JP2019217510A - Device for visualizing the inside of continuous casting mold, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To visualize a state of molten steel in a mold of a continuous casting facility. A visualization device 100 has a first probability density function p (xt | y0: t-Δt) of a state vector xt at a time t and a likelihood function L (xt) of a state vector xt at the time t. By giving | yt) to the algorithm of the filter that performs data assimilation, the second probability density function p (xt | y0: t) of the state vector xt at time t is derived. The visualization device 100 derives the mode value of the second probability density function p (xt | y0: t) as an estimated value of the state vector xt at time t. Further, the visualization device 100 uses the second probability density function p (xt | y0: t) to obtain the numerical analysis data xt at time t + Δt, and the temperature and flow velocity of the molten steel 3 and the parameters of the boundary conditions. To derive multiple. [Selection diagram] Fig. 1

Description

  The present invention relates to a continuous casting mold visualization device, method, and program, and is particularly suitable for use in a continuous casting facility.

  FIG. 7 is a diagram illustrating an example of a schematic configuration of a continuous casting facility. In each of the drawings, the X axis, the Y axis, and the Z axis indicate directions. A cross in a circle indicates a direction from the near side to the far side of the paper.

  Molten steel 3 supplied from ladle 1 to tundish 2 is poured into mold 4. A sliding nozzle 5 is provided at the bottom of the tundish 2. An immersion nozzle 6 is provided below the sliding nozzle 5. The immersion nozzle 6 is disposed at the center of the horizontal section (XY section) of the mold 4. A pair of left and right discharge ports 7 (a pair of discharge ports 7 at both ends in the X-axis direction) are formed on the side surface of the tip of the immersion nozzle 6. The tip (discharge port 7) of the immersion nozzle 6 is immersed in the molten steel 3 supplied into the mold 4 (the area surrounded by the mold 4). FIG. 8 is a diagram illustrating an example of the flow of the molten steel 3 in the mold 4.

  The molten steel 3 supplied to the tundish 2 flows down through the immersion nozzle 6 through the sliding nozzle 5 and is injected into the mold 4 from a pair of left and right discharge ports 7. After colliding with the solidified shell 8, the molten steel 3 discharged from the pair of left and right discharge ports 7 is divided into an ascending flow and a descending flow as indicated by arrows in FIG. 8.

  As shown in FIG. 8A, in a steady state, the amount of molten steel discharged from the pair of left and right discharge ports 7 is substantially equal. However, as shown in FIG. 8B, the amounts of molten steel discharged from the pair of left and right discharge ports 7 may be uneven. Such unevenness in the amount of molten steel discharged from the pair of left and right discharge ports 7 is referred to as drift. When the drift occurs, a difference occurs in the flow velocity of the molten steel 3 on both the left and right sides of the immersion nozzle 6.

  The cause of such a drift is that an oxide such as alumina adheres to the inner surface of the immersion nozzle 6 or the like, or the shape of the discharge port 7 is distorted due to erosion of the discharge port 7. Further, due to the structure of the sliding nozzle 5, the fact that the molten steel 3 does not flow down the inside of the immersion nozzle 6 axisymmetrically but flows down to the left or right is also a cause of the drift.

  When the drift of the molten steel 3 occurs in the mold 4 for the above-described reason, the molten steel 3 is coated on the inner surface of the solidified shell 8 in the region where the amount of the molten steel 3 is large among the left and right regions sandwiching the immersion nozzle 6. Along the top and bottom. The upward flow of the molten steel 3 with strong momentum causes a rise of the molten metal surface (meniscus) of the molten steel 3. Thus, the supply of the flux sprayed on the molten metal surface of the molten steel 3 between the inner wall surface of the mold 4 and the solidified shell 8 is inhibited. Then, the shape of the solidified shell 8 tends to be non-uniform, which causes wrinkles and cracks to be generated in the slab cast by the continuous casting facility.

  Also, the downward flow of the molten steel 3 having a strong momentum reaches deep into the molten steel 3 and hinders the floating of nonmetallic inclusions. The penetration of the non-metallic inclusions deep into the strands causes non-metallic inclusion defect in the slab cast by the continuous casting facility. The metal surface level of the molten steel 3 (the position in the height direction (Z-axis direction) of the metal surface (meniscus) of the molten steel 3) is measured by the metal surface level meter 9. An eddy current sensor or the like is used as the level gauge 9.

  On the other hand, in the region on the left and right sides sandwiching the immersion nozzle 6, in the region on the side where the amount of the molten steel 3 is small, the flow force of the molten steel 3 discharged becomes weak. If the flow of the molten steel 3 is weak, the flow of the molten steel 3 in the discharge port 7 is likely to stagnate, and deposits such as alumina may adhere to the immersion nozzle 6. The adhesion of the precipitate such as alumina causes the flow path in the immersion nozzle 6 to be blocked.

  As described above, the occurrence of the drift in the mold 4 not only hinders the operation of the continuous casting, but also deteriorates the quality of the slab, which is not preferable. Therefore, when the drift occurs, it is necessary to take measures such as changing the casting speed, changing the flux, and replacing the immersion nozzle 6. In order to perform these measures appropriately and promptly, it is necessary to constantly monitor and grasp the state in the mold 4 such as the occurrence of drift.

The inside of the mold 4 is very hot and opaque. Therefore, the state of heat transfer and flow of the molten steel 3 in the mold 4 cannot be directly observed.
Therefore, Patent Document 1 discloses the following technology. First, a heat transfer inverse problem analysis is performed using the temperature measured by the thermocouple embedded in the mutually facing regions of the mold 4. By this inverse problem analysis, time-series information of the heat flux on one side and the other side (N side, S side) of the mutually facing regions of the mold 4 is calculated. A delay vector is calculated from the time-series information of the heat flux, and a trajectory based on a time transition of the delay vector is created, thereby reconstructing the N-side attractor and the S-side attractor. Based on the N-side attractor and the S-side attractor, a recurrence plot is created using the distribution of the N-side heat flux and the distribution of the S-side heat flux as variables, and based on the recurrence plot, the presence or absence of a drift is determined. Diagnose.

  Patent Document 2 discloses the following technology. First, a heat transfer inverse problem analysis is performed using the temperature measured by the thermocouple embedded in the mutually facing regions of the mold 4. By this heat transfer inverse problem analysis, the molten metal level of the molten steel 3 is obtained on both the inner wall surfaces of the mold 4 facing each other based on the component value of the heat flux on the inner wall surface of the mold 4 in the casting direction. The difference in the level of the molten steel 3 is obtained as an index of the drift.

JP-A-2003-305553 JP 2016-175106 A

J. Szekely and T. Yadoya, "The physical and mathematical modeling of the flow field in the mold region in continuous casting systems: Part II.The mathematical representation of the turbulent flow", Metallurgical Transactions, Vo.4, 1379 (1973) Edited by Tomoyuki Higuchi, "Introduction to Data Assimilation", Asakura Shoten, 2011 Genshiro Kitagawa, "Introduction to Time Series Analysis", Iwanami Shoten, 2005 King, Aaron A., Dao Nguyen, and Edward L. Ionides. "Statistical Inference for Partially Observed Markov Processes via the R Package pomp." Journal of Statistical Software 69.i12 (2016)

  In the technology described in Patent Document 1, a recurrence plot is used as an indicator of drift, and in the technology described in Patent Document 2, the difference in the level of the molten steel 3 is used as an indicator of drift. That is, the techniques described in Patent Literatures 1 and 2 merely determine an index of drift. However, these indices cannot always accurately predict (estimate) whether or not there is a problem in the operation of continuous casting or whether or not the quality of the slab is reduced. Even if the prediction (estimation) deviates, there is little information to determine the cause, and it is difficult to take measures such as improving the index. Therefore, if the present inventors can visualize the state of the molten steel in the mold (physical quantities such as temperature and flow velocity), a great deal of information can be obtained, and the causal relationship between the operating state and the quality of the slab is clearer. Therefore, even if inconsistency arises in this causal relationship, it is thought that it is easy to take measures.

  The present invention has been made in view of the above problems, and has as its object to make it possible to visualize the state of molten steel in a mold of a continuous casting facility.

  The continuous casting in-mold visualization device of the present invention, for a state vector that is a vector composed of physical quantities at each calculation position of the visualization target region of the molten metal injected into the mold of the continuous casting equipment, data of the state vector at time t Deriving numerical analysis data for each time interval Δt by numerical simulation, the temperature of the molten metal at time t−Δt before the time interval Δt of time t and the temperature at the time t−Δt. Numerical simulation means for performing each of a plurality of cases in which at least one of a flow rate of the molten metal and at least one of parameters of a boundary condition from the time t-Δt to the time t is different; Means from the numerical analysis data at time t of the plurality of cases derived by the means. First probability density function deriving means for deriving a first probability density function of the vector, and an observation vector which is a vector composed of physical quantities at each observation position of the continuous casting facility, using data of the observation vector at time t. Observation data acquisition means for acquiring at each time interval Δt by measuring certain observation data with sensors arranged at each of the observation positions, and the time from the observation data at time t acquired by the observation data acquisition means a likelihood function deriving means for deriving a likelihood function of the state vector at t, the first probability density function of the state vector at time t derived by the first probability density function deriving means, Data based on Bayesian statistical modeling based on the likelihood function of the state vector at the time t derived by the likelihood function deriving means. Derives a second probability density function of the state vector at the time t by a filter performing the transformation, and estimates the state vector at the time t based on the second probability density function of the state vector. Data assimilation means for deriving a value, wherein the plurality of cases when deriving the numerical analysis data at the time t in the numerical simulation means are the plurality of cases at the time t derived by the data assimilation means. The state vector is derived based on the second probability density function of the state vector at the time t-Δt before the time interval Δt.

  The visualization method in a continuous casting mold of the present invention is a method for visualizing a state vector, which is a vector composed of physical quantities at respective calculation positions of a visualization target region of a molten metal injected into a mold of a continuous casting facility, data of the state vector at time t. Deriving numerical analysis data for each time interval Δt by numerical simulation, the temperature of the molten metal at time t−Δt before the time interval Δt of time t and the temperature at the time t−Δt. A numerical simulation step performed for each of a plurality of cases in which at least one of the flow rate of the molten metal and at least one of the parameters of the boundary condition from the time t-Δt to the time t differs. From the numerical analysis data at the time t of the plurality of cases derived by the process, the state database at the time t is obtained. A first probability density function deriving step of deriving a first probability density function of the vector, and an observation vector that is a vector composed of physical quantities at each observation position of the continuous casting facility. Observation data acquisition step of acquiring certain observation data at each of the time intervals Δt by measuring the sensors with the sensors arranged at the respective observation positions, and the time from the observation data at time t acquired by the observation data acquisition step at the time a likelihood function deriving step of deriving a likelihood function of the state vector at t, the first probability density function of the state vector at time t derived by the first probability density function deriving step, Based on the likelihood function of the state vector at the time t derived in the likelihood function derivation step, based on the Bayesian statistics modeling data Derives a second probability density function of the state vector at the time t by a filter performing the transformation, and estimates the state vector at the time t based on the second probability density function of the state vector. A data assimilation step of deriving a value, wherein the plurality of cases when deriving the numerical analysis data at the time t in the numerical simulation step are performed at the time t derived by the data assimilation step. The state vector is derived based on the second probability density function of the state vector at the time t-Δt before the time interval Δt.

  A program according to the present invention causes a computer to function as each unit of the continuous casting mold visualization device.

  According to the present invention, it is possible to visualize the state of molten steel in a mold of a continuous casting facility.

FIG. 1 is a diagram illustrating an example of a functional configuration of a visualization device in a continuous casting mold. FIG. 2 is a diagram illustrating an example of a thermometer embedded in a mold. FIG. 3 is a flowchart illustrating an example of a process performed by the continuous casting mold visualization device. FIG. 4 is a diagram illustrating an example of observation data (temperature). FIG. 5 is a diagram showing an invention example of visualization data. FIG. 6 is a diagram illustrating a comparative example of the visualization data. FIG. 7 is a diagram illustrating an example of a schematic configuration of a continuous casting facility. FIG. 8 is a diagram illustrating an example of a flow of molten steel in a mold.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram illustrating an example of a functional configuration of a visualization device 100 in a continuous casting mold. The hardware of the continuous casting mold visualization device 100 is realized by using, for example, an information processing device having a CPU, a ROM, a RAM, a HDD, and various interfaces, or dedicated hardware. The continuous casting mold visualization device 100 is a device that creates data for visualizing the state of the flow and temperature of molten steel 3 (molten metal) in the mold 4 of the continuous casting facility. In the present invention, deriving the distribution of the physical quantity (flow velocity, temperature, etc.) of the molten steel (solidified shell in some cases) in all or a part of the region in the continuous casting mold is called visualization, and the distribution of the physical quantity of the molten steel is visualized. Is referred to as a visualization target region. In the following description, the visualization device 100 in a continuous casting mold is abbreviated as the visualization device 100 as necessary.

In the present embodiment, the state of the flow and temperature of the molten steel 3 in the mold 4 of the continuous casting facility shown in FIG. 7 is visualized. A thermometer (thermocouple) is embedded in the mold 4. FIG. 2 is a diagram illustrating an example of the thermometers L1 to L12 and F1 to F12 embedded in the mold 4.
As shown in FIGS. 2A to 2C, at a certain height position (position in the casting direction (Z-axis direction)) of the mold 4, one long side surface (“F Plane)), a plurality of thermometers F1, F3, F5, F7, F9, and F9 are located at point-symmetric positions with the center of the long side of the mold 4 in the width direction (X-axis direction) as a symmetric point. F11 is embedded. In addition, at the height position of the mold 4 (position in the casting direction (Z-axis direction)), the other long side surface (referred to as “L surface”) of the mold 4 is located on the long side of the mold 4. A plurality of thermometers L1, L3, L5, L7, L9, L11 are embedded at point-symmetric positions with the center in the width direction (X-axis direction) as the point of symmetry.

  Further, a plurality of thermometers F2, F4, F6, F8, F10, and F12 are embedded below the plurality of thermometers F1, F3, F5, F7, F9, and F11 on the F surface of the mold 4. The positions of the plurality of thermometers F1 to F12 in the depth direction (Y-axis direction) of the mold 4 are the same. The intervals in the X-axis direction of the plurality of thermometers F1, F3, F5, F7, F9, and F11 and the intervals in the X-axis direction of the plurality of thermometers F2, F4, F6, F8, F10, and F12 are the same. is there. Further, the positions of the thermometers F1 and F2 in the X-axis direction, the positions of the thermometers F3 and F4 in the X-axis direction, the positions of the thermometers F5 and F6 in the X-axis direction, the positions of the thermometers F7 and F8 in the X-axis direction, The positions of the thermometers F9 and F10 in the X-axis direction and the positions of the thermometers F11 and F12 in the X-axis direction are the same.

  Similarly, a plurality of thermometers L2, L4, L6, L8, L10, and L12 are embedded below the plurality of thermometers L1, L3, L5, L7, L9, and L11 on the L surface of the mold 4. . The positions of the plurality of thermometers L1 to L12 in the depth direction (Y-axis direction) of the mold 4 are the same. The intervals in the X-axis direction of the plurality of thermometers L1, L3, L5, L7, L9, L11 and the intervals in the X-axis direction of the plurality of thermometers L2, L4, L6, L8, L10, L12 are the same. is there. Further, the positions of the thermometers L1 and L2 in the X-axis direction, the positions of the thermometers L3 and L4 in the X-axis direction, the positions of the thermometers L5 and L6 in the X-axis direction, the positions of the thermometers L7 and L8 in the X-axis direction, The positions of the thermometers L9 and L10 in the X-axis direction and the positions of the thermometers L11 and L12 in the X-axis direction are the same.

  Further, the positions of the plurality of thermometers F1, F3, F5, F7, F9, and F11 on the upper side on the F side of the mold 4 in the Z-axis direction, and the plurality of thermometers L1 and L3 on the upper side of the L side of the mold 4 , L5, L7, L9, and L11 have the same position in the Z-axis direction. The position of the plurality of thermometers F2, F4, F6, F8, F10, and F12 on the lower side of the F surface of the mold 4 in the Z-axis direction, and the plurality of thermometers L2 and L4 of the lower side of the L surface of the mold 4 , L6, L8, L10, and L12 have the same position in the Z-axis direction.

Further, the positions of the thermometers F1 and L1 in the X-axis direction, the positions of the thermometers F3 and L3 in the X-axis direction, the positions of the thermometers F5 and L5 in the X-axis direction, the positions of the thermometers F7 and L7 in the X-axis direction, X-axis positions of thermometers F9 and L9, X-axis positions of thermometers F11 and L11, X-axis positions of thermometers F2 and L2, X-axis positions of thermometers F4 and L4, thermometer The positions of F6 and L6 in the X-axis direction, the positions of thermometers F8 and L8 in the X-axis direction, the positions of thermometers F10 and L10 in the X-axis direction, and the positions of thermometers F12 and L12 in the X-axis direction are the same. is there.
Further, the distance in the Y-axis direction from the F surface (inner wall surface) of the thermometers F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12, and the thermometers L1, L2, L3 , L4, L5, L6, L7, L8, L9, L10, L11, and L12 have the same distance from the L plane (inner wall surface) in the Y-axis direction.
In the following description, the thermometers F1 to F12 and L1 to L12 are collectively referred to as thermometers F and L as necessary.

Next, a description will be given of how the present inventors have reached an embodiment described later.
The present inventors do not process the time-series data from the thermometers F and L and the level gauge 9 with a simple theoretical formula, but use a non-stationary numerical simulator configured on the assumption of a continuous casting facility. I thought about using. According to the time evolution equation derived from the law of conservation of mass, momentum, and energy, concerning the interior of the continuous casting facility, the numerical simulator uses continuous casting so that the balance of those (mass, momentum, and energy) does not contradict. The physical quantity on the calculation grid point of the numerical model for the equipment can be calculated at an arbitrary time. The present inventors fuse the temperature and flow velocity of the molten steel 3 calculated by the numerical simulator with the temperature and flow velocity of the molten steel 3 obtained as observation data, thereby obtaining the flow and the flow of the molten steel 3 in the continuous casting facility. We thought that the state of temperature could be grasped more accurately.

  Further, the physical variables handled by the numerical simulator can be evaluated at any place in the continuous casting facility. Therefore, an output obtained by fusing the observation data and the data calculated by the numerical simulation can be calculated at an arbitrary place in the continuous casting facility. The present inventors thought that, by this, the occurrence of a phenomenon such as drift could be grasped by visualizing the molten steel 3 inside the mold 4.

  In addition, the present inventors, regarding the fusion method of the observation data and the data calculated by the numerical simulator, all of the observation data and the data calculated by the numerical simulator are regarded as information including noise, and It is reasonable to find the state of molten steel not stochastically, but stochastically, and it is effective in performing the calculation process. That is, an equation derived using the Bayes' theorem from the probability density function of the physical quantity to be observed estimated from the observation data and the probability density function of the state of the molten steel in the mold estimated from the data calculated by the numerical simulation. Was used to obtain a more reliable probability density function of the state of molten steel in the mold. Thereby, the influence of observation noise included in each observation data can be considered. At the same time, the influence of system noise included in the data calculated by the numerical simulator can be considered. The system noise included in the data calculated by the numerical simulator includes noise associated with the setting of initial conditions and boundary conditions, noise in the calculation based on the resolution of the calculation grid points, and the accuracy of the physical model used in the calculation by the numerical simulator. Noise caused by the above. By assuming the existence of these noises as a premise of the theory, it is possible to perform a rational analysis in which the observation data and the data calculated by the numerical simulator are compatible.

  From the above circumstances, the present inventors have reached the following embodiments. Hereinafter, an example of a function of the visualization device 100 of the present embodiment will be described. In the present embodiment, a two-dimensional plane (X-Z plane) determined by the width direction (X-axis direction) of the mold 4 and the casting direction (Z-axis direction) at the center position in the depth direction (Y-axis direction) of the mold 4. The case where the state of the flow and the temperature of the molten steel 3 in () is visualized will be described as an example. In addition, as shown in FIG. 2A, the center position in the width direction (X-axis direction) and the depth direction (Y-axis direction) of the mold 4 corresponds to the position of the axis of the immersion nozzle 6. In the following description, this two-dimensional plane is referred to as a visualization target plane as needed. In the present embodiment, the visualization target surface is an example of the visualization target region.

(Numerical simulation unit 101)
The numerical simulation unit 101 performs a numerical simulation of unsteady heat transfer and flow in the continuous casting facility to be visualized using the operation parameters of the continuous casting facility and the physical properties of the molten steel 3. The operation parameters of the continuous casting facility and the physical properties of the molten steel 3 are stored in the numerical simulation unit 101 in advance.

The numerical simulation of heat transfer and flow in the molten steel 3 can be obtained by solving the Navier-Stokes equation together with a continuous equation and an energy conservation equation. For example, a numerical simulation is executed by discretizing and solving each equation using the finite volume method.
When performing a numerical simulation, it is necessary to set initial conditions and boundary conditions. The boundary conditions of the flow and heat transfer are as follows: the inner wall surface of the mold 4, the molten metal surface of the molten steel 3, the outer wall surface of the immersion nozzle 6, the discharge port 7, the boundary surface between the solidified shell 8 and the molten steel 3, the molten steel 3 Is set at the lower end. The lower end of the molten steel 3 refers to the lowest position (the position of the end in the positive direction of the Z axis) in the visualization target area. Initial conditions of flow and heat transfer are set in the molten steel 3.

  At time t, the numerical simulation unit 101 calculates the temperature of the molten steel 3 at the calculation grid point at time t-Δt, the flow velocity of the molten steel 3 at the calculation grid point at time t-Δt, and the time t-Δt to time t. By executing a numerical simulation for each of a plurality of cases in which at least one of at least one of the parameters (for example, heat flux, flow velocity, and pressure) of the boundary condition is different at time t, The temperature and the flow velocity of the molten steel 3 at the calculation grid point are derived. In the present embodiment, a calculation grid point is an example of a calculation position. Note that the flow velocity has three component values in the X-axis direction, the Y-axis direction, and the Z-axis direction. In the present embodiment, the numerical simulation unit 101 derives the temperature and the flow velocity at each calculation grid point at the time interval of the step width Δt. The contents of the Navier-Stokes equation, the continuous equation, the energy conservation equation, and the initial conditions and boundary conditions for the continuous casting facility are described in, for example, Patent Document 3 and Non-Patent Document 1. Detailed description is omitted.

Numerical simulation unit 101, the temperature of the molten steel 3 in the first time t (= t _0), the flow rate of the molten steel 3 in the first time t (= t _0), from time t ₀ to time t ₀ + Delta] t A preset value is used as an initial value for a plurality of cases in which at least one of at least one of the parameters of the boundary condition between them is different. From the second time t onward, the result derived by the data assimilation unit 105 described later based on the observation data (information) acquired by the observation data acquisition unit 103 described later is calculated based on the temperature of the molten steel 3 at the time t. It is used as a parameter of a flow velocity and a boundary condition from time t to time t + Δt. Details of this point will be described later. In the following description, a vector composed of all of the temperature and the flow velocity of the molten steel 3 at the calculation grid point will be referred to as a state vector as necessary, and the temperature and the flow velocity of the molten steel 3 derived by the numerical simulation unit 101 will be referred to as necessary. This is referred to as numerical analysis data.

(First probability density function deriving unit 102)
The first probability density function deriving unit 102 calculates the state at the time t estimated based on the observation data (information) y _{t0: t-Δt} up to the time t-Δt acquired by the observation data acquisition unit 103 described later. A conditional probability density function p (x _t | y _{t0: t−Δt} ) of the vector x _t is derived. The probability density function p (x _t | y _{t0: t−Δt} ) is a probability density function represented by a plurality of numerical analysis data {x _t ^(k) } _k derived by the numerical simulation unit 101. In the following description, this probability density function p ( _xt | _{yt0: t-Δt} ) is also referred to as a first probability density function as needed. In the present embodiment, the first probability density function deriving unit 102 generates the first probability density function p (x _t | y _{t0: t−)} of the state vector x _t at each time t at intervals of the step width Δt. _Δt ) is derived.

The first probability density function deriving unit 102 calculates a relative frequency of a plurality of pieces of numerical analysis data {x _{t | t−Δt} ^(k) } _k at time t derived by the numerical simulation unit 101 (frequency is _expressed by the total data number). The frequency distribution using the divided value is derived. The frequency distribution is the state vector at time t x the first probability density function p of _{t (x t | y t0:} t-Δt) to become. Further, the frequency distribution of each component (each physical quantity at each calculation grid point j) of the plurality of numerical analysis data ｛ _{xt | t-Δt} ^(k) ｝ _k is derived, The frequency distribution of the numerical analysis data ｛ _{xt | t-Δt} ^(k) ｝ _k may be used. Further, those obtained by approximating these frequency distributions with a predetermined function (for example, a spline function) may be used as the first probability density function.

Further, the first probability density function deriving unit 102 uses the plurality of numerical analysis data {x _{t | t−Δt} ^(k) } _k at time t derived by the numerical simulation unit 101 to perform ensemble approximation (Monte Carlo approximation). ) by performing the state vector at time t x the probability density function of _{t p (x t | y t0} : t-Δt) can also be derived.
The first probability density function deriving unit 102, the state vector at time t x the first probability density function p of _{t (x t | y t0:} t-Δt) is assumed to be Gaussian, The average value and the variance may be derived from the plurality of numerical analysis data {x _t ^(k) } _k at time t derived by the numerical simulation unit 101.
Note that the first probability density function deriving unit 102 calculates the first probability density function p (x _t | y _{t0: t−Δt} ) of the state vector x _t at the time t derived as described above. The correction may be performed using noise having a probability density function such as a Gaussian distribution.

(Observation data acquisition unit 103)
The observation data acquisition unit 103 acquires observation data based on time-series data (measured values) measured in the continuous casting facility.
In the present embodiment, the observation data acquisition unit 103 inputs measurement values including the temperature measured by the thermometers F and L (the temperature in the mold 4) and the level measured by the level gauge 9. I do.

  The temperature measured by the thermometers F and L is the temperature of the mold 4, not the temperature of the molten steel 3. Therefore, in the present embodiment, the observation data acquisition unit 103 determines the two thermometers F for each of the total of 12 thermometers F and L facing each other in the depth direction (Y-axis direction) of the mold 4. , L to derive the arithmetic mean value of the temperatures measured at the same time. The set of the two thermometers F and L is a thermometer F1, L1, a thermometer F2, and the like. This gives 12 temperatures. These temperatures are temperatures at positions (coordinates (X, Z)) on the XZ plane where the two thermometers F and L from which the temperatures are derived are located.

The observation data acquisition unit 103 determines the temperature of the cooling water of the mold 4 and the temperature of the mold 4 on the assumption that the heat transfer state on the long side of the mold 4 is one-dimensional steady heat conduction in the depth direction (Y-axis direction). These 12 temperatures are extrapolated based on the thermal conductivity of the molten steel 3 to derive the temperature of the molten steel 3 at each position on the surface to be visualized.
Further, the observation data acquisition unit 103 determines the casting direction at each position corresponding to the molten steel surface of the molten steel 3 on the surface to be visualized from changes in the plurality of molten metal levels per unit time measured by the molten metal level meter 9. The flow velocity in the Z-axis direction is derived.

  As described above, in the present embodiment, the observation data acquisition unit 103 calculates the temperature of the molten steel 3 at each position on the two-dimensional plane to be visualized and the molten metal surface of the molten steel 3 on the two-dimensional plane to be visualized. The flow velocity in the casting direction at each corresponding position is obtained as observation data. In the following description, the position is referred to as an observation position as necessary, and a vector formed of all of the temperature of the molten steel 3 and the flow velocity in the casting direction obtained at the observation position is referred to as an observation vector. In the present embodiment, the observation data acquisition unit 103 extracts time data corresponding to the time when the numerical simulation is performed by the numerical simulation unit 101 from the time-series data measured in the continuous casting facility, and extracts the extracted data. The temperature of the molten steel 3 at each observation position on the two-dimensional plane to be visualized and the flow velocity in the casting direction at each observation position corresponding to the molten metal surface of the molten steel 3 on the two-dimensional plane to be visualized are used. Is obtained as observation data.

(Likelihood function deriving unit 104)
The likelihood function deriving unit 104 calculates the observation data y _t ⁽⁰⁾ at time t acquired by the observation data acquisition unit 103 (y _t ⁽⁰⁾ is the temperature of the molten steel 3 acquired at the observation position and the flow velocity in the casting direction. Of the observation vector y _t when the state vector x _t at the time _t is obtained by evaluating the observation noise of the observation data of the past from the observation data in the past. p (y _t | x _t) the likelihood function of the state vector x _t for the L | to derive the (x _t y _t). Likelihood function L | A (x _t y _t), the conditional probability density function p | which was regarded as a function of (y _t x _t) of the state vector x _t, observation vector y _t the observation data y _t determined as a function of the state vector x _t by substituting ^(0). In the present embodiment, the likelihood function deriving unit 104 derives a likelihood function L (x _t | y _t ) of the state vector x _t at each time t at intervals of the step width Δt.

  The observation noise follows a Gaussian distribution with an average vector of 0 (zero vector), for example, and the variance-covariance matrix of the observation data can be used as the covariance matrix of the observation noise. In this case, the variance-covariance matrix values of past observation data of the same type are calculated in advance for all types of observation data, and the likelihood function deriving unit 104 stores them. That is, the likelihood function deriving unit 104 stores the variance-covariance matrix value for each type of observation data. Also, the variance-covariance matrix value of the observation data may be a variance value of each component (value at each observation position) of the observation data, and the covariance value may be 0 (zero).

Based on observation data y _t ⁽⁰⁾ at time t and the variance-covariance matrix value of observation noise, likelihood function derivation section 104 generates likelihood function L (x _t of state vector x _t at time _t. | Y _t ).

Observation noise is not limited to following a Gaussian distribution. For example, the likelihood function deriving unit 104, the observation data y _t ⁽⁰⁾ at time t, based on with the observed data y _t of a predetermined period of time before the relevant time t ^(0), these multiple observation data ^{_{{y t-nΔt (0)}} , ···, y t (0)} and derives the average vector m of ^(y _t ^(0)), a plurality of data ^{_{{y t-nΔt (0)}} -m A frequency distribution using a relative frequency (a value obtained by dividing the frequency by the total number of data ^{) of} (y _t ⁽⁰⁾ ),..., Y _t ⁽⁰⁾ −m (y _t ⁽⁰⁾ )} is derived. Then, the likelihood function deriving unit 104 derives the frequency distribution as a probability density function of observation noise at time t. Also, each component of each of the plurality of data {y _t−nΔt ⁽⁰⁾ −m (y _t ⁽⁰⁾ ),..., Y _t ⁽⁰⁾ −m (y _t ⁽⁰⁾ )} (each observation position i ), And the product of these values is taken as a plurality of data {y _{t -nΔt} ⁽⁰⁾ -m (y _t ⁽⁰⁾ ), ..., y _t ⁽⁰⁾ A frequency distribution of −m (y _t ⁽⁰⁾ )｝ may be used. Also, the likelihood function deriving unit 104 may use the frequency distribution approximated by a predetermined function (for example, a spline function) as the probability density function of the observation noise.

(Data assimilation unit 105)
The data assimilation unit 105 calculates the first probability density function p (x _t | y _{0: t−Δt} ) of the state vector x _t at the time t derived by the first probability density function derivation unit 102 and the likelihood The likelihood function L (x _t | y _t ) of the state vector x _t at the time t when the observation data at the time t derived by the function deriving unit 104 is obtained is based on Bayes' theorem. To the algorithm of a filter that performs data assimilation by modeling of the Bayesian statistics obtained, the conditional probability density function p (x _t | y of the state vector x _t at the time t when the observation data up to the time t is obtained. _{t0: t} ) is derived. In the following description, this probability density function p ( _xt | _{yt0: t} ) is also referred to as a second probability density function as needed. In the present embodiment, the data assimilation unit 105 derives a second probability density function p (x _t | y _{0: t} ) of the state vector x _t at each time t at intervals of the step width Δt.

When performing data assimilation, it is necessary to define a system equation (state equation) and an observation equation. System equation is the time interval of the step width Delta] t, an equation defining a relationship between the state vector x _{t + Δt,} x _t before and after the time. In the present embodiment, this relationship is determined by a plurality of numerical simulations by the numerical simulation unit 101. The observation equation shows a relational expression between the observation data y _t and the state vector x _t, and is given by Expression (1).
y _t = H _t x _t + w _t (1)
Here, _Ht is an observation matrix, and _wt is observation noise. For example, if the i-th component of the observation vector is the same as the physical quantity of the j-th component of the state vector, the observation matrix _Ht has the (i, j) component of 1 and the other components of the i-th row being 0 ( Zero). Also, the observation position i do not match any calculation grid point j, it is also possible to define the observation matrix H _t so as to interpolate a state vector.

For example, an ensemble Kalman filter can be used as a filter that performs data assimilation by modeling Bayesian statistics.
In this case, the data assimilation unit 105 calculates the first probability density function p (x _t | y _{0: t−Δt} ) of the state vector x _t at the time t derived by the first probability density function derivation unit 102. , likelihood function L of the state vector x _t at the time t is derived by the likelihood function deriving unit 104 | a (x _t y _t), and ensemble approximation to derive an ensemble member (particles). Each ensemble member x _t-Δt ^(k) at time t-Δt is updated based on the system equation, and the ensemble x _{t | t-Δt} ^(k) of the predicted distribution one period ahead (time t) is set to the first. Derived by the probability density function deriving unit 102. The data assimilation unit 105, ensemble x _t predictive distribution one stage forward _| from _t-Δt ^(k), and derives a filter distribution ensemble x _t ^(k). By deriving such an ensemble of the filter distribution, a second probability density function of the state vector x _t at the time t is derived.

  In the continuous casting facility, it is not possible to measure the flow velocity of the molten steel 3 at all positions. However, in the system equations, the temperature and the flow velocity of the molten steel 3 are coupled, so that the probability density function of the state vector includes the probability density function of the flow velocity of the molten steel 3. In the present embodiment, the flow velocity of the molten steel 3 in the casting direction on the molten metal surface is measured. The accuracy of the density function can be improved.

  A filter that performs data assimilation by modeling Bayesian statistics is not limited to the ensemble Kalman filter. For example, a particle filter may be used. Non-Patent Documents 2 and 3 describe ensemble Kalman filters and particle filters. Non-Patent Document 4 describes a specific calculation algorithm for the ensemble Kalman filter and the particle filter. Therefore, a detailed description thereof will be omitted.

Data assimilation unit 105, the second probability density function p of the state vector x _t at time t | deriving the mode x _m of (x _t y _t), as an estimate of the state vector x _t at time t I do. Further, the respective components of the state vector x _t (the physical quantity in each calculation grid point j), the second probability density function p | derives marginal probability density function of (x _t y _t), each of the marginal probability density function the vector consists of the mode of the component second probability density function p | may be the mode x _m of (x _t y _t).
As described above, in the present embodiment, the data assimilation unit 105 sets the first probability density function p (x _t | y ₀ of the state vector x _t at the time t derived by the first probability density function derivation unit 102. _{: t−Δt} ) and the likelihood function L (x _t | y _t ) of the state vector x _t at the time t derived by the likelihood function deriving unit 102 to obtain the most reasonable value at the time t. A second probability density function p (x _t | y _t ) of the typical state vector x _t is derived, and its mode x _m is derived as an estimated value of the state vector x _t at time t.

Further, the data assimilation unit 105 outputs the probability density function p (x _t | y _t ) of the state vector x _t to the numerical simulation unit 101. The numerical simulation unit 101 calculates the temperature and the flow rate of the molten steel 3 at the time t and the time t to the time t + Δt based on the second probability density function p (x _t | y _t ) of the state vector x _t . A plurality of parameters of the boundary condition are derived. For example, the data assimilation unit 105 uses the ensemble members in the second probability density function p (x _t | y _t ) of the state vector x _t to calculate the temperature and flow velocity of the molten steel 3 at the time t, and the time from the time t to the time A plurality of parameters of the boundary condition up to t + Δt are set. Then, the numerical simulation unit 101 derives a plurality of numerical analysis data at the next time t + Δt.

(Visualization data creation unit 106)
The visualization data creation unit 106 creates display data of at least one of the temperature and the flow velocity of the molten steel 3 at each position constituting the estimated value of the state vector at the time t derived by the data assimilation unit 105.
The visualization data creation unit 106 may create any display data as long as the user of the visualization device 100 can recognize the temperature and the flow velocity of the molten steel 3 at each position at each time. However, it is preferable that the visualization data creation unit 106 creates display data that is easy for the user of the visualization device 100 to intuitively understand.

  For example, when the temperature range assumed as the temperature of the molten steel 3 is divided into a plurality of regions, the visualization data creating unit 106 stores different display modes for each region in advance. As the display mode, for example, at least one of a color, a pattern, and a density can be adopted. The visualization data creation unit 106 specifies the temperature at each position from the temperature of the molten steel 3 at each position at the time t derived by the data assimilation unit 105, and the image at each position on the surface to be visualized becomes the specified temperature. Display data is created so as to be displayed in a corresponding display mode.

  In addition, when the flow velocity range assumed as the flow velocity of the molten steel 3 is divided into a plurality of regions, the visualization data creation unit 106 stores different display modes for each region in advance. As the display mode, for example, at least one of a color, a pattern, and a density can be adopted. The visualization data creation unit 106 specifies the flow velocity at each position from the flow velocity of the molten steel 3 at each position at the time t derived by the data assimilation unit 105, and the image at each position on the visualization target surface corresponds to the specified flow velocity. Display data is created so as to be displayed in a corresponding display mode. In addition, the visualization data creating unit 106 derives a representative direction of the molten steel 3 for each region set in advance with respect to the visualization target surface, and an arrow line pointing in the direction indicates the direction of the region on the visualization target surface. Create display data to be displayed over the image.

(Output unit 107)
The output unit 107 displays the display data created by the visualization data creating unit 106 on a computer display. In addition, instead of or in addition to such display data, the output unit 107 outputs the data of the temperature and the flow velocity of the molten steel 3 at each position constituting the estimated value of the state vector at each time derived by the data assimilation unit 105. Can be output. Examples of the output mode include transmission to a storage medium inside or outside the visualization device 100 and transmission to an external device. By doing so, display data for displaying the temperature and flow velocity of the molten steel 3 at each position at each time can be separately created later.

(Operation flowchart)
Next, an example of the processing of the visualization device 100 will be described with reference to the flowchart of FIG.
First, in step S301, the numerical simulation unit 101 sets the time t to an initial value (t ₀ ).
Next, in step S302, the numerical simulation unit 101 sets the temperature and flow velocity of the molten steel 3 at time t, and the initial values of the parameters of the boundary conditions from time t to time t + Δt.

Next, in step S303, the numerical simulation unit 101 updates time t to time t + Δt, and the process proceeds to step S304.
Next, in step S304, the numerical simulation unit 101 derives the temperature and flow velocity of the molten steel 3 at the calculation grid point at time t.

Next, in step S305, the first probability density function deriving unit 102 determines the first probability density function p (x) of the state vector x _t (temperature and flow velocity of the molten steel 3 at each calculation grid point j) at time t. _t | y _t−Δt ).
Next, in step S306, the observation data acquisition unit 103 acquires the observation data y _t ⁽⁰⁾ (the temperature of the molten steel 3 at each observation position i and the flow velocity in the casting direction (Z-axis direction)) at time t.

Next, in step S307, the likelihood function deriving unit 104 derives a likelihood function L (x _t | y _t ) of the state vector x _t at time t based on the observation data y _t ⁽⁰⁾ .
Next, in step S308, the data assimilation unit 105, a first probability density function p of the state vector x _t at time _{t (x t | y 0:} t-Δt) and the state vector x in the time t _t of the likelihood function L | a (x _t y _t), by providing a filter algorithm to perform data assimilation by modeling Bayesian statistics, the second probability density function p of the state vector x _t at time t ( x _t | y _{t0: t} ).

Next, in step S309, the data assimilation unit 105 estimates the mode value of the second probability density function p (x _t | y _t ) of the state vector x _t at time t by estimating the state vector at time t. Derived as a value.
Next, in step S310, the visualization data creation unit 106 creates display data of the temperature and the flow velocity of the molten steel 3 at each position constituting the estimated value of the state vector at the time t derived by the data assimilation unit 105.

Next, in step S311, the output unit 107 determines whether the time t has reached a preset time T. If the result of this determination is that the time t has not reached the preset time T, the process proceeds to step S312.
In step S312, the numerical simulation unit 101 transmits the temperature and flow velocity of the molten steel 3 at time t, which is data used in the numerical simulation, and the parameters of the boundary conditions from time t to time t + Δt in step S307. derived by the assimilation unit 105, the second probability density function p of the state vector x _t at time _{t (x t | y t0:} t) is derived based on.

Then, the process proceeds to step S303, and the processes of steps S303 to S312 are repeatedly executed until the time t reaches a preset time T. In step S304, the parameters of the temperature and flow velocity of the molten steel 3 and the boundary conditions derived in step S312 immediately before step S304 are used.
When the time t reaches the preset time T as described above, the process proceeds to step S313. In step S313, the output unit 107 outputs the visualized data (the display data created by the visualized data creation unit 106 and the molten steel 3 at each position constituting the estimated value of the state vector at each time derived by the data assimilation unit 105). Temperature and flow velocity data). The display data may be displayed on the computer display every time the display data is created in step S309.

(Example)
Next, examples will be described, but the present invention is not limited to the following examples.
In this embodiment, the visualization device 100 visualized the continuous steel casting machine having the configuration shown in FIG. The length of the long side of the mold 4 is 1500 mm, and the length of the short side is 250 mm.

  In the present embodiment, the numerical simulation unit 101 does not consider generation of the solidified shell 8 (that is, assuming that the solidified shell 8 is not generated), and uses the finite volume method to determine each position of the visualization target surface at each time t. The flow velocity and temperature of the molten steel 3 at were calculated. The width (length in the X-axis direction) of the surface to be visualized was 1500 mm, and the depth (length in the Z-axis direction) was 5000 mm. 2600 calculation grid points were set in the area of the surface to be visualized. In addition, necessary physical properties such as thermal conductivity, specific heat, density, and viscosity coefficient of the molten steel 3 were set.

  Further, the heat transfer boundary conditions were such that a constant heat flux was provided at the outer peripheral boundary of the molten steel 3. The boundary conditions of the flow are such that a vertical component (component in the Z-axis direction) of the flow velocity is given on the surface of the molten steel 3, and the inner wall surface of the mold 4, the outer wall surface of the immersion nozzle 6, the lower end of the molten steel 3, , All the components of the flow velocity are given, and pressure is given to the discharge port 7. Then, 0 (zero) was set (slip condition) as an initial value of the vertical component (component in the Z-axis direction) of the flow velocity on the molten metal surface. The initial values of all components of the flow velocity on the inner wall surface of the mold 4 and the outer wall surface of the immersion nozzle 6 were set to 0 (zero). Further, as initial values of the flow velocity at a position 5000 mm below the molten metal surface (positive direction of the Z axis) (the lower end of the molten steel 3), the X axis direction is 0 (zero), and the Z axis direction is the casting speed (casting speed). (Drawing speed of the piece). The initial value of the pressure at the discharge port 7 has a value other than 0 (zero) at the boundary with the outer wall surface of the immersion nozzle 6, but the average value thereof is set to 0 (zero).

The numerical simulation unit 101 calculates the values of the temperature and the flow velocity of the molten steel 3 at each calculation grid point j at the time t, the heat flux distribution on the outer periphery of the molten steel 3 from the time t to the time t + Δt, Enter pressure and casting speed. Then, numerical simulation section 101 updates time t to time t + Δt, and calculates the temperature and flow velocity of molten steel 3 at each calculation grid point j at time t by numerical simulation. Thereby, numerical analysis data x _t ^(k) (temperature and flow velocity of molten steel 3 at each calculation grid point j ⁾ at each time t is obtained.

At each time t, the numerical simulation unit 101 calculates the temperature of the molten steel 3 at the time t-Δt, the flow velocity of the molten steel 3 at the time t-Δt, and the boundary conditions from the time t-Δt to the time t. Numerical simulation is performed simultaneously and simultaneously for each of up to 100 cases in which at least one of the parameters differs from at least one of the parameters. Thereby, at each time t, a large number of calculation results (an ensemble {x _t ^(k) ｝ _k ) of numerical analysis data (temperature and flow velocity of the molten steel 3 at each calculation grid point j) are obtained.
The first probability density function deriving unit 102 calculates the number of calculation results (an ensemble {x _t ^(k) ｝ _k ) of numerical analysis data (temperature and flow velocity of the molten steel 3 at each calculation grid point j) at each time t. _Derives a first probability density function p (x _t | y _t-Δt ) of the state vector x _t of

In this example, observation data was obtained using the temperatures measured by the thermometers F1 to F12 and L1 to L12 embedded in the mold 4.
The thermometers F1 to F12 and L1 to L12 are arranged as shown in FIG. Therefore, in order to correspond to the numerical simulation of the measurement target surface of the visualization device 100, the observation data acquisition unit 103 calculates a total of 12 thermometers F and L facing each other in the depth direction (Y-axis direction) of the mold 4. For each of the sets, an arithmetic average of the temperatures measured at the same time by the two thermometers F and L is derived. Then, the observation data acquisition unit 103 calculates the arithmetic average value of the position (coordinates (X, Z)) on the XZ plane where the two thermometers F and L from which the temperature is derived exist. The temperature is used, and the time series data is obtained. The observation data acquisition unit 103 extrapolates the time series data of the twelve temperatures obtained in this manner based on the temperature of the cooling water of the mold 4 and the thermal conductivity of the mold 4 to obtain each of the visualization target surfaces. The temperature of the molten steel 3 at the observation position i is derived as observation data y _t ⁽⁰⁾ .

  FIG. 4 is a diagram illustrating an example of observation data (temperature). In FIG. 4, the numerical values correspond to the numbers of the thermometers F1 to F12 and L1 to L12 shown in FIG. For example, “1” shown in FIG. 4A indicates observation data derived based on the arithmetic mean value of the temperatures measured at the same time by the thermometers F1 and L1.

The likelihood function deriving unit 104 calculates a plurality of observation data ｛y _t-nΔt ⁽⁰⁾ ,... Derived as observation noise of the observation vector y _t during a certain period (for example, 6 hours or 24 hours) immediately before measurement. , Y _t ⁽⁰⁾ }. In the present embodiment, the likelihood function deriving unit 104 assumes that the observation noise at time t follows a Gaussian distribution with an average vector of 0 (zero vector), and calculates the variance-covariance matrix value. Thus, the likelihood function L of the state vector x _t at each time _t (x t | y t) is obtained.

Data assimilation unit 105, a first probability density function p of the state vector x _t at each time _{t (x t | y 0:} t-Δt) and, the likelihood function L of the state vector x _t at each time t By applying (x _t | y _t ) to the algorithm of the ensemble Kalman filter, a filter operation is performed. Thus, a second probability of the state vector x _t at time t density function _{p (x t | y t0:} t) is obtained. In (1), the observation matrix H _t is set to derive the temperature of the molten steel 3 at each observation position i from the state vector x _t, observation noise w _t is the mean vector of 0 (zero vector), variance covariance matrix, the thermometer F1 to F12, the variance of the last 24 hours of the variation of the observed data y _t evaluated at the position of the L1 to L12, the covariance value is set to 0 (zero).

Data assimilation unit 105, the second probability density function p of the state vector x _t at time _{t (x t | y t0:} t) deriving the mode of, as an estimate of the state vector x _t at time t I do.

Further, the numerical simulation unit 101 calculates the molten steel 3 at the time t from the second probability density function p (x _t | y _{t0: t} ) of the state vector x _t at the time t derived by the data assimilation unit 105. Approximately 100 sets of parameters of the temperature and flow velocity and the boundary conditions from time t to time t + Δt are constructed at random, and a numerical simulation from time t to time t + Δt is performed. New boundary conditions, only the distribution of pressure at the location of the discharge port 7 of the immersion nozzle 6, the second probability density function of the state vector x _t at time _{t p (x t | y t0} : t) Based The other boundary conditions were fixed as they were at the beginning of the change. The time interval Δt was 10 seconds.

  The visualization data creation unit 106 creates the visualization data based on the temperature and the flow velocity of the molten steel 3 at each position constituting the estimated value of the state vector at the time t, derived by the data assimilation unit 105. The output unit 107 displays the visualized data on the computer display every time the visualized data is generated by the visualized data generating unit 106.

  FIG. 5 is a diagram showing an invention example of visualization data. In FIG. 5, the magnitude of the flow velocity vector is indicated by an isoline, and the direction of the flow velocity vector is indicated by the direction of an arrow line. Further, in FIG. 5, the visualization data obtained every 100 seconds from the time 100 seconds to 900 seconds is shown in order (the numerical value shown below each image in FIG. 5 represents the time). In FIG. 5, only the flow velocity of the molten steel 3 is shown as visualization data.

  FIG. 5 clearly shows that the molten steel 3 injected into the mold 4 separately from the immersion nozzle 6 into the mold 4 does not flow symmetrically but changes every moment. For example, around the time of 100 seconds to 200 seconds, the immersion nozzle 6 discharged and flowed in the horizontal direction more strongly on the left side than the right side. It can be seen that the flow is strong on the left side per second, and is strong on the right side again at time 900 seconds. As described above, in this example, it was confirmed that the state of drift of the molten steel 3 that changes momentarily was visualized.

  FIG. 6 is a diagram illustrating a comparative example of the visualization data. 6, only the flow rate of the molten steel 3 is shown as visualization data, as in FIG. In the comparative example, the visualization device 100 was operated without inputting observation data based on the temperatures measured by the thermometers F1 to F12 and L1 to L12. As shown in FIG. 6, the molten steel 3 flowed almost symmetrically at any time. However, at this time, the temperatures measured by the thermometers F1 to F12 and L1 to L12 changed in a range of several degrees Celsius in a cycle of about 100 seconds in substantially the same manner as in the invention example (see FIG. 4). In the data, the temperature of the molten steel 3 hardly changed with time, and it was not possible to express a drift.

(Summary)
As described above, in the present embodiment, the visualization device 100 determines the first probability density function p (x _t | y _{0: t−Δt} ) of the state vector x _t at the time t and the state vector at the time t. likelihood function L of x _t (x _t | y _t) and the, by providing a filter algorithm to perform data assimilation, a second probability of the state vector x _t at time t density function p (x _t | y _{0: t} ). The visualization device 100 derives the mode value of the second probability density function p (x _t | y _{0: t} ) as the estimated value of the state vector x _t at time t. The visualization apparatus 100, the second probability density function _{p (x t | y 0:} t) based on the temperature and flow rate of the molten steel 3 to determine the numerical analysis data x _t at time t + Delta] t, and boundary Deriving multiple condition parameters. Therefore, the flow and temperature distribution of the molten metal in the continuous casting machine can be visualized as facts based on observation data and rational numerical data obtained by numerical simulation based on the laws of physics. You can know the occurrence of the phenomenon moment by moment. Therefore, it becomes possible to flexibly control the operating conditions of the casting, change the problematic member, and perform the replacement with good timing, and produce a high-quality steel material with good yield and high productivity. .

In the present embodiment, the visualization device 100 derives the mode value of the second probability density function p (x _t | y _{0: t} ) as the estimated value of the state vector x _t at the time t. The average value of the second probability density function p (x _t | y _{0: t} ) may be derived as an estimated value of the state vector x _t at time t, or the second probability density function p (x _t | Y _{0: t} ) may be derived as an estimate of the state vector x _t at time t.
Further, in the present embodiment, the visualization target region is limited to the region where the molten steel 3 exists, but may be a region where the molten steel 3 and the solidified shell 8 exist. In this case, the numerical simulation unit 101 may perform a numerical simulation of unsteady heat transfer and flow accompanied by solidification using the physical property values of the molten steel 3, the physical property values of the solidified shell 8, and the latent heat of solidification.

The embodiments of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, and the like can be used.
In addition, the embodiments of the present invention described above are merely examples of specific embodiments for carrying out the present invention, and the technical scope of the present invention should not be interpreted in a limited manner. Things. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features.

  1: ladle, 2: tundish, 3: molten steel, 4: mold, 5: sliding nozzle, 6: immersion nozzle, 7: discharge port, 8: solidified shell, 9: level gauge, 100: continuous casting mold Internal visualization device, 101: numerical simulation unit, 102: first probability density function derivation unit, 103: observation data acquisition unit, 104: likelihood function derivation unit, 105: data assimilation unit, 106: visualization data creation unit, 107 : Output unit, F1 to F12, L1 to L12: thermometer

Claims (8)

For a state vector that is a vector composed of physical quantities at each calculation position of the visualization target region of the molten metal injected into the mold of the continuous casting equipment, numerical analysis data that is data of the state vector at time t is subjected to time interval by numerical simulation. To derive for each Δt, the temperature of the molten metal at the time t-Δt before the time interval Δt of the time t, the flow rate of the molten metal at the time t-Δt, and the time t-Δt Numerical simulation means for performing each of a plurality of cases in which at least one of at least one of the parameters of the boundary condition is different from t to the time t;
First probability density function deriving means for deriving a first probability density function of the state vector at the time t from numerical analysis data at the time t of the plurality of cases derived by the numerical simulation means;
For the observation vector that is a vector composed of physical quantities at each observation position of the continuous casting facility, the time interval is obtained by measuring observation data that is the data of the observation vector at time t with a sensor arranged at each observation position. Observation data acquisition means for acquiring for each Δt;
A likelihood function deriving unit that derives a likelihood function of the state vector at the time t from observation data at the time t acquired by the observation data acquiring unit;
The first probability density function of the state vector at the time t derived by the first probability density function deriving means, and the state probability vector of the state vector at the time t derived by the likelihood function deriving means. A second probability density function of the state vector at the time t is derived by a filter that performs data assimilation by modeling of Bayesian statistics based on the likelihood function and the second probability density function of the state vector Data assimilation means for deriving an estimated value of the state vector at the time t based on
Has,
The plurality of cases in deriving the numerical analysis data at the time t in the numerical simulation means may include the time t-Δt at the time interval Δt before the time t derived by the data assimilation means. A continuous casting mold visualization device, which is derived based on the second probability density function of a state vector.   There is further provided visualization data creation means for creating display data of the physical quantity at each calculation position of the visualization target area at time t based on the estimated value of the state vector at time t derived by the data assimilation means. The visualization device in a continuous casting mold according to claim 1, wherein:   The method according to claim 1, wherein the data assimilation unit derives a mode value of a second probability density function of the state vector at time t as an estimated value of the state vector at time t. The visualization device in a continuous casting mold as described in the above.   The visualization in the continuous casting mold according to any one of claims 1 to 3, wherein the physical quantity at each calculation position of the visualization target area includes at least one of a temperature and a flow velocity of the molten metal. apparatus.   The sensor includes at least one of a plurality of thermometers embedded in the mold and a level gauge for measuring a position of the molten metal in a height direction. The visualization device in a continuous casting mold according to any one of claims 1 to 4.   The visualization device according to any one of claims 1 to 5, wherein the filter is an ensemble Kalman filter or a particle filter. For a state vector that is a vector composed of physical quantities at each calculation position of the visualization target region of the molten metal injected into the mold of the continuous casting equipment, numerical analysis data that is data of the state vector at time t is subjected to time interval by numerical simulation. To derive for each Δt, the temperature of the molten metal at the time t-Δt before the time interval Δt of the time t, the flow rate of the molten metal at the time t-Δt, and the time t-Δt A numerical simulation step performed for each of a plurality of cases in which at least one of at least one of the parameters of the boundary condition is different from t to the time t;
A first probability density function deriving step of deriving a first probability density function of the state vector at the time t from the numerical analysis data at the time t of the plurality of cases derived by the numerical simulation step;
For the observation vector that is a vector composed of physical quantities at each observation position of the continuous casting facility, the time interval is obtained by measuring observation data that is the data of the observation vector at time t with a sensor arranged at each observation position. An observation data acquisition step for acquiring at each Δt;
A likelihood function deriving step of deriving a likelihood function of the state vector at the time t from the observation data at the time t acquired in the observation data acquiring step;
The first probability density function of the state vector at the time t derived by the first probability density function deriving step; and the state vector at the time t derived by the likelihood function deriving step. A second probability density function of the state vector at the time t is derived by a filter that performs data assimilation by modeling of Bayesian statistics based on the likelihood function and the second probability density function of the state vector A data assimilation step of deriving an estimated value of the state vector at the time t based on
Has,
The plurality of cases in deriving the numerical analysis data at the time t in the numerical simulation step include the time t-Δt at the time interval Δt before the time t derived in the data assimilation step. A visualization method in a continuous casting mold, which is derived based on the second probability density function of a state vector.   A non-transitory computer-readable storage medium storing a program for causing a computer to function as each unit of the continuous casting in-mold visualization device according to claim 1.