JP6375800B2 - State estimation method and estimation apparatus for slab cast by continuous casting machine - Google Patents

Description

  The present invention relates to a method and apparatus for estimating the state of a slab cast by a continuous casting machine. More specifically, the present invention relates to a method and apparatus for estimating the temperature and solid fraction distribution of a slab cooled in a secondary cooling zone of a continuous casting machine.

  In continuous casting of steel, for example, in a vertical bending type continuous casting machine, a slab drawn from a vertical mold is bent once, then drawn with a constant radius of curvature, and then the casting in a state where the bending is eliminated in the correction part. Extract as a piece and cut. The slab is pulled out by driving the slab with a pinch roll while supporting the upper and lower sides with a plurality of pairs of rolls.

  However, since tensile stress is applied to the lower surface of the slab at the bent portion of the strand and to the upper surface of the slab at the correction portion, if the temperature of the surface of the slab is in a range called the embrittlement region, Surface cracks called cracks may occur. For this reason, it is necessary to appropriately set the cooling water amount distribution so that the slab surface portion temperature avoids the embrittlement region in the bent portion and the straightening portion. In order to prevent an operational trouble called out-of-machine bulging where the slab solidified shell expands to the outside due to the molten steel static pressure after the roll pair (the most downstream pair) arranged at the most downstream in the casting longitudinal direction. It is also necessary to determine the amount of cooling water so that the slab is completely solidified by the downstream pair position.

  These objects can be achieved by setting the cooling zone water amount distribution to an appropriate value in advance by simulation or the like when the casting speed is constant. However, when the arrival of the next ladle in continuous casting is delayed, it is necessary to change the casting speed during operation in order to wait for arrival by lowering the casting speed below a predetermined value so that continuous casting is not interrupted. At this time, in the conventional cascade water amount control, the zone water amount set in advance with respect to the casting speed is set by interpolating the casting speed being changed. However, when such control is performed, the cooling history with respect to the time from the mold surface of the slab to the cutting is disturbed, so that there is a risk of slab quality defects such as lateral cracks on the surface, and cooling is insufficient. In such a case, the above-described out-of-machine bulging may also occur. In order to solve these problems, the surface temperature of the slab and the solid phase ratio inside the slab are constantly calculated so that the temperature distribution and solid phase ratio distribution of the entire slab can be grasped even if the casting speed changes. It is necessary to make it.

  For example, Patent Document 1 discloses a solidified state of a slab in continuous casting in which molten steel injected into a mold is solidified by performing secondary cooling while being drawn and continuously manufactured. The solidification state estimation method for estimating the solidification state of a slab by a heat transfer model using a heat flux based on at least a cooling condition of secondary cooling, and at a predetermined measurement position in the longitudinal direction of the slab The slab width of the heat flux is measured so that the estimated temperature estimated by the heat transfer model at the measurement position matches the measured temperature distribution in the slab width direction. A method for estimating the solidification state of a slab that corrects the output of the heat transfer model by correcting the heat flux distribution in the direction is disclosed. Further, in Patent Document 1, (1) in correcting the calculated value of the slab cross-section temperature distribution and re-estimating the calculation, a position upstream from the surface temperature distribution measurement position and upstream from the final solidification position is determined. The temperature distribution of the cross section at the determined upstream position is corrected using an optimization method, and re-estimation calculation is performed using the temperature distribution of the cross section at the corrected upstream position, or (2) in the longitudinal direction of the slab The measurement position is set at two or more locations along the surface, the temperature distribution in the slab width direction is measured at each measurement position, and the estimated temperature estimated by the heat transfer model and the measured slab are measured at each measurement position. It is also disclosed that the correction of the heat flux distribution in the slab width direction of the heat flux is repeated so that the temperature distribution in the width direction matches.

JP 2012-187636 A

  In each of the techniques disclosed in Patent Literature 1, after measuring the temperature distribution in the slab width direction, a series of calculations of the temperature distribution in the slab cross section from the molten steel surface position in the mold to the temperature distribution measurement position is performed. Since the process is repeated several times along the longitudinal direction, there is a problem that a large amount of calculation is required until the temperature distribution calculation result in the slab width direction matches the measured value of the temperature distribution. Therefore, with the technique disclosed in Patent Literature 1, it is difficult to continuously calculate the distribution of the surface temperature and the solid phase ratio at a specific position of the slab. Moreover, in the technique currently disclosed by patent document 1, the casting speed and the amount of secondary cooling water changed before the slab cross section in the measurement position with a thermometer arrives at the position from a molten metal surface position at the present time. In some cases, it is necessary to perform a model calculation that reflects the change, which complicates the management of data used for the calculation.

  Therefore, the present invention provides a state estimation method and an estimation apparatus for a slab cast by a continuous casting machine, capable of continuously calculating a surface temperature distribution and a solid phase ratio distribution at a specific position of the slab. This is the issue.

  The first aspect of the present invention is calculated using the size of the slab perpendicular to the slab longitudinal direction, the casting speed, the molten metal temperature in the mold, the solute component concentration in the molten metal, and the solute component concentration. The operation data grasping process for grasping the operation data of the continuous casting machine, including the liquidus temperature of the molten metal and the cooling conditions at each point on the surface of the slab, and each point on the slab surface using the above cooling conditions Using a heat transfer coefficient estimation parameter for correcting an error between the heat transfer coefficient estimated in the heat transfer coefficient estimation step and the heat transfer coefficient estimated in the heat transfer coefficient estimation step and the true heat transfer coefficient of the slab, By correcting the heat transfer coefficient estimated in the heat transfer coefficient estimation process, the heat transfer coefficient correction process for calculating the corrected heat transfer coefficient, and the corrected heat calculated in the operation data and the heat transfer coefficient correction process. Using the transmission rate, the surface temperature distribution of the slab, Temperature solid phase ratio distribution calculation step for calculating temperature distribution and solid phase ratio distribution inside the slab sequentially, and temperature measuring means at any point from the mold outlet to the location where the slab is cut The surface temperature measurement step of measuring the surface temperature of the slab using the surface temperature of the slab measured in the surface temperature measurement step, the surface temperature by the temperature measurement means calculated in the temperature solid fraction distribution calculation step Heat transfer coefficient correction parameter correction that corrects the heat transfer coefficient correction parameter every time the temperature solid phase ratio distribution calculation process is completed using the deviation between the calculated value of the surface temperature of the slab at the measurement position where the temperature is measured A method for estimating a state of a slab cast by a continuous casting machine.

  Here, in the present invention, the “true heat transfer coefficient of the slab” refers to the actual heat transfer coefficient of the slab, not the heat transfer coefficient predicted by calculation. In the present invention, it is only necessary to correct the heat transfer coefficient correction parameter once for each calculation of the temperature distribution of the cross section at each calculation position in the casting direction, so that the calculation amount can be reduced as compared with the conventional case. Thereby, it is possible to continuously calculate the surface temperature distribution and the solid phase ratio distribution at a specific position of the slab. Further, in the present invention, the calculation position of the cross section for calculating the temperature distribution or the like is predetermined on the slab, and each time the calculation target cross section moves from the calculation position adjacent to the upstream side for each calculation position, When the secondary cooling water amount change or the like is reflected, only the casting speed and cooling conditions during this period need be stored. By adopting such a configuration, it is not necessary to store past operation states over a long period of time, so that management of data used for calculation is facilitated.

  Further, in the first aspect of the present invention, each time each of the above distributions is sequentially calculated in the temperature solid fraction distribution calculation step, it corresponds to the measurement position of the calculated cross section of the slab in which each distribution is calculated. The enthalpy at the calculation point and the variance-covariance matrix of the heat transfer coefficient correction parameter at the calculation point are calculated, and the correction value to be added to the enthalpy at the calculation point and the correction value to be added to the heat transfer coefficient correction parameter at the calculation point are calculated. Therefore, using the variance-covariance matrix, the deviation (the surface temperature of the slab measured in the surface temperature measurement step and the slab of the slab at the measurement position calculated in the temperature solid-phase ratio distribution calculation step) It is preferable to calculate the corrected gain coefficient matrix as a coefficient vector to be multiplied by the deviation of the calculated value of the surface temperature. This facilitates continuous calculation of the surface temperature distribution and the solid fraction distribution at a specific position of the slab.

  Further, in the first aspect of the present invention, using the operation data, the distribution of the surface temperature of the slab, the distribution of the internal temperature of the slab, the distribution of the solid fraction within the slab, and the slab It is preferable to sequentially calculate the distribution of the concentration of the solute component in the liquid phase in the solid-liquid coexistence region inside. By adopting such a configuration, in a continuous casting machine on a practical scale, even if the calculated heat transfer coefficient by the heat transfer coefficient model is different from the actual value, not only the temperature measurement point but also the casting points other than the temperature measurement point It is possible to match the estimated surface temperature of the piece with sufficient accuracy with the temperature measurement result in a continuous caster on a practical scale.

  The second aspect of the present invention is calculated using the size of the slab perpendicular to the slab longitudinal direction, the casting speed, the molten metal temperature in the mold, the solute component concentration in the molten metal, and the solute component concentration. Operation data storage unit for storing operation data of the continuous casting machine including the liquidus temperature of the molten metal and the cooling conditions at each point on the surface of the slab, and each point on the slab surface using the above cooling conditions Using a heat transfer coefficient estimation unit that estimates the heat transfer coefficient in the heat transfer coefficient correction parameter that corrects an error between the heat transfer coefficient estimated by the heat transfer coefficient estimation unit and the true heat transfer coefficient of the slab, By correcting the heat transfer rate estimated by the heat transfer rate estimation unit, the heat transfer rate correction unit that calculates the corrected heat transfer rate, and the corrected heat calculated by the operation data and the heat transfer rate correction unit Using the transmission rate, the surface temperature distribution of the slab and the internal temperature distribution of the slab And the temperature solid phase ratio distribution calculation part which calculates the distribution of the solid fraction in the slab sequentially, and the surface temperature of the slab at any point from the mold outlet to the part where the slab is cut The surface temperature of the slab measured by the temperature measurement means, and the calculated value of the surface temperature of the slab at the measurement position where the surface temperature is measured by the temperature measurement means, calculated by the temperature solid fraction distribution calculation unit. A heat transfer coefficient correction parameter correction unit that corrects the heat transfer coefficient correction parameter each time the calculation by the temperature solid phase ratio distribution calculation unit is completed using the deviation, and is cast by a continuous casting machine. It is the state estimation apparatus of the slab.

  In the present invention, it is only necessary to correct the heat transfer coefficient correction parameter once for each calculation of the temperature distribution of the cross section at each calculation position in the casting direction, so that the calculation amount can be reduced as compared with the conventional case. Thereby, it is possible to continuously calculate the surface temperature distribution and the solid phase ratio distribution at a specific position of the slab. Further, in the present invention, the calculation position of the cross section for calculating the temperature distribution or the like is predetermined on the slab, and each time the calculation target cross section moves from the calculation position adjacent to the upstream side for each calculation position, When the secondary cooling water amount change or the like is reflected, only the casting speed and cooling conditions during this period need be stored. By adopting such a configuration, it is not necessary to store past operation states over a long period of time, so that management of data used for calculation is facilitated.

  Further, in the second aspect of the present invention, each time the distribution is sequentially calculated by the temperature solid fraction distribution calculation unit, the calculation point corresponding to the measurement position of the calculation cross section of the slab in which each distribution is calculated To calculate a correction value to be added to the enthalpy at the calculation point and a correction value to be added to the heat transfer coefficient correction parameter at the calculation point. In addition, using the variance-covariance matrix, the deviation (the surface temperature of the slab measured by the temperature measuring means and the surface temperature of the slab at the measurement position calculated by the temperature solid fraction distribution calculation unit) It is preferable to calculate a corrected gain coefficient matrix as a coefficient vector to be multiplied by the deviation of the calculated value. This facilitates continuous calculation of the surface temperature distribution and the solid fraction distribution at a specific position of the slab.

  Further, in the second aspect of the present invention, using the operation data, the distribution of the surface temperature of the slab, the distribution of the internal temperature of the slab, the distribution of the solid phase ratio inside the slab, and the slab It is preferable to sequentially calculate the distribution of the concentration of the solute component in the liquid phase in the solid-liquid coexistence region inside. By adopting such a configuration, in a continuous casting machine on a practical scale, even if the calculated heat transfer coefficient by the heat transfer coefficient model is different from the actual value, not only the temperature measurement point but also the casting points other than the temperature measurement point It is possible to match the estimated surface temperature of the piece with sufficient accuracy with the temperature measurement result in a continuous caster on a practical scale.

  According to the present invention, there is provided a state estimation method and an estimation device for a slab cast by a continuous casting machine capable of continuously calculating a surface temperature distribution and a solid phase ratio distribution at a specific position of the slab. can do.

It is a figure explaining the continuous casting machine which can apply this invention. It is a figure which simplifies and shows the II-II 'cross section of FIG. It is a figure explaining the state estimation method of the slab cast with the continuous casting machine of this invention. It is a figure explaining the division of the whole slab to which a heat transfer coefficient correction parameter corresponds. It is a figure explaining the boundary line of the calculation object cross section of a slab, arrangement | positioning of a calculation point, and arrangement | positioning of a temperature measuring point. It is a figure explaining the calculation flow per time of the sequential calculation part in the state estimation method of this invention. It is a figure explaining the method shown by 1st Embodiment of patent document 1. FIG. It is a figure explaining the method shown by 2nd Embodiment of patent document 1. FIG. It is a figure explaining the state estimation apparatus of the slab cast with the continuous casting machine of this invention. It is a figure which shows the result of the comparative example which compared the model calculation value in a bending segment exit. It is a figure which shows the result of the comparative example which compared the model calculation value in the correction | amendment segment exit. It is a figure which shows the result of the Example which compared the model calculation value in a bending segment exit. It is a figure which shows the result of the Example which compared the model calculation value in the correction | amendment segment exit. It is a figure explaining the estimation result of the heat transfer coefficient correction parameter in an Example. It is a figure explaining the estimation result of the slab surface temperature of an Example and a comparative example. It is a figure explaining the error distribution of the cross-sectional temperature of the estimation model by a comparative example, and the cross-sectional temperature of a plant model. It is a figure explaining the error distribution of the cross-sectional temperature of the estimation model by an Example, and the cross-sectional temperature of a plant model. It is a figure explaining the error distribution of the solid phase ratio in a section of an estimation model by a comparative example, and the solid phase ratio in a section of a plant model. It is a figure explaining the error distribution of the solid phase ratio in a section of an estimation model by an example, and the solid phase ratio in a section of a plant model. It is a figure explaining transition of the value of a heat transfer coefficient correction parameter at the time of applying a state estimating device of the present invention to operation of a commercial machine of a continuous casting machine. It is a figure explaining the estimation result of the slab surface temperature at the time of applying the state estimation apparatus of this invention to the operation of a practical machine of a continuous casting machine. It is a figure explaining the estimation result of the slab surface temperature at the time of applying the state estimation apparatus of this invention to the operation of a practical machine of a continuous casting machine.

  Embodiments of the present invention will be described below. In the following description, the state estimation method of a slab cast by the continuous casting machine of the present invention may be referred to as “the state estimation method of the present invention”, and the slab cast by the continuous casting machine of the present invention. This state estimation device may be referred to as a “state estimation device of the present invention”. In addition, the form demonstrated below is an illustration of this invention and this invention is not limited to the form demonstrated below.

  FIG. 1 is a diagram illustrating a continuous casting machine to which the present invention can be applied. FIG. 1 schematically shows the configuration of a continuous casting machine. FIG. 2 is a simplified view of the II-II ′ cross section of FIG. 1. A continuous casting machine 10 shown in FIGS. 1 and 2 includes a mold 1, a roll 3 that supports a slab 2 drawn out from the mold 1, and a cooling water spray 4 that discharges cooling water toward the slab 2. And a thermometer 5 for measuring the temperature of the slab 2, a high-order computer 6, and a low-order instrumentation calculation device 7. The host computer 6 includes the size of the slab perpendicular to the longitudinal direction of the slab 2, the temperature of the molten metal in the mold 1, the concentration of the solute component in the molten metal, and the molten metal calculated using the concentration of the solute component. The operation data of the continuous casting machine including the liquidus temperature and the cooling conditions at each point on the surface of the slab 2 are stored. The lower instrumentation calculation device 7 has a casting speed and a thermometer 5. The surface temperature of the slab measured by is stored. That is, the upper computer 6 and the lower instrumentation computer 7 function as an operation data storage unit described later. Operation data stored in the upper computer 6 and the lower instrumentation computer 7 is used in the state estimation device 8 of the present invention. The calculation target region 21 shown in FIG. 2 is based on the assumption that the temperature distribution is symmetric with respect to the center of the slab in the thickness direction and the temperature distribution is symmetric with respect to the center of the slab in the width direction. This is a region where the temperature distribution and the solid fraction distribution according to the present invention are calculated.

1. FIG. 3 is a flow chart for explaining the state estimation method of the present invention. As shown in FIG. 3, the state estimation method of the present invention includes a surface temperature measurement step (S31), an operation data grasping step (S32), a heat transfer rate estimation step (S33), and a heat transfer rate correction step ( S34), a temperature solid phase ratio distribution calculating step (S35), and a heat transfer coefficient correction parameter correcting step (S36). The function of the slab state estimation model used in the state estimation method of the present invention, the setting of the model, and the calculation procedure in each function of the model will be described below with reference to FIG. 3 as appropriate.

<Time in model and coordinates in slab section>
In the slab state estimation model used in the present invention, a process in which a cross section perpendicular to the slab longitudinal direction (hereinafter also referred to as “calculation target cross section”) is drawn from the molten steel surface in the mold to the outlet of the continuous casting machine is traced. Then, the time change due to the progress of solidification of the state variable in this section is calculated. Hereinafter, with respect to time t, the time when the cross section to be tracked is in the mold surface is assumed to be t = 0.

As shown in FIG. 2, among the sides of the cross section perpendicular to the longitudinal direction of the slab in the continuous casting machine, the direction parallel to the side corresponding to the upper surface or the lower surface of the slab is the width direction and the side corresponding to the side surface perpendicular thereto The parallel direction is defined as the thickness direction, the slab width direction is represented by x, and the slab thickness direction is represented by y. The coordinate axis in the slab width direction is the x axis, the coordinate axis in the slab thickness direction is the y axis, and one section corner is the origin of the coordinate system.
Further, as shown in FIG. 1, regarding the position z in the longitudinal direction of the slab, z (0) = 0 and dz / dt = vc (t) when the casting speed is vc (t). Shall be satisfied.

<State variable>
In the molten steel temperature estimation model, the following are set as state variables in the in-section coordinates (x, y) at time t. Here, i is the number of the solute component in the molten steel.
Enthalpy: H (x, y, t), temperature: T (x, y, t), solid phase ratio: f _s (x, y, t), solute component concentration at the solid-liquid interface: C _i (x, y , T).
The physical property parameters in the molten steel temperature estimation model are as follows.
Thermal conductivity (dependent on temperature): λ (x, y, t) = λ (T (x, y, t)), specific heat of steel (dependent on temperature): c (x, y, t) = c ( T (x, y, t)), latent heat of solidification: L, liquidus temperature: T _L.

<Basic equation of model>
Since the enthalpy is the energy at each point in the cross section including the latent heat of solidification, the time change can be expressed by the heat conduction equation (1) representing the heat balance at each point.

Here, q _x represents the heat flux in the x direction, and q _y represents the heat flux in the y direction. The following formulas (2) and (3) hold at the inner points other than the boundary line in the cross section.

Here, λ _x represents the thermal conductivity in the x direction, and λ _y represents the thermal conductivity in the y direction. Therefore, from the equations (2) and (3), the above equation (1) is

It becomes.

<Boundary conditions>
In the cross section boundary on the slab surface of the slab surface to be calculated, the heat flux is expressed by the following formula (5) on the short side surface of the slab of x = 0, and the following formula (6) on the long side surface of the slab of y = 0. ) Represents the heat flux.

However, K _x is the heat transfer coefficient in the slab narrow side, K _y is the heat transfer coefficient in the slab long side surface, it expressed using a model equation based on the mode of cooling. T _a is the external ambient temperature, and ε _x and ε _y are parameters (heat transfer coefficient correction parameters) for correcting the difference between the model value of the heat transfer coefficient and the actual value when the model calculation is applied. On the other hand, at each center line side boundary line of the calculation object cross section, it is assumed that each variable is symmetric with respect to the center line, and there is no heat exchange across the boundary line, and the following equations (7) and (8) ) Holds. In the following formula (7), X / 2 is the center of the slab width direction, and in the following formula (8), Y / 2 is the center of the slab thickness direction.

<Relationship between enthalpy, temperature and solid fraction>
In the solidification of steel, which is an alloy, when the temperature falls below the liquidus temperature _TL determined by the component concentration, solidification starts and the solid phase ratio f _s > 0 until solidification is completed and f _s = 1. The temperature drops. Considering that the solid phase ratio is 0 ≦ f _s ≦ 1, the relationship between enthalpy and temperature is expressed by the following formula (9).

Here, ρ is density.

<Heat conduction equation with enthalpy as a variable>
When both sides of the above formula (9) are partially differentiated by x, the following formula (10) is obtained. Therefore, the heat flux q _{x in the} x direction is represented by the following formula (11).

Similarly, the heat flux q _{y in the} y direction is expressed by the following formula (12).

By substituting the above equations (11) and (12) into the above equation (3), the heat conduction equation can be rewritten to the equation (13) with the enthalpy as a variable at the inner point of the cross section.

  Several models representing the relationship between temperature and solid fraction have been proposed so far. One of them is a model that interpolates a solid phase ratio between a liquidus temperature at which solidification starts and a solidus temperature at which solidification is completed.

Interpolation function is generally monotonic increasing, a method of the first order equation for f _s, there is a method of the quadratic equation for f _s.
Since the above equations (9), (13), and (14) are closed with respect to the variables H, T, and f _s , enthalpy H (x, y in the cross section can be obtained by solving these simultaneously. , T), temperature T (x, y, t), and solid fraction f _s (x, y, t).

  Another model representing the relationship between temperature and solid phase ratio is that the temperature is determined by the solute concentration on the liquid phase side at the interface between the solid phase and the liquid phase in the solid-liquid coexistence region. And (16).

Since the above formula (9), formula (13), formula (15), and formula (16) are closed with respect to the variables H, T, f _s , and C _Li , the cross section is obtained by solving them simultaneously. Enthalpy H (x, y, t), temperature T (x, y, t), solid fraction f _s (x, y, t), and liquid phase side solute concentration C _Li (x , Y, t).

  However, it is difficult to solve these equations analytically. Therefore, in the present invention, a numerical solution is obtained by discretization. In the present invention, a model is used in which the equation (13) is spatially discretized in the cross section of the slab and on the boundary line, and the boundary condition on the slab surface is incorporated and updated at the discretized time.

<Discrete coordinates>
In the longitudinal direction of the slab, calculation points are set at a certain distance Δz from the position of the molten metal surface in the mold. Number of computation position, the mold molten steel surface position and tp = 0, the following drawing direction to tp = 1, 2, ..., and _{T P.} At each calculation position, calculation points are set in common on the slab cross section and on the boundary.
In the following description, as shown in FIG. 2, the calculation target area is set to the center of the slab width direction x = X / 2 and the center of the slab thickness direction y = Y / 2 with the lower left corner of the slab cross section as the origin. The range. The coordinates (x _i , y _j ) of the calculation point are x ₀ = 0 and x _I = X / 2 and y ₀ = 0 for i = 0,..., I, and j = 0,. And y _J = Y / 2, and among these, the minimum interval of the calculation point coordinates in the x-axis direction and the minimum interval of the calculation point coordinates in the y-axis direction always satisfy the stability condition in the numerical solution of the partial differential equation. Arrange the calculation point coordinates at appropriate positions so as to satisfy. As a stability condition, a method of analytically deriving from coefficients of an equation to be solved is known, but in the present invention, it is determined after confirming that a solution obtained by a prior simulation is numerically stable.
In the following, for i = 0,..., I-1 and j = 0,.
x _{i + 1/2} = (x _i + x _{i + 1} ) / 2,
y _{j + 1/2} = (y _j + y _{j + 1} ) / 2,
Δx _i = x _{i + 1} −x _i ,
Δy _j = y _{j + 1} −y _j ,
And
On the other hand, i = 1,..., I-1 and j = 1,.
Δx _{c i} = x _{i + 1/2} −x _{i−1 / 2} ,
Δy _{c j} = y _{j + 1/2} −y _{j−1 / 2} ,
Δx _{c 0} = x _1/2 −x ₀ ,
Δy _{c 0} = y _1/2 −y ₀ ,
Δx _{c I} = x _I −x _{I−1 / 2} ,
Δy _{c J} = y _J −y _{J−1 / 2} ,
And

<Discrete model formula>
In the following description, for variables other than coordinates, the subscript i + 1/2 means an amount at an intermediate position between i and i + 1. In the actual calculation, when given as an argument of a function, the subscript is an average value corresponding to i and i + 1. In the present invention, a model discretized at a point (x _i , y _j ) can be expressed as follows using enthalpy, temperature, solid fraction, and enthalpy and solid fraction at adjacent points. Here, the “adjacent point” refers to the point (i + 1, j), the point (i, j + 1), the point (i−1, j), and the point (i, j) with respect to the coordinate (i, j). -1).

Here, N (i, j) represents a set of the above adjacent points of the point (x _i , y _j ). Further, a ^t _{i, j} is a coefficient applied to H _{i, j, t} when the partial differentiation is discretely approximated by the central difference in Equation (13) and arranged in the form of Equation (17), and α ^t _{i and j} are coefficients similarly applied to fi _{, j and t} . Further, b _{i, j} is always 0 when the point (x _i , y _j ) is not a point on the slab surface boundary, and the point (x _i , y _i ) is a point on the slab surface boundary. Is a coefficient relating to (T _{i, j, t} −T _a ) including the heat transfer coefficient K _x or K _y in the expressions (5) and (6) after the discrete approximation of the expression (17). Also, ω is a variable that takes one of the values 1, 0, and 1/2. In updating the enthalpy, when ω = 1, the explicit method is used, when ω = 0, the implicit method is used, and ω = 1 / In the case of 2, it means that the semi-yang semi-implicit method (Crank-Nicholson method) is used. Further, _p in T _p and H _p is an abbreviated notation representing the point (i, j), and k (p) is a range of values that the temperature T can take in advance divided into a plurality of sections, and the temperature T (p ) Including T ^{k (p)} ≦ T (p). In addition, I _c (T ^{k (p)} ) is a value ^obtained by previously calculating the integration in Equation (9) up to the boundary value T ^{k (p)} from the temperature T ₀ , and c ^* _{k (p) +1/2} is the above It is a representative value of the specific heat c of molten steel in the section k (p).

When the right sides of the above equations (17) and (18) at each point are arranged and the variable values of the respective calculation points at time t are arranged in a vector in an appropriate order, the enthalpy in the tracking plane and the temperature at the temperature measurement point Uses the matrix A _H , A _f , B _T , B _ε, C, and D, and T _p0 that summarizes terms that are not related to H _{p, t} and f _{sp, t} on the right side of equation (18). Can be expressed as follows.

<Sequential estimation of enthalpy and heat transfer coefficient correction parameters>
In the present invention, the slab surface temperature at the slab surface temperature measurement position calculated by the above model and the slab surface temperature measurement value measured by the thermometer each time each cross section moves to the downstream side after being pulled out by a certain length Using the error from the temperature, the enthalpy of the calculation point at the slab surface temperature measurement position, and the value of the heat transfer coefficient correction parameter from the thermometer adjacent to the mold outlet or upstream to the slab surface temperature measurement position Are estimated sequentially.

  The heat transfer coefficient correction parameter is to cope with the possibility that there is a variation in the heat transfer coefficient model and the actual heat transfer coefficient error in the slab width direction and slab thickness direction of the spray in the secondary cooling zone. 4, from the mold outlet to the slab surface temperature measurement position at the most downstream side in the slab longitudinal direction, for each range between thermometer installation positions (upstream part, downstream part, inside and outside in FIG. 4) Assign correction parameters to. When multiple thermometers are installed in the slab width direction as shown in FIGS. 2, 4, and 5, a boundary line is provided in the middle of the thermometer to correct the heat transfer coefficient in the slab width direction. Assign a parameter variable.

The model equation (19) and the right side of the equation (20) at the calculation point of the slab surface temperature measurement position, the equation with the enthalpy h _t and the heat transfer coefficient correction parameter ε _t at the point (x _i , y _j ) as variables, By considering them, the following expressions (21) and (22) are obtained.

Here, H ′ _t is an enthalpy other than the temperature measurement position, and ε ′ _t is a vector of a heat transfer coefficient correction parameter other than the temperature measurement position. Further, a _hh is a coefficient related to h _t when a row related to h _{t + 1} in the equation (20) is extracted, a _hε is a coefficient _related to ε _t , A _hH is a coefficient matrix related to H ′ _t , and A ′ _hε. Is a coefficient concerning ε ′ _t . B ′ _T is also a coefficient according to (T _t −T _a ). Further, c ^T _ph is a row vector obtained by extracting a row at the temperature measurement point for the coefficient matrix C in the equation (20), and d _ph is a coefficient obtained by extracting a row at the temperature measurement point for the coefficient matrix D. In the portion after the mold exit of the slab, the solid phase ratio at the calculation point on the slab surface can be regarded as 1, so the term derived from latent heat release is excluded from the above equation (21).

In the present invention, the expected value E (| U _pt −T _pt | ² ) of variance of errors between the slab surface temperature U _pt measured sequentially and the model estimated value T _pt of the surface temperature at the surface temperature measurement position is minimized. The time series [h _t ε _t ] ^T of the enthalpy and the heat transfer coefficient correction parameter at the surface temperature measurement position is sequentially calculated. This method will be described below.

<Calculation Procedure of State Estimation Method of the Present Invention>
A calculation procedure performed every time the casting progresses by Δz is shown below. For convenience, the description of the surface temperature measurement process is also described below.

1.1. Surface temperature measurement process (S31)
The surface temperature measuring step (S31) is a step of measuring the surface temperature of the slab using a thermometer at an arbitrary point from the mold outlet to the location where the slab is cut.

1.2. Operation data grasping process (S32)
The operation data grasping step (S32) is calculated using the size of the slab perpendicular to the slab longitudinal direction, the casting speed, the molten metal temperature in the mold, the solute component concentration in the molten metal, and the solute component concentration. This is a process of grasping operation data of a continuous casting machine including the liquidus temperature of the molten metal and the cooling conditions at each point on the surface of the slab. In S32, data on the cooling water flow rate in each cooling zone of the secondary cooling zone is acquired, and the cooling water flow rate and the number of cooling water sprays, the arrangement of the cooling water spray, and the spray water discharged from the cooling water spray are the surface of the slab. The cooling water spray density distribution on the entire slab surface is calculated using data (cooling conditions) in the range of collision with the slab.

1.3. Heat transfer coefficient estimation step (S33)
The heat transfer coefficient estimation step (S33) is a step of estimating the heat transfer coefficient at each point on the surface of the slab using the cooling conditions grasped in S32. S33 is specifically the slab longitudinal calculated position tp = 0, ..., in each of between T _P, a portion spraying water collides, divided into and other parts, to each portion the heat transfer coefficient on the section boundary calculation points belongs, the flow density w _d spray water collide in a portion where the sprayed water collides, the air flow velocity v _a of the mist spray, the slab surface temperature T _s of the collision parts Is calculated based on a predetermined model formula (the following formula (23) and formula (24)). Here, K _x0 (0, y, z, t) shown in the following formula (23) is a heat transfer coefficient at the position y in the thickness direction of the slab short side surface at the time t and the casting direction position z. K _y0 (x, 0, z, t) shown in Expression (24) is a heat transfer coefficient at the position x in the width direction of the long side surface of the slab at the time t and the position z in the casting direction. In S33, the heat transfer coefficient at the calculation point on the cross-sectional boundary belonging to the portion where the spray water does not collide (the above “other portion”) is expressed by w _d = 0, v _a = in Equations (23) and (24). 0, and is calculated based on the model formula using only the cast slab surface temperature T _s.

1.4. Heat transfer coefficient correction step (S34)
In the heat transfer coefficient correction step (S34), the heat transfer coefficient correction parameters ε _x and ε _y for correcting the error between the heat transfer coefficient estimated in S33 and the true heat transfer coefficient of the slab are used, and the above S33 is performed. In this step, the corrected heat transfer coefficient is corrected to calculate the corrected heat transfer coefficient. More specifically, in S34, the heat transfer coefficient correction factor parameter for each section in the slab width direction and slab longitudinal direction, which was corrected in the previous model calculation, is caused to act as in the following formulas (25) and (26). This is a step of correcting the heat transfer coefficient calculated in S33.

1.5. Temperature solid fraction distribution calculation step (S35)
In the temperature solid phase ratio distribution calculating step (S35), the surface temperature distribution of the slab and the internal temperature of the slab are calculated using the operation data grasped in S32 and the corrected heat transfer coefficient calculated in S34. And the distribution of the solid phase ratio inside the slab. In S35, specifically, the enthalpy is updated according to the discretized heat conduction equation (17) at each calculation point using the heat transfer coefficient corrected in S34. Thereafter, for the renewed enthalpy, the combination of the above formula (9) and formula (14) converges on the temperature, the solid phase ratio, and the solute concentration at the solid-liquid interface, or the above formula (9), formula (15) is a step in which the model equations of Equation (16) are simultaneously calculated and a numerical solution is obtained by convergence calculation.

1.6. Heat transfer coefficient correction parameter correction step (S36)
In the heat transfer coefficient correction parameter correction step (S36), a deviation between the surface temperature of the slab measured in S31 and the calculated value of the surface temperature of the slab at the surface temperature measurement position calculated in S35 is calculated. This is a step of correcting the heat transfer coefficient correction parameter every time S35 is completed. The contents of S36 will be described below.

1.6.1. Estimated value vector Correction of enthalpy and heat transfer coefficient at the point immediately below the surface temperature measurement position at time t based on the enthalpy, solid phase ratio, and temperature calculation result in the tracking surface at time t-1 calculated in S32 to S35 above The estimated value vector of the rate parameter is represented by [h _{t | t−1} ε _{t | t−1} ] ^T. In the following description, the variable subscript t | t represents a variable estimated value based on the temperature measurement result data obtained at time t, and the subscript t + 1 | t represents a time t + 1 based on the variable estimated result at time t. Represents the estimation result of the value at.

1.6.2. Update of Variance Covariance Matrix Variance covariance matrix V _{t | of} variable vector [h _{t | t−1} ε _{t | t−1} ] ^T using a _hh and a _hε among the coefficients of equation (21). _t-1 is updated as shown in the following formula (27).

Here, v _{hh | t-1} is the variance of h _{t | t-1} , v _{hεt | t-1} is the _covariance of h _{t | t-1} and ε _{t | t-1,} and v _{εεt | t-1} Is the variance of ε _{t | t−1} . Further, Γ is expressed by the following equation (28) using the same coefficient as the above model equation and the system noise v _t that is a random variable with an average of 0 at the surface temperature measurement position. This is a coefficient matrix when assumed.

However, h _t ^″ is the true value of enthalpy, T _t ^″ is the true value of temperature, and ε ^″ is the true value of the heat transfer coefficient correction parameter. Γ is a coefficient matrix for system noise. Q is a variance-covariance matrix of the random variable v _t .

1.6.3. Calculation of Kalman gain and correction of enthalpy and heat transfer coefficient correction parameters Kalman gain is the estimated temperature and surface temperature of the tracking surface at the surface temperature measurement position using the variance-covariance matrix estimated by the above equation (27). It is a gain coefficient matrix for correcting the enthalpy at the calculation point immediately below the surface temperature measurement position as shown in the following equation (29) due to an error from the measurement value.

Here, Ψ _t is the Kalman gain, and R is the variance covariance matrix of the average 0 observation noise added to the temperature measurement value.

1.6.4. Correction of variance-covariance matrix by Kalman gain A variance-covariance matrix V _{t | t} is calculated using the Kalman gain.

Above 1.6.1. To 1.6.4. The series of steps up to are performed at the measurement points at the surface temperature measurement position in the slab longitudinal direction.

<Reflection of enthalpy and heat transfer coefficient correction parameter>
The enthalpy at the temperature measurement point at each surface temperature measurement position is replaced with h _{t | t} calculated in the above procedure, and the heat transfer coefficient correction parameter at the calculation point of the section to which the temperature measurement point belongs, upstream of the temperature measurement point The heat transfer coefficient correction parameter at the calculation point belonging to the same section of each tracking surface is updated. In the tracking surface after the surface temperature measurement position on the most downstream side, the heat transfer coefficient correction parameter is replaced with the value calculated for the temperature measurement point at the surface temperature measurement position on the most downstream side.

  By executing the calculation according to the present invention according to the procedure as described above, a series of calculations of the temperature distribution in the slab cross section from the molten steel surface position in the mold to the measurement position are performed as in the method disclosed in Patent Document 1. There is no need to repeat several times along the casting direction. Therefore, it is possible to eliminate the problem of requiring a large amount of calculation until the model temperature calculation result distribution in the slab width direction matches the distribution of the temperature measurement values. It is possible to calculate the surface temperature distribution and the solidification state at a specific position.

The difference between the state estimation method of the present invention and the method disclosed in Patent Document 1 will be described more specifically. FIG. 6 is a diagram for explaining a calculation flow per time of the sequential calculation portion in the state estimation method of the present invention. On the other hand, FIG. 7A shows a concept of a method for matching the temperature distribution measurement value and the model calculation value at the width direction temperature measurement position shown in the first embodiment of Patent Document 1. Moreover, the conceptual diagram of the method shown in 2nd Embodiment of patent document 1 and matching the temperature distribution measured value and model calculation value in the width direction temperature measurement position is shown to FIG. 7B.
As shown in FIG. 7A and FIG. 7B, in the technique disclosed in Patent Document 1, in order to continuously match the actual results and the calculated values at the temperature measurement position in the slab width direction, In general, a procedure P2 for repeating the calculation procedure P1 for the temperature distribution in the cross section at each calculation target time from the position of the molten metal surface in the mold to the temperature measurement position in the slab width direction, and further, the correction of the optimization target variable in each embodiment is performed as the procedure P2. The procedure P3 to be performed while repeating the above must be repeated as time passes. On the other hand, in the state estimation method of the present invention, as shown in FIG. 6, the calculation of the temperature distribution in the cross section at each calculation position in the longitudinal direction of the slab needs to be repeated as time passes. The correction of the heat transfer coefficient correction parameter may be performed only once for each distribution calculation of the temperature of the cross section at each calculation position in the slab longitudinal direction. This corresponds to that the number of calculations of P2 in the technique disclosed in Patent Document 1 is only one. That is, according to the state estimation method of the present invention, it is possible to reduce the amount of calculation, so that it is possible to solve the problem that required a large amount of calculation in the prior art.
Furthermore, in the method shown in each embodiment of Patent Document 1, the temperature distribution in the cross section from when the calculated cross section at the slab width direction temperature measurement position is at the molten metal surface to the position is reached. Therefore, there is a problem that data such as changes in casting speed and cooling conditions must be stored in correspondence with past times. In contrast, in the state estimation method of the present invention, the calculation position of the cross section for calculating the temperature distribution or the like is predetermined on the slab, and each calculation position moves from the calculation position adjacent to the upstream side for each calculation position. In order to reflect the change in the casting speed and the amount of the secondary cooling water during that time, only the casting speed and the cooling conditions during this period need be stored. Therefore, in the present invention, unlike the technique disclosed in Patent Document 1, it is not necessary to store past operation states over a long period of time.

2. FIG. 8 is a diagram for explaining the state estimation device of the present invention. In FIG. 8, the same components as those shown in FIG. 1 are denoted by the same reference numerals as those used in FIG. 1, and the description thereof is omitted as appropriate. The state estimation device 8 of the present invention shown in FIG. 8 includes an operation data storage unit 81, a heat transfer rate estimation unit 82, a heat transfer rate correction unit 83, a temperature solid phase rate distribution calculation unit 84, and a heat transfer rate. A correction parameter correction unit 85 and an output unit 86 are provided.

  The operation data storage unit 81 is calculated by using the size of the slab perpendicular to the longitudinal direction of the slab, the casting speed, the temperature of the molten metal in the mold, the concentration of the solute component in the molten metal, and the concentration of the solute component. It is a part which memorize | stores the operation data of a continuous casting machine including the liquidus temperature of this, and the cooling conditions in each point of the surface of a slab. The operation data stored in the operation data storage unit 81 is used in S32 and the like.

  The heat transfer coefficient estimation unit 82 is a part that estimates the heat transfer coefficient at each point on the surface of the slab using the cooling conditions stored in the operation data storage unit 81. S33 is performed by the heat transfer coefficient estimation unit 82.

  The heat transfer coefficient correction unit 83 uses a heat transfer coefficient correction parameter that corrects an error between the heat transfer coefficient estimated by the heat transfer coefficient estimation unit 82 and the true heat transfer coefficient of the slab, and uses the heat transfer coefficient correction unit. By correcting the heat transfer coefficient estimated at 82, the heat transfer coefficient after correction is calculated. S34 is performed by the heat transfer coefficient correction unit 83.

  The temperature solid phase ratio distribution calculation unit 84 uses the operation data stored in the operation data storage unit 81 and the corrected heat transfer coefficient calculated by the heat transfer coefficient correction unit 83 to distribute the surface temperature of the slab. This is a part for sequentially calculating the distribution of the internal temperature of the slab and the distribution of the solid phase ratio inside the slab. The above S35 is performed by the temperature solid phase ratio distribution calculation unit 84.

  The heat transfer coefficient correction parameter correcting unit 85 is the surface temperature of the slab measured by the temperature measuring unit and the measurement position calculated by the temperature solid phase rate distribution calculating unit 84 at which the surface temperature is measured by the temperature measuring unit. This is a part for correcting the heat transfer coefficient correction parameter every time the calculation by the temperature solid phase ratio distribution calculation unit 84 is completed using the deviation from the calculated value of the surface temperature of the slab. S36 is performed by the heat transfer coefficient correction parameter correction unit 85.

  The output unit 86 is a part for displaying a calculation result by the temperature solid phase ratio distribution calculating unit 84 and the heat transfer coefficient correction parameter correcting unit 85. The output form of the output unit 86 is not particularly limited. For example, a known form such as display on a display device, storage in a portable storage medium, and transmission to an external device can be employed. The output by the output unit 86 is realized, for example, when the CPU reads out data such as a temperature distribution and a solid phase ratio distribution from an HDD or the like and performs output processing such as creating display data.

  Thus, the state estimation apparatus 8 of the present invention can implement the state estimation method of the present invention. According to the state estimation method of the present invention, it is possible to continuously calculate the surface temperature distribution and the solid phase ratio distribution at a specific position of the slab, so according to the present invention, the surface temperature distribution at the specific position of the slab. And the state estimation apparatus of the slab cast | casted with the continuous casting machine which can calculate a solid-phase-rate distribution continuously can be provided.

  The present invention will be further described with reference to examples.

  The effect of the present invention was confirmed by applying the present invention (Example) and the prior art (Comparative Example) to a vertical bending slab continuous casting machine. In the slab continuous casting machine, the cooling control from the upper and lower surfaces, which are the long sides of the slab rectangular cross section, is important, so in the continuous casting machine used this time, at the exit of the slab bending segment and the exit of the straightening segment, The temperature of the upper and lower surfaces of the slab was measured. As shown in FIGS. 4 and 5, the thermometer arrangement in the width direction at each installation position was a ¼ width position and a ¾ width position on the center line in the slab width direction.

  The state estimation device 8 of the present invention used in this example is calculated from the size of the cross section perpendicular to the slab longitudinal direction (z direction), the molten steel temperature in the mold, the solute component concentration and the solute component concentration in the molten steel. The operating condition data including the liquidus temperature of the steel and the cooling conditions at each point on the surface of the slab are received from the host computer 6 shown in FIG. Each signal related to the measurement result was received from the low-level instrumentation calculation device 7.

  The heat transfer coefficient correction parameter is divided into two sections in the longitudinal direction of the slab, from the mold outlet to the measurement position by the thermometer arranged upstream, and from the measurement position by the thermometer arranged upstream to the secondary cooling zone outlet. did. The slab width direction is from one short side surface to the 3/8 width position of the slab width, from the 3/8 width position to the 5/8 width position, and from the 5/8 position to the opposite short side. In this example, the heat transfer coefficient parameter in the slab width direction is divided into two types by assuming that the temperature distribution and the like are symmetric about the center line in the slab width direction. Limited. As a result, the number of heat transfer coefficient correction factor parameters in the example was four.

(Comparative example)
First, as a comparative example, without using the heat transfer coefficient correction parameter shown in the description of the present invention, using the operation condition data and the boundary condition based on the heat transfer coefficient obtained from the operation condition data, the above formula (9 ), Equation (13), Equation (15), and Equation (16) are used for the calculation results.
The continuous casting machine to be simulated was a slab continuous casting machine having a slab cross section of 2300 mm in width and 250 mm in thickness, and the casting speed was 1.25 m / min. In the simulation using the plant model, a tracking cross-section was generated every time the casting proceeded by 0.25 m, and the temperature and solid-phase ratio distribution of each cross-section were calculated according to S32 to S35 every 0.05 m. The heat transfer coefficient was calculated by a model according to the equipment conditions and operating conditions of the continuous casting machine to be simulated, but the heat transfer coefficient distribution in the slab width direction is the result of model calculation in the range of 600 mm inside the slab center. It was assumed to be 1.05 times and 1.10 times outside that. On the other hand, in the simulation of the slab state estimation model, a tracking cross section is generated every time 0.25 m casting proceeds as in the case of the plant model. The phase distribution was calculated. However, in the comparative example, the heat transfer coefficient correction parameter was fixed to 0, and the calculation was performed without correcting the value of the heat transfer coefficient model calculation result. 9A and 9B show time charts comparing the model calculated values at both the bending segment outlet and the straightening segment outlet of the simulation target continuous casting machine. FIG. 9A is a time chart comparing both model calculated values at the bending segment exit, and FIG. 9B is a time chart comparing both model calculated values at the straightening segment exit. In the comparative example, since the heat transfer coefficient of the estimated model was not corrected, the amount of heat removed from the slab is smaller than that of the plant model. Therefore, as shown in FIGS. 9A and 9B, the temperature calculation result of the estimated model was higher than that of the plant model at the outlet temperature measurement points of both the bending segment and the correction segment.

(Example)
The plant model simulation for calculating the temperature and solid phase ratio of the entire slab during casting of the continuous casting machine, and the surface temperature calculation value at the temperature measurement point at the temperature measurement position in the plant model simulation result, the temperature measurement of the thermometer in the present invention A result of an example in which the state of the entire slab is estimated using the heat transfer coefficient correction parameter will be described. In the simulation calculation in the embodiment, the tracking cross section is generated every time the casting proceeds 0.25 m, and the temperature and the solid phase ratio distribution of each cross section are calculated according to the above S32 to S35 every 0.05 m, thereby generating the tracking cross section. At the same time, the enthalpy and heat transfer coefficient correction parameters at the temperature measurement point were calculated in the tracking cross section at the temperature measurement position at that time.

  The time chart of the calculation result by the plant model of the slab surface temperature at each position where the surface temperature was measured at the bending segment outlet and the straightening segment outlet of the continuous casting machine to be simulated, and the heat transfer coefficient correction according to the present invention FIGS. 10A and 10B show time charts of the slab surface temperature at the same position based on a calculation model in which parameters are sequentially estimated. Moreover, the estimation result of the heat transfer coefficient correction parameter is shown in FIG. 10C.

  As shown in FIGS. 10A and 10B, according to the method of the present invention, the estimation result of the surface temperature at the surface temperature measurement position immediately after the start of the simulation has a deviation from the output temperature of the plant model. It approaches the plant model output value and converges to the same value. Further, as shown in FIG. 10C, the value of the heat transfer coefficient correction parameter at this time is a desirable correction value 0.05 inside the slab width direction and a desirable correction value 0.10 outside the slab width direction. Converged to a close value.

The simulation results of the surface temperature at the center position in the slab width direction by the plant model inside the correction segment further upstream than the surface temperature measurement position at the upstream side in the slab longitudinal direction, and the surface temperature at the same measurement position according to the present invention FIG. 11 shows the result (Example) calculated using the heat transfer coefficient correction parameter and the result calculated without using the heat transfer coefficient correction parameter (Comparative Example). As shown in FIG. 11, in the comparative example in which the heat transfer coefficient correction parameter is not used, the estimated surface temperature is 17 ° C. higher than the plant model output value, but in the embodiment using the heat transfer coefficient correction parameter, the surface temperature is The estimated value matched the plant model output value with an error of 0.6 ° C.
From this result, even when the heat transfer coefficient calculation value by the heat transfer coefficient model is different from the actual value in the continuous casting machine on the practical scale, by calculating the heat transfer coefficient correction parameter sequentially with the present invention, it can be applied to other than the temperature measuring point. It can be seen that the estimated surface temperature of the slab can be matched with a practical scale continuous casting machine with sufficient accuracy.

  Next, regarding the comparative example and the example, the temperature distribution and the solid phase ratio distribution in the slab cross section at the temperature measurement position at the correction segment outlet were compared at each calculation point. The results are shown in FIGS. 12A, 12B, 13A, and 13B. FIG. 12A is a diagram showing an error distribution between the temperature in the cross section of the estimation model according to the comparative example and the temperature in the cross section of the plant model, and FIG. 12B is a diagram showing the temperature in the cross section of the estimation model according to the embodiment and the plant model. It is the figure which represented the error distribution with the temperature in a cross section of a contour map. FIG. 13A is a diagram showing an error distribution between the solid phase ratio in the cross section of the estimation model according to the comparative example and the solid phase ratio in the cross section of the plant model, and FIG. 13B is a diagram of the estimation model according to the embodiment. It is the figure which represented the error distribution of the solid-phase rate in a cross section and the solid-phase rate in a cross section of a plant model with a contour map.

  As shown in FIG. 12A, the absolute value of the error was a maximum of 35 ° C. in the comparative example not using the heat transfer coefficient correction parameter, whereas the implementation using the heat transfer coefficient correction parameter was performed as shown in FIG. 12B. In the example, the error absolute value was 0.5 ° C. at the maximum, and the error absolute value was 1/70 or less of the comparative example. Further, as shown in FIG. 13A, the absolute value of the error was 0.11 at maximum in the comparative example not using the heat transfer coefficient correction parameter, whereas the heat transfer coefficient correction parameter was changed as shown in FIG. 13B. In the example used, the error absolute value was 0.011 at the maximum, and the error absolute value was 1/10 or less of the comparative example. Also from this result, according to the present invention, it was confirmed that the temperature inside the slab and the solid phase ratio could be accurately estimated.

  As a result of calculating the heat transfer coefficient correction coefficient parameter based on the operation condition data and the temperature measurement data when the state estimation device 7 of the present invention is applied to the practical machine operation of the continuous casting machine that is the object of the simulation, And the temperature calculation result by online (in operation) in a temperature measuring point is shown to FIG. 14A-FIG. 14C. As shown in FIG. 14A, the heat transfer coefficient correction parameter almost converged to the estimated value in each section from the initial 0 as the calculation progressed. Further, as shown in FIGS. 14B and 14C, the surface temperature estimation value output by the state estimation device of the present invention with respect to the measurement result of the thermometer installed at the same position as the simulation passes through the transient state immediately after the startup. It almost coincided with the measurement result of the thermometer. From this result, it has been confirmed that according to the present invention, the surface temperature of the slab can be accurately estimated.

DESCRIPTION OF SYMBOLS 1 ... Mold 2 ... Slab 3 ... Roll 4 ... Cooling water spray 5 ... Thermometer (temperature measurement means)
DESCRIPTION OF SYMBOLS 6 ... High-order computer 7 ... Low-order instrumentation calculation apparatus 8 ... State estimation apparatus of the slab cast by the continuous casting machine 10 ... Continuous casting machine 21 ... Calculation object area | region 81 ... Operation data memory | storage part 82 ... Heat transfer coefficient estimation part 83 ... Heat transfer rate correction unit 84 ... Temperature solid phase rate distribution calculation unit 85 ... Heat transfer rate correction parameter correction unit 86 ... Output unit

Claims (4)

Slab size perpendicular to the slab longitudinal direction, casting speed, molten metal temperature in the mold, solute component concentration in the molten metal, liquidus temperature of the molten metal calculated using the solute component concentration, and , Including the cooling conditions at each point on the surface of the slab, grasping operation data of the continuous casting machine, operation data grasping step,
A heat transfer coefficient estimation step of estimating a heat transfer coefficient at each point on the slab surface using the cooling condition;
Using the heat transfer coefficient correction parameter for correcting an error between the heat transfer coefficient estimated in the heat transfer coefficient estimation step and the true heat transfer coefficient of the slab, the heat estimated in the heat transfer rate estimation step A heat transfer coefficient correction step of calculating a heat transfer coefficient after correction by correcting the transfer coefficient;
Using the operation data and the corrected heat transfer coefficient calculated in the heat transfer coefficient correction step, the surface temperature distribution of the slab, the internal temperature distribution of the slab, and the interior of the slab A temperature solid phase ratio distribution calculating step for sequentially calculating a solid phase ratio distribution in
Measuring the surface temperature of the slab using a temperature measuring means at any point from the outlet of the mold to the location where the slab is cut; and
The surface temperature of the slab measured at the surface temperature measurement step, and the surface temperature of the slab at the measurement position where the surface temperature is measured by the temperature measurement means, calculated at the temperature solid phase ratio distribution calculation step. A heat transfer coefficient correction parameter correction step of correcting the heat transfer coefficient correction parameter each time the temperature solid phase ratio distribution calculation step is completed, using the calculated value of
I have a,
Each time the respective distributions are sequentially calculated in the temperature solid phase ratio distribution calculating step, the enthalpy at the calculation point corresponding to the measurement position and the heat at the calculation point of the calculation cross section of the slab in which each distribution is calculated. The variance-covariance matrix of the transmission rate correction parameter is calculated,
In order to calculate a correction value to be added to the enthalpy at the calculation point and a correction value to be added to the heat transfer coefficient correction parameter at the calculation point, correction is performed as a coefficient vector by which the deviation is multiplied using the variance-covariance matrix. A method for estimating a state of a slab cast by a continuous casting machine, wherein a gain coefficient matrix is calculated . Using the operation data, the distribution of the surface temperature of the slab, the distribution of the internal temperature of the slab, the distribution of the solid phase ratio inside the slab, and the solid-liquid coexistence area inside the slab 2. The method for estimating the state of a slab cast by the continuous casting machine according to claim 1, wherein the distribution of the concentration of the solute component in the liquid phase is sequentially calculated. The size of the slab perpendicular to the slab longitudinal direction, the casting speed, the molten metal temperature in the mold, the solute component concentration in the molten metal, the liquidus temperature of the molten metal calculated using the solute component concentration, and Storing operation data of a continuous casting machine, including cooling conditions at each point on the surface of the slab, and an operation data storage unit;
A heat transfer coefficient estimator for estimating a heat transfer coefficient at each point on the surface of the slab using the cooling condition;
The heat transfer coefficient estimated by the heat transfer coefficient estimation unit using a heat transfer coefficient correction parameter that corrects an error between the heat transfer coefficient estimated by the heat transfer coefficient estimation unit and the true heat transfer coefficient of the slab. A heat transfer coefficient correction unit that calculates a heat transfer coefficient after correction by correcting the transfer coefficient;
Using the operation data and the corrected heat transfer coefficient calculated by the heat transfer coefficient correction unit, the surface temperature distribution of the slab, the internal temperature distribution of the slab, and the interior of the slab A temperature solid phase ratio distribution calculating section for sequentially calculating the distribution of the solid phase ratio in
The surface temperature of the slab measured by temperature measuring means for measuring the surface temperature of the slab at an arbitrary point from the outlet of the mold to the location where the slab is cut, and the temperature solid fraction distribution calculation The calculation by the temperature solid phase ratio distribution calculation unit is completed using the deviation of the calculated value of the surface temperature of the slab at the measurement position where the surface temperature is measured by the temperature measuring unit. A heat transfer coefficient correction parameter correction unit for correcting the heat transfer coefficient correction parameter every time;
I have a,
Every time each distribution is sequentially calculated by the temperature solid fraction distribution calculation unit, the enthalpy at the calculation point corresponding to the measurement position and the heat at the calculation point of the calculation cross section of the slab from which each distribution is calculated. The variance-covariance matrix of the transmission rate correction parameter is calculated,
In order to calculate a correction value to be added to the enthalpy at the calculation point and a correction value to be added to the heat transfer coefficient correction parameter at the calculation point, correction is performed as a coefficient vector by which the deviation is multiplied using the variance-covariance matrix. A state estimation device for a slab cast by a continuous casting machine, wherein a gain coefficient matrix is calculated . Using the operation data, the distribution of the surface temperature of the slab, the distribution of the internal temperature of the slab, the distribution of the solid phase ratio inside the slab, and the solid-liquid coexistence area inside the slab The state estimation device for a slab cast by the continuous casting machine according to claim 3 , wherein the distribution of solute component concentration in the liquid phase is sequentially calculated.