Facility, facility status monitoring device, facility status monitoring method, and program

Abstract

In an electric furnace (1), an inner peripheral surface (6a) of a side wall part (6) is composed of a refractory. Further, optical fibers (121 to 122) provided in optical fiber temperature sensors (111, 112) are embedded in a member constituting the side wall part (6).

Description

[Technical field]

[0001] The present disclosure relates to a facility, a facility status monitoring device, a facility status monitoring method, and a program, and is particularly suitable for use in a facility in which molten metal is present during operation. This application claims priority based on Japanese Patent Application No. 2023-065494 filed in Japan on April 13, 2023, the contents of which are incorporated herein by reference in their entirety. [Background technology]

[0002] In facilities that produce molten metal, such as electric furnaces and blast furnaces, molten metal is present inside during operation. This causes the inside of the facilities to become very hot. Therefore, refractories such as firebricks are arranged on the inner circumferential surface of the facilities. As the refractories are exposed to high-temperature molten metal, they are worn out as the facilities are used, with parts of them melting or peeling off. Therefore, technology is required to monitor the condition of the refractories.

[0003] One such technique is described in Patent Document 1. In the technique described in Patent Document 1, the temperature of the inner circumferential surface of the furnace is calculated by solving a one-dimensional inverse heat transfer problem using measurements from two thermocouples embedded in the hearth wall of a blast furnace. Then, in the technique described in Patent Document 1, the position at which the temperature calculated in this way becomes a temperature that defines the inner circumferential surface of the furnace is calculated as the position of the inner circumferential surface of the furnace. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2001-234217 A Summary of the Invention [Problem to be solved by the invention]

[0005] However, the technology described in Patent Document 1 uses the measured value of a thermocouple that is embedded in the refractory material beforehand. Therefore, the temperature measurement positions of the equipment are limited. In addition, it is not easy to install new temperature sensors. Furthermore, when increasing the number of temperature measurement positions, it is necessary to embed many thermocouples in the refractory material. However, it is practically difficult to embed many thermocouples in the refractory material.

[0006] The present disclosure has been made in consideration of the above problems, and aims to make it possible to measure temperatures over a wider range as the temperature of the side wall of equipment containing molten metal during operation. [Means for solving the problem]

[0007] The equipment disclosed herein is an equipment in which molten metal is present during operation, and the inner circumferential surface of a side wall of the equipment is made of a refractory material, and an optical fiber provided in an optical fiber temperature sensor is embedded in a member constituting the side wall. Among the members constituting the side wall portion, the member in which the optical fiber is embedded is a fire-resistant block produced by precasting a molded refractory material in a state in which the optical fiber is embedded. do.

[0008] The equipment status monitoring device of the present disclosure is The equipment has molten metal inside during operation, and the inner circumferential surface of the side wall of the equipment is made of refractory material, and the optical fiber of the optical fiber temperature sensor is embedded in a member constituting the side wall. An equipment status monitoring device that monitors the status of equipment, comprising: an inverse problem analysis means that calculates a temperature distribution of the side wall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on measurement values ​​of a temperature sensor that measures the temperature of the side wall portion; and a refractory position calculation means that calculates a position of the inner circumferential surface based on the temperature distribution calculated by the inverse problem analysis means, wherein the inverse problem analysis means calculates a temperature distribution in a thickness direction of the side wall portion, and the position of the inner circumferential surface calculated by the refractory position calculation means includes a position in the thickness direction of the side wall portion, and the temperature sensor measures a temperature at a position relatively closer to the inner circumferential surface of the side wall portion and a temperature at a position relatively closer to the outer circumferential surface of the side wall portion at a portion of the side wall portion different from the inner circumferential surface of the side wall portion, and the temperature sensor that measures at least the temperature at the position relatively closer to the inner circumferential surface of the side wall portion among the temperature at the position relatively closer to the inner circumferential surface of the side wall portion and the temperature at the position relatively closer to the outer circumferential surface of the side wall portion is the optical fiber temperature sensor.

[0009] The equipment status monitoring method of the present disclosure includes: The equipment has molten metal inside during operation, and the inner circumferential surface of the side wall of the equipment is made of refractory material, and the optical fiber of the optical fiber temperature sensor is embedded in a member constituting the side wall. An equipment status monitoring method for monitoring a status of equipment, the method comprising: an inverse problem analysis step of calculating a temperature distribution of the sidewall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on a measurement value of a temperature sensor that measures a temperature of the sidewall portion; and a refractory position calculation step of calculating a position of the inner circumferential surface based on the temperature distribution calculated by the inverse problem analysis step, wherein the inverse problem analysis step calculates a temperature distribution in a thickness direction of the sidewall portion, and the position of the inner circumferential surface calculated in the refractory position calculation step includes a position in the thickness direction of the sidewall portion, and the temperature sensor measures a temperature at a position relatively closer to the inner circumferential surface of the sidewall portion and a temperature at a position relatively closer to the outer circumferential surface of the sidewall portion at a portion of the sidewall portion different from an inner circumferential surface of the sidewall portion, and at least one of the temperature at the position relatively closer to the inner circumferential surface of the sidewall portion and the temperature at the position relatively closer to the outer circumferential surface of the sidewall portion is calculated. The temperature sensor for measuring the temperature at a position on the inner circumferential surface side of the side wall portion is The optical fiber temperature sensor.

[0010] The program disclosed herein causes a computer to function as each of the means of the equipment status monitoring device. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram showing an example of the configuration of an electric furnace. [Diagram 2] FIG. 2 is a cross-sectional view taken along line II in FIG. [Diagram 3] FIG. 3 is a diagram showing an example of the configuration of a precast block in which optical fibers are embedded. [Figure 4A] FIG. 4A is a diagram conceptually explaining a first example of heat transfer that can be considered in a one-dimensional unsteady heat transfer inverse problem. [Figure 4B] FIG. 4B is a diagram conceptually explaining a second example of heat transfer that can be considered in a one-dimensional unsteady heat transfer inverse problem. [Figure 5A] FIG. 5A is a diagram illustrating a first example of heat transfer that can be considered in a three-dimensional unsteady heat transfer inverse problem. [Figure 5B] FIG. 5B is a diagram illustrating a second example of heat transfer that can be considered in a three-dimensional unsteady heat transfer inverse problem. [Figure 6] FIG. 6 is a diagram illustrating an example of a functional configuration of the facility state monitoring device. [Figure 7] FIG. 7 is a diagram illustrating an example of a hot spot region. [Figure 8A] FIG. 8A is a diagram showing a first example of a position of temperature acquired when performing a three-dimensional unsteady heat transfer inverse problem analysis. [Figure 8B] FIG. 8B is a diagram showing a second example of the positions of temperatures acquired when performing a three-dimensional unsteady heat transfer inverse problem analysis. [Figure 9A] FIG. 9A is a diagram showing an example of a region including a worn portion when the side wall portion is viewed from above. [Figure 9B] FIG. 9B is a diagram showing an example of a region including a worn portion when the side wall portion is viewed from the central axis side of the electric furnace. [Figure 10] FIG. 10 is a flowchart illustrating an example of a facility state monitoring method. [Figure 11A] FIG. 11A is a diagram showing a first example of the relationship between the refractory temperature and the distance in the refractory thickness direction. [Figure 11B] FIG. 11B is a diagram showing a second example of the relationship between the refractory temperature and the distance in the thickness direction of the refractory. [Figure 12] FIG. 12 is a diagram illustrating an example of a hardware configuration of an equipment state monitoring device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings. In addition, the fact that the length, position, size, interval, etc. of the objects being compared are the same includes not only the case where they are exactly the same, but also the case where they are different within the scope of the gist of the present disclosure (for example, the case where they are different within the range of the tolerance determined at the time of design). In addition, in each drawing, for the convenience of explanation and notation, a part of the configuration is omitted or simplified.

[0013] The equipment status monitoring device 100 of the present embodiment described later monitors the state of the inner peripheral surface of the side wall of the equipment in which molten metal exists during operation. The inner peripheral surface of the side wall of the equipment is a surface that contacts a space in which molten metal may exist (for example, a surface facing the central axis (center line) side of the equipment). The inner peripheral surface of the side wall of the equipment is made of refractory material. In the present embodiment, an arc melting furnace, which is a type of electric furnace, is exemplified as such equipment. However, the equipment monitored by the equipment status monitoring device 100 is not limited. In the arc melting furnace, raw materials such as scrap are charged into the furnace for each charge (ch). After that, the raw materials are melted and fused by the arc generated from the arc electrode. As a result, molten metal (for example, molten steel) and molten slag are produced. In the present embodiment, the period from the timing of charging the raw materials into the furnace to the timing of discharging the molten metal and molten slag out of the furnace is called a charge. The side wall of the arc melting furnace is exposed to high temperatures. Therefore, refractories such as firebricks are used to form the sidewalls of the arc melting furnace. As described above, the equipment monitored by the equipment status monitoring device 100 is not limited to the arc melting furnace. For example, the equipment monitored by the equipment status monitoring device 100 may be an electric furnace other than the arc melting furnace, or may be an industrial furnace such as a blast furnace or a converter.

[0014] <Equipment> Fig. 1 is a diagram showing an example of the configuration of an electric furnace 1. Fig. 1 is a vertical cross-sectional view of the electric furnace 1. For convenience of notation and explanation, hatching indicating a cut surface is omitted in Fig. 1. In this embodiment, an electric furnace 1 includes an upper lid 2, arc electrodes 3a to 3c, a furnace bottom electrode 4, a furnace bottom portion 5, and a side wall portion 6. As shown in FIG. Fig. 1 illustrates an example in which the electric furnace 1 includes three arc electrodes 3a-3c. Fig. 1 also illustrates an example in which the three arc electrodes 3a-3c are installed at equal intervals (120° intervals) around the central axis (center line) O of the electric furnace 1. In the following description, the direction around the central axis (center line) O of the electric furnace 1 will be referred to as the circumferential direction as necessary. In the following description, the central axis (center line) O of the electric furnace 1 will be abbreviated to the central axis O as necessary.

[0015] 1 illustrates an example in which the side wall portion 6 is installed so as to surround the central axis O. In addition, in the present embodiment, FIG. 1 illustrates an example in which the side wall portion 6 has wear bricks 7, permanent bricks 8, precast blocks 9, and an iron shell 10. Refractory bricks are used to form the wear bricks 7. Of the faces of the wear bricks 7, the face facing the central axis O forms the inner circumferential surface 6a of the side wall portion 6 of the electric furnace 1. In the following description, the inner circumferential surface 6a side of the side wall portion 6 of the electric furnace 1 will be referred to as the inner side as necessary. The inner side is the side closer to the central axis O of the electric furnace 1. The side opposite the inner side will be referred to as the outer side as necessary. The outer side is the outer circumferential surface 6b side of the side wall portion 6 of the electric furnace 1 (the side farther from the central axis O of the electric furnace 1).

[0016] Firebricks are used to form the permanent bricks 8. The permanent bricks 8 are installed outside the wear bricks 7. The outer end of the wear brick 7 and the inner end of the permanent brick 8 are connected (fixed) to each other, for example, via a material that is heat-resistant and adhesive. The material that is heat-resistant and adhesive is, for example, mortar. The shell 10 is placed outside the permanent bricks 8. The shell 10 constitutes the outer peripheral surface 6b of the side wall portion 6 of the electric furnace 1. The inner end of the shell 10 and the outer end of the permanent bricks 8 are connected (fixed) to each other, for example, via a heat-resistant and adhesive material. The heat-resistant and adhesive material is, for example, mortar.

[0017] The above-mentioned configuration of the electric furnace is a general configuration of the electric furnace. The configuration of the electric furnace is not limited to the above-mentioned configuration of the electric furnace. In the electric furnace 1 of the present embodiment, a precast block 9 is installed in a part of the area where the permanent bricks 8 are installed in such a general electric furnace. The precast block 9 is an example of a precast refractory block. As described later, in the present embodiment, a case is illustrated in which the precast block 9 is produced by precasting an amorphous refractory with an optical fiber provided in the optical fiber temperature sensor embedded therein.

[0018] In the electric furnace 1 illustrated in FIG. 1, when scrap, which is the raw material, melts down, the side wall 6 becomes locally extremely hot due to radiant heat generated by the arc discharge. Therefore, the temperature distribution of the side wall 6 in a virtual plane parallel to the inner circumferential surface 6a has a local maximum value (local maximum value). In the following description, such a position where the temperature is locally maximum will be referred to as a hot spot as necessary. Note that in an electric furnace (arc melting furnace) equipped with arc electrodes 3a to 3c, there are at least as many hot spots as the number of arc electrodes per virtual plane parallel to the inner circumferential surface 6a (in the example illustrated in FIG. 1, there are at least three hot spots).

[0019] In this embodiment, a case will be illustrated in which the precast blocks 9 are installed so as to satisfy all of the following (A) to (D). (A) The position of the outer edge of the precast block 9 is the same as the outer edge of the permanent brick 8 or is located more inward than the outer edge of the permanent brick 8. (B) The position of the inner end of the precast block 9 is the same as the inner end of the permanent brick 8, or is further outboard than the inner end of the permanent brick 8. (C) The circumferential position of the precast block 9 includes the circumferential position of the area where hot spots are expected to occur. (D) The height position of precast block 9 includes the height position of the area where hot spots are expected to occur.

[0020] The precast block 9 is used to install a temperature sensor on the side wall 6 for measuring the temperature of the side wall 6. In this embodiment, an optical fiber temperature sensor is used as a temperature sensor for measuring the temperature of the side wall 6. In FIG. 1, in this embodiment, an optical fiber temperature sensor is used as an example. The optical fiber temperature sensors 111-112 include optical fibers 121-122 and measuring instruments 131-132. The measuring instruments 131-132 output light (e.g., infrared light) into the optical fibers 121-122. The light output into the optical fibers 121-122 is scattered in the optical fibers 121-122. The measuring instruments 131-132 input the light that is scattered and returned in the optical fibers 121-122. The measuring instruments 131-132 calculate the temperature at each position in the optical fibers 121-122 based on the intensity, speed, and time of the input and output light. Since the optical fiber temperature sensors 111-112 themselves can be realized by known technology, a detailed description of the optical fiber temperature sensors 111-112 will be omitted here.

[0021] Optical fibers 121-122 are embedded in the precast block 9. The optical fiber 121 is installed at a relatively inner position so that both the temperature distribution in the height direction of the side wall portion 6 and the temperature distribution in the circumferential direction of the side wall portion 6 can be measured. The optical fiber 122 is installed at a relatively outer position so that both the temperature distribution in the height direction of the side wall portion 6 and the temperature distribution in the circumferential direction of the side wall portion 6 can be measured. In the following description, the optical fiber installed at a relatively inner position is referred to as an inner optical fiber as necessary. Also, the optical fiber installed at a relatively outer position is referred to as an outer optical fiber as necessary. Also, the height direction of the side wall portion 6 and the circumferential direction of the side wall portion 6 are abbreviated to the height direction and the circumferential direction, respectively, as necessary.

[0022] FIG. 2 is a cross-sectional view taken along line II in FIG. 1. For convenience of notation and explanation, hatching showing a cut surface is omitted in FIG. 2 as well. As shown in FIG. 2, in this embodiment, the electric furnace 1 is provided with a plurality of precast blocks 9a to 9r. The plurality of precast blocks 9a to 9r are arranged in the circumferential direction of the electric furnace 1. In this embodiment, the plurality of precast blocks 9a to 9r are configured in the same manner. However, the shape and size of at least one of the plurality of precast blocks 9a to 9r may be different from the other precast blocks. At least one physical property value (i.e., the material constituting the precast block) of the plurality of precast blocks 9a to 9r may also be different from the other precast blocks. However, it is preferable that the physical property values ​​of the plurality of precast blocks 9a to 9r are substantially the same, and it is more preferable that they are the same. This is because there is no need to change the physical property values ​​of the precast blocks used when performing a three-dimensional unsteady heat transfer inverse problem analysis described later depending on the location.

[0023] Among the precast blocks 9a to 9r, the circumferential ends of two adjacent precast blocks (e.g., precast blocks 9a to 9b) are connected (fixed) to each other via, for example, a material having heat resistance and adhesive properties. In addition, the outer end of the wear brick 7 and the inner end of the precast blocks 9a to 9r are also connected (fixed) to each other via, for example, a material having heat resistance and adhesive properties. In addition, the inner end of the steel shell 10 and the outer end of the precast blocks 9a to 9r are also connected (fixed) to each other via, for example, a material having heat resistance and adhesive properties. The material (material having heat resistance and adhesive properties) for connecting (fixing) the precast blocks 9a to 9r in the above manner is, for example, mortar.

[0024] As shown in FIG. 2, in this embodiment, the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r are installed in each of the precast blocks 9a to 9r. In addition, in this embodiment, the inner optical fibers 121 to 121r have the same configuration. In addition, in this embodiment, the outer optical fibers 122a to 122r have the same configuration. In addition, in this embodiment, the inner optical fibers 121 to 121r and the outer optical fibers 122a to 122r are relatively arranged in the same manner in each of the precast blocks 9a to 9r. As described above, in this embodiment, the precast blocks 9a to 9r have the same configuration. Therefore, in a relative coordinate system with the reference position (for example, the position of the center of gravity) of each of the precast blocks 9a to 9r as the origin, the coordinates of the positions where the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r are present are the same. That is, in this embodiment, the precast blocks 9a to 9r have the same configuration, including the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r. Also, in this embodiment, even if at least two of the precast blocks 9a to 9r are replaced, the same state as before the replacement is achieved.

[0025] The precast block 9 shown in FIG. 1 is one of the precast blocks 9a to 9r. In the following description, when the description of the precast blocks 9a to 9r is not limited to the individual precast blocks 9a to 9r, the precast block is designated by the reference symbol 9. The inner optical fiber 121 and the outer optical fiber 122 shown in FIG. 1 are each one of the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r. When the description of the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r is not limited to the individual inner optical fibers 121a to 121r and the individual outer optical fibers 122a to 122r, the inner optical fiber and the outer optical fiber are designated by the reference symbols 121 and 122, respectively.

[0026] FIG. 3 is a diagram showing an example of the configuration of a precast block 9 in which an inner optical fiber 121 and an outer optical fiber 122 are embedded. As described above, the inner optical fiber 121 is disposed relatively inside, and the outer optical fiber 122 is disposed relatively outside. 3, in this embodiment, the case where the inner optical fiber 121 is installed so as to meander on the imaginary plane 31a with the circumferential direction as the traveling direction is illustrated. The imaginary plane 31a is a plane parallel to the inner circumferential surface 6a of the side wall portion 6. When the inner optical fiber 121 is installed in this manner, the height direction position of the region where the above-mentioned hot spot is expected to occur is included within the height direction range of the region where the inner optical fiber 121 meanders.

[0027] Similarly, in this embodiment, the outer optical fiber 122 is disposed so as to meander on the imaginary plane 31b with the circumferential direction as the traveling direction. The imaginary plane 31b is a plane parallel to the inner circumferential surface 6a of the side wall portion 6. When the outer optical fiber 122 is disposed in this manner, the height direction position of the region where the aforementioned hot spot is expected to occur is included within the height direction range of the region where the outer optical fiber 122 meanders. In the following description, the areas within the imaginary planes 31a and 31b in which the optical fibers 121 and 122 are installed will be referred to as installation areas of the optical fibers 121 and 122, as necessary.

[0028] In addition, in order to simplify the notation and explanation, Fig. 3 illustrates an example in which the shape of the precast block 9 is a rectangular column shape with a hollow fan-shaped bottom. However, the shape of the precast block 9 is not limited to this shape. For example, the shape of the precast block 9 may be a rectangular parallelepiped.

[0029] As shown in FIG. 3, both ends of the inner optical fiber 121 and the outer optical fiber 122 are drawn out to the outside of the precast block 9. The inner optical fibers 121a to 121r are connected in series. The outer optical fibers 122a to 122r are also connected in series. One end of the inner optical fibers 121a to 121r connected in series is connected to a measuring device 131 shown in FIG. 1. The other end of the inner optical fibers 121a to 121r connected in series may be embedded in the precast block 9 or may be drawn out to the outside of the precast block 9. One end of the outer optical fibers 122a to 122r connected in series is connected to a measuring device 132 shown in FIG. 1. Similarly, the other end of the outer optical fibers 122a to 122r connected in series may be embedded in the precast block 9 or may be drawn out to the outside of the precast block 9.

[0030] An example of a method for connecting the remaining end of the inner optical fiber 121 embedded in the precast block 9 is as follows. In the following description, the right and left sides in the circumferential direction when the side wall portion 6 (precast block 9) is viewed from the central axis O of the electric furnace 1 with the upward direction in the height direction of the electric furnace 1 being the upward direction will be simply referred to as the right side and the left side, respectively (see "circumferential direction", "right side", and "left side" in FIG. 3).

[0031] Of both ends of the inner optical fiber 121 embedded in the precast block 9, the end drawn out from the right side is connected to the end drawn out from the left side of both ends of the inner optical fiber 121 embedded in the precast block 9 adjacent to the right side of the precast block 9. For example, in Fig. 2, of both ends of the inner optical fiber 121a embedded in the precast block 9a, the end drawn out from the right side is connected to the end drawn out from the left side of both ends of the inner optical fiber 121b embedded in the precast block 9b adjacent to the right side of the precast block 9a.

[0032] Of both ends of the inner optical fiber 121 embedded in the precast block 9, the end drawn out from the left side is connected to the end drawn out from the right side of both ends of the inner optical fiber 121 embedded in the precast block 9 adjacent to the left side of the precast block 9. For example, in Fig. 2, of both ends of the inner optical fiber 121a embedded in the precast block 9a, the end drawn out from the left side is connected to the end drawn out from the right side of both ends of the inner optical fiber 121r embedded in the precast block 9r adjacent to the left side of the precast block 9a.

[0033] By configuring and installing the inner optical fibers 121a to 121r as described above, the inner optical fibers 121a to 121r are installed so as to surround the central axis O of the electric furnace 1 while meandering on the imaginary plane 31a with the circumferential direction as the traveling direction.

[0034] Similarly, of both ends of the outer optical fiber 122 embedded in the precast block 9, the end drawn out from the right side is connected to the end drawn out from the left side of both ends of the outer optical fiber 122 embedded in the precast block 9 adjacent to the right side of the precast block 9. For example, in Fig. 2, of both ends of the outer optical fiber 122a embedded in the precast block 9a, the end drawn out from the right side is connected to the end drawn out from the left side of both ends of the outer optical fiber 122b embedded in the precast block 9b adjacent to the right side of the precast block 9a.

[0035] Of both ends of the outer optical fiber 122 embedded in a precast block 9, the end drawn out from the left side is connected to the end drawn out from the right side of both ends of the outer optical fiber 122 embedded in a precast block 9 adjacent to the left side of the precast block 9. For example, in Fig. 2, of both ends of the outer optical fiber 122a embedded in a precast block 9a, the end drawn out from the left side is connected to the end drawn out from the right side of both ends of the outer optical fiber 122r embedded in a precast block 9r adjacent to the left side of the precast block 9a.

[0036] By configuring and installing the outer optical fibers 122a to 122r as described above, the outer optical fibers 122a to 122r are installed so as to surround the central axis O of the electric furnace 1 while meandering on the imaginary plane 31b with the circumferential direction as the traveling direction.

[0037] As described above, in this embodiment, the optical fiber temperature sensor 111 that measures the temperature at a relatively inner position and the optical fiber temperature sensor 112 that measures the temperature at a relatively outer position are separate temperature sensors. However, this is not necessarily the case. For example, a single optical fiber temperature sensor may measure both the temperature at a relatively inner position and the temperature at a relatively outer position. In this case, a single optical fiber may be installed in the installation area of ​​the optical fibers 121 and 122.

[0038] The precast block 9 is manufactured, for example, as follows. The amorphous refractory is placed in a form having a shape and size according to the outer shape of the precast block 9. Thereafter, the inner optical fiber 121 and the outer optical fiber 122 are placed in the form so as to be embedded in the above-mentioned position in the precast block 9 before the amorphous refractory hardens. The amorphous refractory is hardened (dried) in a state in which the inner optical fiber 121 and the outer optical fiber 122 are placed in the form. It is preferable that the positions (coordinates of the above-mentioned relative coordinate system) of the inner optical fiber 121 and the outer optical fiber 122 in the precast block 9 are specified even in a state in which they are embedded in the precast block 9. For this purpose, for example, it is preferable to suppress the change in the positions of the inner optical fiber 121 and the outer optical fiber 122 in the precast block 9 (preferably prevent the positions from changing) by using a jig (not shown) that holds the inner optical fiber 121 and the outer optical fiber 122 outside the form from when the inner optical fiber 121 and the outer optical fiber 122 are placed in the form until the amorphous refractory hardens.

[0039] For example, a jig having a configuration capable of adjusting the position of the object to be held in the formwork so that the position of the object to be held in the formwork can be specified may be used. The inner optical fiber 121 and the outer optical fiber 122 are placed in the formwork while attached to such a jig. Then, the jig is adjusted to set the inner optical fiber 121 and the outer optical fiber 122 to predetermined positions in the formwork. Then, the jig holds the positions of the inner optical fiber 121 and the outer optical fiber 122 in the precast block 9 until the monolithic refractory hardens.

[0040] After the inner optical fiber 121 and the outer optical fiber 122 are placed in the formwork, the monolithic refractory material may be placed in the formwork. In addition, as the material for the amorphous refractory material, a material is used such that the mechanical strength of the precast block 9 has the mechanical strength required for the side wall portion 6 and the heat resistance of the precast block 9 satisfies the heat resistance required for the side wall portion 6.

[0041] In addition, the lengths of the inner optical fiber 121 and the outer optical fiber 122 drawn out from the precast block 9 can be specified even in a state where they are embedded in the precast block 9. Therefore, if the positions of the inner optical fiber 121 and the outer optical fiber 122 in the precast block 9 are specified, the lengths from the measuring instruments 131-132 to the positions of the inner optical fiber 121 and the outer optical fiber 122 can also be specified.

[0042] In this embodiment, a case in which all of the following (E) to (G) are satisfied will be illustrated. (E) The distance from the inner circumferential surface 6a of the side wall portion 6 to the inner optical fibers 121a to 121r is constant. (F) The distance from the inner circumferential surface 6a of the side wall portion 6 to the outer optical fibers 122a to 122r is constant. (G) The intervals (the distances in the thickness direction of the side wall portion 6) between the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r are constant.

[0043] Doing so is preferable because it reduces the calculation load, such as temperature interpolation calculations using the temperatures measured by the optical fiber temperature sensors 111-112, in the equipment status monitoring device 100 described below. However, this is not necessarily required as long as the lengths from the measuring instruments 131-132 to each position in the inner optical fiber 121 and the outer optical fiber 122 can be specified.

[0044] Moreover, if the inner optical fiber and the outer optical fiber (e.g., the inner optical fiber 121a and the outer optical fiber 122a) that are in the same circumferential position are embedded in the same precast block 9, the inner optical fiber 121 and the outer optical fiber 122 can be easily installed, which is preferable. However, this is not necessarily required. For example, the inner optical fiber and the outer optical fiber that are in the same circumferential position may be embedded in different precast blocks. Moreover, if the inner optical fiber and the outer optical fiber (e.g., the inner optical fiber 121a and the outer optical fiber 122a) are in the same circumferential position, it is preferable because the calculation load when performing a three-dimensional unsteady heat transfer inverse problem analysis described later can be reduced. However, the circumferential positions of the inner optical fiber and the outer optical fiber (e.g., the inner optical fiber 121a and the outer optical fiber 122a) do not have to be the same.

[0045] Moreover, a temperature sensor other than the optical fiber temperature sensor may be used instead of the optical fiber temperature sensor 112. The temperature sensor other than the optical fiber temperature sensor does not need to be embedded in the side wall 6. The temperature sensor other than the optical fiber temperature sensor may be, for example, a temperature sensor that measures the temperature distribution on the outer surface of the iron shell 10. Such a temperature sensor may be a radiation thermometer or a thermocouple. Moreover, such a temperature sensor is installed at a position outside the optical fiber temperature sensor (optical fiber) so that both the temperature distribution in the height direction of the side wall 6 and the temperature distribution in the circumferential direction of the side wall 6 can be measured. Moreover, such a temperature sensor is installed at a position where it can measure the temperature of the area where the above-mentioned hot spot is expected to occur.

[0046] Further, a permanent brick may be installed outside the permanent brick 8. In this case, the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded is preferably installed in a part of the area in which the permanent brick 8 closest to the iron shell 10 is installed. For example, this is because the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded is easily installed and maintained. However, the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded may be installed in a part of the area in which the permanent brick other than the permanent brick closest to the iron shell 10 is installed. The wear brick 7 constitutes the inner peripheral surface 6a of the side wall portion 6 of the electric furnace 1. For this reason, there is a risk that the thickness of the wear brick 7 will decrease due to melting or the like. Therefore, it is preferable that the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded does not constitute the inner peripheral surface 6a of the side wall portion 6 of the electric furnace 1. For example, it is preferable that the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded is not installed in an area in which the wear bricks 7 are installed. In this case, the precast block 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded is installed in an area in which the permanent bricks, which are refractory materials that do not constitute the inner peripheral surface 6a of the side wall portion 6 of the electric furnace 1, are installed, for example.

[0047] <Outline of equipment status monitoring device and equipment status monitoring method> Although details will be described later, the equipment status monitoring device 100 of this embodiment calculates the temperature distribution in the thickness direction of the side wall 6 by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the measured values ​​of the optical fiber temperature sensors 111-112. The temperature distribution in the thickness direction of the side wall 6 is information indicating the relationship between the position in the thickness direction of the side wall 6 and the temperature of the side wall 6. The equipment status monitoring device 100 may further calculate the temperature distribution in other directions (for example, the height direction and the circumferential direction). The temperature distribution in the thickness direction of the side wall 6 is calculated in a range assumed as a range in which the inner circumferential surface 6a of the side wall 6 may exist. That is, the temperature distribution in the thickness direction of the side wall 6 may include the temperature of the region inside the furnace in addition to the region where the side wall 6 actually exists.

[0048] The equipment status monitoring device 100 then calculates the position of the inner circumferential surface 6a based on the temperature distribution in the thickness direction of the side wall 6. The position of the inner circumferential surface 6a calculated by the equipment status monitoring device 100 includes the position in the thickness direction of the side wall 6. The thickness direction of the side wall 6 is the direction in which a straight line connecting the inner circumferential surface 6a and the outer circumferential surface 6b at the shortest distance extends (the radial direction of the electric furnace 1). The position in the thickness direction of the side wall 6 is represented, for example, by the value of the coordinate axis when the straight line is used as the coordinate axis. In the following description, the thickness direction of the side wall 6 will be abbreviated to thickness direction as necessary.

[0049] Here, the unsteady heat transfer inverse problem refers to a problem based on the unsteady heat conduction equation governing the calculation domain, and refers to a problem of estimating at least one of the boundary conditions of physical quantities (temperature, heat flux, etc.) at the domain boundary and the initial conditions of the physical quantities at the domain boundary, with the temperature information inside the domain being known. In this embodiment, the unsteady heat transfer inverse problem refers to a problem of estimating the temperature at the domain boundary (the temperature of the inner circumferential surface 6a). Note that the unsteady heat transfer forward problem refers to a problem of estimating temperature information inside the domain based on the known boundary conditions.

[0050] As mentioned above, Patent Document 1 discloses solving a one-dimensional unsteady heat transfer inverse problem. However, when using the one-dimensional unsteady heat transfer inverse problem, it is not possible to sufficiently improve the estimation accuracy of the temperature distribution in the thickness direction of the side wall portion 6. This will be described with reference to Figs. 4A, 4B, 5A, and 5B. Figs. 4A and 4B are diagrams for explaining an example of heat transfer that can be considered in the one-dimensional unsteady heat transfer inverse problem. Figs. 5A and 5B are diagrams for explaining an example of heat transfer that can be considered in the three-dimensional unsteady heat transfer inverse problem.

[0051] As described later, in this embodiment, a three-dimensional unsteady heat transfer inverse problem is exemplified in a three-dimensional Cartesian coordinate system (xyz coordinate system). Therefore, xyz coordinates are shown in each figure. However, the origin of the xyz coordinates shown in each figure is not limited to the position shown in each figure. Also, in each figure, a symbol with a black circle in a white circle indicates an arrow line going from the back side of the paper to the front side (the coordinate axis with the positive direction going from the back side of the paper to the front side).

[0052] Here, the x-axis direction corresponds to the thickness direction. The y-axis direction corresponds to the circumferential direction. The z-axis direction corresponds to the height direction. In this embodiment, the inner circumferential surface 6a of the side wall portion 6 is not a flat surface. Therefore, in this embodiment, the circumferential direction and the height direction of the side wall portion 6 that appear as a flat surface by cutting the side wall portion 6 along the height direction at one point in the circumferential direction and developing it are respectively set as the y-axis direction and the z-axis direction, and the y-coordinate and the z-coordinate of each position of the side wall portion 6 are determined. Similarly, in this embodiment, the y-coordinate and the z-coordinate of each position of the side wall portion 6 are determined in the same manner as the inner circumferential surface 6a also in the planes (virtual planes 31a, 31b, etc.) parallel to the inner circumferential surface 6a.

[0053] 4A and 4B, the heat flux is from the inside, which is at a higher temperature, to the outside. When using a one-dimensional unsteady heat transfer inverse problem, the temperature distribution in the thickness direction of the side wall 6 is calculated assuming that the heat transfer occurs only in the thickness direction (x-axis direction) of the side wall 6.

[0054] Therefore, when solving a one-dimensional unsteady heat transfer inverse problem to calculate the temperature distribution in the thickness direction of the side wall 6, as shown in Figures 4A and 4B, the temperature measurement positions 41a to 41b, 41c to 41d, 41e to 41f, 41g to 41h, 41i to 41j, and 41k to 41l are aligned in the thickness direction of the side wall 6. In this case, the direction of heat transfer that can be considered in the unsteady heat transfer inverse problem is limited to the direction in which the temperature measurement positions 41a to 41b, 41c to 41d, 41e to 41f, 41g to 41h, 41i to 41j, and 41k to 41l are aligned (the direction along the arrow line shown in Figures 4A and 4B). In addition, in FIGS. 4A and 4B, for convenience of explanation and notation, temperature measurement positions 41a to 41b, 41c to 41d, 41e to 41f, 41g to 41h, 41i to 41j, and 41k to 41l are shown exaggeratedly large (the same applies to FIGS. 5A and 5B).

[0055] However, the actual direction of heat transfer is not limited to the thickness direction (x-axis direction) of the side wall 6. When a one-dimensional unsteady heat transfer inverse problem is solved to calculate the temperature distribution in the thickness direction of the side wall 6, the direction of heat transfer is limited to the thickness direction of the side wall 6. Therefore, even if the number of temperature measurement positions is increased, there is a limit to improving the estimation accuracy of the temperature distribution in the thickness direction of the side wall 6. Furthermore, when a two-dimensional unsteady heat transfer inverse problem is solved to calculate the temperature distribution in the side wall 6, the direction of heat transfer is limited to the thickness direction of the side wall 6 and only one of the circumferential direction and the height direction of the side wall 6.

[0056] In contrast, when estimating the temperature of the inner circumferential surface 6a by solving a three-dimensional unsteady heat transfer inverse problem, it is possible to take into account heat transfer from the inner temperature measurement positions 51a, 51c, 51e, 51g, 51i, and 51k toward the outer temperature measurement positions 51b, 51d, 51f, 51h, 51j, and 51l, respectively, as shown in Figures 5A and 5B. Therefore, the direction of heat transfer that can be taken into account in the unsteady heat transfer inverse problem is not limited to the direction in which the temperature measurement positions 51a to 51b, 51c to 51d, 51e to 51f, 51g to 51h, 51i to 51j, and 51k to 41l are aligned. That is, the direction of heat transfer that can be considered in the inverse problem of unsteady heat transfer is each direction from any one of the temperature measurement positions 51a, 51c, 51e, 51g, 51i, and 51k on the inside toward any one of the temperature measurement positions 51b, 51d, 51f, 51h, 51j, and 51l on the outside (directions along the arrows shown in FIG. 5A and FIG. 5B). In this way, in the inverse problem of unsteady heat transfer, all directions including the thickness direction of the side wall portion 6, the circumferential direction of the side wall portion 6, and the height direction of the side wall portion 6 can be considered. Therefore, if the temperature distribution in the thickness direction of the side wall portion 6 is calculated by solving the three-dimensional inverse problem of unsteady heat transfer, the estimation accuracy of the temperature distribution in the thickness direction of the side wall portion 6 can be improved. This can improve the estimation accuracy of the position in the thickness direction of the inner circumferential surface 6a. Therefore, in this embodiment, a three-dimensional unsteady heat transfer inverse problem analysis is performed to calculate the temperature distribution in the thickness direction of the side wall portion 6.

[0057] Furthermore, in order to calculate the temperature distribution in the thickness direction of the side wall 6 over as wide a range as possible, the temperature measurement positions also need to be located over as wide a range as possible. When using thermocouples as temperature sensors as described in Patent Document 1, it is practically difficult to install a large number of thermocouples in the side wall 6 at precisely determined positions. Therefore, in this embodiment, optical fiber temperature sensors 111 and 112 are used as temperature sensors.

[0058] Furthermore, when the temperature measurement position is between the wear brick 7 and the permanent brick 8, or between each permanent brick 8, the measurement accuracy of the temperature measured at that temperature measurement position may be lower than the measurement accuracy of the temperature measured at other temperature measurement positions. This is because the temperature measured at that temperature measurement position is affected by the properties and gaps around that temperature measurement position (temperature sensor). Therefore, the accuracy of the temperature measured by the temperature sensor may vary depending on the temperature measurement position. On the other hand, if the physical property values ​​around the temperature sensor are approximately the same (preferably the same), such temperature variation can be suppressed. Furthermore, when the temperature sensor is embedded in the bricks, the workload is large.

[0059] Therefore, in this embodiment, a case where the temperature sensor is embedded in a precast block 9 having approximately the same physical property values ​​(preferably the same physical property values) is illustrated. However, for example, if the physical property values ​​around the temperature measurement position are approximately the same (preferably the same), the temperature sensor does not necessarily need to be embedded in the precast block 9. For example, optical fiber temperature sensors 111-112 may be embedded in the permanent bricks 8. In this case, it is preferable that only positions inside the permanent bricks 8 are used as temperature measurement positions. Furthermore, in this case, the precast block 9 does not need to be installed in the electric furnace 1.

[0060] <Facility status monitoring device 100> Next, an example of the equipment status monitoring device 100 will be described. FIG. 6 is a diagram showing an example of the functional configuration of the equipment status monitoring device 100. The equipment status monitoring device 100 has, as hardware, one or more hardware processors such as a CPU (Central Processing Unit) and one or more memories such as a RAM (Random Access Memory) and a ROM (Read Only Memory). The equipment status monitoring device 100 executes various calculations by executing one or more programs stored in the memory by one or more hardware processors. Furthermore, the equipment status monitoring device 100 has, as hardware, an input device and an output device. At least one of the input device and the output device may be outside the equipment status monitoring device 100. In this case, the equipment status monitoring device 100 performs wired communication or wireless communication with the input device and the output device.

[0061] In this embodiment, an example is shown in which the equipment status monitoring device 100 includes a temperature acquisition unit 61, an inverse problem analysis unit 62, a refractory position calculation unit 63, and an output unit 64. An example of the function of each unit is described below. Note that information that can be set in advance in the calculation described below is assumed to be stored in the equipment status monitoring device 100 via an input device, for example.

[0062] <<Temperature acquisition section 61>> The temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111-112. As described above, in this embodiment, the temperature at each position in the optical fibers 121-122 is calculated by the measuring instruments 131-132. Therefore, in this embodiment, the temperature acquisition unit 61 acquires the temperatures at each position in the optical fibers 121-122 calculated by the measuring instruments 131-132 as the measured values ​​of the optical fiber temperature sensors 111-112. The temperature acquisition unit 61 may acquire the measured values ​​of the optical fiber temperature sensors 111-112 by performing wired or wireless communication with the measuring instruments 131-132. Furthermore, the temperature acquisition unit 61 may acquire the measured values ​​of the optical fiber temperature sensors 111-112 via devices other than the measuring instruments 131-132. Furthermore, the temperature acquisition unit 61 may have the functions of the measuring instruments 131-132.

[0063] The positions at which the optical fiber temperature sensors 111-112 obtain their measured values ​​are set in advance from among the positions within the optical fibers 121-122. It is preferable that the positions at which the optical fiber temperature sensors 111-112 obtain their measured values ​​are as wide as possible and as numerous as possible. This is because this improves the accuracy of calculating the temperature at the temperature acquisition positions (center of gravity of the hotspot, positions around the hotspot) described below. However, if there are too many positions at which the optical fiber temperature sensors 111-112 obtain their measured values, the calculation load may become too high. Therefore, it is preferable that the positions at which the optical fiber temperature sensors 111-112 obtain their measured values ​​are set in advance from the viewpoint of balancing between reducing the calculation load and improving the calculation accuracy.

[0064] The temperature acquisition unit 61 may acquire the measured values ​​during charging as the measured values ​​of the optical fiber temperature sensors 111-112. In this way, the equipment status monitoring device 100 can calculate the position in the thickness direction of the inner circumferential surface 6a even when the state of the inner circumferential surface 6a of the side wall portion 6 cannot be measured by a profile meter or the like because raw materials are present in the furnace. However, the timing at which the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111-112 is not limited to such timing. For example, the temperature acquisition unit 61 may acquire the measured values ​​between charges as the measured values ​​of the optical fiber temperature sensors 111-112. The period between charges is, for example, the period from when the molten metal and molten slag are discharged out of the furnace to when the next raw material is inserted.

[0065] In this embodiment, a case is illustrated in which the optical fiber temperature sensors 111-112 measure the temperatures at each position in the optical fibers 121-122 at a constant time period. Also, in this embodiment, a case is illustrated in which the temperature acquisition unit 61 acquires the measurement values ​​of the optical fiber temperature sensors 111-112 at each time period. In the following description, the time period in which the temperature acquisition unit 61 acquires the measurement values ​​of the optical fiber temperature sensors 111-112 is referred to as a temperature measurement period, as necessary.

[0066] <<Inverse problem analysis section 62>> The inverse problem analyzing unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the measured values ​​of the optical fiber temperature sensors 111-112.

[0067] When performing a three-dimensional unsteady heat transfer inverse problem analysis, N temperatures can be used per location in the thickness direction of the side wall portion 6 as temperatures for calculating one position in the thickness direction of the inner circumferential surface 6a. In this embodiment, such a case is illustrated. N is an integer of 2 or more. N is preferably an integer of 3 or more, and more preferably 5 (this will be described later).

[0068] In addition, when performing a three-dimensional unsteady heat transfer inverse problem analysis, it is considered that the estimation accuracy of one position in the thickness direction of the inner circumferential surface 6a is higher when a large number of temperatures are used as the temperature for calculating one position in the thickness direction of the inner circumferential surface 6a. However, the present inventors have found that this is not necessarily the case, and that it is preferable to use five temperatures per location in the thickness direction of the side wall portion 6 as the temperature for calculating one position in the thickness direction of the inner circumferential surface 6a. In other words, even if the number of temperatures (=N) for calculating one position in the thickness direction of the inner circumferential surface 6a is not greater than five, the estimation accuracy of the position in the thickness direction of the inner circumferential surface 6a can satisfy the accuracy required in practice (can be brought close to the actual measured value) (see the calculation example (FIG. 11) described later).

[0069] Therefore, in this embodiment, the inverse problem analyzing unit 62 acquires five temperatures per location in the thickness direction of the side wall 6 as temperatures for calculating one position in the thickness direction of the inner circumferential surface 6a based on the measured values ​​of the optical fiber temperature sensors 111-112, and performs three-dimensional unsteady heat transfer inverse problem analysis based on the acquired temperatures. As described above with reference to Figs. 1-3, this embodiment illustrates a case where there are two installation regions (regions in the imaginary surfaces 31a, 31b) of the optical fibers 121, 122 in the thickness direction of the side wall 6. Therefore, this embodiment illustrates a case where the inverse problem analyzing unit 62 acquires a total of 10 temperatures (=5 x 2) to calculate one position in the thickness direction of the inner circumferential surface 6a.

[0070] The five temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall 6 may be the measured values ​​of the optical fiber temperature sensors 111-112, or may be temperatures calculated based on the measured values ​​of the optical fiber temperature sensors 111-112. As described above, it is preferable that the number of temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall 6 is five. However, the number of temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall 6 is not limited to five, and may be, for example, a number greater than five. However, if the number of temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall 6 is too large, a large number of measured values ​​are required as the measured values ​​of the temperatures. In addition, the weighting coefficient w in the equation (3) described later, which is calculated by performing a three-dimensional unsteady heat transfer inverse problem analysis, i,j,k、l There is a risk that the calculation accuracy of decreases (specifically, overfitting occurs). Therefore, it is preferable to set the number of temperatures acquired by the inverse problem analysis unit 62 taking these points into consideration. Furthermore, the optimal value of the number of temperatures (=N) for calculating one position in the thickness direction of the inner circumferential surface of the side wall portion may vary depending on, for example, the equipment. In this case, the number of temperatures (=N) for calculating one position in the thickness direction of the inner circumferential surface of the side wall portion may be more than 5 or less than 5.

[0071] In addition, the thickness of the side wall 6 (wear brick 7) is likely to decrease near the hot spot. Therefore, in this embodiment, the position of the five temperatures acquired by the inverse problem analysis unit 62 at one point in the thickness direction of the side wall 6 is as follows. 7 is a diagram illustrating an example of a hot spot region. As described above, a hot spot is a position where the temperature is locally maximum. A hot spot region is a region that includes a hot spot. In this embodiment, a case is illustrated in which a hot spot region is defined in each of the x coordinates of the installation regions (regions within virtual planes 31a and 31b) of optical fibers 121 and 122.

[0072] 7, the temperature distribution in the installation area (area within virtual surfaces 31a and 31b) of the optical fibers 121 and 122 is shown on the yz plane. The temperature distribution shown in Fig. 7 is calculated based on the measured values ​​of the optical fiber temperature sensors 111-112. For example, the temperature distribution shown in Fig. 7 is calculated by interpolating the measured values ​​of the optical fiber temperature sensors 111-112. The method of interpolation is not limited, and may be any known method such as linear approximation, spline interpolation, or polynomial interpolation.

[0073] If the position where the temperature is locally maximum can be clearly determined as one point from the measured values ​​of the optical fiber temperature sensors 111-112, the position may be determined as the position of the hot spot area. In this case, the temperature of the position may be determined as the temperature of the hot spot area. In addition, the hot spot area may be searched for in each of a plurality of temperature sections obtained by dividing the temperature range measurable by the optical fibers 121 and 122 into a plurality of sections. In this case, the area of ​​the temperature section showing the highest temperature among the plurality of temperature sections may be determined as the hot spot area. In this case, the representative position of the hot spot area may be determined as the position of the hot spot area, and the temperature of the position may be determined as the temperature of the hot spot area. In FIG. 7, a case where the area of ​​the temperature section of 500° C. to 525° C. is the hot spot area 71 is illustrated. The representative position of the hot spot area 71 is, for example, the position of the center of gravity of the hot spot area 71.

[0074] In this embodiment, a case will be illustrated in which the inverse problem analyzing unit 62 calculates the temperature of the hotspot region 71 for the entire installation region (region within the imaginary planes 31a, 31b) of the optical fibers 121, 122 based on the measured values ​​of the optical fiber temperature sensors 111-112. In this case, the temperature of the hotspot region 71 will be one of the five temperatures described above. If there are multiple hotspot regions 71 in each of the installation regions (region within the imaginary planes 31a, 31b) of the optical fibers 121, 122, the temperature of each hotspot region 71 will be one of the five temperatures described above.

[0075] In addition, when the yz coordinates of the representative position of the hot spot region 71 in the installation region of the inner optical fiber 121 (region in the virtual surface 31a) and the yz coordinates of the representative position of the hot spot region 71 in the installation region of the outer optical fiber 122 (region in the virtual surface 31b) do not match, it is preferable that the inverse problem analysis unit 62 calculates the temperature of the hot spot region 71 in the installation region of the optical fibers 121 and 122 as follows. That is, in this case, it is preferable that the inverse problem analysis unit 62 matches the yz coordinates of the representative positions of the hot spot region 71 in the installation region of the optical fibers 121 and 122, and calculates the temperature of the matched yz coordinate as the temperature of the hot spot region 71 in the installation region of the optical fibers 121 and 122. For example, the inverse problem analysis unit 62 may take the arithmetic average values ​​of the y coordinates and z coordinates of the hot spot region 71 in the installation region of the optical fibers 121 and 122 as the y coordinates and z coordinates of each of the hot spot regions 71. Furthermore, the inverse problem analyzing unit 62 may set one of the y coordinates and z coordinates of the hotspot region 71 in the installation region of the optical fibers 121, 122 as the other y coordinate and z coordinate.

[0076] In this embodiment, of the five temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall portion 6, four positions other than the position of the hot spot region 71 are distributed around the position of the hot spot region 71. The distribution means that, for example, when the four positions are projected onto the same plane, three or more of the four positions are not on the same line. FIG. 8A and FIG. 8B are diagrams showing an example of the positions of the temperatures acquired when performing a three-dimensional unsteady heat transfer inverse problem analysis. In the following description, the position of the hot spot region 71 is referred to as the hot spot center position as necessary.

[0077] Fig. 8A is a diagram showing an example of five temperature positions 81a to 81e acquired in the installation area (area in imaginary plane 31a) of the inner optical fiber 121. Fig. 8B is a diagram showing an example of five temperature positions 82a to 82e acquired in the installation area (area in imaginary plane 31b) of the outer optical fiber 122.

[0078] In Fig. 8A, the coordinate values ​​of the hotspot centroid position 81a in the installation area of ​​the inner optical fiber 121 are (x^1, y^1, z^1). Note that x^, y^, and z^ correspond to the symbols with ^ above x, y, and z, respectively, in the mathematical expressions described below. As shown in Fig. 8A, in this embodiment, a case is illustrated in which four positions 81b to 81e are determined around the hotspot centroid position 81a on the yz plane at the position where the x coordinate is x1. The coordinate values ​​of the positions 81b, 81c, 81d, and 81e are (x^1, y^0, z^1), (x^1, y^1, z^0), (x^1, y^2, z^1), and (x^1, y^1, z^2), respectively.

[0079] In Fig. 8A, three or more of the four positions 81b to 81e around the hotspot centroid position 81a are not located on the same line. Therefore, the positions 81b to 81e are distributed around the hotspot centroid position 81a. Note that Fig. 8A illustrates an example in which only two of the four positions 81b to 81e around the hotspot centroid position 81a (e.g., positions 81b and 81d) are located on the same line.

[0080] Similarly, in Fig. 8B, the coordinate values ​​of the hotspot centroid position 82a in the installation area of ​​the outer optical fiber 122 are (x2, y1, z1). As shown in Fig. 8B, in this embodiment, four positions 82b to 82e are determined around the hotspot centroid position 82a on the yz plane at a position where the x coordinate is x2. The coordinate values ​​of the positions 82b, 82c, 82d, and 82e are (x^2, y^0, z^1), (x^2, y^1, z^0), (x^2, y^2, z^1), and (x^2, y^1, z^2), respectively.

[0081] Distances Δy1, Δy2, Δz1, and Δz2 in the y-axis and z-axis directions from the hotspot centroid positions 81a and 82a to the four positions 81b-81e and 82b-82e around the hotspot centroid positions 81a and 82a are set before performing a three-dimensional unsteady heat transfer inverse problem analysis. In the following description, the four positions around the hotspot centroid positions 81a and 82a are referred to as hotspot peripheral positions as necessary. In addition, distances Δy1, Δy2, Δz1, and Δz2 in the y-axis and z-axis directions from the hotspot centroid positions 81a and 82a to the hotspot peripheral positions 81b-81e and 82b-82e are abbreviated as distances Δy1, Δy2, Δz1, and Δz2 as necessary.

[0082] The distances Δy1, Δy2, Δz1, and Δz2 are not limited, so long as they are determined so that the calculation accuracy of the position in the thickness direction of the inner surface 6a, calculated, for example, as described below, satisfies the accuracy required for practical use.

[0083] For example, distances Δy1, Δy2, Δz1, Δz2 that satisfy the accuracy required for practical use of the calculation accuracy of the position in the thickness direction of the inner circumferential surface 6a may be searched for by trial and error. In this case, for example, a test furnace simulating an electric furnace 1 is used to perform a three-dimensional unsteady heat transfer inverse problem analysis described later to calculate the position in the thickness direction of the inner circumferential surface 6a, with the distances Δy1, Δy2, Δz1, Δz2 being different. Next, the calculated values ​​of the positions in the thickness direction of the inner circumferential surface 6a at the respective distances Δy1, Δy2, Δz1, Δz2 are compared with the actual measured values ​​in the test furnace. Finally, based on the results of this comparison, distances Δy1, Δy2, Δz1, Δz2 that satisfy the accuracy required for practical use of the calculation accuracy of the position in the thickness direction of the inner circumferential surface 6a are searched for.

[0084] In addition, as in this embodiment, when the hotspot centroid positions 81a, 82a are included in the five temperatures acquired by the inverse problem analysis unit 62 at one location in the thickness direction of the side wall portion 6, the wear brick 7 at the position intersecting the virtual line connecting the hotspot centroid positions 81a, 82a and the central axis O of the electric furnace 1 at the shortest distance may be worn out. When the wear brick 7 is worn out like this, the region of the inner circumferential surface 6a where the wear brick 7 is located is recessed more than other regions. In this case, it is preferable to determine the distances Δy1, Δy2, Δz1, and Δz2 based on the size of the recessed portion. In the following description, the portion of the inner circumferential surface 6a recessed due to the wear of the wear brick 7 is referred to as a worn portion as necessary. The wear of the wear brick 7 occurs due to melting or peeling of the wear brick 7.

[0085] 9A and 9B are diagrams showing an example of a worn part. FIG. 9A is a diagram showing an example of a region including a worn part when the side wall 6 is viewed from above. FIG. 9B is a diagram showing an example of a region including a worn part when the side wall 6 is viewed from the central axis O side of the electric furnace 1. Note that FIG. 9A and FIG. 9B show a state assumed as a state in which the side wall 6 is cut along the height direction at one point in the circumferential direction and developed. Also, FIG. 9A and FIG. 9B show only a part of the side wall 6 (a region corresponding to one precast block 9). Note that, in FIG. 9A and FIG. 9B, hatching showing a cut surface is omitted for convenience of notation and explanation.

[0086] In FIG. 9A, the wear brick 7 on which the damaged portion 92 is formed is the wear brick 7 located at a position intersecting an imaginary line 91 that connects the hot spot gravity center positions 81a, 82a and the central axis O of the electric furnace 1 at the shortest distance.

[0087] The distances Δy1 and Δy2 are, for example, the length WL of the worn portion 92 in the circumferential direction (y-axis direction). y Specifically, the distances Δy1 and Δy2 are determined based on the circumferential length WL of the worn portion 92. yIn this way, hot spot peripheral positions 81b-81e, 82b-82e can be determined between both ends of worn portion 92 in the y-axis direction. y It has been found that setting the thickness of the inner circumferential surface 6a to 1 / 4 is preferable because it improves the accuracy of calculation of the position in the thickness direction of the inner circumferential surface 6a.

[0088] The distances Δz1 and Δz2 are, for example, the length WL of the worn portion 92 in the height direction (z-axis direction). z Specifically, the range of distances Δz1 and Δz2 is determined based on the circumferential length WL of worn portion 92. z In this way, the hot spot peripheral positions 81b to 81e and 82b to 82e can be determined between both ends of the worn portion 92 in the z-axis direction. z , Δy z is the circumferential length WL of the worn portion 92. z It has been found that setting the thickness of the inner circumferential surface 6a to 1 / 4 is preferable because it improves the accuracy of calculation of the position in the thickness direction of the inner circumferential surface 6a.

[0089] Also, for example, the depth WL of the worn portion 92 x For example, the distances Δy1, Δy2, Δz1, and Δz2 may be adjusted depending on the depth WL of the worn portion 92. x The longer the distances Δy1, Δy2, Δz1, and Δz2, the longer or shorter they may be made. Note that the depth of worn portion 92 is the length of worn portion 92 in its thickness direction (x-axis direction).

[0090] For the sake of simplicity, Figures 9A and 9B show an example in which the shape of the space that is the damaged portion 92 is a right square prism. However, the shape of the actual damaged portion L is more complicated than a right square prism. In this case, the lengths WL of the damaged portion 92 in each direction are x , W.L. y , W.L. zmay be set to the characteristic length in each direction, for example.

[0091] For example, the width WL of the worn portion 92 y and the height WL of the worn part 92 z may be the length at the open end 92a (mouth portion) of the worn portion 92. The width of the worn portion 92 is the length in the circumferential direction (y-axis direction). The height of the worn portion 92 is the length in the height direction (z-axis direction).

[0092] Also, for example, the length WL of the worn portion 92 in each direction x , W.L. y , W.L. z For example, the length WL of the worn portion 92 in each direction may be the maximum length in each direction. x , W.L. y , W.L. z may be the length at the center of gravity of worn portion 92.

[0093] Here, the length WL of the worn portion 92 in each direction x , W.L. y , W.L. z For example, may be a measurement value of a profile meter measured between charges, or may be a visual observation value observed between charges. Measurement by a profile meter is realized by known technology as described in JP 2018-185253 A and the like, and therefore detailed description thereof is omitted here. In addition, a test furnace simulating an electric furnace 1 was used to measure the temperature of the hotspot region 71 and the length WL of the worn portion 92 in each direction. x , W.L. y , W.L. z Then, based on the result of the investigation of the relationship, the relationship between the temperature of the hot spot region 71 and the length WL of the worn portion 92 in each direction may be calculated. x , W.L. y , W.L. z In this case, the inverse problem analyzing unit 62 may generate a formula or a lookup table showing the relationship between the length WL of the worn part 92 in each direction corresponding to the temperature of the hot spot region 71. x , W.L. y , W.L. zRead out.

[0094] The inverse problem analysis unit 62 calculates hotspot peripheral positions 81b to 81e, 82b to 82e based on the distances Δy1, Δy2, Δz1, and Δz2 determined as described above and the hotspot centroid positions 81a, 82a, and acquires the temperatures of the hotspot peripheral positions 81b to 81e, 82b to 82e.

[0095] As described above, the inverse problem analysis unit 62 calculates the temperature u^ at the coordinates (x^1, y^1, z^1) and (x^2, y^1, z^1) of the hotspot centroid positions 81a and 82a at each time t1 to t n Similarly, the inverse problem analysis unit 62 obtains the temperature u^ at the coordinates (x^1,y^0,z^1), (x^1,y^1,z^0), (x^1,y^2,z^1), (x^1,y^1,z^2), (x^2,y^0,z^1), (x^2,y^1,z^0), (x^2,y^2,z^1), (x^2,y^1,z^2) of the hotspot peripheral positions 81b to 81e, 82b to 82e, and calculates the temperature u^ at each time t1 to t n Obtain the temperature u^ at

[0096] Then, the inverse problem analysis unit 62 solves a three-dimensional unsteady heat transfer inverse problem. An example of a three-dimensional unsteady heat transfer inverse problem will be described below. In the following description, the hot spot centroid positions 81a, 82a and the hot spot peripheral positions 81b to 81e, 82b to 82e will be referred to as temperature acquisition positions 81a to 81e, 82a to 82e as necessary. First, the three-dimensional unsteady heat conduction equation is expressed by the following equation (1).

[0097]

number

[0098] Here, U is the temperature. x, y, and z are the x, y, and z coordinates in the xyz coordinate system, respectively. t is time. α is the square root of thermal diffusivity. The thermal diffusivity is calculated using the thermal conductivity, specific heat, and density (specific gravity). Basis function φ(xx c ,yy c ,zz c ,tt c ) is expressed by the following equation (2). c ,yy c ,zz c ,tt c ) is a function expressed in the form of a fundamental solution that satisfies the unsteady heat conduction equation (1), and the center point c (reference position x c and the reference time t c ) is a function based on

[0099]

number

[0100] Here, T is a constant (model parameter) that represents the variance of the spatial distribution of the fundamental solution of the unsteady heat conduction equation (1), and is called the time shift. c ,y c ,z c ,t c is a set of space-time coordinates called source terms, which are set values ​​(i.e., x c ,y c ,z c ,t c are not unknowns when solving the unsteady heat transfer inverse problem). For example, the information of the temperature acquisition positions 81a to 81e and 82a to 82e is c ,y c ,z c ,t c In this case, t cis the time when the measurement values ​​of the optical fiber temperature sensors 111-112 used to acquire the temperatures at the temperature acquisition positions 81a-81e, 82a-82e were obtained. In the following description, the time when the measurement values ​​of the optical fiber temperature sensors 111-112 were obtained will be referred to as measurement time as necessary.

[0101] Here, the variable that identifies the position of the temperature acquisition positions 81a-81e, 82a-82e in the x-axis direction (thickness direction) is i (i = 1, 2). Furthermore, the variable that identifies the position of the temperature acquisition positions 81a-81e, 82a-82e in the y-axis direction (circumferential direction) is j (i = 0, 1, 2). The variable that identifies the position of the temperature acquisition positions 81a-81e, 82a-82e in the z-axis direction (height direction) is k (k = 0, 1, 2). Furthermore, the variable that identifies the time when the temperature was measured is l (l = 1,..., 2m).

[0102] The temperature of the side wall 6 is calculated by the interpolation temperature u(x, y, z, t) using 10×m basis functions φ(xx i ,yy j ,zz k ,tt l ). In this case, the internal / extrapolated temperature u(x,y,z,t) for calculating the temperature of the side wall portion 6 is expressed by the following formula (3). The "10" in "10×m" corresponds to the number of temperature acquisition positions 81a to 81e, 82a to 82e. The "m" in "10×m" corresponds to the temperature measurement time (1 to m, m+1 to 2m). The internal / extrapolated temperature u(x,y,z,t) is a temperature that satisfies the three-dimensional unsteady heat conduction equation expressed by formula (1). The internal / extrapolated temperature u(x,y,z,t) is an approximate solution of the temperature U(x,y,z,t).

[0103]

number

[0104] (3) 10×m weighting coefficients Weighting coefficient w i,j,k、l Therefore, it is necessary to determine the temperature u^(x^) at each of the 10 temperature acquisition positions 81a to 81e and 82a to 82e at 2×n times.i ,y^ j ,z^ k ,t l ) where n ≥ m. You can also use n = m. In addition, the coordinate value of the space-time coordinate (x^ i ,y^ j ,z^ k ,t l ) is the source term (x i ,y j ,z k ,t l ) can be the same as the 10 × m weighting coefficients w i,j,k、l The 20×n simultaneous equations for determining are expressed by the following equation (4). Note that, for convenience of notation, only two of the 20×n simultaneous equations (simultaneous equations for l=1, 2n) are shown in equation (4).

[0105]

number

[0106] Let U(∈R (2n×5)×1 ) is written as Φ(∈R (2n×5)×(2m×5) ) is written as the matrix (vector) that stores the weight coefficient w in equation (4). (2m×5)×1 ) is denoted as e(∈ (2n×5)×1 ) Then, equation (4) can be rewritten as equation (5) below. Note that T indicates the transpose matrix. In order to obtain the least squares solution for matrix W, we use the cost function J:R (2n×5)×1 →R is used. Here, γ(∈R) is a regularization coefficient for ensuring the stability of the solution. The matrix W when the value of the cost function J is minimized is the matrix W that satisfies the following equation (7). Specifically, the matrix W when the value of the cost function J is minimized is expressed by the following equation (8). Here, I(∈Z (2m×5)×(2m×5) ) is a unit matrix. Note that the cost function J is not limited to equation (6) as long as it is a function that evaluates the error between the left and right sides of equation (4).

[0107]

number

[0108] From equation (8), we obtain the matrix W (weighting coefficient w i,j,k、l However, in an inverse problem, when the inverse matrix of the right-hand side of equation (8) is solved, the error is amplified, and the solution may not be stable. Therefore, in this embodiment, the matrix Φ is subjected to singular value decomposition as shown in the following equation (9). Here, S(∈R (2n×5)×(2n×5) ) is the left singular matrix. Σ(∈R (2n×5)×(2m×5) ) is a diagonal matrix that stores singular values. V(∈R (2m×5)×(2m×5) ) is a right singular value matrix. Then, the matrix W is expressed by the following equation (10). In this embodiment, a case where the inverse problem analyzing unit 62 calculates the matrix W by equation (10) is illustrated.

[0109]

number

[0110] The inverse problem analysis unit 62 performs the above process, for example, every time the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111-112. As a result, the matrix W (with the weighting coefficient w i,j,k、l ) is calculated.

[0111] Then, the inverse problem analysis unit 62 calculates the weighting coefficient w i,j,k、l and the thermal diffusivity α of the precast block 9 2 and the time (reference time) t when the measurement values ​​of the optical fiber temperature sensors 111 to 112 are acquired. c (=t l ) and the coordinates (x^ i, y^ j, z^ k )(=(x i, y j, z k)) into equation (3), the value of the interpolation / extrapolation temperature function u(x,y,z,t) is calculated, and this value is set as the temperature u(x,y,z,t).

[0112] Here, the heat transfer in the thickness direction of the region where the precast block 9 exists is in the order of inside the furnace → deposits on the inner peripheral surface 6a → wear bricks 7 → precast block 9 → steel shell 10 → outside the furnace. Note that there may be no deposits on the inner peripheral surface 6a. As described above, the region between the wear bricks 7 and the precast block 9 and the region between the precast block 9 and the steel shell 10 each have materials for connecting (fixing) them. Also, there may be voids in these regions. Therefore, these regions become regions that hinder heat transfer. Therefore, when performing heat transfer calculations strictly, it is necessary to take into account the physical properties of these regions. Therefore, a three-dimensional unsteady heat transfer inverse problem may be formulated taking into account the physical properties of these regions. However, it is not easy to determine the physical properties of these regions. Also, since the physical properties differ depending on the type of deposit, it is not easy to determine the physical properties of the deposit.

[0113] The present inventors have conducted intensive research in light of the above. As a result, the present inventors have determined that the weighting coefficient w i,j,k,l When calculating the weighting factor w, if the thermal diffusivity of the precast block 9 is used as the thermal diffusivity (square root of α), i,j,k,l It was found that the accuracy of the temperature calculated by the interpolation / extrapolation temperature function u(x, y, z, t) satisfies the accuracy required for practical use (approaching the actual measured value) without using other thermal diffusivities when calculating (see the calculation example (Figure 11) described later).

[0114] When the thermal diffusivity of the precast block 9 is used as the thermal diffusivity (square root of α), the value of the internal / extrapolation temperature function u(x,y,z,t) is essentially the temperature of the precast block 9. In other words, when the thermal diffusivity of the precast block 9 is used as the thermal diffusivity (square root of α), the range of coordinates (x,y,z) in the xyz coordinate system to which the internal / extrapolation temperature function u(x,y,z,t) is applied must be the coordinates of the area of ​​the precast block 9. However, the present inventors have found that even if the coordinates (x,y,z) are treated as the coordinates of an area other than the precast block 9, the accuracy of the value of the internal / extrapolation temperature function u(x,y,z,t) satisfies the accuracy required for practical use. Therefore, in this embodiment, a case is illustrated in which the thermal diffusivity of the precast block 9 is used as the thermal diffusivity (square root of α) included in the internal / extrapolation temperature function u(x,y,z,t) and the thermal diffusivity of other members is not used. For example, when the optical fibers 121 to 122 are embedded in the permanent brick 8, the thermal diffusivity of the permanent brick 8 is used, and the thermal diffusivity of other members is not used.

[0115] As described above, this embodiment illustrates a case where the temperature of each position of the electric furnace 1 including the side wall 6 is calculated based on the value of the internal / extrapolation temperature function u(x, y, z, t) in equation (3). This embodiment illustrates a case where the equipment status monitoring device 100 calculates the position in the thickness direction of the inner circumferential surface 6a. Therefore, this embodiment illustrates a case where the inverse problem analyzing unit 62 calculates at least the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 based on the value of the internal / extrapolation temperature function u(x, y, z, t) in equation (3).

[0116] More specifically, in this embodiment, a case is illustrated in which the inverse problem analyzing unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 at the y and z coordinates of the hotspot centroid positions 81a, 82a. It is preferable to set the hotspot centroid positions 81a, 82a as the positions (y and z coordinates) for calculating the temperature distribution in the thickness direction (x-axis direction) of the side wall 6. This is because it is possible to calculate the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 at the position where wear is expected to be most advanced.

[0117] However, the positions (y coordinate and z coordinate) for calculating the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 are not limited to the hot spot centroid positions 81a and 82a. For example, the inverse problem analyzing unit 62 may calculate the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 at the hotspot peripheral positions 81b to 81e and 82b to 82e in addition to or instead of the hotspot centroid positions 81a and 82a.

[0118] Also, for example, there are cases where the hot spot region 71 cannot be identified. In this case, the inverse problem analysis unit 62 does not need to identify the hot spot region 71. For example, the inverse problem analysis unit 62 may replace the position of the hot spot region 71 with a preset position and calculate the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 at that position as described above. The position (the preset position) to which the position of the hot spot region 71 is replaced may be, for example, a position where a hot spot is expected to occur. Also, the position to which the position of the hot spot region 71 is replaced may be a position planned to be repaired, or may be another position (for example, a position determined to manage the time transition of the state of the electric furnace 1).

[0119] <<Refractory position calculation unit 63>> The refractory position calculation unit 63 calculates the position in the thickness direction of the inner circumferential surface 6a based on the temperature distribution in the thickness direction of the side wall portion 6 calculated by the inverse problem analysis unit 62. In this embodiment, a case is illustrated in which the inverse problem analysis unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 at the y coordinates and z coordinates of the hotspot centroid positions 81a, 82a. Therefore, a case is illustrated in which the refractory position calculation unit 63 calculates the x coordinate of the inner circumferential surface 6a at the y coordinates and z coordinates of the hotspot centroid positions 81a, 82a.

[0120] For example, the refractory position calculation unit 63 calculates the position (x coordinate) in the thickness direction where the temperature is the same as the temperature of the molten metal in the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 as the x coordinate of the inner circumferential surface 6a. The temperature of the molten metal may be a measured value or an estimated value (target value or calculated value). When the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 is calculated at y coordinates and z coordinates different from the y coordinates and z coordinates of the hot spot gravity center positions 81a, 82a, for example, the temperature of a position in the furnace having the same y coordinates and z coordinates as the positions different from the hot spot gravity center positions 81a, 82a may be used instead of the temperature of the molten metal.

[0121] Since the wear brick 7 constitutes the inner peripheral surface 6a, the state of the wear brick 7 can be identified by the x-coordinate of the inner peripheral surface 6a. For example, when the xyz coordinate system is defined as shown in Figures 9A and 9B, a decrease in the value of the x-coordinate indicates a decrease in the depth WL of the worn portion 92. x The x-coordinate value increases as the depth of the inner circumferential surface 6a (the wear brick 7) increases (i.e., the thickness of the wear brick 7 decreases). On the other hand, the x-coordinate value increases as the amount of deposits on the inner circumferential surface 6a (the wear brick 7) increases.

[0122] Here, the length in the thickness direction (x-axis direction) from the shell 10 to the inner circumferential surface 6a is referred to as the refractory equivalent length. In this embodiment, the refractory equivalent length is obtained by calculating the difference between the x coordinate of the shell 10 and the x coordinate of the inner circumferential surface 6a in the y coordinate and z coordinate of the hotspot centroid positions 81a, 82a.

[0123] For example, the refractory position calculation unit 63 stores the refractory equivalent length in a new electric furnace 1 as the current value of the refractory equivalent length. The refractory equivalent length in a new electric furnace 1 is, for example, a design value. If the refractory equivalent length calculated thereafter is shorter than the current value of the refractory equivalent length, the refractory position calculation unit 63 determines that the thickness of the wear brick 7 has decreased. Then, the refractory position calculation unit 63 updates the current value of the refractory equivalent length to the calculated refractory equivalent length. On the other hand, if the calculated refractory equivalent length is longer than the current value of the refractory equivalent length, the refractory position calculation unit 63 calculates the difference between the calculated refractory equivalent length and the current value of the refractory equivalent length as the thickness of the deposit (length in the thickness direction (x-axis direction)). Note that the method of managing the state of the wear brick 7 using the refractory equivalent length is not limited to the above method. For example, the refractory position calculation unit 63 may calculate the increase or decrease in the refractory equivalent length from the previous value.

[0124] <<Output section 64>> The output unit 64 outputs the inner circumferential surface state information. The inner circumferential surface state information is information related to the x coordinate of the inner circumferential surface 6a (the position in the thickness direction of the inner circumferential surface 6a) calculated by the refractory position calculation unit 63. The inner circumferential surface state information is not limited to the x coordinate of the inner circumferential surface 6a. For example, the inner circumferential surface state information may be information calculated using the x coordinate of the inner circumferential surface 6a. For example, the output unit 64 outputs at least one of the current value of the x coordinate of the inner circumferential surface 6a and the current value of the refractory equivalent length. The output of information by the output unit 64 is performed, for example, by at least one of displaying on a computer display, transmitting to an external device, and storing in a storage medium outside the equipment status monitoring device 100.

[0125] When the measured values ​​of the optical fiber temperature sensors 111-112 are acquired during charging, the output unit 64 can output the inner circumferential surface state information during the charging. Therefore, the inner circumferential surface state information can identify the repaired portion of the inner circumferential surface 6a during charging. The repaired portion of the inner circumferential surface 6a may be identified by an operator or by the equipment status monitoring device 100. For example, the equipment status monitoring device 100 may have a repaired portion identifying unit that identifies the repaired portion based on the current value of the x coordinate of the inner circumferential surface 6a. In this case, the repaired portion identifying unit, for example, determines whether or not the current value of the refractory equivalent length is less than a threshold value. If the current value of the refractory equivalent length is less than the threshold value as a result of this determination, the repaired portion identifying unit identifies the position of the inner circumferential surface 6a used when calculating the refractory equivalent length as the repaired portion. In addition, the threshold value is determined, for example, based on the thickness (length in the x-axis direction) of the wear brick 7 at which the function as a refractory is impaired. When the equipment status monitoring device 100 calculates the repair location in this manner, the output unit 64 may output information indicating the repair location as inner circumferential surface status information. The repair location identified in the above manner is then repaired. The repair is performed, for example, by filling the worn portion 92 with a repair material. Note that the method of repairing the refractory material is realized by a known technique, and therefore a detailed description of the method will be omitted here.

[0126] In addition, the inner peripheral surface state information can be used to determine whether or not to interrupt or stop the operation because there is a risk that the contents (molten metal, etc.) in the furnace may be discharged from the side wall portion 6 to the outside of the furnace during charging. This determination may be made by an operator or may be specified by the equipment state monitoring device 100. For example, the equipment state monitoring device 100 may have an operation continuation determination unit that determines whether or not to continue the operation of the electric furnace 1 based on the current value of the x coordinate of the inner peripheral surface 6a. The operation continuation determination unit may determine not to continue the operation (i.e., to interrupt or stop) when the current value of the refractory equivalent length is less than a threshold value. The threshold value is determined based on, for example, the thickness (length in the x-axis direction) of the wear brick 7 at which the function as a refractory is impaired. It is preferable that the threshold value used in determining whether or not to continue the operation of the electric furnace 1 is smaller than the threshold value used in calculating the repair location described above. In this case, the latter threshold value is a length with a larger margin than the former threshold value with respect to the thickness of the wear brick 7 at which the function as a refractory material is impaired. In this way, when the equipment status monitoring device 100 judges whether or not to continue the operation of the electric furnace 1, the output unit 64 may output information indicating the result of the judgment as the inner peripheral surface status information.

[0127] <Flowchart> Next, an example of an equipment status monitoring method performed using the equipment status monitoring device 100 of this embodiment will be described with reference to the flowchart of Fig. 10. Note that information that can be set in advance before the flowchart of Fig. 10 starts is stored in the equipment status monitoring device 100 via an input device. Also, the flowchart of Fig. 10 is realized, for example, by a processor included in the equipment status monitoring device 100 executing a program stored in a memory.

[0128] First, in step S1001, the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111 to 112. In this embodiment, the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111 to 112 at a plurality of times t1, . . . , t m 1, a case in which temperatures at respective positions in the optical fibers 121 to 122 are acquired will be illustrated.

[0129] Next, in step S1002, the inverse problem analysis unit 62 calculates the temperatures u^(x^) at the temperature acquisition positions 81a to 81e and 82a to 82e based on the measurements of the optical fiber temperature sensors 111 to 112. i ,y^ j ,z^ k ,t l ) is calculated. Then, the process of step S1003 is performed.

[0130] Here, the temperature acquisition positions 81a-81e, 82a-82e include the hotspot centroid positions 81a, 82a (position of the hotspot region 71). In step S1002, when a plurality of positions are obtained as the hotspot centroid positions 81a, 82a (position of the hotspot region 71), hotspot peripheral positions 81b-81e, 82b-82e are calculated for each of the plurality of hotspot centroid positions 81a, 82a.

[0131] In FIG. 10, the temperature u^(x^) at the temperature acquisition positions 81a to 81e and 82a to 82e for one hot spot region 71 is acquired in one process of steps S1003 to S1106. i ,y^ j ,z^ k ,t l ) is used as an example.

[0132] In step S1003, the inverse problem analysis unit 62 calculates the temperature u^(x^ i ,y^ j ,z^ k ,t l ), the weighting factor w of the internal / extrapolated temperature function u(x,y,z,t) in Eq. (3) is i,j,k、l Calculate.

[0133] Next, in step S1004, the inverse problem analysis unit 62 calculates the weighting coefficient w i,j,k、l and the time coordinates (x^ i ,y^ j ,z^k ,t l )((=(x i, y j, z k ,t l )) and the thermal diffusivity α of the precast block 9 2 By substituting and into equation (3), the value of the interpolation / extrapolation temperature function u(x,y,z,t) (i.e., the temperature u(x,y,z,t)) is calculated.

[0134] Next, in step S1005, the inverse problem analysis unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 at the y-coordinates and z-coordinates of the hotspot center of gravity positions 81a, 82a based on the value of the internal / extrapolation temperature function u(x, y, z, t).

[0135] Next, in step S1006, the refractory position calculation unit 63 calculates the position (x coordinate) in the thickness direction of the inner surface 6a at the y coordinate and z coordinate of the hotspot center of gravity positions 81a, 82a based on the temperature distribution in the thickness direction (x axis direction) of the side wall portion 6 at the y coordinate and z coordinate of the hotspot center of gravity positions 81a, 82a calculated in step S1005.

[0136] Next, in step S1007, the equipment status monitoring device 100 judges whether or not processing has been performed for all hot spot regions 71. If the result of this judgment is that processing has not been performed for all hot spot regions 71 (NO in step S1007), the processing of step S1003 is performed. Then, in steps S1003 to 1006, the inverse problem analyzing unit 62 and the refractory position calculating unit 63 calculate the positions in the thickness direction of the inner circumferential surface 6a of the hot spot centroid positions 81a, 82a of the unprocessed hot spot regions 71 in the y coordinate and z coordinate.

[0137] Then, in step S1007, when it is determined that the processing has been performed on all the hot spot regions 71 (YES in step S1007), the processing of step S1008 is performed. In step S1008, the output unit 64 outputs the inner circumferential surface state information. If multiple hot spot regions 71 are obtained in step S1002, the same number of positions as the number of hot spot regions 71 are calculated as positions in the thickness direction of the inner circumferential surface 6a in the repeated processing of steps S1003 to S1006. Therefore, in this case, the output unit 64 outputs the inner circumferential surface state information for each of the multiple positions in the thickness direction of the inner circumferential surface 6a. When the processing of step S1008 is completed, the processing according to the flowchart of FIG. 10 is completed.

[0138] <Calculation example> Next, a calculation example will be described. In this calculation example, the side wall 6 to be subjected to the three-dimensional unsteady heat transfer inverse problem analysis is a side wall modeled as shown in Fig. 9A and Fig. 9B. In this calculation example, the x coordinate of the inner circumferential surface 6a of the side wall 6 modeled in this way is calculated in each of the cases where the three-dimensional unsteady heat transfer inverse problem analysis is performed as described in this embodiment and where the one-dimensional unsteady heat transfer inverse problem is performed.

[0139] The damaged portion 92 is formed at the center of the yz plane of the model. The lengths WL of the damaged portion 92 in each direction are x , W.L. y , W.L. z 0.14m, 0.2m, and 0.2m (WL x =0.14, W.L. y =WL z =0.2). The height (length in the height direction (z-axis direction)) ZB, width (length in the circumferential direction (y-axis direction)) YB, and thickness (length in the thickness direction (x-axis direction)) XB of the modeled side wall portion 6 were set to 1 m, 1 m, and 0.46 m (ZB=YB=1, XB=0.46), respectively. The distance Δx from the outer peripheral surface 6b of the modeled side wall portion 6 to the inner optical fiber 121 in the thickness direction (x-axis direction) in 0.14m(Δx in= 0.14), and the distance Δx from the outer peripheral surface 6b of the modeled side wall portion 6 to the outer optical fiber 122 in the thickness direction (x-axis direction) out 0.04m(Δx out =0.04). The distances Δy1 and Δy2 shown in FIG. 8A and FIG. 8B were each set to 0.05 m (Δy1=Δy2=0.05). That is, the distances Δy1 and Δy2 were set to the width WL of the worn portion 92. y 8A and 8B are set to 0.05 m (Δz1=Δz2=0.05). z The ratio was set at 1 / 4.

[0140] Under the above conditions, the temperatures in the thickness direction (x-axis direction) of the side wall portion 6 at the y-coordinate and z-coordinate of the hotspot gravity center positions 81a, 82a were calculated. In this case, the temperature measurement period was set to 0.01 Hr. The number of temperature measurement times m was set to 50 (m=50). As a model parameter of the unsteady heat transfer inverse problem, the time shift T (see equation (1)) was set to 35 Hr. The regularization coefficient γ (see equation (6)) was set to 0.00000000001 (γ=0.00000000001). The model parameters of the unsteady heat transfer inverse problem may be determined according to the degree of unsteadiness.

[0141] Moreover, the temperature of each part of the model was given as a true value. The true values ​​(temperatures) at the temperature acquisition positions 81a to 81e and 82a to 82e were extracted to solve the unsteady heat transfer inverse problem. In the one-dimensional unsteady heat transfer inverse problem, the temperature acquisition positions were the two hot spot gravity center positions 81a and 82a. The y and z coordinates of the position of the gravity center of the damaged portion 92 were the y and z coordinates of the hot spot gravity center positions 81a and 82a. Moreover, the temperature T of the inner circumferential surface 6a M is 1665℃(T M =1665).

[0142] 11A and 11B are diagrams showing an example of the relationship between the refractory temperature and the refractory thickness direction distance. The refractory temperature is the value (temperature) of an internal / extrapolated temperature function u(x, y, z, t) calculated by performing a non-steady heat transfer inverse problem analysis. The refractory thickness direction distance is the distance in the thickness direction (x-axis direction) from the outer peripheral surface 6b of the model.

[0143] Fig. 11A shows the results of a three-dimensional unsteady heat transfer inverse problem analysis performed as described in this embodiment. Fig. 11B shows the results of a one-dimensional unsteady heat transfer inverse problem analysis performed by limiting the heat transfer direction to only the thickness direction in the three-dimensional unsteady heat transfer inverse problem analysis described in this embodiment.

[0144] As described above, the temperature T of the inner circumferential surface 6a M is 1665℃(T M = 1665). The temperature T M The distance in the thickness direction of the refractory at (=1665°C) is the above-mentioned equivalent length of the refractory.

[0145] As shown in FIG. 11A, in the method described in this embodiment, the calculated value is close to the true value. M 9A and 9B, the thickness of the side wall 6 at the worn portion 92a (=XB-WL x ) is 0.32 (=0.46-0.14). The temperature T M It can be seen that the refractory thickness direction distance (=0.323 m) at the temperature (=1665° C.) is close to the thickness (=0.32 m) of the side wall portion 6 at the worn portion 92a.

[0146] In contrast, when a one-dimensional unsteady heat transfer inverse problem analysis was performed as shown in FIG. 11B, the calculated value was lower than the true value. M The refractory thickness direction distance at (=1665℃) was 0.371 m, which deviated significantly from the true value (=0.32 m).

[0147] 11A and 11B, if heat transfer in the y-axis and z-axis directions is not taken into consideration, the calculation accuracy of the position in the thickness direction of the inner circumferential surface 6a may be reduced, whereas the calculation accuracy of the position in the thickness direction of the inner circumferential surface 6a can be improved by taking heat transfer in the y-axis and z-axis directions into consideration as in this embodiment. Also, from FIG. 11A, it can be seen that the position in the thickness direction of the inner circumferential surface 6a can be calculated with high accuracy by using the thermal diffusivity of the precast block 9 as the thermal diffusivity (square root of α) included in the internal / extrapolation temperature function u(x,y,z,t) without using the thermal diffusivity of other members.

[0148] <Hardware> Next, a description will be given of an example of hardware of the equipment status monitoring device 100. In Fig. 12, the equipment status monitoring device 100 has a CPU 1201, a main memory device 1202, an auxiliary memory device 1203, a communication circuit 1204, a signal processing circuit 1205, an image processing circuit 1206, an I / F circuit 1207, a user interface 1208, a display 1209, and a bus 1210.

[0149] The CPU 1201 performs overall control of the equipment status monitoring device 100. The CPU 1201 uses the main memory device 1202 as a work area to execute programs stored in the auxiliary memory device 1203. The main memory device 1202 temporarily stores data. The auxiliary memory device 1203 stores various types of data in addition to the programs executed by the CPU 1201.

[0150] The communication circuit 1204 is a circuit for communicating with the outside of the equipment status monitoring device 100. The communication circuit 1204 may perform wireless communication or wired communication with the outside of the equipment status monitoring device 100.

[0151] The signal processing circuit 1205 performs various signal processing operations on signals received by the communication circuit 1204 and signals input under the control of the CPU 1201 . The image processing circuit 1206 performs various types of image processing on the input signal under the control of the CPU 1201. The signal that has undergone this image processing is output to a display 1209, for example. The user interface 1208 is a part where an operator gives instructions to the equipment status monitoring device 100. The user interface 1208 has, for example, buttons, switches, dials, etc. The user interface 1208 may also have a graphical user interface using a display 1209.

[0152] The display 1209 displays an image based on a signal output from the image processing circuit 1206. The I / F circuit 1207 exchanges data with devices connected to the I / F circuit 1207. In FIG. 12, a user interface 1208 and a display 1209 are shown as devices connected to the I / F circuit 1207. However, the devices connected to the I / F circuit 1207 are not limited to these. For example, a portable storage medium may be connected to the I / F circuit 1207. Furthermore, at least a part of the user interface 1208 and the display 1209 may be located outside the equipment status monitoring device 100.

[0153] The CPU 1201, the main memory device 1202, the auxiliary memory device 1203, the signal processing circuit 1205, the image processing circuit 1206, and the I / F circuit 1207 are connected to a bus 1210. Communication between these components is performed via the bus 1210. The hardware of the equipment status monitoring device 100 is not limited to the hardware shown in FIG. 12 as long as it can realize the functions of the equipment status monitoring device 100 described above. For example, a GPU may be used as a processor instead of or in addition to the CPU 1201. The hardware of the equipment status monitoring device 100 is also realized by, for example, the same hardware as the hardware of the equipment status monitoring device 100 shown in FIG. 12. Therefore, detailed explanation of a specific example of the hardware of the equipment status monitoring device 100 is omitted here.

[0154] <Summary> As described above, in this embodiment, in the electric furnace 1, which is an example of equipment in which molten metal exists during operation, the inner circumferential surface 6a of the side wall 6 is made of refractory material. Also, the optical fibers 121-122 provided in the optical fiber temperature sensors 111, 112 are embedded in the members constituting the side wall 6. Therefore, it is possible to measure the temperature of the side wall 6 over a wider range.

[0155] In this embodiment, a precast block 9 is used as a member constituting the side wall portion 6. The precast block 9 is a fire-resistant block produced by precasting an amorphous refractory material with the optical fibers 121-122 embedded therein. This makes it easy to install the optical fibers 121, 122. In addition, it is possible to suppress variation in temperature measurement errors by the optical fiber temperature sensors 111-112.

[0156] In this embodiment, the equipment status monitoring device 100 calculates the temperature distribution in the thickness direction of the side wall 6 by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the measured values ​​of the optical fiber temperature sensors 111-112. Then, the equipment status monitoring device 100 calculates a position including the position in the thickness direction of the side wall 6 as the position of the inner circumferential surface 6a based on the temperature distribution in the thickness direction of the side wall 6. Therefore, the state of the inner circumferential surface 6a can be easily and highly accurately monitored. Also, the state of the inner circumferential surface 6a can be monitored even when molten metal or the like is present in the furnace.

[0157] Furthermore, in this embodiment, the equipment status monitoring device 100 acquires five temperatures per location in the thickness direction of the side wall 6 as temperatures for calculating one position in the thickness direction of the inner circumferential surface 6a. Therefore, it is possible to optimize the number of temperatures used when performing a three-dimensional unsteady heat transfer inverse problem analysis.

[0158] Furthermore, in this embodiment, the equipment status monitoring device 100 acquires the temperatures at the hotspot centroid positions 81a, 82a, making it possible to take into account heat transfer in each three-dimensional direction in an area including a hotspot.

[0159] In addition, in this embodiment, the equipment status monitoring device 100 performs a three-dimensional unsteady heat transfer inverse problem analysis using only the physical property values ​​(thermal diffusivity) of the precast block 9 among the physical property values ​​(thermal diffusivity) of the members constituting the side wall portion 6. Therefore, it is possible to prevent the unsteady heat transfer inverse problem from becoming a complicated problem. In addition, it is possible to prevent a decrease in calculation accuracy caused by introducing assumptions about events that are difficult to estimate into the unsteady heat transfer inverse problem.

[0160] In this embodiment, the optical fiber temperature sensor 111 that measures the temperature at a relatively inner position and the optical fiber temperature sensor 112 that measures the temperature at a relatively outer position are separate temperature sensors, which makes it easy to install the optical fiber temperature sensors 111-112.

[0161] In this embodiment, the precast blocks 9 in which the optical fibers 121, 122 are embedded are installed in a part of the area where the permanent bricks 8 are installed. Therefore, wear of the precast blocks 9 can be suppressed.

[0162] (Other embodiments) The above-described embodiment of the present disclosure can be realized by a computer executing a program. A computer-readable recording medium having the program recorded thereon and a computer program product such as the program can also be applied as an embodiment of the present disclosure. Examples of the recording medium that can be used include a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, and a ROM.

[0163] Furthermore, the above-described embodiments of the present disclosure are merely examples of specific implementations of the present disclosure, and the technical scope of the present disclosure should not be interpreted as being limited by these. In other words, the present disclosure can be implemented in various forms without departing from its technical concept or main features. [Industrial Applicability]

[0164] The present disclosure can be used, for example, in equipment in which molten metal is present during operation.

Claims

1. Equipment in which molten metal is present during operation, The inner circumferential surface of the side wall of the equipment is made of refractory material, an optical fiber provided in an optical fiber temperature sensor is embedded in a member constituting the side wall portion, Among the components constituting the side wall portion, the component in which the optical fiber is embedded is a fire-resistant block produced by precasting an amorphous refractory material with the optical fiber embedded in it.

2. a temperature sensor for measuring a temperature at a position on the inner circumferential surface side of the side wall portion; a temperature sensor for measuring a temperature at a position on the outer circumferential surface side of the side wall portion, The facility according to claim 1 , wherein the temperature sensor that measures the temperature at a position on the relatively inner circumferential surface side of the side wall portion is the optical fiber temperature sensor.

3. The equipment according to claim 2 , wherein the temperature sensor for measuring the temperature at a position relatively closer to the outer circumferential surface of the side wall portion is the optical fiber temperature sensor.

4. The facility according to any one of claims 1 to 3, wherein the member is located closer to the outer circumferential surface of the side wall portion than a refractory material constituting the inner circumferential surface of the side wall portion.

5. An equipment status monitoring device for monitoring the status of equipment in which molten metal is present during operation, the equipment having an inner circumferential surface of a side wall portion thereof constructed of a refractory material, and an optical fiber provided with an optical fiber temperature sensor embedded in a member constituting the side wall portion, an inverse problem analysis means for calculating a temperature distribution of the side wall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on a measurement value of a temperature sensor that measures a temperature of the side wall portion; a refractory position calculation means for calculating a position of the inner circumferential surface based on the temperature distribution calculated by the inverse problem analysis means; having The inverse problem analysis means calculates a temperature distribution in a thickness direction of the side wall portion, the position of the inner circumferential surface calculated by the refractory position calculation means includes a position of the side wall portion in a thickness direction, the temperature sensor measures a temperature at a position relatively closer to the inner circumferential surface of the sidewall portion and a temperature at a position relatively closer to the outer circumferential surface of the sidewall portion in a portion of the sidewall portion that is different from the inner circumferential surface of the sidewall portion; an optical fiber temperature sensor that measures at least the temperature at a position relatively closer to the inner periphery of the side wall portion, out of the temperature at a position relatively closer to the inner periphery of the side wall portion and the temperature at a position relatively closer to the outer periphery of the side wall portion.

6. An equipment status monitoring device as described in claim 5, wherein, among the components constituting the side wall portion, the component in which the optical fiber is embedded is a fire-resistant block manufactured by precasting an amorphous refractory material with the optical fiber embedded therein.

7. 7. An equipment status monitoring device as described in claim 5 or 6, wherein the temperature sensor that measures the temperature at a position relatively closer to the inner periphery of the side wall portion and the temperature at a position relatively closer to the outer periphery of the side wall portion is an optical fiber temperature sensor having an optical fiber embedded in a member constituting the side wall portion.

8. 7. The equipment status monitoring device according to claim 5, wherein, among the components constituting the side wall portion, a component in which the optical fiber is embedded is located closer to the outer circumferential surface of the side wall portion than a refractory material constituting an inner circumferential surface of the side wall portion.

9. the inverse problem analysis means acquires N temperatures at one location in the thickness direction of the side wall portion based on measurements by the temperature sensor as temperatures for calculating one position on the inner circumferential surface in the thickness direction of the side wall portion, and calculates a temperature distribution in the thickness direction of the side wall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the N temperatures; 7. The facility status monitoring device according to claim 5, wherein N is an integer of 2 or more.

10. 10. The facility status monitoring device according to claim 9, wherein N is 5.

11. 7. The equipment status monitoring device according to claim 5 or 6, wherein the inverse problem analysis means acquires temperatures of hot spot regions including positions where the temperature is locally maximized based on measurements of the temperature sensors, and calculates a temperature distribution in a thickness direction of the side wall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the acquired temperatures.

12. 7. The equipment status monitoring device according to claim 5, wherein the inverse problem analysis means performs a three-dimensional unsteady heat transfer inverse problem analysis using only physical property values ​​of a member in which the temperature sensor is embedded, among physical property values ​​of members constituting the side wall portion.

13. An equipment status monitoring method for monitoring the status of equipment in which molten metal is present during operation, the equipment having an inner circumferential surface of a side wall portion thereof made of a refractory material, and an optical fiber provided with an optical fiber temperature sensor is embedded in a member constituting the side wall portion, comprising: an inverse problem analysis step of calculating a temperature distribution of the side wall portion by performing a three-dimensional unsteady heat transfer inverse problem analysis based on a measurement value of a temperature sensor that measures the temperature of the side wall portion; a refractory position calculation step of calculating a position of the inner circumferential surface based on the temperature distribution calculated by the inverse problem analysis step; having The inverse problem analysis step calculates a temperature distribution in a thickness direction of the side wall portion, The position of the inner circumferential surface calculated in the refractory position calculation step includes a position of the side wall portion in a thickness direction, the temperature sensor measures a temperature at a position relatively closer to the inner circumferential surface of the sidewall portion and a temperature at a position relatively closer to the outer circumferential surface of the sidewall portion in a portion of the sidewall portion that is different from the inner circumferential surface of the sidewall portion; an optical fiber temperature sensor that measures at least the temperature at a position relatively closer to the inner periphery of the side wall portion, out of the temperature at a position relatively closer to the inner periphery of the side wall portion and the temperature at a position relatively closer to the outer periphery of the side wall portion.

14. A program for causing a computer to function as each of the means of the facility status monitoring device according to claim 5 or 6.

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