to predict the erosion boundary, one of the reliable ways is to establish an inverse solution through Fourier's law in heat transfer. The traditional one-dimensional calculation model is easy to analyze and understand, but the calculation results have large errors and the accuracy is not high enough; the three-dimensional model is too complex and difficult. Therefore, in comparison, the two-dimensional calculation model can greatly improve the analysis accuracy and has high practical application value. It is the most practical method at present. The commonly used numerical analysis method in the two-dimensional calculation model is the finite difference method. It is relatively simple in concept and easy to implement, but the limitation of the finite difference method is that the solution area must be divided into linear units, that is, the grid division must be regular, but the erosion boundary of the blast furnace hearth causes the solution area to be irregular, so the erosion boundary obtained by the finite difference method has a large error.

[0006] Unlike the finite difference method, which uses differences to approximate differentials, the finite element method uses interpolation functions to approximate differentials. By leveraging the variational principle or weighted residuals, it can calculate nonlinear and irregular regional problems and accurately simulate regional boundaries. However, existing finite element methods for calculating hearth erosion boundaries only consider temperature constraints, resulting in a more theoretically accurate calculated erosion boundary. The actual hearth erosion boundary is relatively smooth, and its accuracy needs to be further improved. Summary of the Invention

[0007] In order to obtain an accurate erosion boundary of the longitudinal section of the furnace hearth, the present invention provides a finite element method for calculating the erosion boundary of the longitudinal section of the furnace hearth. The method establishes a finite element model of the erosion boundary of the blast furnace hearth based on finite element heat conduction analysis; considers the curvature constraint of the erosion boundary of the blast furnace hearth, and uses an improved particle swarm algorithm to determine the position of the erosion boundary.

[0008] Optionally, the method includes:

[0009] Step 1: The boundary formed by connecting thermocouples near the outer wall of the furnace is used as the outer boundary, and the hearth erosion boundary is used as the inner boundary. Based on the temperatures and corresponding coordinates of the points on the inner and outer boundaries, a geometric model of the blast furnace is established. The geometric model is then divided using a triangular mesh for finite element heat conduction analysis, thereby obtaining the temperature domain of the longitudinal section of the furnace. The hearth erosion boundary is composed of several moving boundary points.

[0010] Step 2: Considering the curvature constraint of the blast furnace hearth erosion boundary, design the objective function of the particle swarm algorithm and the end condition of the particle iterative update;

[0011] Step 3: During the particle optimization process, the fitness value of each particle is calculated according to the objective function, and the minimum fitness value is recorded as the current optimal fitness value. It is judged whether the current optimal fitness value meets the set particle iterative update end condition; if it meets the condition, the erosion boundary corresponding to the current optimal fitness value is output as the calculated erosion boundary position.

[0012] Optionally, in Step 1, it is assumed that the hearth erosion boundary is composed of p moving boundary points, of which l moving boundary point is located in the corner area of ​​the hearth erosion boundary; it is assumed that, except for the l moving boundary points in the corner area, the erosion boundary points in the horizontal direction are evenly spaced horizontally, and the erosion boundary points in the vertical direction are evenly spaced vertically, then the p moving boundary points have a total of p+l unknown coordinates. In the subsequent optimization process using the particle swarm algorithm, the dimension of each particle is p+l, corresponding to the p+l unknown coordinates of the p moving boundary points; the movable range of the p moving boundary points is the particle swarm search space;

[0013] The thermocouple close to the outer wall of the furnace is called the outer thermocouple, denoted as P i,out , the corresponding actual temperature is recorded as T i,out The thermocouple close to the iron layer of the furnace is called the inner parameter thermocouple, denoted as P i,in , the corresponding actual temperature is recorded as T i,in In the finite element heat conduction analysis, the temperature at the location of the inner parameter thermocouple is calculated based on the temperature domain of the furnace longitudinal section, which is recorded as The temperature domain of the furnace longitudinal section corresponding to the different furnace erosion boundaries formed by the moving boundary points is calculated. With T i,in The difference is used as one of the conditions for the end of particle iterative update, and the curvature of the corresponding erosion boundary is combined to determine whether the particle iterative update is ended.

[0014] Optionally, the objective function of the particle swarm algorithm in Step 2 is:

[0015]

[0016] Where s is the inner parameter thermocouple P i,in The number of i,in Indicates the actual temperature corresponding to the i-th inner layer parameter thermocouple, represents the calculated temperature corresponding to the i-th inner layer parameter thermocouple, r represents the number of line segments formed by the moving boundary points in the erosion boundary, ψ k is the angle between two adjacent line segments, α is a positive parameter with a value range of

[0017] Optionally, the particle iterative update end condition includes:

[0018] The current optimal fitness value fitness is less than or equal to e;

[0019] Where e is set according to the number of inner layer parameter thermocouples s.

[0020] Optional, s = 1.5s ~ 3s.

[0021] Optionally, if the current optimal fitness value fitness is less than or equal to e, it means that the erosion boundary determined by the p+l coordinate values ​​corresponding to the particle dimension of the current optimal fitness value satisfies:

[0022] Condition (1): Calculated based on the temperature domain of the longitudinal section of the furnace corresponding to the erosion boundary With T i,in The difference is less than or equal to 1℃, that is:

[0023] Condition (2): On the erosion boundary, except for the line segment formed by the inflection point, the angle between the other two adjacent line segments is

[0024] Optionally, in the particle optimization process, the dimension of each particle corresponds to an erosion boundary, and N particles correspond to N different erosion boundaries, corresponding to the finite element heat conduction analysis, that is, different erosion boundaries are used as inner boundaries to determine the temperature domain of the corresponding furnace longitudinal section;

[0025] After each iteration, the fitness value of each particle is calculated according to the objective function, the minimum fitness value is selected as the current optimal fitness value, and it is judged whether the current optimal fitness value meets the end condition of particle iteration update. In the corresponding finite element heat conduction analysis, the temperature value at the location of the inner parameter thermocouple is calculated using the temperature domain of different furnace longitudinal sections. Thus, comparison With T i,in Whether the difference of satisfies condition (1); at the same time, compare whether the angles between the two adjacent line segments on the erosion boundary, except the line segment formed by the inflection point, meet condition (2).

[0026] Optionally, in the finite element heat conduction analysis, the temperature at locations on the outer boundary other than the outer thermocouples is calculated using linear interpolation.

[0027] Optionally, the temperature at each location on the inner boundary is the solidification temperature of the molten iron.

[0028] The beneficial effects of the present invention are:

[0029] The location of the hearth erosion boundary is calculated by obtaining temperature values ​​detected by a set of thermocouples placed in the hearth carbon bricks. The calculation of the erosion boundary is transformed into a function optimization problem, which is solved using a particle swarm optimization algorithm. During the optimization process, the finite element method is used for heat conduction analysis. This method uses the finite element method for heat conduction analysis, improving the accuracy of temperature calculations. By considering the smooth continuity of the actual erosion boundary and designing the objective function of the optimization process, a smoother erosion boundary is obtained, making the calculated erosion boundary of the blast furnace hearth closer to the actual erosion boundary. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 It is a schematic diagram of the computational domain mesh in the geometric structure model disclosed in one embodiment of the present invention.

[0032] Figure 2 The diagram is a schematic diagram of a triangular discrete unit in a process of using a triangular mesh to segment a geometric structure model disclosed in an embodiment.

[0033] Figure 3 It is a specific implementation flow chart of the finite element method for calculating the erosion boundary of the longitudinal section of the furnace disclosed in one embodiment of the present invention.

[0034] Figure 4 This is a schematic diagram of erosion boundary simulation obtained using the method of this application. DETAILED DESCRIPTION

[0035] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0036] Thermocouples, as temperature sensors, are installed in the furnace wall of a blast furnace to monitor the furnace temperature in real time. In this application, for ease of modeling, the thermocouples near the outer wall of the furnace are referred to as outer thermocouples, and the thermocouples near the condensed iron layer of the furnace are referred to as inner parameter thermocouples. In actual application scenarios, the position coordinates of the outer and inner parameter thermocouples are known, and the actual temperature at these locations can be directly read.

[0037] Example 1:

[0038] This embodiment provides a finite element method for calculating the erosion boundary of a hearth longitudinal section. This method establishes a finite element model of the blast furnace hearth erosion boundary based on finite element heat conduction analysis. Taking into account the curvature constraint of the blast furnace hearth erosion boundary, an improved particle swarm algorithm is used to determine the location of the erosion boundary. The method specifically includes the following steps:

[0039] Step 1: The boundary formed by connecting thermocouples near the outer wall of the furnace is used as the outer boundary, and the hearth erosion boundary is used as the inner boundary. Based on the temperatures and corresponding coordinates of the points on the inner and outer boundaries, a geometric model of the blast furnace is established. The geometric model is then divided using a triangular mesh for finite element heat conduction analysis, thereby obtaining the temperature domain of the longitudinal section of the furnace. The hearth erosion boundary is composed of several moving boundary points.

[0040] In this step, it is assumed that the hearth erosion boundary is composed of p moving boundary points, of which l moving boundary points are located in the corner area of ​​the hearth erosion boundary; it is assumed that, except for the l moving boundary points in the corner area, the erosion boundary points in the horizontal direction are equally spaced horizontally, and the erosion boundary points in the vertical direction are equally spaced vertically (equally spaced distribution means that the coordinates in the corresponding direction are considered known), then the p moving boundary points have a total of p+l unknown coordinates. In the subsequent optimization process using the particle swarm algorithm, the dimension of each particle is p+l, corresponding to the p+l unknown coordinates of the p moving boundary points; the movable range of the p moving boundary points is the particle swarm search space;

[0041] The most original inner boundary in this step can be the inner boundary after the blast furnace is built, or the actual erosion boundary after a major overhaul, and the subsequent particle swarm initialization is performed based on its corresponding coordinates.

[0042] The outer thermocouple is denoted as P i,out , the corresponding actual temperature is recorded as T i,out ; The inner parameter thermocouple is denoted as P i,in , the corresponding actual temperature is recorded as T i,in In the finite element heat conduction analysis, the temperature at the location of the inner parameter thermocouple is calculated based on the temperature domain of the furnace longitudinal section, which is recorded as The temperature domain of the furnace longitudinal section corresponding to the different furnace erosion boundaries formed by the moving boundary points is calculated. With T i,in The difference is used as one of the conditions for the end of particle iterative update, and the curvature of the corresponding erosion boundary is combined to determine whether the particle iterative update is ended.

[0043] Step 2: Considering the curvature constraint of the blast furnace hearth erosion boundary, design the objective function of the particle swarm algorithm and the end condition of the particle iterative update;

[0044] The objective function of the particle swarm optimization algorithm is:

[0045]

[0046] Where s is the inner parameter thermocouple P i,in The number of i,in Indicates the actual temperature corresponding to the i-th inner layer parameter thermocouple, represents the calculated temperature corresponding to the i-th inner layer parameter thermocouple, r represents the number of line segments formed by the moving boundary points in the erosion boundary, ψ k is the angle between two adjacent line segments, α is a positive parameter with a value range of

[0047] The particle iterative update end condition requires that the corresponding erosion boundary satisfies:

[0048] Condition (1): Calculated based on the temperature domain of the longitudinal section of the furnace corresponding to the erosion boundary With T i,in The difference is less than or equal to 1℃, that is:

[0049] Condition (2): On the erosion boundary, except for the line segment formed by the inflection point, the angle between the other two adjacent line segments is

[0050] Combining the above conditions (1) and (2), the corresponding particle iterative update end condition is that the current optimal fitness value fitness is less than or equal to e, and e is set according to the number of inner layer parameter thermocouples s, e = 1.5s ~ 3s.

[0051] Step 3: During the particle optimization process, the fitness value of each particle is calculated according to the objective function, and the minimum fitness value is recorded as the current optimal fitness value. It is judged whether the current optimal fitness value meets the set particle iterative update end condition; if it meets the condition, the erosion boundary corresponding to the current optimal fitness value is output as the calculated erosion boundary position.

[0052] In the particle optimization process, the dimension of each particle corresponds to an erosion boundary, so N particles correspond to N different erosion boundaries. In the finite element heat conduction analysis, different erosion boundaries are used as inner boundaries to determine the temperature domain of the corresponding furnace longitudinal section.

[0053] After each iteration, the fitness value of each particle is calculated according to the objective function, the minimum fitness value is selected as the current optimal fitness value, and it is judged whether the current optimal fitness value meets the end condition of particle iteration update. In the corresponding finite element heat conduction analysis, the temperature value at the location of the inner parameter thermocouple is calculated using the temperature domain of different furnace longitudinal sections. Thus, comparison With T i,in Whether the difference of satisfies condition (1); at the same time, compare whether the angles between the two adjacent line segments on the erosion boundary, except the line segment formed by the inflection point, meet condition (2).

[0054] The dimension of the particle corresponding to the current optimal fitness value that meets the end condition of the particle iterative update is the unknown coordinates corresponding to each moving boundary point on the final required erosion boundary. By assigning the dimension value of the particle to the unknown coordinates corresponding to each moving boundary point, the specific position of each moving boundary point can be obtained, and the connection is the obtained erosion boundary.

[0055] Example 2:

[0056] This embodiment provides a finite element method for calculating the erosion boundary of a furnace longitudinal section, the method comprising:

[0057] Step 1: Based on the finite element heat conduction analysis, establish the blast furnace hearth erosion boundary finite element model:

[0058] Step 1.1 Determine the temperature and position of the outer boundary layer. The outer boundary layer refers to the boundary formed by the thermocouple connection close to the outer wall of the furnace. In this application, the thermocouple close to the outer wall of the furnace is called the outer layer thermocouple, denoted as P i,out The thermocouple close to the iron layer of the furnace is called the inner parameter thermocouple, denoted as P i,in .like Figure 1 As shown, the outer thermocouple is represented by a square black dot, and the inner parameter thermocouple is represented by a triangular black dot.

[0059] According to the existing outer thermocouple P i,out , the temperature T of the outer thermocouple i,out and coordinates, and the temperature at any position on the outer boundary is calculated using the linear interpolation method, that is, the outer thermocouple temperature T on the outer boundary is used. i,out The temperatures of all nodes on the outer boundary are completed by interpolation.

[0060] Step 1.2 determines the temperature and location of the erosion boundary. Figure 1 As shown, the moving boundary points on the inner wall of the furnace represent the movable erosion boundary points ( Figure 1 Indicated by black origins in the figure), assuming that the erosion boundary is composed of p boundary points connected by lines. Except for the moving boundary points in the corner area, the other erosion boundary points in the horizontal direction are equally spaced horizontally, and the other erosion boundary points in the vertical direction are equally spaced vertically. Therefore, except for the l boundary points in the corner area ( Figure 1The dotted circle in the middle represents the corner region, which is determined based on the estimated erosion situation. All other boundary points have fixed coordinates (x or y) in one direction, which is known. The unfixed coordinates are optimized using the particle swarm optimization algorithm. The x and y coordinates of the boundary points within the corner region are unknown and are all optimized using the particle swarm optimization algorithm.

[0061] In the optimization process of the particle swarm algorithm, assuming that there are N particles in total, each particle has p+l dimensions, that is, the coordinates of the boundary points in the corner area in two directions are determined by the two dimensions corresponding to the particles, while the non-fixed coordinates of other boundary points are determined by one dimension corresponding to the particles.

[0062] Since the solidification temperature of molten iron is 1150℃, the temperature of all nodes on the erosion boundary is 1150℃.

[0063] Step 1.3: Establish the corresponding geometric structure model according to the erosion boundary and the outer boundary, and use the triangular mesh to divide the model as follows: Figure 2 shown.

[0064] The temperature of the erosion boundary and the outer boundary is used as the boundary condition to carry out the finite element heat conduction analysis, thereby obtaining the temperature domain of the boiler longitudinal section. i,in The corresponding calculated temperature at the location is recorded as Inner layer parameter thermocouple P i,in The temperature actually measured by the thermocouple at the corresponding position is recorded as T i,in .

[0065] Finite element heat conduction analysis:

[0066] Considering a two-dimensional steady-state heat conduction problem, and ignoring the second and third boundary conditions in this invention (in thermodynamic conduction analysis, the second boundary condition is the heat flow boundary condition, which gives the heat flux density value on the boundary; the third boundary condition is the convection heat transfer boundary condition, which gives the heat transfer coefficient between the object on the boundary and the surrounding fluid and the surrounding fluid temperature), the governing equation can be described as:

[0067]

[0068] In this invention, it is assumed that the heat transfer coefficients in the x and y directions are the same and are both k, so the functional of the control equation can be expressed as:

[0069]

[0070] The governing equation is solved by finding the minimum of the above functional. Obviously, solving the minimum of the above functional is equivalent to the following two-dimensional heat conduction differential equation:

[0071]

[0072] By choosing a suitable test function N i (x,y) is used to replace the true solution of temperature, as follows:

[0073]

[0074] Where C i (i=1,2,…,n) is the parameter to be determined, and n is the number of nodes of the triangular mesh in the computational domain after finite element discretization.

[0075] Using the Galerkin weighted residual method, the weak form of the above two-dimensional heat conduction differential equation can be written as:

[0076]

[0077] The finite element method is to divide the entire computational domain Ω into a large number of overlapping subdomains, or finite elements Ω e Therefore, in unit Ω e Complete the derivation of the formula and quickly extend it to the entire domain Ω.

[0078] The entire structure is discretized into M triangular elements. Assume that the temperature distribution law of the element is called the temperature function. Take an element e from the divided three-node triangular element. The nodes are numbered a, b, and c. Each node has only one degree of freedom - temperature, which are set as like Figure 2 shown.

[0079] Assume the temperature interpolation function is:

[0080]

[0081] Substituting the node temperature value into the above formula, we can get:

[0082]

[0083] Solving the above formula, we get:

[0084]

[0085] Where: Δ e is the area of ​​the triangular unit e.

[0086] Therefore, the temperature interpolation function can be written as follows:

[0087]

[0088] Where shape function and as follows

[0089]

[0090] make Available

[0091] T e (x,y)=N e (x,y)T e

[0092] Then for unit e, we need to solve the following integral:

[0093]

[0094] T e Substituting the expression of (x,y) into the above formula, we get:

[0095]

[0096] The above formula can be written as follows:

[0097] K e T e =0

[0098] In the formula is the unit heat conduction matrix, which is expressed as follows:

[0099]

[0100] Therefore, by setting each unit K e After assembling the numbers, the overall heat transfer equation is obtained:

[0101] KT=0

[0102] Where K is the overall heat conduction matrix, T=[T1,T2,…,T n ] is the node temperature matrix of the triangular mesh.

[0103] The overall heat conduction matrix K is assembled as follows:

[0104]

[0105] At this point, the constant temperature boundary condition (Dirichlet condition), that is, the temperature value of the grid node located on the boundary of the computational domain, is loaded into the above heat transfer equation. By solving the equation using Gaussian elimination, the temperature value T of all nodes can be obtained. Then, through the temperature interpolation function, the temperature of all locations in the entire computational domain Ω can be obtained.

[0106] Step 2: Determine the objective function and output conditions of the optimization process.

[0107] Through step 1, the inner thermocouple P in the temperature domain can be calculated i,inThe calculated temperature corresponding to the location is recorded as Inner thermocouple P i,in The temperature actually measured by the thermocouple at the corresponding position is recorded as T i,in .

[0108] Since the actual hearth erosion boundary is relatively smooth, the curvature of the erosion boundary needs to be considered during the optimization process in order to obtain an erosion boundary that is closer to the actual one. Therefore, the objective function of the optimization process not only considers the error between the calculated temperature and the measured temperature of the inner layer parameter thermocouple, but also considers the angle between the various line segments that make up the erosion boundary. The objective function of the optimization process is designed as:

[0109]

[0110] Where: s is the inner parameter thermocouple P i,in , r is the number of line segments formed by boundary points in the erosion boundary, ψ k is the angle between two adjacent line segments, and α is a designed positive parameter.

[0111] Assign the values ​​of all dimensions of a particle in the particle swarm algorithm to the moving boundary point, and through step 1, we can obtain the required temperature value and angle, substitute them into the objective function fitness, and obtain the fitness value of the particle.

[0112] In one iteration, the fitness values ​​of all particles in the particle population are calculated respectively, and the minimum fitness value is recorded as the optimal fitness value.

[0113] In the algorithm, we hope that in the early stage of iteration, the size of the particle fitness value is more determined by the actual temperature T of the inner parameter thermocouple. i,in and calculated temperature The difference is determined by the value of Approximate the measured actual temperature T i,in When , the particle adaptation value is determined by the temperature difference and the curvature of the erosion boundary.

[0114] Output condition: calculated temperature of each inner parameter thermocouple With the actual temperature T i,in The difference The angle between two adjacent line segments of the erosion boundary except the corner area

[0115] The parameter α is related to the number of line segments r and the number of inner parameter thermocouples s.

[0116] Therefore, the output condition e of the algorithm can be set according to the number s of the inner parameter thermocouples, e = 1.5s ~ 3s. When the optimal fitness value in the optimization process is less than the set output condition, the algorithm in the following step 3 will stop iterating and output the position of the erosion boundary corresponding to the optimal fitness value, which is considered to be the erosion boundary of the boiler at this time.

[0117] Step 3: Use the particle swarm algorithm to calculate the optimization problem in step 2 and determine the optimal position of the erosion boundary. The specific algorithm steps are as follows:

[0118] (a) Set the initial parameters: number of particles N, particle dimension p+l, maximum number of iterations k max , the initial position of the particle, the individual optimal position, the global optimal position of the group, the objective function of the optimization process, and the output conditions;

[0119] (b) For each particle, assign the corresponding values ​​of its current dimensions to the moving boundary points in step (1). Then, according to step 1, a finite element model of the blast furnace hearth erosion boundary is established and a finite element heat conduction analysis is performed to obtain the inner layer parameter thermocouple P. i,in The calculated temperature corresponding to the location The angle ψ between two adjacent line segments to the erosion boundary k ;

[0120] (c) Calculate the fitness value of each particle according to the objective function, record the minimum fitness value as the current optimal fitness value, and update the optimal position G of the group according to the optimal fitness value best The position of the particle corresponding to the optimal fitness value, and the individual optimal position of each particle is updated at the same time The current position of each particle;

[0121] (d) Each particle will update its velocity and position using the following formula:

[0122]

[0123] X i (k+1)=X i (k)+V i (k+1)

[0124] Among them, X i (k), V i (k) represents the position and velocity of the i-th particle in the k-th iteration, G best(k) represents the optimal individual position and group position of the i-th particle in the k-th iteration, r1 and r2 range from 0 to 1 and are randomly generated numbers; w is the inertia weight coefficient, and c1 and c2 are training coefficients. The calculation formula of w is as follows:

[0125]

[0126] Among them, k max is the maximum number of iterations, w max is 0.9, w min is 0.4;

[0127] (e) Check whether the optimal fitness value meets the output condition. If so, exit the iteration, end and output the position of the erosion boundary, otherwise return to step (b).

[0128] In order to verify the effectiveness of the algorithm designed by the present invention, MATLAB was used as the experimental platform. Figure 1 The erosion boundary shown is taken as the real erosion boundary, so the thermocouple P is calculated. i,out and P i,in The temperature at the location is the actual temperature T measured by the thermocouple i,out With T i,in .

[0129] The following is a detailed description of the finite element method for calculating the erosion boundary of the furnace longitudinal section proposed by the present invention, combined with experimental results and accompanying drawings. Figure 3 Schematic diagram of the steps for calculating the erosion boundary.

[0130] The parameters used in the particle swarm algorithm are as follows:

[0131] Assume that the number of particles N = 50, the particle dimension p + l = 48, and the maximum number of iterations k max = 500, the initial position of each particle is the same as Figure 4 As shown (ie, the particles are initialized using the inner boundary after the blast furnace is built), the output condition is e=5, the positive parameter α=4, and the number of inner layer parameter thermocouples s=13.

[0132] As shown in Figure 4, the final erosion boundary is Figure 1 The real erosion boundary is basically consistent with the inner thermocouple P i,in The actual temperature T i,in and calculated temperature As shown in the following table.

[0133] Table 1. Calculated and actual temperatures of the inner layer thermocouple parameters

[0134]

[0135] As shown in Table 1, the calculated temperature of the inner layer parameter thermocouple is basically consistent with the actual temperature, with the difference less than 1°C. The simulation results show that the finite element method for erosion boundary calculation proposed in this application can obtain a smooth erosion boundary that is closer to the actual one.

[0136] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0137] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A finite element method for calculating the erosion boundary of a furnace longitudinal section, characterized in that: The method is based on finite element heat conduction analysis to establish a finite element model of the blast furnace hearth erosion boundary; considering the curvature constraint of the blast furnace hearth erosion boundary, an improved particle swarm algorithm is used to determine the position of the erosion boundary; The method comprises: Step 1: The boundary formed by connecting thermocouples near the outer wall of the furnace is used as the outer boundary, and the hearth erosion boundary is used as the inner boundary. Based on the temperatures and corresponding coordinates of the points on the inner and outer boundaries, a geometric model of the blast furnace is established. The geometric model is then divided using a triangular mesh for finite element heat conduction analysis, thereby obtaining the temperature domain of the longitudinal section of the furnace. The hearth erosion boundary is composed of several moving boundary points. Step 2: Considering the curvature constraint of the blast furnace hearth erosion boundary, design the objective function of the particle swarm algorithm and the end condition of the particle iterative update; Step 3: During the particle optimization process, the fitness value of each particle is calculated according to the objective function, and the minimum fitness value is recorded as the current optimal fitness value. It is judged whether the current optimal fitness value meets the set particle iterative update end condition; if it does, the erosion boundary corresponding to the current optimal fitness value is output as the calculated erosion boundary position; In Step 1, it is assumed that the hearth erosion boundary is composed of p moving boundary points, of which l moving boundary points are located in the corner area of ​​the hearth erosion boundary; it is assumed that, except for the l moving boundary points in the corner area, the erosion boundary points in the horizontal direction are evenly spaced horizontally, and the erosion boundary points in the vertical direction are evenly spaced vertically. Then, the p moving boundary points have a total of p+l unknown coordinates. In the subsequent optimization process using the particle swarm algorithm, the dimension of each particle is p+l, corresponding to the p+l unknown coordinates of the p moving boundary points respectively; the movable range of the p moving boundary points is the particle swarm search space; The thermocouple close to the outer wall of the furnace is called the outer thermocouple, denoted as P i,out , the corresponding actual temperature is recorded as T i,out The thermocouple close to the iron layer of the furnace is called the inner parameter thermocouple, denoted as P i,in , the corresponding actual temperature is recorded as T i,in In the finite element heat conduction analysis, the temperature at the location of the inner parameter thermocouple is calculated based on the temperature domain of the furnace longitudinal section, which is recorded as The temperature domain of the furnace longitudinal section corresponding to the different furnace erosion boundaries formed by the moving boundary points is calculated. With T i,in The difference is used as one of the conditions for the end of particle iterative update, and the curvature of the corresponding erosion boundary is combined to determine whether the particle iterative update is ended.

2. The method according to claim 1, characterized in that The objective function of the particle swarm algorithm in Step 2 is: Where s is the inner parameter thermocouple P i,in The number of i,in Indicates the actual temperature corresponding to the i-th inner layer parameter thermocouple, represents the calculated temperature corresponding to the i-th inner layer parameter thermocouple, r represents the number of line segments formed by the moving boundary points in the erosion boundary, ψ k is the angle between two adjacent line segments, α is a positive parameter with a value range of 3. The method according to claim 2, characterized in that The particle iterative update end conditions include: The current optimal fitness value fitness is less than or equal to e; Where e is set according to the number of inner layer parameter thermocouples s.

4. The method according to claim 3, characterized in that e=1.5s~3s.

5. The method according to claim 4, characterized in that The current optimal fitness value fitness is less than or equal to e, which means that the erosion boundary determined by the p+l coordinate values ​​corresponding to the particle dimension of the current optimal fitness value satisfies: Condition (1): Calculated based on the temperature domain of the longitudinal section of the furnace corresponding to the erosion boundary With T i,in The difference is less than or equal to 1℃, that is: Condition (2): On the erosion boundary, except for the line segment formed by the inflection point, the angle between the other two adjacent line segments is 6. The method according to claim 5, characterized in that In the particle optimization process, the dimension of each particle corresponds to an erosion boundary, so N particles correspond to N different erosion boundaries. In the finite element heat conduction analysis, different erosion boundaries are used as inner boundaries to determine the temperature domain of the corresponding furnace longitudinal section. After each iteration, the fitness value of each particle is calculated according to the objective function, the minimum fitness value is selected as the current optimal fitness value, and it is judged whether the current optimal fitness value meets the end condition of particle iteration update. In the corresponding finite element heat conduction analysis, the temperature value at the location of the inner parameter thermocouple is calculated using the temperature domain of different furnace longitudinal sections. Thus, comparison With T i,in Whether the difference of satisfies condition (1); at the same time, compare whether the angles between the two adjacent line segments on the erosion boundary, except the line segment formed by the inflection point, meet condition (2).

7. The method according to claim 6, characterized in that In the finite element heat conduction analysis, the temperature at locations on the outer boundary excluding the outer layer thermocouples is calculated using the linear interpolation method.

8. The method according to claim 1, characterized in that The temperature at each point on the inner boundary is the temperature at which the molten iron solidifies.

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