JP7016706B2 - Equipment monitoring equipment, equipment monitoring methods, and programs - Google Patents

Description

The present invention relates to equipment monitoring equipment, equipment monitoring methods, and programs, and is particularly suitable for use in monitoring the state of refractories constituting the inner peripheral surface of equipment in which molten metal is present.

Examples of the furnace for producing molten metal include a submerged arc furnace (SAF) and an electric furnace. The submerged arc furnace is also referred to as a resistance heating type melting treatment furnace, a closed electric iron making furnace, or the like. In a submerged arc furnace, a raw material molded into a predetermined shape is melted by being energized and heated by an electrode. In an electric furnace, iron scrap is melted by arc discharge. In such a furnace, the temperature inside the furnace becomes high, so refractory materials such as refractory bricks are arranged on the inner peripheral surface of the furnace.

Since refractories are exposed to high-temperature molten metal (hot metal, slag, etc.), some of them are melted or peeled off with the use of the furnace, resulting in wear. Therefore, a technique for monitoring the state of wear of refractories is required. As this kind of technique, there is a technique described in Patent Documents 1 and 2.

In Patent Document 1, a temperature sensor is arranged inside a refractory material of an electric furnace, and the difference between the time when the energization starts and the time when the temperature measured by the temperature sensor becomes the maximum value is monitored as a delay time. This shortening of the delay time corresponds to the close distance between the temperature sensor and the molten metal. Utilizing this fact, when the delay time is shorter than the preset reference time, it is determined that the refractory erosion is progressing.

In Patent Document 2, a temperature sensor is arranged inside a fire-resistant material of an electric furnace, and the temperature measured by the temperature sensor is measured by the temperature sensor by utilizing the fact that the amount of wear of the fire-resistant material is in a proportional relationship. It is stated that the amount of wear of the fireproof material can be estimated from the above temperature.

Japanese Unexamined Patent Publication No. 3-223658 Japanese Unexamined Patent Publication No. 8-94264 JP-A-2015-227733 Japanese Patent No. 3403093

However, in the technique described in Patent Document 1, since it is determined whether or not the refractory is eroded by comparing the delay time with the reference time, it is possible to know exactly how much the refractory is worn. It's not easy. Further, it is not easy to set the set value of the reference time so that a desired determination result can be obtained. Furthermore, it is only possible to determine if refractory erosion has occurred at a specific time.

Further, in the technique described in Patent Document 2, the relationship between the temperature measured by the temperature sensor and the amount of wear of the refractory must be prepared in advance offline. Further, in the technique described in Patent Document 2, the residual thickness of the refractory is calculated from the measured value of the temperature of the refractory and the thermal conductivity of the refractory. However, it is not easy to calculate the residual thickness of the refractory with high accuracy only by considering the measured value of the temperature of the refractory and the thermal conductivity of the refractory. Therefore, it is not easy to accurately determine the degree of wear of the refractory.

In addition, the temperature measured by the temperature sensor changes with each charge. Therefore, the residual thickness of the refractory differs depending on the time point at which the temperature is measured. In the same charge, the residual thickness of the refractory does not change according to the change in temperature measured by the temperature sensor. Therefore, in the technique described in Patent Document 2, the temperature measured by the temperature sensor used to obtain the residual thickness of the refractory in each charge must be the temperature under a predetermined common condition. Patent Document 2 shows an example in which the temperature measured by the temperature sensor used to determine the residual thickness of the refractory is the maximum temperature at each charge. Therefore, even in the technique described in Patent Document 2, the timing for obtaining the residual thickness of the refractory is limited.

The present invention has been made in view of the above problems so that the state of the refractory constituting the inner peripheral surface of the equipment in which the molten metal exists can be accurately monitored in real time. The purpose is to do.

The equipment monitoring device of the present invention is equipment in which molten metal is present inside, has a fire-resistant material constituting the inner peripheral surface of the equipment, and is in a state where the inside of the fire-resistant material is in contact with the molten metal or other. An equipment monitoring device that monitors equipment that is arranged with substances in between and is arranged with the outside of the fireproof material in contact with the cooling medium or with other substances in between. The temperature measured by the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means, which are arranged at different positions inside the fireproof material, and the temperature of the cooling medium are measured. Using the temperature acquisition means for acquiring the temperature measured by the temperature measuring means of No. 4, the temperature measured by the first temperature measuring means, and the temperature measured by the second temperature measuring means. The temperature on the surface of the outer part of the equipment, which is the part where the outside of the fireproof material is in contact with the cooling medium or the part in contact with the substance existing between the cooling medium, and the surface of the outer part of the equipment. The first derivation means for deriving the value of the component of the heat flux vector in the heat transfer direction of the fireproof material based on the result of the one-dimensional non-stationary heat transfer reverse problem analysis, and the outside of the equipment. Measured by a fourth temperature measuring means for measuring the temperature on the surface of the portion , the value of the component of the heat transfer vector on the surface of the outer portion of the equipment in the heat removal direction of the fireproof material, and the temperature of the cooling medium. A second derivation means for deriving a heat transfer coefficient between the material constituting the refractory material and the cooling medium, and a temperature measured by the third temperature measuring means, and the temperature measured by the third temperature measuring means. Using the heat transfer coefficient derived by the second derivation means, the temperature matching position, which is the position in the heat removal direction of the fireproof material where the temperature of the molten metal becomes equal to the temperature, and the molten metal of the equipment. A third derivation means for deriving the value of the component of the heat flux vector on the surface of the contacting portion in the heat removal direction of the refractory material based on the result of one-dimensional non-stationary heat transfer reverse problem analysis. The position of the first temperature measuring means in the direction perpendicular to the heat transfer direction of the fireproof material and the position of the second temperature measuring means in the direction perpendicular to the heat transfer direction of the fireproof material are substantially the same. Yes, the position of the third temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material and the position perpendicular to the heat removal direction of the fireproof material of the first temperature measuring means and the second temperature measuring means. It is characterized in that the positions in different directions are different.

The equipment monitoring method of the present invention is a facility in which molten metal is present inside, has a fire resistant material constituting the inner peripheral surface of the facility, and is in a state where the inside of the fire resistant material is in contact with the molten metal or other. It is an equipment monitoring method for monitoring equipment having a configuration in which substances are arranged in a state where they are present in between and the outside of the fireproof material is in contact with a cooling medium or in a state where other substances are present in between. The temperature measured by the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means, which are arranged at different positions inside the fireproof material, and the temperature of the cooling medium are measured. Using the temperature acquisition step of acquiring the temperature measured by the temperature measuring means of No. 4, the temperature measured by the first temperature measuring means, and the temperature measured by the second temperature measuring means. The temperature on the surface of the outer part of the equipment, which is the part where the outside of the fireproof material is in contact with the cooling medium or the part in contact with the substance existing between the cooling medium, and the surface of the outer part of the equipment. The first derivation step of deriving the value of the component of the heat flux vector in the heat transfer direction of the fireproof material based on the result of the one-dimensional non-stationary heat transfer reverse problem analysis, and the outside of the equipment. Measured by a fourth temperature measuring means for measuring the temperature on the surface of the portion , the value of the component of the heat transfer vector on the surface of the outer portion of the equipment in the heat removal direction of the fireproof material, and the temperature of the cooling medium. The second derivation step of deriving the heat transfer coefficient between the material constituting the refractory material and the cooling medium using the obtained temperature, and the temperature measured by the third temperature measuring means, Using the heat transfer coefficient derived by the second derivation step, the temperature matching position, which is the position in the heat removal direction of the fireproof material where the temperature of the molten metal becomes equal to the temperature, and the molten metal of the equipment. A third derivation step of deriving the value of the component of the heat flux vector on the surface of the contacting portion in the heat removal direction of the refractory material based on the result of one-dimensional non-stationary heat transfer reverse problem analysis. The position of the first temperature measuring means in the direction perpendicular to the heat transfer direction of the fireproof material and the position of the second temperature measuring means in the direction perpendicular to the heat transfer direction of the fireproof material are substantially the same. Yes, the position of the third temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material and the position perpendicular to the heat removal direction of the fireproof material of the first temperature measuring means and the second temperature measuring means. It is characterized in that the positions in different directions are different.

The program of the present invention is for making a computer function as each means of the equipment monitoring device.

According to the present invention, it is possible to accurately monitor the state of the refractory material constituting the inner peripheral surface of the equipment in which the molten metal is present in real time.

It is a figure which shows an example of the structure of the submerged arc furnace. It is a figure which shows an example of the functional configuration of the equipment monitoring apparatus. It is a figure which shows an example of the coordinate system of the unsteady heat transfer inverse problem in the 1st inverse problem analysis part. It is a figure which shows an example of the coordinate system of the unsteady heat transfer inverse problem in the 2nd inverse problem analysis part. It is a figure which shows an example of the calculation result by the equipment monitoring apparatus. It is a flowchart explaining an example of the equipment monitoring method using the equipment monitoring apparatus.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In this embodiment, a submerged arc furnace will be described as an example of equipment in which molten metal is present. Therefore, first, an outline of the configuration of the submerged arc furnace will be described. Since the configuration of the submerged arc furnace itself is realized by the known techniques described in Patent Documents 3, 4, etc., the outline thereof will be described here and detailed description thereof will be omitted. The submerged arc furnace may have a configuration different from that described below as long as it has a configuration in which a raw material molded into a predetermined shape is melted by energizing and heating with an electrode.

(Composition of submerged arc furnace)
FIG. 1 is a diagram showing an example of the configuration of a submerged arc furnace 100. FIG. 1A is a diagram showing the overall configuration of the submerged arc furnace 100. FIG. 1B is a perspective view of the bottom of the submerged arc furnace 100, and is a diagram illustrating the position of the thermometer embedded in the refractory material constituting the bottom of the submerged arc furnace 100. .. FIG. 1C is a perspective view of the refractory material constituting the bottom of the submerged arc furnace 100 from the side thereof, and is a diagram illustrating the position of the thermometer embedded in the refractory material.

In the example shown in FIG. 1, the submerged arc furnace 100 has a bottomed cylindrical furnace body 111 having an opening on the upper surface and a furnace lid 112 that closes the opening on the upper surface of the furnace body 111. The furnace body 111 and the furnace lid 112 are both formed by using a refractory material.
When the furnace lid 112 is installed in the opening on the upper surface of the furnace main body 111, a space (filling portion) for filling the raw material is formed inside. In the following description, this space is referred to as the inside of the furnace as necessary, and the outside of the submerged arc furnace 100 is referred to as the outside of the furnace as necessary.

On the furnace lid 112, cylindrical raw material charging chutes 121 and 122 for charging raw materials into the furnace are arranged. Further, the furnace lid 112 is arranged with cylindrical exhaust portions 131 and 132 for exhausting the exhaust gas generated in the furnace to the outside of the furnace.

Near the center of the furnace lid 112, electrodes 151, 152, 153 for melting the raw material filled in the furnace by energization heating (resistance heating) to form the slag 141 and the hot metal 142 are installed. .. The electrodes 151, 152, and 153 are arranged at equal intervals, for example, with their tips arranged in the furnace. The raw material is energized and heated by applying three-phase AC power to the electrodes 151, 152, and 153. The slag 141 is discharged to the outside of the furnace from the slag opening 161 formed on the side wall of the furnace main body 111. The hot metal 142 is discharged to the outside of the furnace from the hot metal outlet 162 formed on the side wall of the furnace main body 111. Further, here, the structure in which the slag 141 and the hot metal 142 are separately discharged to the outside of the furnace has been described as an example, but even if the structure is such that the slag 141 and the hot metal 142 are discharged to the outside of the furnace from the same outlet. good.

An air flow path 171 is arranged on the bottom of the furnace body 111, which is the bottom surface of the furnace body 111. In the example shown in FIG. 1 (a), air is circulated in the flow path 171 in the direction of the arrow lines (negative direction of the y-axis) attached to both sides of the flow path 171 in FIG. 1 (a). .. The distribution path 171 is configured so that the air flowing through the distribution path 171 directly hits the entire lower part of the bottom of the furnace body 111 at a uniform wind speed.

Thermometers 181 and 182 are arranged in the distribution channel 171. The thermometer 181 measures the temperature of the air flowing inside the distribution path 171 at a predetermined position on the upstream side of the furnace main body 111. The thermometer 182 measures the temperature of the air flowing inside the distribution path 171 at a predetermined position on the downstream side of the furnace main body 111. In the following description, the thermometer 181 will be referred to as an upstream thermometer 181 as necessary, and the thermometer 182 will be referred to as a downstream thermometer 182 as necessary.

A thermometer 183 for measuring the temperature of the hot metal 142 is arranged in the furnace main body 111. In the following description, the thermometer 183 will be referred to as a hot metal thermometer 183, if necessary.
Further, thermometers 191 to 193 are arranged (buried) inside the refractory material of the portion constituting the bottom of the furnace body 111. The thermometers 191 to 193 are, for example, thermocouples. In the following description, the refractory of the portion constituting the bottom of the furnace body 111 will be referred to as a refractory of the bottom, if necessary.

In the example shown in FIG. 1 (c), the refractory furnace bottom has a refractory castable 111a, a perm brick 111b, a ware brick A111c, and a ware brick B111d. The refractory castable 111a, the perm brick 111b, the ware brick A111c, and the ware brick B111d are arranged in this order from the outside of the furnace. As described above, in the present embodiment, the furnace bottom refractory is arranged by arranging four kinds of materials having different thermal conductivitys side by side in the direction parallel to the furnace core 101 (the direction in which heat is transferred from the inside of the furnace). It is composed. The refractory material at the bottom of the furnace may be made of one kind of material or may be made of two or more kinds of materials other than four kinds.

As shown in FIGS. 1 (a) to 1 (c), the thermometer 191 is located at a position substantially coincide with the furnace core 101 (axis of the submerged arc furnace 100) and is closer to the outside of the furnace than inside the furnace. Placed in the area. In this embodiment, the thermometer 191 is embedded in the refractory castaple 111a. For example, the thermometer 191 is embedded at a position where the distance L ₁ from the bottom of the furnace body 111 is 50 mm. The reason why the thermometer 191 is placed at a position substantially coincide with the furnace core 101 in this way is that the temperature of the hot metal 142 tends to be the highest in the furnace core 101, so that the state of the surface inside the furnace bottom is monitored. This is because it is preferable to obtain the heat flux at a position as close as possible to the furnace core 101. In the following description, the inner surface of the furnace bottom will be referred to as the inner wall surface of the furnace bottom, if necessary. Further, the outer surface of the furnace bottom refractory is referred to as a furnace bottom outer wall surface as necessary. If deposits are attached to the refractory material on the bottom of the furnace, the deposits form the inner wall surface of the bottom of the furnace. Further, the outer surface of the furnace bottom refractory may be covered with an iron skin. No deposits adhere to the outer wall surface of the furnace bottom, and the outer wall surface of the furnace bottom is composed of the refractory material (iron skin covering the bottom). The direction connecting the inner wall surface of the furnace bottom and the outer wall surface of the furnace bottom at the shortest distance is the heat extraction direction (x-axis direction). The x-axis direction (direction along the furnace core 101 (direction in which heat is transferred from the inside of the furnace)) is the heat removal direction of the refractory material at the bottom of the furnace.

The thermometer 192 is located at a position away from the furnace core 101 (thermometer 191) and is arranged in a region closer to the outside of the furnace than inside the furnace. In this embodiment, the thermometer 192 is embedded in the refractory castaple 111a. For example, the thermometer 192 is embedded at a position where the distance L ₂ from the bottom of the furnace body 111 is 50 mm and the distance L 4 from the furnace core 101 is 550 mm. In FIG. 1 (c), the distances L ₁ and L ₂ of the thermometers 191 and 192 from the bottom of the furnace body 111 do not have to be the same.

The thermometer 193 is located at a position away from the furnace core 101 and is located in a region closer to the outside of the furnace than inside the furnace. In this embodiment, the thermometer 193 is embedded in the refractory castaple 111a. The thermometer 193 is buried inside the furnace more than the thermometer 192. The thermometers 192 and 193 have different positions along the furnace core 101 (direction in which heat is transferred from the furnace, x-axis direction), and other directions (y-axis direction and z-axis direction (vertical to the furnace core 101). The positions of)) are almost the same. For example, the thermometer 193 is embedded at a position where the distance L ₃ from the bottom of the furnace body 111 is 100 mm and the distance L ₅ from the furnace core 101 is 550 mm. In FIG. 1 (c), the distances L ₄ and L ₅ from the furnace core 101 may be the same or different (this point will be described in the following paragraphs). Further, in FIG. 1 (b), the thermometer 193 is located at a position overlapping the thermometer 192, so that the thermometer 193 is not shown in FIG. 1 (b).

It is preferable that the thermometers 192 and 193 have the same positions (positions on the yz plane) in the y-axis direction and the z-axis direction (direction of the plane perpendicular to the furnace core 101). However, if the accuracy of the heat transfer coefficient _ha derived as described later is within the range of the accuracy required for practical use, the positions of the thermometers 192 and 193 in the y-axis direction and the z-axis direction are different. May be. However, the distance between the thermometer 192 and the thermometer 193 in the direction of the plane perpendicular to the furnace core 101 (yz plane) is the distance between the thermometer 191 and the thermometer 192 in the direction of the plane perpendicular to the furnace core 101. And, it is preferable that the distance between the thermometer 191 and the thermometer 193 is smaller than the distance in the direction of the plane perpendicular to the core 101.

When obtaining the heat flux in the x-axis direction (direction along the furnace core 101 (direction in which heat is transferred from the inside of the furnace)) at the position of the furnace core 101, the heat flux is arranged on the furnace core 101 with an interval in the x-axis direction. If the temperature can be measured by the two thermometers, the heat flux in the x-axis direction at the position of the core 101 (thermometer 191) can be derived by the unsteady heat transfer reverse problem. ~ 193 can be expanded, but in the example shown in FIG. 1 (a), it is a region under the distribution path 171 and a pillar is formed in the vicinity of the core 101. Therefore, the furnace bottom. It is not possible (or very costly and difficult) to add a thermometer other than the thermometer 191 in the area of the fireproof material, which is the area of the furnace core 101 and its vicinity.

Therefore, since the bottom of the furnace body 111 is forcibly air-cooled, the present inventors have changed the heat transfer coefficient between the refractory material (refractory 111a) at the bottom and the air flowing inside the flow path 171 over time. Obtained the finding that there is not much difference between the core 101 and the position away from the core 101. Based on such findings, the present inventors are in the case where it is not possible (or difficult) to add a thermometer to the area of the furnace core 101 or its vicinity in the area of the fire bottom refractory material. Also found that the heat flux in the x-axis direction at the position of the furnace core 101 (thermometer 191) can be derived by the unsteady heat transfer reverse problem.

Details will be described later, but in the present embodiment, the temperature at each time measured by the thermometers 192 and 193 is used to determine the position of the outer wall surface of the furnace bottom, and the thermometers 192 and 193 and the y-axis direction and the z-axis. The heat flux in the x-axis direction at the same position in the direction is derived at each time by the one-dimensional unsteady heat transfer reverse problem, and the derived heat flux is used in the y-axis direction and z-axis of the thermometers 192 and 193. The heat transfer coefficient between the fire bottom fire resistant material (fire resistant castable 111a) and the air flowing inside the flow path 171 at the position in the direction (position on the yz plane) is derived at each time. Then, using the heat transfer coefficient at each time and the temperature at each time measured by the thermometer 191 at the position of the inner wall surface of the furnace bottom, the core 101 (thermometer 191) and the y-axis direction and z. The heat flux in the x-axis direction at the same position in the axial direction is derived at each time by the one-dimensional unsteady heat transfer inverse problem. Here, the unsteady heat transfer inverse problem is a boundary condition or initial condition such as temperature and heat flux at the region boundary, assuming that the temperature information inside the region is known based on the unsteady heat conduction equation that governs the calculation region. Refers to the problem of estimating. On the other hand, the unsteady heat transfer quasi-problem refers to the problem of estimating the temperature information inside the region based on the known boundary conditions.

The heat transfer coefficient between the refractory at the bottom of the furnace (fireproof castable 111a) and air at the same positions as the thermometers 192 and 193 in the y-axis direction and the z-axis direction is determined by the furnace core 101 (thermometer 191) and y. Even if it is regarded as the heat transfer coefficient between the refractory (fireproof castable 111a) at the bottom of the furnace and the air at the same position in the axial direction and the z-axis direction, the furnace core 101 can obtain the accuracy required for practical use. Distances _L4 and _L5 from are determined. Further, when deriving the heat flux in the x-axis direction at the position of the inner wall surface of the furnace bottom at the same position as the furnace core 101 (thermometer 191) in the y-axis direction and the z-axis direction, the thermometer 191 is used. When the temperature measured by the thermometer 192 or 193 is used, the distances L ₄ and L ₅ from the furnace core 101 are increased so that the accuracy of the heat flux is not practically required. It is preferable to do. Even if there are no two thermometers in the direction of heat transfer from the inside of the furnace (even if only the thermometer 191), it is the position of the inner wall surface of the bottom of the furnace, and the core 101 (thermometer 191) and the y-axis. This is because the heat flux in the x-axis direction can be accurately derived at the same position in the direction and the z-axis direction. From the above viewpoint, the positions of the thermometers 191 to 193 are determined.

In the following description, the thermometer 191 is referred to as a core thermometer 191 as necessary, the thermometer 192 is referred to as a core peripheral thermometer 192 as necessary, and the thermometer 193 is referred to as a core as necessary. It is called a peripheral furnace inner thermometer 193.

(Configuration of equipment monitoring device)
FIG. 2 is a diagram showing an example of a functional configuration of the equipment monitoring device 200. The hardware of the equipment monitoring device 200 is realized by using, for example, a CPU, a ROM, a RAM, an HDD, an information processing device having various interfaces, or dedicated hardware.
<Temperature acquisition unit 201>
The temperature acquisition unit 201 is measured by an upstream thermometer 181, a downstream thermometer 182, a hot metal thermometer 183, a core thermometer 191 and a core peripheral furnace outer thermometer 192, and a core peripheral furnace inner thermometer 193. To get the temperature. In the present embodiment, the temperature acquisition unit 201 includes an upstream thermometer 181, a downstream thermometer 182, a hot metal thermometer 183, a core thermometer 191 and a core peripheral furnace outer thermometer 192, and a core peripheral furnace inner temperature. Input the temperature measured by the total 193, upstream side thermometer 181, downstream side thermometer 182, hot metal thermometer 183, core thermometer 191 and core peripheral furnace outside thermometer 192, and core peripheral furnace inside temperature. Acquire the temperature measured at the same time with a total of 193. The temperature acquisition unit 201 outputs such a temperature at predetermined sampling times. For example, the temperature acquisition unit 201 can periodically and repeatedly acquire these temperatures. As a result, each time measured by the upstream thermometer 181, the downstream thermometer 182, the hot metal thermometer 183, the core thermometer 191 and the core peripheral thermometer 192, and the core peripheral thermometer 193. Temperature is obtained.

<First inverse problem analysis unit 202>
In the present embodiment, the internal / external temperature function T ^ (x, t) indicating the temperature in the heat removal direction (x-axis direction) of the bottom refractory is set to 1 in the heat removal direction (x-axis direction) of the bottom refractory. It is a mathematical formula that predicts the time change of the temperature distribution in the dimensional region. Interpolation / extrapolation By using the temperature function T ^ (x, t), the temperature can be interpolated and extrapolated by determining the coordinates x on the x-axis and the time t. In the first inverse problem analysis unit 202, the internal / external temperature function T ^ (x, t) is set in the heat removal direction of the fire bottom refractory material at the same positions in the y-axis direction and the z-axis direction as the thermometers 192 and 193. It is used as a formula for predicting the time change of the temperature distribution in the one-dimensional region (in the x-axis direction).

FIG. 3 is a diagram showing an example of the coordinate system of the unsteady heat transfer inverse problem in the first inverse problem analysis unit 202. FIG. 3 shows a definition point of an amount of information on a two-dimensional cross section of space x-time t. FIG. 3 shows a two-dimensional cross section of two-dimensional coordinates (coordinates of space x-time t).

In FIG. 3, the x-axis is an axis in which the outer wall surface of the furnace bottom is x = 0, and indicates the position of the refractory material in the furnace bottom in the heat removal direction. The t-axis is a time axis.

In FIG. 3, the plots indicated by white circles are the definition points of the amount of information. The definition points of the amount of information indicated by the white circles indicate the position of the furnace outside thermometer 192 around the core and the time when the temperature was measured by the furnace outside thermometer 192 around the core. The plots shown by black circles are also the definition points of the amount of information. The definition points of the amount of information indicated by the black circles indicate the position of the furnace core peripheral thermometer 193 and the time when the temperature was measured by the furnace core peripheral furnace inner thermometer 193. The amount of information at the definition point indicated by the white circle includes the temperature measured by the furnace outside thermometer 192 around the furnace core and the measurement time of the temperature. The amount of information at the definition point indicated by the black circle includes the temperature measured by the furnace inside thermometer 193 around the core and the measurement time of the temperature.

The first inverse problem analysis unit 202 uses each of the points on the two-dimensional coordinates of the x-axis and the t-axis shown by the plots shown by the white circles and the plots shown by the black circles shown in FIG. 3 as the definition points of the amount of information.
In FIG. 3, the timing t _N is the timing at which the latest temperature is measured by the thermometers 192 and 193. In FIG. 3, each time the temperature measured by the thermometers 192 and 193 is acquired, eight temperature measurement timings (eight timings from timing t _O to t _N ) are set in order from the newest to the definition point of the amount of information. This will be described by taking as an example the case where the time t is adopted. That is, when the temperature newly measured by the thermometers 192 and 193 is newly acquired, the first inverse problem analysis unit 202 includes 2 of the 8 temperature measurement timings, including the oldest temperature measurement timing. Is excluded from the definition points of 16 (8 × 2) information quantities. Then, the first inverse problem analysis unit 202 adds the definition points of the two information amounts including the latest temperature measurement timing to the definition points of the 16 information amounts. The number of time t that defines the definition point of the amount of information is not limited to eight.

The first inverse problem analysis unit 202 derives the weight vector α (element α _j ) included in the internal / external temperature function T ^ (x, t) based on the amount of information at the definition point of the above amount of information. ..
Here, an example of the internal / external temperature function T ^ (x, t) will be described.
First, the one-dimensional unsteady heat conduction equation is expressed by the following equation (1).

In equation (1), λ is the thermal conductivity [kcal / (m · hr · K)] of the refractory of the fire bottom (refractory 111a), and ρ is the specific gravity of the refractory of the bottom (refractory 111a). It is [kg / m ³ ], and C _p is the specific heat [kcal / (kg · K)] of the refractory material (fireproof castable 111a) at the bottom. λ / ρC _p corresponds to the thermal diffusivity [m ² / s] of the refractory refractory (fireproof castable 111a). Further, 0 <x <1 indicates that the coordinates of the x-axis are normalized by [0,1].

Here, as shown in FIG. 1 (c), the refractory material at the bottom of the furnace has a refractory castable 111a, a perm brick 111b, a wear brick A111c, and a wear brick B111d, and has physical property values (thermal conductivity λ, density ρ). , Specific heat C _p ) is different. Therefore, if a one-dimensional unsteady heat conduction equation is constructed for each refractory, the thermal resistance due to contact of different refractories must be considered. The present inventors assume that the refractory material at the bottom of the furnace is composed only of the refractory material (fireproof castable 111a) in which thermometers 191 to 193 are embedded, and that the heat transfer phenomenon of the refractory material at the bottom of the furnace is not one-dimensional. Modeled by the steady heat transfer equation, with a length corresponding to the length (thickness) of the entire refractory refractory in the heat removal direction (x-axis direction) when the refractory refractory is composed only of the refractory 111a. Even if a certain considerable length is set appropriately, the one-dimensional non-stationary heat transfer equation is solved, and the positions of the heat flux and the inner wall surface of the furnace bottom are derived based on the solution, they can be derived accurately. I found. Further, since it is difficult to construct an equation (model) that accurately expresses the thermal resistance due to the contact of different refractories, the error of the model becomes larger when the thermal resistance due to the contact of different refractories is taken into consideration. Therefore, in the present embodiment, a one-dimensional unsteady heat conduction equation is constructed assuming that the refractory at the bottom of the fire is composed only of the refractory castable 111a.

Here, when the refractory furnace bottom is composed of only the refractory castable 111a, a considerable length corresponding to the length (thickness) in the heat removal direction (x-axis direction) of the entire refractory furnace bottom is predetermined. investigate. Specifically, when the inner wall surface of the bottom of the submerged arc furnace 100 is the same as when it is new, the internal / external temperature of the equation (4) described later in the section <1st inverse problem analysis unit 202> will be described later. The x-axis coordinates when the function T ^ (x, t) becomes equal to the temperature of the hot metal 142 are derived as the reference values of the x-axis coordinates of the inner wall surface of the furnace bottom. When the inner wall surface of the bottom of the submerged arc furnace 100 is the same as when it is new, for example, the first operation of the submerged arc furnace 100 can be mentioned. The equivalent length shall be represented by the coordinates of the x-axis of the inner wall surface of the furnace bottom when the coordinates of the x-axis of the outer wall surface of the furnace bottom are set to "0".

Therefore, in the present embodiment, the x-axis coordinates are determined so that the reference value of the x-axis coordinates of the inner wall surface of the furnace bottom is "1" and the coordinates of the x-axis of the outer wall surface of the furnace bottom are "0". The same shall apply in other explanations). t _max is the time when the calculation end condition is satisfied.

Further, the following equations (2) and (3) are used as boundary conditions (functions of temperature) for temperature.

x ₁ ^* is the coordinates of the x-axis of the furnace outside thermometer 192 around the furnace core. obs1 (t) is the temperature measured by the furnace outside thermometer 192 around the furnace core at time t. T ₁ (x ₁ ^* , t) is a function indicating the temperature measured by the core peripheral thermometer 192, and is the x-axis coordinate x ₁ ^* and time t of the core peripheral thermometer 192. Is a function of. x ₁ ^* ∈ [0, 1] indicates that the x-axis coordinates x ₁ ^* of the furnace core peripheral thermometer 192 are normalized by [0, 1]. That is, the x-axis coordinates of the furnace outside thermometer 192 around the furnace core so that the reference value of the x-axis coordinates of the inner wall surface of the furnace bottom is "1" and the coordinates of the x-axis on the outer wall surface of the furnace bottom are "0". To determine.

x ₂ ^* is the coordinates of the x-axis of the furnace core peripheral thermometer 193. obs2 (t) is the temperature measured by the furnace core peripheral thermometer 193 at time t. T ₂ (x ₂ ^* , t) is a function indicating the temperature measured by the core peripheral thermometer 193, and the x-axis coordinates x ₂ ^* and time t of the core peripheral thermometer 193. Is a function of. x ₂ ^* ∈ [0, 1] indicates that the x-axis coordinates x ₂ ^* of the furnace core peripheral thermometer 193 are normalized by [0, 1]. That is, the x-axis of the furnace core peripheral thermometer 193 so that the x-axis coordinate on the inner wall surface of the furnace bottom refractory is "1" and the x-axis coordinate on the outer wall surface of the furnace bottom is "0". Determine the coordinates of.

Under the boundary conditions of Eqs. (2) and (3), the one-dimensional unsteady heat conduction equation of Eq. (1) will be solved. Here, the numerical calculation of Eq. (1) is performed as follows. An example of solving a one-dimensional unsteady heat conduction equation will be described.
First, the internal / external temperature function T ^ (x, t) is expressed by the following equation (3).

In the equation (3), the internal / external temperature function T ^ (x, t) is a temperature satisfying the one-dimensional unsteady heat conduction equation shown in the equation (1), and is an approximate solution of the temperature T.

x _j is an arbitrary reference position (coordinates on the x-axis). t _j is an arbitrary reference time. The point on the two-dimensional coordinates determined by the reference position x _j and the reference time t _j is called the center point. Normally, the reference x _j and the reference time t _j are made to match the above-mentioned definition points of the amount of information, and thus this is also done in this embodiment. However, the reference position x _j and the reference time t _j do not have to match the above-mentioned definition points of the amount of information.

j is a variable that identifies the above-mentioned center point (a point on the two-dimensional coordinates determined by the reference position x _j and the reference time t _j ), and is an integer in the range of 1 to m + l.

m is represented by n _p1 × n _t , and l is represented by n _p2 × n _t .
n _p1 is the position of the furnace outside thermometer 192 around the furnace core. The position of the outer peripheral side thermometer 192 around the core is set so that the internal / external temperature function T ^ (x, t) satisfies the equation (2), and n _p2 is the thermometer 193 around the core. The position. The position of the furnace inner thermometer 193 around the furnace core is set so that the internal / external temperature function T ^ (x, t) satisfies the equation (3). n _t is the number of times. This time is set so that the internal / external temperature function T ^ (x, t) satisfies the equations (2) and (3). As described above, m is the number of center points j determined by the position and time of the furnace outside thermometer 192 around the furnace core. Further, l is the number of center points j determined by the position and time of the furnace inside thermometer 193 around the furnace core.

In the present embodiment, the center point j coincides with the definition point of the amount of information. Therefore, in the example shown in FIG. 3, the maximum value m + l of j is the sum of the plots shown by the black circles and the white circles. However, in reality, for example, the number m of the center point j determined by the position and time of the furnace outside thermometer 192 around the furnace core can be set to 30 when the sampling cycle is 300 seconds. Similarly, the number of center points j determined by the position and time of the furnace inside thermometer 193 around the furnace core can be set to 30 when the sampling period is 300 seconds.

φ (xx _j , tt _j ) is a basis function determined by the following equations (5) and (6).

In equation (6), H (t) is a Heaviside function. Equation (6) is an equation expressed in the form of a fundamental solution satisfying the one-dimensional unsteady heat conduction equation shown in equation (1). The fundamental solution is a solution (temperature T) of a one-dimensional unsteady heat conduction equation when the initial condition of the temperature T is expressed by a δ function. In equation (5), S is a parameter for adjusting the diffusion profile of the fundamental solution of the one-dimensional unsteady heat conduction equation, and is set in advance. S is a value exceeding 0.

As described above, the basis function φ (x-x _j , t-t _j ) is a one-dimensional unsteady heat conduction equation when the center point j (reference position x _j and reference time t _j ) is used as a reference. It is a function expressed in the form of a satisfying basic solution.

Here, let α be a weight vector representing the weight of the basis function φ (x−x _j , t−t _j ) with respect to the internal / external temperature function T ^ (x, t), and let α _j be its element. The weight vector α has an effect on the internal / external temperature function T ^ (x, t) of the basis function φ (x-x _j , t-t _j ) and the basis function φ (x-x _j , t-t _j ). It is determined by the balance with the influence of other basis functions φ (x-x _j , t-t _j ) different from the above on the internal / external temperature function T ^ (x, t). The basis function φ (x−x _j , t−t _j ) exists at each center point j, and the element α _j of the weight vector α also exists at each center point j.

As described above, the internal / external temperature function T ^ (x, t) is the product of the basis function φ (xx _j , tt _j ) and the element α _j of the weight vector α at each of the center points j. It is expressed as the sum of the values.
The weight vector α and its element α _j are represented by the following equations (7) to (10).

In Eqs. (8) and (10), k is a variable that identifies the definition point of the amount of information, and is an integer from 1 to m (k = 1, ..., M). s is a variable that identifies the definition point of the amount of information, and is an integer from m + 1 to l (s = m + 1, ... , L ). j is an integer from 1 to m + l (j = 1, ..., m + l).
The matrix A is a (m + l) × (m + l) matrix. b and α are (m + l) dimensional column vectors. As described above, (m + l) is the number of center points j.

In the equation (8), "φ (x _s − x _j , t _s − t _j )” in [] of A = [] represents the k-row j-column component of the matrix A, and “φ (x _s −”. x _j , t _s −t _j ) ”represents the s row j column component of the matrix A.

Obs1 (t) represented by the equation (2) is given to obs1 _k in [] of b = []. Obs1k in this [] represents the _k -row component of the matrix b. Further, obs2 (t) represented by the equation (3) is given to obs2 _sm in [] of b = []. The obs2 _sm in this [] represents the s row component of the matrix b.

As described above, k is a variable that identifies the definition point of the amount of information, and is an integer from 1 to m (k = 1, ..., M). m is represented by n _p1 × n _t . n _p1 is the number of center points j at the position of the furnace outside thermometer 192 around the furnace core. s is a variable that identifies the definition point of the amount of information, and is an integer from m + 1 to l (s = m + 1, ..., L). l is represented by n _p2 × n _t . n _p2 is the number of center points j at the position of the furnace inside thermometer 193 around the furnace core.

Equations (7) to (10) are the one-dimensional non-stationary heat conduction equation of equation (1), the temperature function (boundary condition) of equations (2) and (3), and the internal / external temperature of equation (4). In order to satisfy the function, the information of the definition point of the amount of information is given the measurement result (temperature, temperature measurement position, and temperature measurement time) by the furnace outside thermometer 192 around the core, and the equation (4) and the periphery of the core. An equation for deriving the weight vector α by substituting the simultaneous equations of equation (4) given the measurement results (temperature, measurement position, and temperature measurement time) by the furnace inside thermometer 193 and solving the simultaneous equations. Is. The information of the definition point of the information amount to be substituted into the simultaneous equation includes the position of the definition point of the information amount, the temperature of the core peripheral furnace outside thermometer 192 and the core peripheral furnace inside thermometer 193, and the core peripheral furnace outside temperature. The temperature measurement time of the total 192 and the thermometer 193 around the core, the thermal conductivity λ, the density ρ, and the specific heat C _p of the refractory refractory (fireproof castable 111a) are included. The thermal conductivity λ, the density ρ, and the specific heat C _p of the refractory material (fireproof castable 111a) may be different or the same depending on the definition point of the amount of information. Further, when solving the simultaneous equations, the position of the center point j is also substituted into the simultaneous equations.

The first inverse problem analysis unit 202 derives the weight vector α (element α _j ) from the equations (7) to (10) as described above.
The first inverse problem analysis unit 202 performs the above processing every time the temperature measured by the thermometers 192 and 193 is acquired from the temperature acquisition unit 201. As a result, the weight vector α (element α _j ) is derived at each time t.

<Heat transfer coefficient derivation unit 203>
The heat transfer coefficient derivation unit 203 includes the weight vector α (element α _j ) at time t derived by the first inverse problem analysis unit 202, the heat conductivity λ of the fire bottom fireproof material (fireproof castable 111a), and the density. By substituting ρ, the specific heat C _p , the reference time t _j , the number m + l of the center point j, and the x-axis coordinate x (= 0) on the outer wall surface of the furnace bottom into equation (4), at time t It is the temperature Tv of the temperature of the outer wall surface of the furnace bottom, and _derives the temperature _Tv at the same positions as the thermometers 192 and 193 in the y-axis direction and the z-axis direction. In the following description, this temperature will be referred to as the temperature _Tv of the outer wall surface of the furnace bottom, if necessary.

Further, the heat transfer coefficient derivation unit 203 includes the weight vector α (element α _j ) at time t derived by the first inverse problem analysis unit 202 and the thermal conductivity λ of the fire bottom fireproof material (fireproof castable 111a). , Density ρ, and specific heat C _p , reference time t _j , number m + l of center point j, and x-axis coordinate x (= 0) on the outer wall surface of the furnace bottom by the following equation (11) or (11)' By substituting into the equation, it is the value q _v of the x-axis direction (heat extraction direction) component of the heat flux vector at time t, the position of the outer wall surface of the furnace bottom, and the thermometers 192, 193 and the y-axis direction. And the value q _v of the x-axis direction (heat extraction direction) component of the heat flux vector at the same position in the z-axis direction is derived. In the following description, the value of the x-axis direction (heat extraction direction) component of this heat flux vector is referred to as a heat flux on the outer wall surface side of the bottom of the furnace core around the furnace core, if necessary. (11)'In the equation, x represents the coordinates of the x-axis on the inner wall surface of the furnace bottom, Δx represents the minute distance in the x-axis direction from the inner wall surface of the furnace bottom to the outer wall surface side of the furnace bottom (outside the furnace), for example, 1 mm. You can set the value of the degree.

The heat transfer coefficient derivation unit 203 was measured by the thermometers 192 and 193 acquired from the temperature acquisition unit 201 each time the weight vector α (element α _j ) was derived by the first inverse problem analysis unit 202. The above processing is performed using the temperature. As a result, the heat flux q _v (t) on the outer wall surface of the furnace bottom around the furnace core at each time t and the temperature T _v (t) of the outer wall surface of the furnace bottom at each time t are derived.

Then, the heat transfer coefficient derivation unit 203 includes the heat flux q _v (t) on the outer wall surface of the furnace bottom around the core at time t, the temperature T _v (t) of the outer wall surface of the furnace bottom at time t, and air cooling at time t. By substituting the temperature T _a (t) into the following equation (12), it is the heat transfer coefficient between the fire bottom fire resistant material (fire resistant castable 111a) and the air flowing inside the flow path 171 at time t. Then, the heat transfer coefficient h _a (t) [W / (m ² · K)] at the same position in the y-axis direction and the z-axis direction as the thermometers 192 and 193 is derived. In the following description, this heat transfer coefficient will be referred to as a furnace bottom heat transfer coefficient, if necessary.

Here, the air cooling temperature T _a (t) at time t is expressed by the following equation (13).

In the equation (13), T _c (t) is the temperature of the air flowing inside the distribution path 171 at the time t measured by the downstream thermometer 182. _Th (t) is the temperature of the air flowing inside the distribution path 171 at time t measured by the upstream thermometer 181. As described above, in the present embodiment, the air cooling temperature T _a (t) is the temperature of the air flowing inside the flow path 171 at a predetermined position on the upstream side of the furnace body 111 and the predetermined temperature on the downstream side of the furnace body 111. The case where it is expressed by the arithmetic mean value with the temperature of the air flowing inside the flow path 171 at the position of is taken as an example.

The heat transfer coefficient derivation unit 203 measures the thermometers 181 and 182 acquired by the temperature acquisition unit 201 each time the heat flux q _v on the outer wall surface side of the furnace bottom around the core and the temperature T _v of the outer wall surface of the furnace bottom are derived. Perform the above processing using temperature. As _a result, the bottom heat transfer coefficient ha at each time t is derived.

<Second inverse problem analysis unit 204>
Two boundary conditions are required to solve the one-dimensional unsteady heat conduction equation in Eq. (1). The only thermometer arranged in the furnace core 101 is the furnace core thermometer 191. Therefore, the value of the x-axis direction (heat extraction direction) component of the heat flux vector at the position of the inner wall surface of the furnace bottom at the same position as the furnace core thermometer 191 in the y-axis direction and the z-axis direction is (1). In order to solve by the equation, the boundary condition is not enough only by the temperature function (boundary condition about temperature) as in the equations (2) and (3).

As described above, the present inventors have determined that the heat transfer coefficient between the fire bottom refractory (fireproof castable 111a) and the air flowing inside the flow path 171 is a thermometer at positions in the y-axis direction and the z-axis direction. It was found that there is not much difference between the same position as 192 and 193 and the same position as the furnace core thermometer 191. From this, the present inventors use the furnace bottom heat transfer coefficient _ha at each time t, and the positions of the outer wall surface of the furnace bottom in the y-axis direction and the z-axis direction are the furnace core thermometers 191. I thought that it would be better to set the boundary condition at the same position as. Hereinafter, an example of processing in the second inverse problem analysis unit 204 based on this will be described. In the following description of the second inverse problem analysis unit 204, detailed description of the same parts as those described in the section <1st inverse problem analysis unit 202> will be omitted.

In the second inverse problem analysis unit 204, the internal / external temperature function T ^ (x, t) is set in the heat removal direction (x) of the fire bottom refractory material at the same positions in the y-axis direction and the z-axis direction as the thermometer 191. It is used as a formula for predicting the time change of the temperature distribution in the one-dimensional region (in the axial direction).
The second inverse problem analysis unit 204 replaces equations (2) and (3) with the following equations (14) and (as boundary conditions for solving the one-dimensional unsteady heat conduction equation of equation (1). 15) Equation is used.

Equation (14) is an equation showing the balance of heat flux on the outer wall surface of the furnace bottom. That is, the equation (14) is an equation showing that the following first heat flux and the second heat flux are equal to each other. The first heat flux is a heat flux based on the temperature gradient of the refractory refractory in the heat removal direction (x-axis direction) on the outer wall surface of the refractory and the thermal conductivity λ of the refractory refractory (fireproof castable 111a). be. The second heat _flux is between the difference between the temperature T (1, t) and the air cooling temperature Ta on the outer wall surface of the furnace bottom, and between the refractory material (refractory 111a) at the bottom and the air flowing inside the flow path 171. It is a heat flux based on the heat transfer coefficient h _a of.

In equation (15), x ₃ ^* is the coordinates of the x-axis of the furnace core thermometer 191. obs3 (t) is the temperature measured by the furnace core thermometer 191 at time t. T ₃ (x ₃ ^* , t) is a function indicating the temperature measured by the core thermometer 191 and is a function of the x-axis coordinates x ₃ ^* of the core thermometer 191 and the time t. x ₃ ^* ∈ [0, 1] indicates that the x-axis coordinate x ₃ ^* of the core thermometer 191 is normalized by [0, 1]. That is, the x-axis coordinates of the furnace core thermometer 191 are set so that the x-axis coordinates on the inner wall surface of the furnace bottom refractory are "1" and the x-axis coordinates on the outer wall surface of the furnace bottom are "0". stipulate.

In the second inverse problem analysis unit 204, the equation (14) is used as a boundary condition. Therefore, the second inverse problem analysis unit 204 uses the following equation (16) as the matrix A in the equation (7) and the following equation (17) as the (m + l) dimensional column vector b.

In equation (16), "λ ∂φ / ∂x (x _k -x _j , tk-t _j ) ₊ ha φ ( _{x k} -x _j , tk-t _j ) in [] of A ₌ []. ) Represents the k-row-j-column component of the matrix A, and "φ (x _s -x _j , t _s -t _j )" represents the s-row-j column component of the matrix A.

g (t) shown in the following equation (18) is given to g _k in [] of b = []. G _k in this [] represents the k-row component of the matrix b. Further, obs3 (t) represented by the equation (15) is given to obs3 _sm in [] of b = []. The obs3 _sm in this [] represents the s row component of the matrix b.

Here, m is represented by n _p3 × n _t , and l is represented by n _p4 × n _t .
n _p3 is the number of center points j on the outer wall surface of the furnace bottom. The number of center points j on the outer wall surface of the furnace bottom (the position of the outer wall surface of the furnace bottom and the positions in the y-axis direction and the z-axis direction are the same as those of the furnace core thermometer 191) is the internal / external temperature function T ^ (x). , T) is set so as to satisfy the equation (14). n _p4 is the position of the furnace core thermometer 191. The position of the furnace core thermometer 191 is set so that the internal / external temperature function T ^ (x, t) satisfies the equation (15). n _t is the number of times. This time is set so that the internal / external temperature function T ^ (x, t) satisfies the equations (14) and (15). As described above, m is the number of center points j determined by the position and time on the outer wall surface of the furnace bottom. Further, l is the number of center points j determined by the position and time of the furnace core thermometer 191.

FIG. 4 is a diagram showing an example of the coordinate system of the unsteady heat transfer inverse problem in the second inverse problem analysis unit 204. FIG. 4 shows a definition point of an amount of information on a two-dimensional cross section of space x-time t. FIG. 4 shows a two-dimensional cross section of two-dimensional coordinates (coordinates of space x-time t).

In FIG. 4, the x-axis is an axis in which the inner wall surface of the furnace bottom is x = 0, and indicates the position of the refractory material in the furnace bottom in the heat removal direction. The t-axis is a time axis.
In FIG. 4, the plots indicated by white circles are the definition points of the amount of information, respectively. The definition point of the amount of information indicated by this white circle is the position of the outer wall surface of the bottom of the furnace, the position where the position in the y-axis direction and the position in the z-axis direction is the same as that of the furnace core thermometer 191 and the time when the heat flux at that position is estimated. And. In the present embodiment, the only thermometer arranged in the furnace core 101 is the furnace core thermometer 191. Therefore, the amount of information at the definition point indicated by the white circle is defined as the furnace bottom heat transfer coefficient _ha .

The plots shown by black circles are also the definition points of the amount of information. The definition points of the amount of information indicated by the black circles indicate the position of the core thermometer 191 and the time when the temperature was measured by the core thermometer 191.
The amount of information at the definition points indicated by white circles includes the bottom heat transfer coefficient h _a , the estimated time of the bottom heat transfer coefficient h _a , the thermal conductivity λ of the refractory refractory (fireproof castable 111a), the density ρ, and the specific heat. C _p is included. The amount of information at the definition points indicated by black circles includes the temperature of the core thermometer 191, the temperature measurement time of the core thermometer 191, the thermal conductivity λ of the refractory refractory (fireproof castable 111a), the density ρ, and the specific heat C. _p is included. The thermal conductivity λ, the density ρ, and the specific heat C _p of the refractory material (fireproof castable 111a) may be different or the same depending on the definition point of the amount of information.

In FIG. 4, the timing t _N is the timing at which the latest temperature is measured by the furnace core thermometer 191. In FIG. 4, each time the temperature measured by the furnace core thermometer 191 is acquired, eight temperature measurement timings (eight timings from timing t _O to t _N ) are set in order from the newest to the definition point of the amount of information. This will be described by taking as an example the case where the time t is adopted. That is, when the temperature newly measured by the core thermometer 191 is newly acquired, the second inverse problem analysis unit 204 includes 2 of the 8 temperature measurement timings, which is the oldest temperature measurement timing. Is excluded from the definition points of 16 (8 × 2) information quantities. Then, the second inverse problem analysis unit 204 adds the definition points of the two information amounts including the latest temperature measurement timing to the definition points of the 16 information amounts. The number of time t that defines the definition point of the amount of information is not limited to eight.

The second inverse problem analysis unit 204 converts the weight vector (element α _j ) included in the internal / external temperature function T ^ (x, t) into (7) based on the amount of information at the definition point of the above amount of information. ), (9), (16), and (17).

Equations (7), (9), (16), and (17) are the one-dimensional non-stationary heat conduction equation of equation (1), the boundary condition of equation (14), and the temperature function of equation (15). (Boundary condition) and the information of the definition point of the amount of information so as to satisfy the internal / external temperature function of the equation (4), the measurement result (temperature, temperature measurement position, and temperature measurement time) by the core thermometer 191 It is an equation for deriving the weight vector α by substituting the given equations (4) and (14) into the simultaneous equations and solving the simultaneous equations. As described above, the information of the definition point of the information amount to be substituted into the simultaneous equation includes the position of the definition point of the information amount, the bottom heat transfer coefficient h _a , the estimated time of the bottom heat transfer coefficient h _a , and the core. It includes the temperature of the thermometer 191 and the temperature measurement time of the core thermometer 191, the thermal conductivity λ of the fire bottom fireproof material (fireproof castable 111a), the density ρ, and the specific heat C _p . Further, when solving the simultaneous equations, the position of the center point j is also substituted into the simultaneous equations.
The second inverse problem analysis unit 204 performs the above processing every time the temperature measured by the furnace core thermometer 191 is acquired from the temperature acquisition unit 201. As a result, the weight vector α (element α _j ) is derived at each time t.

<Heat flux / wall position derivation unit 205>
When the submerged arc furnace 100 is used, the coordinates of the x-axis of the inner wall surface of the furnace bottom change due to melting damage of the refractory material at the bottom of the furnace. Therefore, in the present embodiment, the x-axis coordinates of the fire bottom refractory when the internal / external temperature function T ^ (x, t) becomes equal to the temperature of the hot metal 142 are set as the x-axis coordinates of the inner wall surface of the furnace bottom. From this, the heat flow flux / wall surface position derivation unit 205 has the weight vector α (element α _j ) at time t derived by the first inverse problem analysis unit 202 and the fire bottom fireproof material (fireproof castable 111a). Thermal conductivity λ, density ρ, specific heat C _p , reference time t _j , number m + l of center point j, and temperature measured at time t by the hot metal thermometer 183 acquired by the temperature acquisition unit 201 (hot metal 142). (Temperature) is substituted into Eq. (4), and the x-axis coordinates of the bottom fireproof material when the internal / external temperature function T ^ (x, t) in Eq. Derived as the x-axis coordinates of the bottom inner wall surface. If the temperature of the hot metal 142 is set to the temperature measured by the hot metal thermometer 183 as in the present embodiment, it is preferable because the accuracy of the temperature of the hot metal 142 can be improved, but it is not always necessary to do so. .. For example, a preset temperature assumed as the temperature of the hot metal 142 may be used as the temperature of the hot metal 142.

Further, the heat flux / wall surface position derivation unit 205 has the weight vector α (element α _j ) at time t derived by the second inverse problem analysis unit 204 and the heat conduction of the fire bottom fireproof material (fireproof castable 111a). Bottom fire resistance when rate λ, density ρ, specific heat C _p , reference time t _j , number m + l of center point j, and internal / external temperature function T ^ (x, t) become equal to the temperature of hot metal 142 By substituting the x-axis coordinates of the object into Eq. (11), the x of the heat flux vector at the position of the inner wall surface of the furnace bottom, where the positions in the y-axis direction and the z-axis direction are the same as those of the thermometer 191. The value q _v of the axial (heat removal direction) component is derived. In this way, at each time t, the position of the inner wall surface of the furnace bottom in the y-axis direction and the z-axis direction is the same as that of the thermometer 191 in the x-axis direction (heat extraction direction) of the heat flux vector. The value q _v of the component is obtained. In the following description, the value q _v of the x-axis direction (heat extraction direction) component of this heat flux vector is referred to as the heat flux q _v on the inner wall surface side of the furnace core, if necessary.

As described above, the heat flux / wall surface position derivation unit 205 is the bottom refractory material when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142 at each time t. Derive the x-axis coordinates. As described above, in the present embodiment, the one-dimensional unsteady heat conduction equation is constructed assuming that the refractory at the bottom of the fire is composed only of the refractory castable 111a. Therefore, the x-axis coordinates of the bottom refractory when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142 are such that the bottom refractory consists of only the fireproof castable 111a. It is the x-axis coordinate of the inner wall surface of the furnace bottom, assuming that the temperature is increased.

Therefore, the heat flux / wall surface position derivation unit 205 is a time series of the x-axis coordinates of the fire bottom refractory when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. By deriving the change, the relative change of the x-axis coordinates of the inner wall surface of the furnace bottom can be obtained. In addition, the heat flux / wall surface position derivation unit 205 has the x-axis coordinates of the fire bottom refractory and the bottom when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. The relative change of the x-axis coordinates of the inner wall surface of the furnace bottom can also be obtained by comparing with the reference value of the x-axis coordinates of the inner wall surface. The reference value of the x-axis coordinates of the inner wall surface of the furnace bottom is the case where the inner wall surface of the furnace bottom of the submerged arc furnace 100 is the same as when it is new, and the internal / external temperature function T ^ of the equation (4). (X, t) is the x-axis coordinate of the fire bottom refractory when the temperature of the hot metal 142 becomes equal.

However, if the above is done, the information on the position of the inner wall surface of the furnace bottom itself cannot be obtained.
Therefore, in the present embodiment, the heat flow flux / wall surface position derivation unit 205 is used to position the boundary between the fireproof castable 111a, the perm brick 111b, the wear brick A111c, and the wear brick B111d constituting the refractory fireproof material as follows. (X-axis coordinates), the length (thickness) in the heat removal direction (x-axis direction), and the position of the inner wall surface of the furnace bottom (x-axis coordinates) are derived. It should be noted that these x-axis coordinates are the x-axis coordinates at the position of the furnace core 101, and the length in the heat removal direction (x-axis direction) is the heat removal direction at the position of the furnace core 101 (the x-axis direction). It shall be the length in the x-axis direction). Further, as shown in the equation (1), the coordinates of the x-axis are normalized by [0,1], but the actual coordinates are obtained by multiplying the normalized x-axis coordinates by the above-mentioned equivalent length. It is assumed that it has been converted to.

First, the x-axis coordinates x _{4_1} at the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom (the boundary between the ware brick B111d and the ware brick A111c) are expressed by the following equation (19). The x-axis coordinates x _{3_1} at the position of the end of the ware brick A111c on the outer wall surface side of the furnace bottom (the boundary between the ware brick A111c and the perm brick 111b) are expressed by the following equation (20). The x-axis coordinates x _{2_1} at the position of the end of the perm brick 111b on the outer wall surface side of the furnace bottom (the boundary between the perm brick 111b and the refractory castable 111a) are expressed by the following equation (21).

Here, x _{4_n} is derived from the reference value of the x-axis coordinate of the inner wall surface of the furnace bottom (inside and outside of equation (4), which is derived when the inner wall surface of the bottom of the submerged arc furnace 100 is new and unchanged. It is the x-axis coordinate of the fire bottom refractory when the temperature insertion function T ^ (x, t) becomes equal to the temperature of the hot metal 142). λ ₁ is the thermal conductivity of the fireproof castable 111a, λ ₂ is the thermal conductivity of the perm brick 111b, λ ₃ is the thermal conductivity of the wear brick A111c, and λ ₄ is the thermal conductivity of the wear brick B111d. Thermal conductivity. L ₄₁ is the length of the new wear brick B111d in the heat removal direction (x-axis direction), and L ₃₁ is the length of the new wear brick _A111c in the heat removal direction (x-axis direction). Is the length in the heat removal direction (x-axis direction) of the new perm brick 111b.

The x-axis coordinates of the surface inside the furnace bottom are measured in a state where raw materials and the like are not charged into the furnace during the operation of the submerged arc furnace 100. The method of measuring the x-axis coordinates of the surface inside the furnace bottom is not particularly limited, but it is realized by using, for example, a laser range finder or the like. In addition, a measuring rod with a scale indicating the distance from the tip is inserted into the furnace, and the scale when the tip of the measuring rod reaches the inner surface of the furnace bottom can be read. The x-axis coordinates of the surface inside the furnace can be measured. Let x _min be the lowest value among the x-axis coordinates of the inner wall surface of the furnace bottom measured by the current time t in this way. Then, the length (thickness) l ₄ of the wear brick B111d in the heat removal direction (x-axis direction) at time t, and the length (thickness) l of the wear brick A111c in the heat removal direction (x-axis direction) at time t. _3. The length (thickness) l ₂ in the heat removal direction (x-axis direction) of the perm brick 111b at time t is represented by the following equations (22) to (24). Here, it is assumed that the length (thickness) of the refractory castable 111a in the heat removal direction (x-axis direction) does not change from the new state.

In the equation (22), the minimum value x _min of the x-axis coordinate of the inner wall surface of the furnace bottom is equal to or more than the x-axis coordinate x _{4_1} of the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom. Represents l ₄ , l ₃ , and l ₂ . In equation (23), the minimum value x _min of the x-axis coordinates of the inner wall surface of the ware brick A111c is greater than or equal to the x-axis coordinates x _{3_1} of the position of the end of the ware brick A111c on the outer wall surface side of the outer wall surface of the ware brick B111d. Represents each length l ₄ , l ₃ , l ₂ when the coordinates of the x-axis of the position of the edge on the outer wall surface side are less than x _{4_1} . In equation (24), the minimum value x _min of the x-axis coordinates of the inner wall surface of the furnace bottom is the x-axis coordinates x _{2_1} or more of the position of the end of the perm brick 111b on the outer wall surface side of the furnace bottom, and the bottom of the wear brick A111c. Represents each length l ₄ , l ₃ , l ₂ when the coordinates of the x-axis of the position of the edge on the outer wall surface side are less than x _{3_1} .

Residual amount Δl ₄ of the length (thickness) of the wear brick B111d in the heat removal direction (x-axis direction) at time t, the length (thickness) of the wear brick A111c in the heat removal direction (x-axis direction) at time t The residual amount Δl ₃ and the residual amount Δl ₂ of the length (thickness) of the perm brick 111b in the heat removal direction (x-axis direction) at time t are derived by any of the equations (22) to (24). It is derived by subtracting the new lengths L ₄₁ , L ₃₁ , and L ₂₁ from the lengths l ₄ , l ₃ , and l ₂ , and is expressed by the following equation (25).

Further, the x-axis coordinates x _{4_2} of the bottom refractory when the internal / external temperature function T ^ (x, t) of Eq. (4) derived at each time t becomes equal to the temperature of the hot metal 142, and the furnace. If the difference from the minimum value x _min of the x-axis coordinates of the inner wall surface of the bottom is defined as the length d in the heat removal direction (x-axis direction) of the deposit, the length in the heat removal direction (x-axis direction) of the deposit is defined. The (thickness of the deposit) d is expressed by the following equations (26) to (31).

In the equation (26), the minimum value x _min of the x-axis coordinate of the inner wall surface of the furnace bottom is equal to or more than the x-axis coordinate x _{4_1} of the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom. The length d in the heat removal direction (x-axis direction).
In the equation (27), the minimum value x _min of the x-axis coordinate of the inner wall surface of the furnace bottom is the x-axis coordinate x _{3_1} or more of the position of the end of the outer wall surface side of the outer wall surface of the ware brick A111c, and the bottom of the ware brick B111d. Fire bottom fire resistant material when the x-axis coordinate x _{4_1} of the position of the end on the outer wall surface side and the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. This is the length d in the heat removal direction (x-axis direction) of the deposit when the x-axis coordinate x _{4_2} of the ware brick B111d exceeds the x-axis coordinate x _{4_1} at the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom.

In equation (28), the minimum value x _min of the x-axis coordinates of the inner wall surface of the ware brick A111c is greater than or equal to the x-axis coordinates x _{3_1} of the position of the end of the ware brick A111c on the outer wall surface side of the outer wall surface of the ware brick B111d. A fireproof material at the bottom of the furnace when the coordinates of the x-axis of the end position on the outer wall surface side are less than x _{4_1} and the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. The x-axis coordinate x _{4_2} is the length d in the heat removal direction (x-axis direction) of the deposit when the x-axis coordinate x _{4_1} or less of the position of the end of the wear brick B111d on the outer wall surface side of the furnace bottom. ..

In equation (29), the minimum value x _min of the x-axis coordinates of the inner wall surface of the furnace bottom is equal to or more than the x-axis coordinates x _{2_1} of the position of the end of the perma brick 111b on the outer wall surface side of the outer wall surface of the furnace bottom, and the bottom of the ware brick A111c. Fire bottom fire resistant material when the x-axis coordinate x _{3_1} of the position of the end on the outer wall surface side and the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. This is the length d in the heat removal direction (x-axis direction) of the deposit when the x-axis coordinate x _{4_2} of the ware brick B111d exceeds the x-axis coordinate x _{4_1} at the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom.

In equation (30), the minimum value x _min of the x-axis coordinates of the inner wall surface of the furnace bottom is the x-axis coordinates x _{2_1} or more of the position of the end of the perm brick 111b on the outer wall surface side of the furnace bottom, and the bottom of the wear brick A111c. A fireproof material at the bottom of the furnace when the coordinates of the x-axis of the end position on the outer wall surface side are less than x _{3_1} and the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. The x-axis coordinates x _{4_2} are the x-axis coordinates x _{3_1} of the position of the end of the ware brick A111c on the outer wall surface side of the furnace bottom, and the x-axis coordinates x _{4_1} of the position of the end of the ware brick B111d on the outer wall surface side of the furnace bottom. It is the length d in the heat removal direction (x-axis direction) of the deposit in the following cases.

In equation (31), the minimum value x _min of the x-axis coordinates of the inner wall surface of the furnace bottom is greater than or equal to the x-axis coordinates x _{2_1} of the position of the end of the perm brick 111b on the outer wall surface side of the furnace bottom, and the bottom of the wear brick A111c. A fireproof material at the bottom of the furnace when the coordinates of the x-axis of the end position on the outer wall surface side are less than x _{3_1} and the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. The x-axis coordinate x _{4_2} is the length d in the heat removal direction (x-axis direction) of the deposit when the x-axis coordinate x _{3_1} or less of the position of the end of the wear brick A111c on the outer wall surface side of the furnace bottom. ..

As described above, the heat flux / wall surface position deriving unit 205 is in the heat extraction direction (x-axis direction) of the wear brick B111d, the wear brick A111c, and the perm brick 111b at time t according to the equations (22) to (24). The lengths (thickness) l ₄ , l ₃ , and l ₂ are derived. Further, the heat flux / wall surface position derivation unit 205 has a residual amount of length (thickness) in the heat removal direction (x-axis direction) of the wear brick B111d, the wear brick A111c, and the perm brick 111b at time t according to the equation (25). Derivation of Δl ₄ , Δl ₃ , and Δl ₂ . Further, the heat flux / wall surface position derivation unit 205 derives the length (thickness of the deposit) d in the heat removal direction (x-axis direction) of the deposit by the formulas (26) to (31).

Here, the length (thickness of the deposit) d in the heat removal direction (x-axis direction) of the deposit does not become a negative value (d ≧ 0). Therefore, the heat flux / wall surface position derivation unit 205 has the x-axis coordinates x _{4_2} of the fire bottom fireproof material when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. When the minimum value x _min of the x-axis coordinates of the inner wall surface of the furnace bottom is exceeded, the length (thickness of the deposit) d in the heat removal direction (x-axis direction) of the deposit is derived.

The heat flow flux / wall surface position derivation unit 205 has lengths (thicknesses) l ₄ , l ₃ , l ₂ in the heat removal direction (x-axis direction) of the wear brick B111d, the wear brick A111c, and the perm brick 111b at time t. The length (thickness) of the fireproof castable 111a in the heat removal direction (x-axis direction) and the length (thickness) d of the heat removal direction (x-axis direction) of the deposit at time t are determined. The value added to the x-axis coordinates of the outer wall surface is derived as the x-axis coordinates of the inner wall surface of the furnace bottom at time t.

<Output unit 206>
The output unit 206 outputs the heat flux q _v on the inner wall surface side of the furnace core and the x-axis coordinates of the inner wall surface of the furnace bottom at each time t derived by the heat flux / wall surface position derivation unit 205. As the form of output, for example, at least one of display on a computer display, storage in an internal or external storage medium of the equipment monitoring device 200, and transmission to an external device can be adopted. Further, in place of or in addition to these information, the output unit 206 has lengths (thicknesses) l ₄ , l ₃ , l in the heat removal direction (x-axis direction) of the wear brick B111d, the wear brick A111c, and the perm brick 111b. ₂ , the length (thickness) residual amount of the wear brick B111d, the wear brick A111c, and the perm brick 111b in the heat removal direction (x-axis direction) residual amounts Δl ₄ , Δl ₃ , Δl ₂ , and the heat removal direction (x-axis) of the deposit. At least one of the length (thickness of the deposit) d in the direction) may be output.

(Calculation example)
FIG. 5 is a diagram showing an example of the calculation result by the equipment monitoring device 200. FIG. 5A shows the relationship between the position of the inner wall surface of the furnace bottom and time, FIG. 5B shows the relationship between heat flux and time, and FIG. 5C shows the heat transfer coefficient and time. 5 (d) shows the relationship between the temperature measured by the thermocouple (thermocouple temperature) and time.

In FIG. 5A, the position of the inner wall surface of the furnace bottom indicates the coordinates of the x-axis of the inner wall surface of the furnace bottom. Here, the value on the x-axis at the position of the outer wall surface of the furnace bottom is set to "0 (zero)". The furnace bottom inner wall surface position (calculation) indicates the x-axis coordinates of the furnace bottom inner wall surface derived by the heat flux / wall surface position deriving unit 205. The position of the inner wall surface of the furnace bottom (actual measurement) is the x-axis coordinate of the inner wall surface of the furnace bottom measured between the operations of the submerged arc furnace 100. The position of the inner wall surface of the furnace bottom (minimum value of actual measurement) is the minimum value of the x-axis coordinates of the inner wall surface of the furnace bottom x _min (the lowest value of the position of the inner wall surface of the furnace bottom (actual measurement)) (the position of the inner wall surface of the furnace bottom (actual measurement). ) Is obtained in the period before the period shown in FIG. 5 (a)).

In FIG. 5B, the heat flux is the heat flux q _v on the inner wall surface side of the furnace core, which is derived by the heat flux / wall surface position lead-out unit 205.
In FIG. 5 (c), the heat transfer coefficient is the furnace bottom heat transfer coefficient h _a (t) derived by the heat transfer coefficient derivation unit 203.
In FIG. 5D, the core temperature is the temperature measured by the core thermometer 191 and the core peripheral temperature (inner wall surface side) is the temperature measured by the core peripheral furnace inner thermometer 193. Yes, the core peripheral temperature (outer wall surface side) is the temperature measured by the furnace core peripheral thermometer 192, and the air cooling temperature is the air cooling temperature _Ta (t).

In FIG. 5A, since the position of the inner wall surface of the furnace bottom (calculation) is larger than the position of the inner wall surface of the furnace bottom (minimum value of actual measurement) at all time zones, the deposits are attached to the refractory material of the bottom of the furnace. Is shown. When a time zone in which the position of the inner wall surface of the furnace bottom (calculation) is smaller than the position of the inner wall surface of the furnace bottom (minimum value of actual measurement) appears, it indicates that the time zone is the time zone in which the refractory in the bottom of the furnace is melted. Further, as shown in FIGS. 5 (b) and 5 (c), it can be seen that the heat flux and the heat transfer coefficient of the bottom of the furnace change from moment to moment.

(flowchart)
Next, an example of the equipment monitoring method using the equipment monitoring device 200 will be described with reference to the flowchart of FIG.
In step S601, the equipment monitoring device 200 sets the time t to the initial value t _ini . Steps S602 to S609 are executed as processing for the time t.
Next, in step S602, the temperature acquisition unit 201 includes an upstream thermometer 181, a downstream thermometer 182, a hot metal thermometer 183, a core thermometer 191 and a core peripheral furnace outside thermometer 192, and a core peripheral furnace. The temperature measured by the inner thermometer 193 is acquired.

Next, in step S603, the first inverse problem analysis unit 202 derives the weight vector α (element α _j ) (see equations (7) to (10)).
Next, in step S604, the heat transfer coefficient derivation unit 203 derives the temperature T _v (t) of the outer wall surface of the furnace bottom and the heat flux q _v (t) on the outer wall surface of the outer wall surface around the furnace core ((4). ) And equation (11)).

Next, in step S605, the heat transfer coefficient deriving unit 203 derives the heat transfer coefficient h _a (t) from the bottom (see Eq. (12)).
Next, in step S606, the second inverse problem analysis unit 204 derives the weight vector α (element α _j ) (Equation (7), Eq. (9), Eq. (16), and Eq. (17)). See).

Next, in step S607, the heat flux / wall surface position derivation unit 205 includes the x-axis coordinates of the bottom refractory material when the internal / external temperature function T ^ (x, t) becomes equal to the temperature of the hot metal 142, and the furnace. Derivation of the heat flux q _v on the inner wall surface side of the core furnace bottom (see equations (4), (11), and (11)').
Next, in step S608, the heat flux / wall surface position deriving unit 205 derives the x-axis coordinates of the actual inner wall surface of the furnace bottom (see equations (22) to (31)).
Next, in step S609, the output unit 206 outputs the heat flux q _v on the inner wall surface side of the furnace core and the x-axis coordinates of the inner wall surface of the furnace bottom.

Next, in step S610, the equipment monitoring device 200 determines whether or not to end the monitoring of the submerged arc furnace 100. This determination can be made, for example, by whether or not the time t _max has elapsed. Further, this determination can also be made by an instruction from the operator to the equipment monitoring device 200. Further, this determination can also be made by an instruction from a higher-level computer that manages the operation of the submerged arc furnace 100.

As a result of this determination, when the monitoring of the submerged arc furnace 100 is terminated, the process according to the flowchart of FIG. 6 is terminated. On the other hand, if the monitoring of the submerged arc furnace 100 is not completed, the process proceeds to step S611. In step S611, the equipment monitoring device 200 adds Δt to the time t to update the time t. Then, the processes of steps S602 to S609 are executed at the updated time t.
The process of step S609 may be performed after it is determined in step S610 that the monitoring of the submerged arc furnace 100 is completed.

(summary)
As described above, in the present embodiment, the equipment monitoring device 200 solves the one-dimensional unsteady heat transfer reverse problem based on the temperature measured by the core peripheral furnace outside thermometer 192 and the core peripheral furnace inside thermometer 193. As a result, the heat transfer flux q _v (t) on the outer wall surface side of the furnace bottom around the furnace core and the temperature T _v (t) on the outer wall surface of the furnace bottom are derived, and these and the air cooling temperature T _a (t) are used to derive the temperature T v (t). The heat transfer coefficient h _a (t) is derived. Then, the equipment monitoring device 200 solves the one-dimensional unsteady heat transfer inverse problem based on the temperature measured by the core thermometer 191 and the bottom heat transfer coefficient _ha (t), thereby causing the one-dimensional unsteady heat transfer. By solving the steady heat transfer reverse problem, the heat flux q _v on the inner wall surface side of the core furnace bottom and the x of the fire bottom fire resistant material when the internal / external temperature function T ^ (x, t) becomes equal to the temperature of the hot metal 142. Derive the coordinates of the axis. Therefore, even if the furnace core 101 has only one thermometer, the one-dimensional unsteady heat transfer inverse problem can be solved accurately, and the heat flux at the position of the furnace core 101 on the inner wall surface of the furnace bottom and the coordinates of the position. Can be derived in real time. Therefore, it is possible to accurately monitor the state of the refractory material constituting the inner peripheral surface of the equipment in which the molten metal is present in real time.

Further, in the present embodiment, a one-dimensional unsteady heat conduction equation is constructed assuming that the refractory at the bottom of the fire is composed only of the refractory castable 111a. Therefore, the one-dimensional unsteady heat conduction equation can be solved without considering the thermal resistance due to the contact of different refractories. Therefore, the model error can be reduced.
Further, in the present embodiment, the equipment monitoring device 200 has the thermal conductivity λ ₁ to λ ₄ of the fireproof castable 111a, the perm brick 111b, the ware brick A111c, and the ware brick B111d, and the coordinates of the x-axis of the inner wall surface of the furnace bottom. Using the minimum value x _min and the x-axis coordinates x _{4_n} , x _{4_2} of the bottom fire resistant material when the internal / external temperature function T ^ (x, t) in Eq. (4) becomes equal to the temperature of the hot metal 142. , Wear brick B111d, wear brick A111c, length (thickness) l ₄ , l ₃ , l ₂ in the heat removal direction (x-axis direction) of wear brick B111d, wear brick A111c, and perma brick 111b. Derivation of the length (thickness) residual amount Δl ₄ , Δl ₃ , Δl ₂ in the thermal direction (x-axis direction) and the length (thickness) d in the heat removal direction (x-axis direction) of the deposit. .. Therefore, it is possible to monitor the more detailed state of the refractory at the bottom of the fire.

In this embodiment, the submerged arc furnace has been described as an example. However, the equipment in which the molten metal is present has a refractory material constituting the inner peripheral surface of the equipment, and the inside of the refractory material is in contact with the molten metal or other substances are present in between. If the equipment is arranged in a state where the outside of the refractory is in contact with the cooling medium or in a state where other substances are present in between, the method of the present embodiment is other than the submerged arc furnace. It can also be applied to the equipment of. The equipment may be equipment for producing molten metal, equipment for processing molten metal, or equipment for accommodating molten metal. Further, the cooling medium may be a gas (for example, air) or a liquid (for example, water) as in the present embodiment.

The embodiment of the present invention described above can be realized by executing a program by a computer. 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 non-volatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of embodiment of the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

100: Submerged arc furnace, 101: furnace core, 111: furnace body, 111a: refractory castable, 111b: perma brick, 111c: ware brick A, 111d: ware brick B, 112: furnace lid, 121-122: raw material packaging Enter chute, 131-132: Exhaust part, 141: Slag, 142: Hot metal, 151-153: Electrode, 161: Outlet port, 162: Outlet port, 171: Distribution channel, 181-183: Thermometer, 191- 193: Thermometer (thermocouple)

Claims (14)

Equipment in which molten metal is present, with refractory material constituting the inner peripheral surface of the equipment, and in a state where the inside of the refractory material is in contact with the molten metal or in a state where other substances are present in between. An equipment monitoring device that monitors equipment that is arranged and is arranged so that the outside of the refractory is in contact with the cooling medium or has other substances in between.
The temperature measured by the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means, which are arranged at different positions inside the fireproof material, and the temperature of the cooling medium are measured. The temperature acquisition means for acquiring the temperature measured by the temperature measuring means of No. 4, and the temperature acquisition means for acquiring the temperature.
Using the temperature measured by the first temperature measuring means and the temperature measured by the second temperature measuring means, the part of the equipment where the outside of the fireproof material comes into contact with the cooling medium or The temperature on the surface of the outer part , which is the part in contact with the substance existing between the cooling medium, and the value of the component of the heat transfer vector on the surface of the outer part of the equipment in the heat removal direction of the fireproof material. The first derivation means to derive based on the result of one-dimensional unsteady heat transfer reverse problem analysis,
A fourth measure of the temperature on the surface of the outer portion of the equipment, the value of the component of the heat flux vector on the surface of the outer portion of the equipment in the heat removal direction of the fireproof material, and the temperature of the cooling medium. A second derivation means for deriving the heat transfer coefficient between the material constituting the refractory material and the cooling medium using the temperature measured by the temperature measuring means, and
Using the temperature measured by the third temperature measuring means and the heat transfer coefficient derived by the second derivation means, the temperature and the temperature of the molten metal become equal to each other in the heat removal direction of the refractory material. A one-dimensional non-stationary heat transfer reverse problem analysis was performed on the temperature matching position, which is the position, and the value of the component of the heat flux vector on the surface of the part in contact with the molten metal of the equipment in the heat removal direction of the fireproof material. It has a third derivation means, which derives based on the result.
The position of the first temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material and the position of the second temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material are substantially the same. The position of the third temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material, and the position of the first temperature measuring means and the second temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material. Equipment monitoring equipment characterized by different positions. The temperature acquisition means further acquires the temperature measured by the fifth temperature measuring means for measuring the temperature of the molten metal.
The equipment monitoring device according to claim 1, wherein the third derivation means derives the temperature matching position by using the temperature measured by the fifth temperature measuring means as the temperature of the molten metal. The refractory is a plurality of types of refractories arranged in the heat removal direction of the refractory, and has a plurality of types of refractories having different thermal conductivitys.
The first temperature measuring means, the second temperature measuring means, and the third temperature measuring means are arranged inside the same type of refractory among the plurality of types of refractories.
In the one-dimensional unsteady heat transfer reverse problem analysis, the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means are arranged among the physical property values of the plurality of types of fireproof materials. The equipment monitoring device according to claim 1 or 2, wherein only the physical property values of the fireproof material are used. Other than the third temperature measuring means, the temperature measuring means for measuring the temperature at the same position as the position in the direction perpendicular to the heat removal direction of the fireproof material, which is the position of the temperature measured by the third temperature measuring means. The equipment monitoring device according to any one of claims 1 to 3, wherein the equipment monitoring device is not provided. Further having a fourth derivation means for deriving the current position of the surface of the portion of the equipment in contact with the molten metal in the heat removal direction of the refractory.
The refractory is a plurality of types of refractories arranged in the heat removal direction of the refractory, and has a plurality of types of refractories having different thermal conductivitys.
The first temperature measuring means, the second temperature measuring means, and the third temperature measuring means are arranged inside the same type of refractory among the plurality of types of refractories.
In the one-dimensional unsteady heat transfer reverse problem analysis, the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means are arranged among the physical property values of the plurality of types of fireproof materials. Only the physical properties of the fireproof material are used,
The fourth derivation means is the fire resistance of the thermal conductivity of the plurality of types of refractories, the temperature matching position derived by the third derivation means, and the surface of the portion of the facility in contact with the molten metal. The refractory material on the surface of the part of the equipment in contact with the molten metal , using the measured value of the position of the object in the heat removal direction, which indicates the position closest to the surface of the outer part of the equipment. The equipment monitoring device according to any one of claims 1 to 4, wherein the current position in the heat removal direction is derived. The one-dimensional unsteady heat transfer inverse problem analysis is a non-stationary heat transfer inverse problem analysis using an internal / external temperature function that satisfies the one-dimensional unsteady heat transfer equation.
The internal / external temperature function is characterized by being a function T ^ (x, t) indicating the temperature inside the refractory at a position x in the x-axis direction, which is the heat removal direction of the refractory, and a time t. The equipment monitoring device according to any one of claims 1 to 5. The extrapolation temperature function T ^ (x, t) is the value of the product of the basis function φ _j determined for each center point j and the weight vector α _j determined for each center point j at each of the center points j. Expressed as sum
The center point j is a point determined from the reference position x _j in the x-axis direction of the fireproof object and the reference time t _j , and is on two-dimensional coordinates determined by the position and time in the x-axis direction of the fireproof object. Is the point,
The sixth aspect of claim 6, wherein the basis function φ _j is a function expressed in the form of a fundamental solution satisfying the one-dimensional unsteady heat conduction equation when the center point j is used as a reference. Equipment monitoring device. The first derivation means includes the one-dimensional non-stationary heat conduction equation, the first temperature function T ₁ (x ₁ ^* , t), and the second temperature function T ₁ (x ₂ ^* , t). The internal / external temperature function T ^ (x, t) and the second The weight is solved by substituting the information of the definition point of the first information amount into the simultaneous equation with the internal / external temperature function T ^ (x, t) to which the measurement result by the temperature measuring means is given. Derivation of the vector α _j ,
The definition point of the first information amount is a point determined by the position and time of the temperature measured by the first temperature measuring means, and is two-dimensional determined by the position and time of the fireproof object in the x-axis direction. A point on the coordinates, a point determined by the position and time of the temperature measured by the second temperature measuring means, and a point on the two-dimensional coordinates determined by the position and time in the x-axis direction of the fireproof object. Including
The first temperature function T ₁ (x ₁ ^* , t) is the first temperature position x ₁ ^* and time t measured by the first temperature measuring means in the x-axis direction of the fireproof object. It is a function that expresses the temperature measured by the temperature measuring means.
The second temperature function T ₂ (x ₂ ^* , t) is the second temperature at the temperature position x ₁ ^* and time t measured by the second temperature measuring means in the x-axis direction of the refractory material. The equipment monitoring device according to claim 7, wherein the equipment is a function representing a temperature measured by a temperature measuring means. The weight vector α _j is calculated by the following equations (A) to (D).
The following m is the number of the center points j determined by the position and time of the temperature measured by the first temperature measuring means.
The following l is the number of the center points j determined by the position and time of the temperature measured by the second temperature measuring means, and the following k is for identifying the definition point of the first information amount. It is an integer from 1 to m of
The following s is an integer from m + 1 to l for identifying the definition point of the first information amount.
The following j is an integer from 1 to m + l for identifying the center point j, and is an integer.
The following A is a (m + l) × (m + l) matrix.
The φ (x _k − x _j , tk −t _j ) in [] of A below is the value of the k-by- _j -column component of the matrix A.
The φ (x _s − x _j , t _s − t _j ) in [] of A below is the value of the s row j column component of the matrix A.
The following x are the coordinates of the x-axis.
The following t is the time,
The following b is a (m + l) dimensional column vector.
Obs1 _k in [] of b below is the value of the k-row component of the matrix b, and is the temperature measured by the first temperature measuring means.
_Obs2k in [] of b below is the value of the s row component of the matrix b, and is the temperature measured by the second temperature measuring means.
The equipment monitoring device according to claim 8, wherein α below is a (m + l) dimensional column vector.

The third derivation means includes the one-dimensional non-stationary heat conduction equation, the boundary conditions in the one-dimensional non-stationary heat conduction equation, the third temperature function T ₃ (x ₃ ^* , t), and the internal / extrapolation. The internal / external temperature function T ^ (the boundary condition in the one-dimensional non-stationary heat conduction equation and the measurement result by the third temperature measuring means are given so as to satisfy the temperature function T ^ (x, t). By substituting the information of the definition point of the second information amount into the simultaneous equations with x, t) and solving the simultaneous equations, the weight vector α _j is derived.
The definition point of the second amount of information is the position of the surface of the outer portion of the equipment, which is determined by the position and time of the third temperature measuring means in the direction perpendicular to the heat removal direction. A point on two-dimensional coordinates determined by the position and time of the fireproof object in the x-axis direction, and a point determined by the position and time of the temperature measured by the third temperature measuring means, which is the fire resistance. Includes points on two-dimensional coordinates determined by the position of the object in the x-axis direction and the time.
The boundary conditions in the one-dimensional non-stationary heat conduction equation are a heat flux based on the temperature gradient in the x-axis direction on the surface of the outer portion of the equipment and the thermal conductivity of the material constituting the refractory material, and the heat flux. The difference between the temperature on the surface of the outer portion of the equipment and the temperature of the cooling medium, and the thermal transfer coefficient between the material constituting the fireproof material derived by the second derivation means and the cooling medium. It is an equation showing that the heat flux based on is equal to each other.
The third temperature function T ₁ (x ₃ ^* , t) is the third temperature function T 1 (x 3 *, t) at the temperature position x ₃ ^* measured by the third temperature measuring means in the x-axis direction of the fireproof object and at time t. The equipment monitoring device according to any one of claims 7 to 9, wherein the equipment is a function representing a temperature measured by a temperature measuring means. The weight vector α _j is calculated by the following equations (E) to (H).
The following m is the number of the center points j determined by the position and time of the surface of the outer portion of the equipment.
The following l is the number of the center points j determined by the position and time of the temperature measured by the third temperature measuring means, and the following k is for identifying the definition point of the second information amount. It is an integer from 1 to m of
The following s is an integer from m + 1 to l for identifying the definition point of the second information amount.
The following j is an integer from 1 to m + l for identifying the center point j, and is an integer.
The following A is a (m + l) × (m + l) matrix.
Λ ∂φ / ∂x (x _k - _{x j} , tk-t _j ) + ha (x _k -x _j , tk -t _j ) φ ( _{x k-x j , in [} ] of A below tk −t _j ) is the value of the k-by- _j -column component of the matrix A.
The φ (x _s − x _j , y _s − y _j , t _s −t _j ) in [] of A below is the value of the s row j column component of the matrix A.
The following λ is the thermal conductivity of the material constituting the refractory.
The following ha is _a heat transfer coefficient between the material constituting the refractory and the cooling medium derived by the second derivation means.
The following x are the coordinates of the x-axis.
The following t is the time,
The following b is a (m + l) dimensional column vector.
The following g _k is the value of the k-row component of the matrix b, and is between the temperature of the cooling medium and the material constituting the refractory derived by the second derivation means and the cooling medium. It is the product of the heat transfer coefficient h _a and
The following obs3 _sm is the value of the s row component of the matrix b, and is the temperature measured by the third temperature measuring means.
The equipment monitoring device according to claim 10, wherein α below is a (m + l) dimensional column vector.

The equipment monitoring device according to any one of claims 1 to 11, wherein the equipment is a submerged arc furnace in which a raw material molded into a predetermined shape is energized and heated by an electrode. Equipment in which molten metal is present, with refractory material constituting the inner peripheral surface of the equipment, and in a state where the inside of the refractory material is in contact with the molten metal or in a state where other substances are present in between. An equipment monitoring method for monitoring equipment that is arranged and is arranged so that the outside of the refractory is in contact with the cooling medium or has other substances in between.
The temperature measured by the first temperature measuring means, the second temperature measuring means, and the third temperature measuring means, which are arranged at different positions inside the fireproof material, and the temperature of the cooling medium are measured. The temperature acquisition step of acquiring the temperature measured by the temperature measuring means of No. 4 and
Using the temperature measured by the first temperature measuring means and the temperature measured by the second temperature measuring means, the part of the equipment where the outside of the fireproof material comes into contact with the cooling medium or The temperature on the surface of the outer part , which is the part in contact with the substance existing between the cooling medium, and the value of the component of the heat transfer vector on the surface of the outer part of the equipment in the heat removal direction of the fireproof material. The first derivation step, which is derived based on the result of one-dimensional unsteady heat transfer reverse problem analysis,
A fourth measure of the temperature on the surface of the outer portion of the equipment, the value of the component of the heat flux vector on the surface of the outer portion of the equipment in the heat removal direction of the fireproof material, and the temperature of the cooling medium. A second derivation step of deriving the heat transfer coefficient between the material constituting the refractory material and the cooling medium using the temperature measured by the temperature measuring means, and
Using the temperature measured by the third temperature measuring means and the heat transfer coefficient derived by the second derivation step, the temperature of the molten metal becomes equal to the temperature in the heat removal direction of the refractory material. A one-dimensional non-stationary heat transfer reverse problem analysis was performed on the temperature matching position, which is the position, and the value of the component of the heat flux vector on the surface of the part in contact with the molten metal of the equipment in the heat removal direction of the fireproof material. It has a third derivation step, which is derived based on the result.
The position of the first temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material and the position of the second temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material are substantially the same. The position of the third temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material, and the position of the first temperature measuring means and the second temperature measuring means in the direction perpendicular to the heat removal direction of the fireproof material. Equipment monitoring method characterized by different locations. A program for operating a computer as each means of the equipment monitoring device according to any one of claims 1 to 12.

Images