Facility, facility state monitoring device, facility state 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

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

[0001] The present disclosure relates to equipment, equipment status monitoring devices, equipment status monitoring methods, and programs, which are particularly suitable for use in equipment in which molten metal is present during operation. This application claims priority to Japanese Patent Application No. 2023-065494, filed on April 13, 2023, the contents of which are incorporated herein by reference in their entirety.

[0002] In facilities that produce molten metal, such as electric furnaces and blast furnaces, molten metal is present inside during operation. This causes the interior of the facility to become very hot. Refractories such as firebricks are therefore installed on the inner periphery of the facility. Because the refractories are exposed to high-temperature molten metal, they are subject to wear and tear, such as melting or peeling, as the facility is used. Therefore, there is a need for technology to monitor the condition of the refractories.

[0003] One such technique is described in Patent Document 1. In this technique, 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 the blast furnace. Then, in this technique, the position at which the temperature calculated in this manner 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.

[0004] Japanese Patent Application Laid-Open No. 2001-234217

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

[0006] The present disclosure has been made in consideration of the above-mentioned 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.

[0007] The equipment disclosed herein is equipment in which molten metal is present inside during operation, the inner surface of the side wall of the equipment is made of refractory material, and the optical fiber provided in the optical fiber temperature sensor is embedded in the material that makes up the side wall.

[0008] The equipment status monitoring device disclosed herein is an equipment status monitoring device that monitors the status of the equipment, and includes: 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 that is 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 out of 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 disclosed herein is an equipment status monitoring method for monitoring the status of the equipment, and includes an inverse problem analysis step of calculating a temperature distribution of the side wall portion by performing 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 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 side wall portion, and the position of the inner circumferential surface calculated in the refractory position calculation step includes a position of the side wall portion in the thickness direction, 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 at least 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.

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

[0011] FIG. 1 is a diagram illustrating an example of the configuration of an electric furnace. FIG. 2 is a cross-sectional view taken along line II of FIG. 1. FIG. 3 is a diagram illustrating an example of the configuration of a precast block with embedded optical fibers. FIG. 4A is a diagram conceptually illustrating a first example of heat transfer that can be considered in a one-dimensional inverse problem of unsteady heat transfer. FIG. 4B is a diagram conceptually illustrating a second example of heat transfer that can be considered in a one-dimensional inverse problem of unsteady heat transfer. FIG. 5A is a diagram illustrating a first example of heat transfer that can be considered in a three-dimensional inverse problem of unsteady heat transfer. FIG. 5B is a diagram illustrating a second example of heat transfer that can be considered in a three-dimensional inverse problem of unsteady heat transfer. FIG. 6 is a diagram illustrating an example of the functional configuration of an equipment status monitoring device. FIG. 7 is a diagram illustrating an example of a hot spot region. FIG. 8A is a diagram illustrating a first example of temperature locations acquired when performing a three-dimensional inverse problem of unsteady heat transfer. FIG. 8B is a diagram illustrating a second example of temperature locations acquired when performing a three-dimensional inverse problem of unsteady heat transfer. FIG. 9A is a diagram illustrating an example of a region including a worn portion when viewing a sidewall from above. 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. Fig. 10 is a flowchart explaining an example of an equipment condition monitoring method. Fig. 11A is a diagram showing a first example of a relationship between a refractory temperature and a distance in the thickness direction of the refractory. Fig. 11B is a diagram showing a second example of a relationship between a refractory temperature and a distance in the thickness direction of the refractory. Fig. 12 is a diagram showing an example of the hardware configuration of an equipment condition monitoring device.

[0012] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings. The term "same length, position, size, spacing, etc.," as used herein, refers to objects being exactly the same, as well as objects being different within the scope of the present disclosure (e.g., within the tolerances established at the time of design). In addition, some components are omitted or simplified in each drawing for ease of explanation and description.

[0013] The equipment status monitoring device 100 of this embodiment, which will be described later, monitors the condition of the inner peripheral surface of the sidewall of equipment in which molten metal is present during operation. The inner peripheral surface of the sidewall of the equipment is the surface that contacts a space where molten metal may be present (e.g., the surface facing the central axis (center line) of the equipment). The inner peripheral surface of the sidewall of the equipment is made of refractory material. In this embodiment, an arc melting furnace, which is a type of electric furnace, is used as an example of such equipment. However, the equipment monitored by the equipment status monitoring device 100 is not limited thereto. In an arc melting furnace, raw materials such as scrap are charged into the furnace for each charge (ch). The raw materials are then melted by an arc generated from an arc electrode. This produces molten metal (e.g., molten steel) and molten slag. In this embodiment, the period from when the raw materials are charged into the furnace to when the molten metal and molten slag are discharged from the furnace is referred to as a "charge." The sidewall 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 arc melting furnaces. For example, the equipment monitored by the equipment status monitoring device 100 may be an electric furnace other than an arc melting furnace, or may be an industrial furnace such as a blast furnace or a converter.

[0014] <Equipment> FIG. 1 is a diagram illustrating an example of the configuration of an electric furnace 1. Note that FIG. 1 is a longitudinal cross-sectional view of the electric furnace 1. For ease of illustration and description, hatching indicating cross sections is omitted in FIG. 1 . In this embodiment, FIG. 1 illustrates an example in which the electric furnace 1 includes an upper lid 2, arc electrodes 3a to 3c, a bottom electrode 4, a furnace bottom 5, and a side wall 6. FIG. 1 illustrates an example in which the electric furnace 1 includes three arc electrodes 3a to 3c. Also, FIG. 1 illustrates an example in which the three arc electrodes 3a to 3c are installed at equal intervals (120° intervals) around the central axis (center line) O of the electric furnace 1. Note that 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. Also, in the following description, the central axis (center line) O of the electric furnace 1 will be abbreviated as the central axis O as necessary.

[0015] In addition, in this embodiment, FIG. 1 illustrates an example in which the side wall portion 6 is installed to surround the central axis O. In addition, in this embodiment, FIG. 1 illustrates an example in which the side wall portion 6 has wear bricks 7, permanent bricks 8, precast blocks 9, and a steel shell 10. Refractory bricks are used to form the wear bricks 7. Of the surfaces of the wear bricks 7, the surface 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 of the side wall portion 6 of the electric furnace 1 will be referred to as the "inner side" as necessary. Note that the "inner side" refers to the side closer to the central axis O of the electric furnace 1. Note that the side opposite the inner side will be referred to as the "outer side" as necessary. Note that the "outer side" refers to the outer circumferential surface 6b 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] Refractory bricks are used to form the permanent set bricks 8. The permanent set bricks 8 are placed outside the wear bricks 7. The outer ends of the wear bricks 7 and the inner ends of the permanent set bricks 8 are connected (fixed) to each other via, for example, a heat-resistant and adhesive material. The heat-resistant and adhesive material is, for example, mortar. The steel shell 10 is placed outside the permanent set bricks 8. The steel shell 10 forms the outer peripheral surface 6b of the side wall portion 6 of the electric furnace 1. The inner ends of the steel shell 10 and the outer ends of the permanent set bricks 8 are connected (fixed) to each other via, for example, a heat-resistant and adhesive material. The heat-resistant and adhesive material is, for example, mortar.

[0017] The above-described configuration of the electric furnace is that of a general electric furnace. The configuration of the electric furnace is not limited to the above-described configuration. In the electric furnace 1 of this 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 will be described later, this embodiment illustrates a case in which the precast block 9 is produced by precasting a monolithic refractory material with an optical fiber provided in an optical fiber temperature sensor embedded therein.

[0018] In the electric furnace 1 illustrated in FIG. 1 , when scrap, the raw material, melts, the side wall 6 becomes extremely hot locally due to radiant heat generated by arc discharge. Therefore, the temperature distribution of the side wall 6 in a virtual plane parallel to the inner circumferential surface 6 a has a local maximum value (local maximum value). In the following description, such a location 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 3 a to 3 c, there are at least as many hot spots as there are arc electrodes per virtual plane parallel to the inner circumferential surface 6 a (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 end of the precast block 9 is the same as the outer end of the permanent brick 8, or is located more inward than the outer end 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 located more outward than the inner end of the permanent brick 8. (C) The circumferential position of the precast block 9 includes the circumferential position of an area where hot spots are expected to occur. (D) The heightwise position of the precast block 9 includes the heightwise position of an 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 example is shown in which an optical fiber temperature sensor is used as the temperature sensor for measuring the temperature of the side wall 6. In this embodiment, FIG. 1 illustrates an example in which the optical fiber temperature sensors 111-112 include optical fibers 121-122 and measuring devices 131-132. The measuring devices 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 within the optical fibers 121-122. The measuring devices 131-132 input the light that has been scattered within the optical fibers 121-122 and returned. The measuring devices 131-132 calculate the temperature at each position within the optical fibers 121-122 based on the intensity, speed, and time of the input and output light. The optical fiber temperature sensors 111 and 112 themselves can be realized by known techniques, and therefore detailed description of the optical fiber temperature sensors 111 and 112 will be omitted here.

[0021] Optical fibers 121 and 122 are embedded in the precast block 9. The optical fiber 121 is installed at a relatively inner position so that it can measure 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. The optical fiber 122 is installed at a relatively outer position so that it can measure 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. In the following description, the optical fiber installed at a relatively inner position will be referred to as the inner optical fiber as needed. Furthermore, the optical fiber installed at a relatively outer position will be referred to as the outer optical fiber as needed. Furthermore, the height direction of the side wall 6 and the circumferential direction of the side wall 6 will be abbreviated as the height direction and the circumferential direction, respectively, as needed.

[0022] Figure 2 is a cross-sectional view taken along the line I-I in Figure 1. Note that, for ease of illustration and description, hatching indicating cross sections is omitted in Figure 2 as well. As shown in Figure 2, this embodiment illustrates an electric furnace 1 equipped with multiple precast blocks 9a-9r. The multiple precast blocks 9a-9r are arranged circumferentially around the electric furnace 1. This embodiment illustrates an electric furnace 1 equipped with multiple precast blocks 9a-9r having the same configuration. However, the shape and size of at least one of the multiple precast blocks 9a-9r may be different from those of the other precast blocks. At least one physical property value (i.e., the material constituting the precast block) of the multiple precast blocks 9a-9r may also be different from those of the other precast blocks. However, it is preferable, and even more preferable, that the physical properties of the multiple precast blocks 9a-9r be substantially identical. This is because there is no need to vary the physical properties of the precast blocks depending on the location when performing the three-dimensional unsteady heat transfer inverse problem analysis described below.

[0023] Among the precast blocks 9a to 9r, the circumferential ends of two adjacent precast blocks (e.g., precast blocks 9a to 9r) are connected (fixed) to each other, for example, via a heat-resistant and adhesive material. The outer ends of the wear bricks 7 and the inner ends of the precast blocks 9a to 9r are also connected (fixed) to each other, for example, via a heat-resistant and adhesive material. The inner ends of the shells 10 and the outer ends of the precast blocks 9a to 9r are also connected (fixed) to each other, for example, via a heat-resistant and adhesive material. The material (heat-resistant and adhesive material) used to connect (fix) the precast blocks 9a to 9r in this manner is, for example, mortar.

[0024] As shown in FIG. 2 , this embodiment illustrates a case in which inner optical fibers 121a to 121r and outer optical fibers 122a to 122r are installed in each of the precast blocks 9a to 9r. This embodiment also illustrates a case in which the inner optical fibers 121 to 121r have the same configuration. This embodiment also illustrates a case in which the outer optical fibers 122a to 122r have the same configuration. This embodiment also illustrates a case in which the inner optical fibers 121 to 121r and the outer optical fibers 122a to 122r are relatively arranged in the same manner within each of the precast blocks 9a to 9r. As described above, this embodiment illustrates a case in which the precast blocks 9a to 9r have the same configuration. Therefore, in a relative coordinate system with the reference position (e.g., 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 located 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, this embodiment illustrates a case where even if at least two of the precast blocks 9a to 9r are interchanged, the same state as before the interchange is achieved.

[0025] Note that the precast block 9 shown in Figure 1 is one of the precast blocks 9a to 9r. In the following explanation, when describing the precast blocks 9a to 9r without being limited to the individual precast blocks 9a to 9r, the reference numeral 9 will be used to represent the precast block. Furthermore, the inner optical fiber 121 and the outer optical fiber 122 shown in Figure 1 are each one of the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r, respectively. When describing the inner optical fibers 121a to 121r and the outer optical fibers 122a to 122r without being limited to the individual inner optical fibers 121a to 121r and the individual outer optical fibers 122a to 122r, the reference numerals 121 and 122 will be used to represent the inner optical fiber and the outer optical fiber, 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 installed relatively inward. The outer optical fiber 122 is installed relatively outward. As shown in FIG. 3 , this embodiment illustrates a case in which the inner optical fiber 121 is installed so as to meander on an imaginary plane 31a with the circumferential direction as the traveling direction. 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 of the region where the aforementioned hot spot is expected to occur is included within the height direction range of the region in which the inner optical fiber 121 meanders.

[0027] Similarly, this embodiment illustrates a case in which the outer optical fiber 122 is installed 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 installed in this manner, the height direction 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 regions within the imaginary planes 31a and 31b where the optical fibers 121 and 122 are installed will be referred to as the installation regions of the optical fibers 121 and 122 as necessary.

[0028] 3, for the sake of simplicity, the precast block 9 is shown as having a rectangular columnar shape with a hollow fan-shaped bottom. However, the shape of the precast block 9 is not limited to this. For example, the precast block 9 may have a rectangular parallelepiped shape.

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

[0030] An example of a method for connecting the remaining ends of the inner optical fibers 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 Figure 3).

[0031] Of both ends of the inner optical fiber 121 embedded in a 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 precast block 9 on 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 precast block 9a on the right side of the precast block 9a.

[0032] Of both ends of the inner optical fiber 121 embedded in a precast block 9, the end drawn out from the left side is mutually 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 precast block 9 on 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 mutually 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 precast block 9a on the left side of the precast block 9a.

[0033] By configuring and installing the inner optical fibers 121a to 121r in the manner 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 in the circumferential direction on the imaginary plane 31a.

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

[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 the precast block 9 adjacent to the precast block 9 on the left 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 left side is connected to the end drawn out from the right side of both ends of the outer optical fiber 122r embedded in the precast block 9r adjacent to the precast block 9a on the left side of the precast block 9a.

[0036] By configuring and installing the outer optical fibers 122a to 122r in the manner 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 in the circumferential direction on the imaginary plane 31b.

[0037] As described above, this embodiment illustrates a case where the optical fiber temperature sensor 111, which measures the temperature at a relatively inner position, and the optical fiber temperature sensor 112, which 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 the temperature at both a relatively inner position and 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: Monolithic refractory is placed in a mold having a shape and size corresponding to the outer shape of the precast block 9. Then, before the monolithic refractory hardens, the inner optical fiber 121 and the outer optical fiber 122 are placed in the mold so that they are embedded in the above-mentioned positions within the precast block 9. The monolithic refractory is hardened (dried) with the inner optical fiber 121 and the outer optical fiber 122 placed in the mold. It is preferable that the positions (coordinates in the relative coordinate system described above) of the inner optical fiber 121 and the outer optical fiber 122 within the precast block 9 can be identified even when they are embedded in the precast block 9. To this end, for example, it is preferable to use a jig (not shown) that holds the inner optical fiber 121 and the outer optical fiber 122 outside the formwork, thereby preventing the inner optical fiber 121 and the outer optical fiber 122 from changing position (preferably preventing their positions from changing) within the precast block 9 from the time the inner optical fiber 121 and the outer optical fiber 122 are placed in the formwork until the amorphous refractory material hardens.

[0039] For example, a jig having a configuration capable of adjusting the position of the object to be held within the mold may be used. The inner optical fiber 121 and the outer optical fiber 122 are placed in the mold while attached to such a jig. The jig is then adjusted to position the inner optical fiber 121 and the outer optical fiber 122 at predetermined positions within the mold. The jig then maintains the positions of the inner optical fiber 121 and the outer optical fiber 122 within the precast block 9 until the monolithic refractory material hardens.

[0040] The castable refractory may be placed in the formwork after the inner optical fiber 121 and the outer optical fiber 122 are placed in the formwork. The castable refractory is made of a material that satisfies the mechanical strength of the precast block 9 required for the side wall portion 6 and the heat resistance of the precast block 9 required for the side wall portion 6.

[0041] Furthermore, the lengths of the inner optical fiber 121 and the outer optical fiber 122 pulled out from the precast block 9 can be determined even when they are embedded in the precast block 9. Therefore, once the positions of the inner optical fiber 121 and the outer optical fiber 122 within the precast block 9 are determined, the lengths from the measuring devices 131 and 132 to the respective positions within the inner optical fiber 121 and the outer optical fiber 122 can also be determined.

[0042] In this embodiment, a case where all of the following (E) to (G) are satisfied is 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 (distance 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] This is preferable because it reduces the calculation load, such as temperature interpolation calculations, that use the temperatures measured by the optical fiber temperature sensors 111 and 112 in the equipment status monitoring device 100 (described later). However, this is not necessarily required as long as the lengths from the measuring devices 131 and 132 to each position in the inner optical fiber 121 and the outer optical fiber 122 can be specified.

[0044] Furthermore, it is preferable to embed the inner optical fiber and the outer optical fiber (e.g., the inner optical fiber 121a and the outer optical fiber 122a) that are positioned in the same circumferential direction in the same precast block 9, as this facilitates the installation of the inner optical fiber 121 and the outer optical fiber 122. However, this is not necessarily required. For example, the inner optical fiber and the outer optical fiber that are positioned in the same circumferential direction may be embedded in different precast blocks. Furthermore, it is preferable that the inner optical fiber and the outer optical fiber (e.g., the inner optical fiber 121a and the outer optical fiber 122a) are positioned in the same circumferential direction, as this reduces the computational load when performing the three-dimensional unsteady heat transfer inverse problem analysis described below. However, 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 positioned in the same circumferential direction.

[0045] Furthermore, 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 shell 10. Such a temperature sensor may be a radiation thermometer or a thermocouple. Furthermore, such a temperature sensor is installed at a position outside the optical fiber temperature sensor (optical fiber) so as to be able to measure 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. Furthermore, such a temperature sensor is installed at a position where it can measure the temperature in the area where the aforementioned hot spot is expected to occur.

[0046] Further, permanent-heat-treated bricks may be installed outside the permanent-heat-treated bricks 8. In this case, the precast blocks 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded are preferably installed in a portion of the area in which the permanent-heat-treated brick 8 closest to the steel shell 10 is installed. This is because, for example, installation and maintenance of the precast blocks 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded are facilitated. However, the precast blocks 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded may be installed in a portion of the area in which permanent-heat-treated bricks other than the permanent-heat-treated brick closest to the steel shell 10 are installed. Note that the wear bricks 7 form the inner circumferential surface 6a of the sidewall 6 of the electric furnace 1. For this reason, there is a risk that the thickness of the wear bricks 7 will decrease due to melting or the like. Therefore, it is preferable that the precast blocks 9 in which the inner optical fiber 121 and the outer optical fiber 122 are embedded do not form the inner circumferential surface 6a of the sidewall 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 where 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 where the permanent bricks, which are refractory materials that do not form the inner peripheral surface 6 a of the side wall 6 of the electric furnace 1, are installed.

[0047] <Overview of Equipment Status Monitoring Device and Equipment Status Monitoring Method> As will be described in detail 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 measurements 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 also calculate temperature distributions in other directions (e.g., the height direction and the circumferential direction). The temperature distribution in the thickness direction of the side wall 6 is calculated within a range assumed to be the range in which the inner circumferential surface 6a of the side wall 6 may exist. In other words, 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 6 a based on the temperature distribution in the thickness direction of the side wall portion 6. The position of the inner circumferential surface 6 a calculated by the equipment status monitoring device 100 includes the position in the thickness direction of the side wall portion 6. The thickness direction of the side wall portion 6 is the direction in which a straight line connecting the inner circumferential surface 6 a and the outer circumferential surface 6 b at the shortest distance extends (the radial direction of the electric furnace 1). The position in the thickness direction of the side wall portion 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 portion 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, in which temperature information inside the domain is known and 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 is estimated. In this embodiment, the unsteady heat transfer inverse problem is 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 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 explained with reference to Figures 4A, 4B, 5A, and 5B. Figures 4A and 4B are diagrams illustrating an example of heat transfer that can be considered in the one-dimensional unsteady heat transfer inverse problem. Figures 5A and 5B are diagrams illustrating an example of heat transfer that can be considered in the three-dimensional unsteady heat transfer inverse problem.

[0051] As will be described later, this embodiment illustrates a case where a three-dimensional unsteady heat transfer inverse problem is formulated 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. Furthermore, in each figure, a symbol with a black circle inside a white circle indicates an arrow line pointing from the back side of the page to the front side (the coordinate axis with the positive direction being from the back side of the page 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 height direction of the side wall portion 6, which appear as a flat surface when the side wall portion 6 is cut along the height direction at one circumferential location and unfolded, are defined as the y-axis direction and the z-axis direction, respectively, and the y-coordinate and z-coordinate of each position on the side wall portion 6 are determined. Similarly, in this embodiment, the y-coordinate and z-coordinate of each position on a surface (such as the imaginary surface 31a or 31b) parallel to the inner circumferential surface 6a are also determined in the same manner as for the inner circumferential surface 6a.

[0053] 4A and 4B, the heat flux is directed 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 direction is 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 portion 6, as shown in Figures 4A and 4B, 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 portion 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 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 arrows shown in Figures 4A and 4B). In Figures 4A and 4B, for the sake of explanation and notation, the 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 Figures 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 calculating the temperature distribution in the thickness direction of the side wall 6 by solving a one-dimensional inverse problem of unsteady heat transfer, 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 accuracy of estimating the temperature distribution in the thickness direction of the side wall 6. Furthermore, when calculating the temperature distribution in the side wall 6 by solving a two-dimensional inverse problem of unsteady heat transfer, 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 consider heat transfer from inner temperature measurement positions 51a, 51c, 51e, 51g, 51i, and 51k to outer temperature measurement positions 51b, 51d, 51f, 51h, 51j, and 51l, as shown in Figures 5A and 5B. Therefore, the direction of heat transfer that can be considered in the unsteady heat transfer inverse problem is not limited to the direction in which temperature measurement positions 51a to 51b, 51c to 51d, 51e to 51f, 51g to 51h, 51i to 51j, and 51k to 51l are aligned. That is, the heat transfer direction that can be considered in the unsteady heat transfer inverse problem is each direction (direction along the arrows shown in FIGS. 5A and 5B ) from any one of the inner temperature measurement positions 51a, 51c, 51e, 51g, 51i, and 51k toward any one of the outer temperature measurement positions 51b, 51d, 51f, 51h, 51j, and 51l. In this way, the unsteady heat transfer inverse problem can consider all directions, including the thickness direction of the side wall 6, the circumferential direction of the side wall 6, and the height direction of the side wall 6. Therefore, by solving a three-dimensional unsteady heat transfer inverse problem to calculate the temperature distribution in the thickness direction of the side wall 6, the estimation accuracy of the temperature distribution in the thickness direction of the side wall 6 can be improved. This improves the estimation accuracy of the position in the thickness direction of the inner circumferential surface 6a. Therefore, in this embodiment, the temperature distribution in the thickness direction of the side wall 6 is calculated by performing a three-dimensional unsteady heat transfer inverse problem analysis.

[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 must also be spread 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 at precisely determined positions on the side wall 6. Therefore, in this embodiment, optical fiber temperature sensors 111-112 are used as temperature sensors.

[0058] Furthermore, if the temperature measurement position is located between a wear brick 7 and a permanent brick 8, or between individual permanent bricks 8, the accuracy of the temperature measured at that temperature measurement position may be lower than the 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 voids 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 properties around the temperature sensor are approximately the same (preferably the same), such temperature variation can be suppressed. Furthermore, embedding a temperature sensor in a brick increases the workload.

[0059] Therefore, in this embodiment, a case where the temperature sensor is embedded in a precast block 9 having substantially 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 substantially the same (preferably the same), the temperature sensor does not necessarily have to be embedded in the precast block 9. For example, the optical fiber temperature sensors 111-112 may be embedded in the permanent-set bricks 8. In this case, it is preferable to use only positions inside the permanent-set bricks 8 as temperature measurement positions. Furthermore, in this case, the precast block 9 does not need to be installed in the electric furnace 1.

[0060] <Equipment 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 includes, as hardware, one or more hardware processors, such as a central processing unit (CPU), and one or more memories, such as random access memory (RAM) and read-only memory (ROM). The equipment status monitoring device 100 executes various calculations by using one or more hardware processors to execute one or more programs stored in the memory. The equipment status monitoring device 100 also includes, as hardware, an input device and an output device. At least one of the input device and the output device may be external to the equipment status monitoring device 100. In this case, the equipment status monitoring device 100 communicates with the input device and the output device via wired or wireless communication.

[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 will be described below. Note that information that can be set in advance in the calculations described below is assumed to be stored in the equipment status monitoring device 100 via an input device, for example.

[0062] <<Temperature Acquisition Unit 61>> The temperature acquisition unit 61 acquires the measurements of the optical fiber temperature sensors 111-112. As described above, this embodiment illustrates a case in which the measuring devices 131-132 calculate the temperatures at each position within the optical fibers 121-122. Therefore, this embodiment illustrates a case in which the temperature acquisition unit 61 acquires the temperatures at each position within the optical fibers 121-122 calculated by the measuring devices 131-132 as the measurements of the optical fiber temperature sensors 111-112. The temperature acquisition unit 61 may acquire the measurements of the optical fiber temperature sensors 111-112 by performing wired or wireless communication with the measuring devices 131-132. Furthermore, the temperature acquisition unit 61 may acquire the measurements of the optical fiber temperature sensors 111-112 via devices other than the measuring devices 131-132. Furthermore, the temperature acquisition unit 61 may have the functions of the measuring devices 131-132.

[0063] The positions at which the optical fiber temperature sensors 111-112 obtain measurements 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 measurements 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 (hotspot centroid positions, hotspot peripheral positions), which will be described later. However, if there are too many positions at which the optical fiber temperature sensors 111-112 obtain measurements, the calculation load may become too high. Therefore, it is preferable that the positions at which the optical fiber temperature sensors 111-112 obtain measurements are set in advance from the perspective of balancing between reducing the calculation load and improving the calculation accuracy.

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

[0065] This embodiment illustrates a case where the optical fiber temperature sensors 111-112 measure the temperatures at respective positions within the optical fibers 121-122 at regular time intervals. This embodiment also illustrates a case where the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111-112 at each time interval. In the following description, the time interval during which the temperature acquisition unit 61 acquires the measured values ​​of the optical fiber temperature sensors 111-112 will be referred to as the temperature measurement interval, as necessary.

[0066] <<Inverse problem analysis unit 62>> The inverse problem analysis unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 by performing a three-dimensional unsteady heat transfer inverse problem analysis based on the measurement 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 the temperature for calculating one position in the thickness direction of the inner circumferential surface 6a. This embodiment illustrates such a case. 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] Furthermore, when performing a three-dimensional unsteady heat transfer inverse problem analysis, it is thought that using a large number of temperatures to calculate a position in the thickness direction of the inner circumferential surface 6 a would increase the accuracy of estimating that position in the thickness direction of the inner circumferential surface 6 a. 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 6 to calculate a position in the thickness direction of the inner circumferential surface 6 a. In other words, even if the number of temperatures (= N) to calculate a position in the thickness direction of the inner circumferential surface 6 a is not greater than five, the accuracy of estimating the position in the thickness direction of the inner circumferential surface 6 a can satisfy the accuracy required in practice (approaching the actual measured value) (see the calculation example ( FIG. 11 ) described later).

[0069] Therefore, in this embodiment, the inverse problem analysis unit 62 acquires five temperatures per location in the thickness direction of the side wall 6 based on the measurements of the optical fiber temperature sensors 111-112 as temperatures for calculating one position in the thickness direction of the inner circumferential surface 6a, and performs a three-dimensional unsteady heat transfer inverse problem analysis based on the acquired temperatures. As described above with reference to FIGS. 1 to 3, this embodiment illustrates a case where there are two installation regions (regions within the imaginary planes 31a and 31b) of the optical fibers 121 and 122 in the thickness direction of the side wall 6. Therefore, this embodiment illustrates a case where the inverse problem analysis unit 62 acquires a total of 10 temperatures (= 5 × 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 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 ​​will be required as temperature measurements. In addition, the weighting coefficient w in Equation (3) described below, 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 (specifically, overfitting) will decrease. 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 for 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] Furthermore, the thickness of the side wall 6 (wear brick 7) is likely to decrease near the hot spot. Therefore, in this embodiment, a case where the five temperature positions acquired by the inverse problem analysis unit 62 at one point in the thickness direction of the side wall 6 are the following positions is illustrated. FIG. 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 maximized. A hot spot region is a region that includes a hot spot. In this embodiment, a case where a hot spot region is defined on each of the x coordinates of the installation regions of the optical fibers 121 and 122 (regions within the imaginary planes 31a and 31b) is illustrated.

[0072] 7 shows the temperature distribution in the installation area of ​​the optical fibers 121 and 122 (area within the imaginary surfaces 31a and 31b) 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 and 112. For example, the temperature distribution shown in FIG. 7 is calculated by interpolating the measured values ​​of the optical fiber temperature sensors 111 and 112. There are no particular restrictions on the method of interpolation, and any known method such as linear approximation, spline interpolation, or polynomial interpolation may be used.

[0073] If the location where the temperature is locally highest can be clearly determined from the measurements of the optical fiber temperature sensors 111-112, that location may be determined as the location of the hotspot region. In this case, the temperature at that location may be determined as the temperature of the hotspot region. Alternatively, hotspot regions may be searched for in each of multiple temperature ranges obtained by dividing the temperature range measurable by the optical fibers 121 and 122 into multiple sections. In this case, the area in the temperature range showing the highest temperature among the multiple temperature ranges may be determined as the hotspot region. In this case, a representative location of the hotspot region may be determined as the location of the hotspot region, and the temperature at that location may be determined as the temperature of the hotspot region. Figure 7 illustrates an example in which the area in the temperature range of 500°C to 525°C is the hotspot region 71. The representative location of the hotspot region 71 is, for example, the position of the center of gravity of the hotspot region 71.

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

[0075] If the y-z coordinates of the representative positions of the hot spot regions 71 in the installation area of ​​the inner optical fiber 121 (the area within the imaginary plane 31a) and the y-z coordinates of the representative positions of the hot spot regions 71 in the installation area of ​​the outer optical fiber 122 (the area within the imaginary plane 31b) do not match, the inverse problem analysis unit 62 preferably calculates the temperatures of the hot spot regions 71 in the installation areas of the optical fibers 121 and 122 as follows. That is, in this case, the inverse problem analysis unit 62 preferably matches the y-z coordinates of the representative positions of the hot spot regions 71 in the installation areas of the optical fibers 121 and 122, and calculates the temperature at the matched y-z coordinates as the temperature of the hot spot regions 71 in the installation areas of the optical fibers 121 and 122. For example, the inverse problem analysis unit 62 may use the arithmetic mean values ​​of the y-coordinates and z-coordinates of the hot spot regions 71 in the installation areas of the optical fibers 121 and 122 as the y-coordinates and z-coordinates of the hot spot regions 71, respectively. Furthermore, the inverse problem analyzing unit 62 may set one 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 other y coordinates and z coordinates.

[0076] In this embodiment, an example is shown in which, 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 locations other than the hot spot region 71 are distributed around the hot spot region 71. The distribution refers to, for example, when the four locations are projected onto the same plane, three or more of the four locations are not on the same line. Figures 8A and 8B are diagrams showing an example of temperature locations acquired when performing a three-dimensional unsteady heat transfer inverse problem analysis. In the following description, the location of the hot spot region 71 will be referred to as the hot spot centroid 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 within imaginary plane 31a) of 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 within imaginary plane 31b) of outer optical fiber 122.

[0078] In FIG. 8A, the coordinate value of the hot spot centroid position 81a in the installation area of ​​the inner optical fiber 121 is (x^ １ , y^ １ , z^ １ ) where x^, y^, and z^ correspond to the symbols x, y, and z with ^ above them, respectively, in the formulas described below. As shown in FIG. 8A, in this embodiment, when the x coordinate is x １ In this example, four positions 81b to 81e are determined around the hot spot center of gravity position 81a on the yz plane. The coordinate values ​​of the positions 81b, 81c, 81d, and 81e are respectively (x^ １ , y^ ０ , z^ １ ), (x^ １ , y^ １ , z^ ０ ), (x^ １ , y^ ２ , z^ １ ), (x^ １ , y^ １ , z^ ２ )

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

[0080] Similarly, in FIG. 8B, the coordinate value of the hot spot centroid position 82a in the installation area of ​​the outer optical fiber 122 is (x ２ , y １ , z １ ) As shown in FIG. 8B, in this embodiment, the x-coordinate is x ２ In this example, four positions 82b to 82e are determined around the hot spot center of gravity position 82a on the yz plane. The coordinate values ​​of the positions 82b, 82c, 82d, and 82e are respectively (x^ ２ , y^ ０ , z^１ ), (x^ ２ , y^ １ , z^ ０ ), (x^ ２ , y^ ２ , z^ １ ), (x^ ２ , y^ １ , z^ ２ )

[0081] Distances Δy in the y-axis direction and z-axis direction from the hot spot centroid positions 81a, 82a to the four positions 81b to 81e, 82b to 82e around the hot spot centroid positions 81a, 82a １ , Δy ２ , Δz １ , Δz ２ is set before performing a three-dimensional unsteady heat transfer inverse problem analysis. In the following explanation, the four positions around the hot spot centroid positions 81a and 82a will be referred to as hot spot peripheral positions as necessary. In addition, the distances Δy in the y-axis direction and z-axis direction from the hot spot centroid positions 81a and 82a to the hot spot peripheral positions 81b to 81e and 82b to 82e are １ , Δy ２ , Δz １ , Δz ２ and, if necessary, the distance Δy １ , Δy ２ , Δz １ , Δz ２ It is abbreviated as.

[0082] distance Δy １ , Δy ２ , Δz １ , Δz ２ is not limited as long as the calculation accuracy of the position in the thickness direction of the inner circumferential surface 6a, which is calculated as described below, is determined to satisfy the accuracy required in practice.

[0083] For example, the distance Δy １ , Δy ２ , Δz １ , Δz ２In this case, for example, the distance Δy may be calculated by performing a three-dimensional unsteady heat transfer inverse problem analysis described later on a test furnace simulating the electric furnace 1. １ , Δy ２ , Δz １ , Δz ２ Next, the distance Δy １ , Δy ２ , Δz １ , Δz ２ Finally, based on the results of this comparison, the distance Δy is determined so that the calculation accuracy of the position of the inner circumferential surface 6a in the thickness direction satisfies the accuracy required for practical use. １ , Δy ２ , Δz １ , Δz ２ Explore.

[0084] Furthermore, as in this embodiment, when the hot spot gravity center 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 where the hot spot gravity center positions 81a, 82a intersect with the imaginary line connecting the hot spot gravity center positions 81a, 82a and the central axis O of the electric furnace 1 at the shortest distance may be worn. When the wear brick 7 is worn in this way, the region of the inner circumferential surface 6a where the wear brick 7 is located is recessed compared to other regions. In this case, the distance Δy １ , Δy ２ , Δz １ , Δz ２ It is preferable to determine the recessed portion based on the size of the recessed portion. In the following description, the recessed portion of the inner peripheral surface 6a due to wear of the wear brick 7 will be referred to as a worn portion as necessary. 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 portion. FIG. 9A shows an example of a region including a worn portion when the side wall portion 6 is viewed from above. FIG. 9B shows an example of a region including a worn portion when the side wall portion 6 is viewed from the central axis O side of the electric furnace 1. Note that FIGS. 9A and 9B show an assumed state in which the side wall portion 6 is cut along the height direction at one location in the circumferential direction and then unfolded. Also, FIGS. 9A and 9B show only a portion of the side wall portion 6 (the region corresponding to one precast block 9). Note that for ease of illustration and explanation, hatching indicating the cut surface is omitted in FIGS. 9A and 9B.

[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 with 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] distance Δy １ , Δy ２ is, for example, the length WL of the worn portion 92 in the circumferential direction (y-axis direction). ｙ (See FIGS. 9A and 9B). Specifically, the distance Δy １ , Δy ２ is the circumferential length WL of the worn portion 92 ｙ In this way, it is possible to determine the hot spot peripheral positions 81b to 81e and 82b to 82e between both ends of the worn portion 92 in the y-axis direction. １ , Δy ２ is the circumferential length WL of the worn portion 92 ｙ It has been found that setting the thickness to 1 / 4 is preferable because it improves the accuracy of calculating the position of the inner peripheral surface 6a in the thickness direction.

[0088] Also, the distance Δz １ , Δz ２ is, for example, the length WL of the worn portion 92 in the height direction (z-axis direction). ｚ (See FIG. 9B). Specifically, the distance Δz １ , Δz ２ The range of the circumferential length WL of the worn portion 92 isｚ In this way, it is possible to determine the hot spot peripheral positions 81b to 81e and 82b to 82e 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 to 1 / 4 is preferable because it improves the accuracy of calculating the position of the inner peripheral surface 6a in the thickness direction.

[0089] In addition, for example, the depth WL of the worn portion 92 ｘ Depending on １ , Δy ２ , Δz １ , Δz ２ For example, the depth WL of the worn portion 92 may be adjusted. ｘ The longer the distance Δy １ , Δy ２ , Δz １ , Δz ２ The depth of the damaged portion 92 is the length of the damaged portion 92 in the thickness direction (x-axis direction).

[0090] 9A and 9B illustrate a case where the shape of the space that is the worn portion 92 is a rectangular prism. However, the shape of the actual worn portion L is more complex than a rectangular prism. In this case, the length WL of the worn portion 92 in each direction is ｘ , W.L. ｙ , W.L. ｚ may be set to the representative 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 portion 92 ｚ The length 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] In addition, for example, the length WL of the worn portion 92 in each direction ｘ , W.L. ｙ , W.L. ｚFor 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 the 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, the values ​​may be measured by a profile meter between charges, or may be visually observed values ​​between charges. Measurements using a profile meter are realized by known techniques as described in JP 2018-185253 A and the like, and therefore detailed explanations thereof will be omitted here. In addition, a test furnace simulating the electric furnace 1 was used to measure the temperature of the hot spot 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 can be calculated. ｘ , W.L. ｙ , W.L. ｚ In this case, the inverse problem analysis unit 62 may generate a mathematical expression or a lookup table showing the relationship between the length WL of the worn portion 92 in each direction corresponding to the temperature of the hot spot region 71. ｘ , W.L. ｙ , W.L. ｚ Read out.

[0094] The inverse problem analysis unit 62 calculates the distance Δy １ , Δy ２ , Δz １ , Δz ２ and the hot spot centroid positions 81a, 82a, the hot spot peripheral positions 81b to 81e, 82b to 82e are calculated, and the temperatures of the hot spot peripheral positions 81b to 81e, 82b to 82e are acquired.

[0095] In this way, the inverse problem analysis unit 62 calculates the coordinates (x^ １ , y^ １ , z^１ ), (x^ ２ , y^ １ , z^ １ ) at each time t １ ~t ｎ Similarly, the inverse problem analysis unit 62 obtains the temperature u^ at the hot spot peripheral positions 81b to 81e and 82b to 82e. 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 ) at each time t １ ~t ｎ The temperature u^ at

[0096] The inverse problem analysis unit 62 then solves a three-dimensional unsteady heat transfer inverse problem analysis. An example of a three-dimensional unsteady heat transfer inverse problem will be described below. In the following description, the hotspot centroid positions 81a, 82a and the hotspot 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]

[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 the time. α is the square root of the thermal diffusivity. The thermal diffusivity is calculated using the thermal conductivity, specific heat, and density (specific gravity). The basis function φ(x-x ｃ , y-y ｃ , z-z ｃ , t-t ｃ ) is expressed by the following equation (2). ｃ , y-y ｃ , z-z ｃ , t-t 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]

[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 unknown quantities 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 ｃ is 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 the measurement time as necessary.

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

[0102] The internal / extrapolated temperature u(x, y, z, t) for calculating the temperature of the side wall 6 is calculated using 10×m basis functions φ(x−x ｉ , y-y ｊ , z-z ｋ , t-t 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 x m" corresponds to the number of temperature acquisition positions 81a to 81e, 82a to 82e. The "m" in "10 x m" corresponds to the temperature measurement time (1 to m, m + 1 to 2 m). 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]

[0104] 10 × m weighting coefficients in equation (3) Weighting coefficient w ｉ，ｊ，ｋ、ｌ Therefore, it is necessary to determine the temperature u^(x^ ｉ , y^ ｊ , z^ ｋ , t ｌ ) where n≧m. It is also possible to set 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) may be the same as the 10 × m weighting coefficients w ｉ，ｊ，ｋ、ｌ The 20×n simultaneous equations for determining l are expressed by the following equation (4): Note that, for convenience of notation, equation (4) shows only two of the 20×n simultaneous equations (simultaneous equations for l=1, 2n).

[0105]

[0106] The matrix storing the temperature u^ in equation (4) is U(∈R （２ｎ×５）×１ ) and the matrix storing the basis function φ in equation (4) is denoted as Φ(∈R （２ｎ×５）×（２ｍ×５） ) and the matrix (vector) storing the weighting coefficient w in equation (4) is expressed as W(∈R （２ｍ×５）×１ ) is denoted as the matrix (vector) that stores the error terms between the left and right sides of equation (4). （２ｎ×５）×１ ) Then, equation (4) can be rewritten as equation (5) below. Note that T represents a transposed matrix. In order to obtain a least squares solution for matrix W, the cost function J:R in equation (6) below for matrix e is （２ｎ×５）×１ →R is used. Here, γ(∈R) is a regularization coefficient for compensating for 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]

[0108] From equation (8), the matrix W (weighting coefficient w ｉ，ｊ，ｋ、ｌ ) may be calculated. However, in the inverse problem, when the inverse matrix of the right-hand side of equation (8) is solved, the error may be 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. （２ｎ×５）×（２ｍ×５） ) is a diagonal matrix that stores singular values. （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 analysis unit 62 calculates the matrix W using equation (10) is illustrated.

[0109]

[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 weighting coefficients 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 111-112 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, heat transfer in the thickness direction of the region where the precast blocks 9 are present is in the following order: inside the furnace → deposits on the inner peripheral surface 6a → wear bricks 7 → precast blocks 9 → steel shell 10 → outside the furnace. Note that there may be no deposits on the inner peripheral surface 6a. As mentioned above, materials connecting (fixing) the regions between the wear bricks 7 and the precast blocks 9 and between the precast blocks 9 and the steel shell 10 exist. Furthermore, voids may exist in these regions. Therefore, these regions hinder heat transfer. Therefore, when performing rigorous heat transfer calculations, the physical properties of these regions must be taken into account. Therefore, a three-dimensional unsteady heat transfer inverse problem may be formulated taking the physical properties of these regions into account. However, determining the physical properties of these regions is not easy. Furthermore, since the physical properties vary depending on the type of deposit, determining the physical properties of the deposits is not easy.

[0113] The present inventors have conducted extensive research based on the above. As a result, the present inventors have found that the weighting coefficient w ｉ，ｊ，ｋ，ｌ When calculating the weighting coefficient 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 in practice (approaching the actually measured value) even without using other thermal diffusivities when calculating (see the calculation example (FIG. 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 / extrapolated 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 / extrapolated 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 coordinates of an area other than the precast block 9, the accuracy of the value of the internal / extrapolated temperature function u(x, y, z, t) satisfies the accuracy required in practical use. Therefore, in this embodiment, the thermal diffusivity of the precast block 9 is used as the thermal diffusivity (square root of α) included in the internal / extrapolated temperature function u(x, y, z, t), and the thermal diffusivity of other components 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 the other members is not used.

[0115] As described above, this embodiment illustrates a case in which the temperature at 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 in which 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 in which the inverse problem analysis 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, the inverse problem analysis unit 62 calculates the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 at the y-coordinates and z-coordinates of the hot spot centroid positions 81 a, 82 a. It is preferable to set the hot spot centroid positions 81 a, 82 a as the positions (y-coordinates 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 positions where wear is expected to be most advanced.

[0117] However, the positions (y coordinates and z coordinates) for calculating the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 6 are not limited to the hotspot centroid positions 81a and 82a. For example, the inverse problem analysis unit 62 may calculate the temperature distribution in the thickness direction (x-axis direction) of the side wall portion 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] Furthermore, for example, there may be cases where the hot spot region 71 cannot be identified. In such cases, 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 predetermined 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 predetermined position) to which the hot spot region 71 is replaced may be, for example, a position where a hot spot is expected to occur. Furthermore, the position to which 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 for managing 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 of the inner circumferential surface 6a in the thickness direction, 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, an example is shown 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, an example is shown 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 (x-axis direction) of the side wall 6 at which the temperature is the same as the temperature of the molten metal 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 (a target value or a calculated value). Note that, when the temperature distribution in the thickness direction (x-axis direction) of the side wall 6 is calculated at y-coordinates and z-coordinates different from the y-coordinates and z-coordinates of the hot spot centroid positions 81a, 82a, for example, the temperature of a position in the furnace having the same y-coordinates and z-coordinates as the position different from the hot spot centroid 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 x-y-z 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 On the other hand, an increase in the x-coordinate value corresponds to the adhesion of deposits to the inner circumferential surface 6a (wear brick 7).

[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 hot spot 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 (the 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 Unit 64>> The output unit 64 outputs inner circumferential surface state information. The inner circumferential surface state information is information related to the x coordinate of the inner circumferential surface 6 a (the position of the inner circumferential surface 6 a in the thickness direction) 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 6 a. For example, the inner circumferential surface state information may be information calculated using the x coordinate of the inner circumferential surface 6 a. For example, the output unit 64 outputs at least one of the current value of the x coordinate of the inner circumferential surface 6 a 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 the information on a computer display, transmitting the information to an external device, and storing the information in a storage medium external to the equipment status monitoring device 100.

[0125] When the measurement values ​​of the optical fiber temperature sensors 111-112 are acquired during charging, the output unit 64 can output inner circumferential surface condition information during the charging. Therefore, the inner circumferential surface condition information can be used to identify the location of the inner circumferential surface 6a to be repaired during charging. The location of the inner circumferential surface 6a to be repaired can be identified by an operator or by the equipment status monitoring device 100. For example, the equipment status monitoring device 100 may have a repair location identification unit that identifies the location of the repair based on the current x-coordinate of the inner circumferential surface 6a. In this case, the repair location identification unit determines, for example, whether 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 repair location identification unit identifies the position of the inner circumferential surface 6a used in calculating the refractory equivalent length as the location to be repaired. 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 refractory function is impaired. When the equipment status monitoring device 100 calculates the repair locations in this manner, the output unit 64 may output information indicating the repair locations as inner circumferential surface status information. The repair locations identified in the above manner are then repaired. The repair is performed, for example, by filling the worn portions 92 with repair material. Note that the method of repairing refractory materials is realized by known technology, and therefore a detailed description of the method will be omitted here.

[0126] Furthermore, the inner peripheral surface condition information can be used to determine whether to suspend or stop operation due to the risk of the furnace contents (e.g., molten metal) being discharged from the sidewall 6 during charging. This determination may be made by an operator or by the equipment status monitoring device 100. For example, the equipment status monitoring device 100 may have an operation continuation determination unit that determines whether to continue 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 (i.e., to suspend or stop) the operation if, for example, the current value of the refractory equivalent length is less than a threshold value. The threshold value is determined, for example, based on the thickness (length in the x-axis direction) of the wear bricks 7 at which their refractory function is impaired. Note that the threshold value used to determine whether to continue operation of the electric furnace 1 is preferably smaller than the threshold value used to calculate the repair location described above. In this case, the latter threshold value is a length that has a larger margin than the former threshold value with respect to the thickness of the wear bricks 7 at which the function as refractory material is impaired. In this way, when the equipment condition monitoring device 100 determines whether or not to continue the operation of the electric furnace 1, the output unit 64 may output information indicating the result of the determination as inner circumferential surface condition 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 in Fig. 10. Note that information that can be set in advance before the flowchart in Fig. 10 starts is assumed to be stored in the equipment status monitoring device 100 via an input device. Furthermore, the flowchart in Fig. 10 is realized, for example, by a processor included in the equipment status monitoring device 100 executing a program stored in 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 ​​at a plurality of times t １ , ..., t ｍ 1, a case where temperatures at respective positions in the optical fibers 121 and 122 are acquired will be exemplified.

[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 to 81e and 82a to 82e include the hotspot centroid positions 81a and 82a (the position of the hotspot region 71). In step S1002, if multiple positions are obtained as the hotspot centroid positions 81a and 82a (the position of the hotspot region 71), hotspot peripheral positions 81b to 81e and 82b to 82e are calculated for each of the multiple hotspot centroid positions 81a and 82a.

[0131] Therefore, in FIG. 10, in one processing of steps S1003 to S1106, the temperature u^(x^ 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 coefficient w of the interpolated / extrapolated temperature function u(x, y, z, t) in equation (3) is calculated. 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 and are substituted into equation (3) to calculate the value of the interpolation / extrapolation temperature function u(x, y, z, t) (i.e., the temperature u(x, y, z, t)).

[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 centroid positions 81a, 82a based on the value of the internal / extrapolated temperature function u(x, y, z, t).

[0135] Next, in step S1006, the refractory position calculation unit 63 calculates the positions (x coordinates) in the thickness direction of the inner surface 6a at the y coordinates and z coordinates of the hotspot centroid positions 81a, 82a, based on 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, calculated in step S1005.

[0136] Next, in step S1007, the equipment status monitoring device 100 determines whether or not processing has been performed on all hot spot regions 71. If this determination shows that processing has not been performed on all hot spot regions 71 (NO in step S1007), the processing of step S1003 is performed. Then, in steps S1003 to S1006, the inverse problem analysis unit 62 and the refractory position calculation 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 coordinates and z coordinates.

[0137] Then, in step S1007, if it is determined that processing has been performed on all hot spot regions 71 (YES in step S1007), processing in step S1008 is performed. In step S1008, the output unit 64 outputs 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 inner circumferential surface state information for each of the multiple positions in the thickness direction of the inner circumferential surface 6a. When processing in step S1008 is completed, the processing according to the flowchart of FIG. 10 ends.

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

[0139] The damaged portion 92 is assumed to be formed at the center of the yz plane of the model. The length WL of the damaged portion 92 in each direction is ｘ , W.L. ｙ , W.L. ｚ , respectively, 0.14 m, 0.2 m, 0.2 m (WL ｘ = 0.14, WL 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 distance Δy １ , Δy ２ 0.05 m (Δy １ =Δy ２ = 0.05). That is, the distance Δy １ , Δy ２ , the width WL of the worn portion 92 ｙ In addition, the distance Δz shown in FIGS. １ , Δz ２ 0.05 m (Δz １ = Δz ２ = 0.05). That is, the distance Δz １ , Δz ２ , the height WL of the worn portion 92 ｚ It was set at 1 / 4 of that.

[0140] Under the above conditions, the temperatures in the thickness direction (x-axis direction) of the side wall portion 6 were calculated at the y-coordinate and z-coordinate of the hot spot gravity center positions 81a and 82a. 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 for 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 for the unsteady heat transfer inverse problem may be determined according to the degree of unsteadiness.

[0141] In addition, 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 are the two hot spot centroid positions 81a and 82a. The y and z coordinates of the position of the centroid of the damaged part 92 were the y and z coordinates of the hot spot centroid positions 81a and 82a. In addition, the temperature T of the inner circumferential surface 6a Ｍ is 1665°C (T Ｍ = 1665).

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

[0143] 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 in the three-dimensional unsteady heat transfer inverse problem analysis described in this embodiment, with the heat transfer direction limited to the thickness direction only.

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

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

[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 distance in the thickness direction of the refractory at (=1665°C) was 0.371 m, which was significantly different from the true value (=0.32 m).

[0147] 11A and 11B, it can be seen that the accuracy of calculating the position of the inner circumferential surface 6a in the thickness direction can be improved by considering heat transfer in the y-axis and z-axis directions as in this embodiment, whereas the accuracy of calculating the position of the inner circumferential surface 6a in the thickness direction can be improved by considering heat transfer in the y-axis and z-axis directions as in this embodiment. Furthermore, it can be seen from Fig. 11A that the thermal diffusivity (square root of α) included in the internal / extrapolation temperature function u(x, y, z, t) is the thermal diffusivity of the precast block 9, and the position of the inner circumferential surface 6a in the thickness direction can be calculated with high accuracy without using the thermal diffusivities of other components.

[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 on signals received by the communication circuit 1204 and signals input under control of the CPU 1201. The image processing circuit 1206 performs various image processing on signals input under control of the CPU 1201. The signals after this image processing are output to, for example, a display 1209. 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, and dials. The user interface 1208 may also have a graphical user interface using the 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 portion of the user interface 1208 and the display 1209 may be external to the equipment status monitoring device 100.

[0153] The CPU 1201, main memory device 1202, auxiliary memory device 1203, signal processing circuit 1205, image processing circuit 1206, and 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 may also be realized by the same hardware as the hardware of the equipment status monitoring device 100 shown in FIG. 12, for example. Therefore, a detailed description of a specific example of the hardware of the equipment status monitoring device 100 will be 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 is present during operation, the inner circumferential surface 6a of the side wall 6 is made of refractory material. In addition, the optical fibers 121-122 provided in the optical fiber temperature sensors 111, 112 are embedded in the material that constitutes 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 component constituting the side wall 6. The precast block 9 is a fire-resistant block made by precasting a monolithic refractory material with the optical fibers 121-122 embedded therein. This facilitates the installation of the optical fibers 121, 122. Furthermore, it is possible to suppress variations in temperature measurement errors by the optical fiber temperature sensors 111-112.

[0156] Furthermore, 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 measurements of the optical fiber temperature sensors 111-112. Then, based on the temperature distribution in the thickness direction of the side wall 6, 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. Therefore, the condition of the inner circumferential surface 6a can be monitored easily and with high accuracy. Furthermore, the condition 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 the temperature for calculating one position in the thickness direction of the inner circumferential surface 6 a. Therefore, it is possible to optimize the number of temperatures used when performing a three-dimensional unsteady heat transfer inverse problem analysis.

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

[0159] Furthermore, in this embodiment, the equipment status monitoring device 100 performs a three-dimensional unsteady heat transfer inverse problem analysis using only the physical property value (thermal diffusivity) of the precast block 9 out of the physical property values ​​(thermal diffusivity) of the components constituting the sidewall portion 6. This prevents the unsteady heat transfer inverse problem from becoming a complicated problem. It also prevents a decrease in calculation accuracy due to the introduction of 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, which measures the temperature at a relatively inner position, and the optical fiber temperature sensor 112, which measures the temperature at a relatively outer position, are separate temperature sensors, which makes it easy to install the optical fiber temperature sensors 111 and 112.

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

[0162] (Other Embodiments) The above-described embodiments of the present disclosure can be realized by a computer executing a program. Furthermore, a computer-readable recording medium on which the program is recorded and a computer program product such as the program can also be applied as embodiments of the present disclosure. Examples of recording media that can be used include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, non-volatile memory cards, and ROMs.

[0163] Furthermore, the above-described embodiments of the present disclosure are merely examples of specific embodiments for carrying out 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 embodied in various forms without departing from its technical concept or main features.

[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 exists during operation, The inner circumferential surface of the side wall of the equipment is made of refractory material, The equipment, wherein an optical fiber of an optical fiber temperature sensor is embedded in a member constituting the side wall portion.

2. The equipment described in claim 1, 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.

3. 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 or 2, 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.

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

5. The facility according to claim 1 or 2, wherein the member 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.

6. 3. An equipment status monitoring device for monitoring a status of the equipment according to claim 1 or 2, 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.

7. An equipment status monitoring device as described in claim 6, 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 amorphous refractory material with the optical fiber embedded therein.

8. 7. The equipment status monitoring device according to claim 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 that constitutes the side wall portion.

9. An equipment status monitoring device as described in Claim 6, wherein among the components constituting the side wall portion, the component in which the optical fiber is embedded is located closer to the outer surface of the side wall portion than the refractory material constituting the inner surface of the side wall portion.

10. 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; The facility status monitoring device according to claim 6 , wherein N is an integer of 2 or more.

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

12. 7. The equipment status monitoring device according to claim 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.

13. 7. The equipment status monitoring device according to claim 6, 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.

14. 3. An equipment status monitoring method for monitoring a status of the equipment according to claim 1 or 2, 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; The equipment status monitoring method, wherein at least one 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 is detected by the optical fiber temperature sensor.

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

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