Installation in which molten metal is present during operation, device and method for monitoring the condition of the installation, and program.

Description

/ 68 INSTALLATION, DEVICE AND METHOD FOR MONITORING THE INSTALLATION'S STATE, AND COMPUTER-READABLE NON-TRANSIENTIAL STORAGE MEDIUM TECHNICAL FIELD

[001] The present description relates to an installation, a device for monitoring the installation's status, a method for monitoring the installation's status, and a program, and is particularly suitable for use in an installation where molten metal is present during operation. This application is based on and claims the benefit of priority of prior Japanese patent application No. 2023-065494, filed April 13, 2023, the full content of which is incorporated herein by reference. FUNDAMENTALS OF THE TECHNIQUE

[002] In installations that produce molten metal, such as electric arc furnaces and blast furnaces, molten metal is present inside during operation. This causes the interior of the installation to become very hot. Therefore, refractories such as refractory bricks are placed on an internal circumferential surface of the installation. The refractories are exposed to high-temperature molten metal, as above, and therefore wear down as a result of erosion or scaling of some of the refractories as the installation is used. Therefore, there is a demand for a technique to monitor the condition of the refractories.

[003] There is a technique described in Patent Literature 1 as a technique of this type. In the technique described in Patent Literature 1, the temperature of an inner circumferential surface of a furnace is calculated by solving an inverse one-dimensional heat transfer problem using measured values ​​from two thermocouples embedded in a wall of the blast furnace. Then, in the technique described in Patent Literature 1, the position at which the temperature calculated in this way becomes the Petition 870250088767, dated 09 / 30 / 2025, page 97 / 171 / 68 The temperature that defines the inner circumferential surface of the furnace is calculated as the position of the inner circumferential surface of the furnace. LIST OF CITATIONS Patent Literature

[004] Patent Literature 1: Japanese patent publication open to public inspection No. 2001-234217 SUMMARY OF THE INVENTION TECHNICAL PROBLEM

[005] However, in the technique described in Patent Literature 1, the measured values ​​of thermocouples previously incorporated into the refractory are used. Therefore, the positions at which the installation temperature is measured are limited. Furthermore, installing new temperature sensors is not easy. In addition, increasing the number of positions at which the temperature is measured requires incorporating a large number of thermocouples into the refractory. However, incorporating a large number of thermocouples into the refractory is practically difficult.

[006] The present description was made taking into account the problems above, and one of its objectives is to make it possible to measure temperatures over a wider range, such as the temperature of a portion of the side wall of an installation in which molten metal is present during operation. SOLUTION TO THE PROBLEM

[007] The installation in the present description is an installation in which molten metal is present during operation, in which an inner circumferential surface of a portion of the side wall of the installation is formed of a refractory material, and an optical fiber included in a fiber optic temperature sensor is incorporated into a member that forms the side wall portion.

[008] The installation status monitoring device in this description is an installation status monitoring device. Petition 870250088767, dated 09 / 30 / 2025, page 98 / 171 / 68, which monitors a state of the installation, the device including: an inverse problem analysis means that calculates a temperature distribution of the sidewall portion by performing a three-dimensional non-steady-state inverse heat transfer problem analysis based on a measured value from a temperature sensor that measures a temperature of the sidewall 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 of the sidewall portion in a thickness direction, the position of the inner circumferential surface to be calculated by the refractory position calculation means includes a position of the sidewall portion in the thickness direction,The temperature sensor measures a temperature at a position on the sidewall portion on one side of the relatively inner circumferential surface and a temperature at a position on the sidewall portion on one side of the relatively outer circumferential surface in a portion of the sidewall that is different from the inner circumferential surface of the sidewall portion, and the temperature sensor that measures at least the temperature at the position on the sidewall portion on the relatively inner circumferential surface among the temperature at the position on the sidewall portion on the relatively inner circumferential surface and the temperature at the position on the sidewall portion on the relatively outer circumferential surface is the fiber optic temperature sensor.

[009] The installation status monitoring method described herein is an installation status monitoring method that monitors an installation status; the method includes: an inverse problem analysis step that calculates a temperature distribution of the sidewall portion by performing an inverse transfer problem analysis. Petition 870250088767, dated 09 / 30 / 2025, page 99 / 171 / 68 of non-steady-state three-dimensional heat based on a measured value from a temperature sensor that measures a temperature of the side wall portion; and a refractory position calculation step that calculates a position of the inner circumferential surface based on the temperature distribution calculated by the inverse problem analysis step, in which the inverse problem analysis step calculates a temperature distribution of the side wall portion in a thickness direction, the position of the inner circumferential surface to be calculated in the refractory position calculation step includes a position of the side wall portion in the thickness direction,The temperature sensor measures a temperature at a position on the sidewall portion on one side of the relatively inner circumferential surface and a temperature at a position on the sidewall portion on one side of the relatively outer circumferential surface in a portion of the sidewall that is different from the inner circumferential surface of the sidewall portion, and the temperature sensor that measures at least the temperature at the position on the sidewall portion on the relatively inner circumferential surface among the temperature at the position on the sidewall portion on the relatively inner circumferential surface and the temperature at the position on the sidewall portion on the relatively outer circumferential surface is the fiber optic temperature sensor.

[0010] The program in the present description is a program to make a computer function as each means of the installation status monitoring device. BRIEF DESCRIPTION OF THE DRAWING

[0011] [Fig. 1] Fig. 1 is a view illustrating an example of an electric arc furnace configuration.

[0012] [Fig. 2] Fig. 2 is a cross-sectional view taken along line II in Fig. 1. Petition 870250088767, dated 09 / 30 / 2025, page 100 / 171 / 68

[0013] [Fig. 3] Fig. 3 is a view illustrating an example of a pre-molded block configuration in which optical fibers are incorporated.

[0014] [Fig. 4A] Fig. 4A is a view that conceptually explains a first example of heat transfer that can be considered in a one-dimensional non-steady-state inverse heat transfer problem.

[0015] [Fig. 4B] Fig. 4B is a view that conceptually explains a second example of heat transfer that can be considered in the inverse problem of one-dimensional non-steady-state heat transfer.

[0016] [Fig. 5A] Fig. 5A is a view that conceptually explains a first example of heat transfer that can be considered in a three-dimensional non-steady-state inverse heat transfer problem.

[0017] [Fig. 5B] Fig. 5B is a view that conceptually explains a second example of heat transfer that can be considered in the inverse problem of three-dimensional non-steady-state heat transfer.

[0018] [Fig. 6] Fig. 6 is a diagram illustrating an example of a functional configuration of a facility status monitoring device.

[0019] [Fig. 7] Fig. 7 is a view that explains an example of a hotspot region.

[0020] [Fig. 8A] Fig. 8A is a view illustrating a first example of temperature positions to be acquired when performing the inverse analysis of the three-dimensional non-steady-state heat transfer problem.

[0021] [Fig. 8B] Fig. 8B is a view illustrating a second Petition 870250088767, dated 09 / 30 / 2025, p. 101 / 171 / 68 example of the temperature positions to be acquired when performing the inverse problem analysis of three-dimensional non-steady-state heat transfer.

[0022] [Fig. 9A] Fig. 9A is a view illustrating an example of a region including a worn portion when a portion of the side wall is viewed from above.

[0023] [Fig. 9B] Fig. 9B is a view illustrating an example of the region including the worn portion when the side wall portion is viewed from the side of the central axis of the electric arc furnace.

[0024] [Fig. 10] Fig. 10 is a flowchart that explains an example of a method for monitoring the installation status.

[0025] [Fig. 11A] Fig. 11A is a view illustrating a first example of the relationship between a refractory temperature and a refractory thickness direction distance.

[0026] [Fig. 11B] Fig. 11B is a view illustrating a second example of the relationship between refractory temperature and distance from the refractory thickness direction.

[0027] [Fig. 12] Fig. 12 is a diagram illustrating an example of a hardware configuration for the facility status monitoring device. DESCRIPTION OF THE MODALITIES

[0028] Next, an embodiment of the present description will be explained with reference to the drawings. Furthermore, the fact that the objects to be compared, such as lengths, positions, sizes, and intervals, are equal includes the case where they are strictly equal, as well as the case where they are different within a range that does not depart from the essence of the present description (for example, the case where they are different within a tolerance range defined at the time of design). In addition, in each of the drawings, for convenience of explanation and notation, some configurations Petition 870250088767, dated 09 / 30 / 2025, pages 102 / 171 / 68 will be omitted or simplified.

[0029] A facility status monitoring device 100 described later in this embodiment monitors the status of an inner circumferential surface of a portion of the side wall of a facility in which molten metal is present during operation. The inner circumferential surface of the side wall portion of the facility is a surface that is in contact with the space in which molten metal may be present (e.g., the surface facing the central axis (centerline) of the facility). The inner circumferential surface of the side wall portion of the facility is formed by a refractory material. In this embodiment, an arc melting furnace, which is a type of electric arc furnace, is explained as an example of such a facility. However, the facility to be monitored by the facility status monitoring device 100 is not limited. In the arc melting furnace, a raw material, such as scrap metal, is loaded into the furnace for each charge (ch).Next, the raw material is melted and fused by arcs generated by arc electrodes. In this way, molten metal (e.g., molten steel) and molten slag are produced. In this method, the period between when the raw material is loaded into the furnace and when the molten metal and molten slag are discharged from the furnace is called the charging period. The side wall of the arc melting furnace is exposed to high temperatures. Therefore, refractories such as refractory bricks are used to construct the side wall of the arc melting furnace. As described earlier, the installation to be monitored by the installation status monitoring device 100 is not limited to the arc melting furnace. For example, the installation to be monitored by the installation status monitoring device 100 could be an electric arc furnace other than the arc melting furnace, or an industrial furnace such as a blast furnace or a converter. <Instalação> Petition 870250088767, dated 09 / 30 / 2025, p. 103 / 171 / 68

[0030] Fig. 1 is a view illustrating an example of an electric arc furnace configuration 1. In fact, Fig. 1 is a vertical cross-sectional view of the electric arc furnace 1. For convenience of notation and explanation, the hatching indicating cut surfaces has been omitted in Fig. 1.

[0031] In Fig. 1, this embodiment explains, by way of example, the case in which the electric arc furnace 1 includes a top cover 2, arc electrodes 3a to 3c, a furnace bottom electrode 4, a furnace bottom portion 5 and a side wall portion 6.

[0032] Fig. 1 illustrates, by way of example, the case where the electric arc furnace 1 includes the three arc electrodes 3a to 3c. Furthermore, Fig. 1 illustrates, by way of example, the case where the three arc electrodes 3a to 3c are installed at equal intervals (120° intervals) around a central axis (centerline) O of the electric arc furnace 1. In fact, in the following explanation, the direction around the central axis (centerline) O of the electric arc furnace 1 is referred to as the circumferential direction, as needed. Furthermore, in the following explanation, the central axis (centerline) O of the electric arc furnace 1 is abbreviated to a central axis O, as needed.

[0033] Furthermore, in Fig. 1, this embodiment explains, as an example, the case where the side wall portion 6 is installed so as to encircle the central axis O. Furthermore, this embodiment explains, as an example, the case where the side wall portion 6 includes a wear brick 7, a permanent brick 8, a precast block 9 and a furnace shell 10.

[0034] Refractory bricks are used to form the wear brick 7. Of the surfaces of the wear brick 7, the surface facing the central axis O forms an inner circumferential surface 6a of the side wall portion 6 of the electric arc furnace 1. In the following explanation, the inner circumferential surface 6a of the side wall portion 6 of the electric arc furnace 1 is referred to as an inner side, as Petition 870250088767, dated 09 / 30 / 2025, page 104 / 171 / 68 necessary. Incidentally, the inner side is the side closest to the central axis O of the electric arc furnace 1. Furthermore, the side opposite the inner side is called the outer side, as necessary. Incidentally, the outer side is the side of the outer circumferential surface 6b of the side wall portion 6 of the electric arc furnace 1 (the side furthest from the central axis O of the electric arc furnace 1).

[0035] Refractory bricks are used to form the permanent brick 8. The permanent brick 8 is installed on the outside in relation to the wear-resistant brick 7. Moreover, the outer end of the wear-resistant brick 7 and the inner end of the permanent brick 8 are connected (fixed) to each other by means of an adhesive and heat-resistant material, for example. The heat-resistant and adhesive material is mortar, for example.

[0036] The furnace casing 10 is installed on the outside in relation to the permanent brick 8. The furnace casing 10 forms the outer circumferential surface 6b of the side wall portion 6 of the electric arc furnace 1. The inner end of the furnace casing 10 and the outer end of the permanent brick 8 are connected (fixed) to each other by means of an adhesive and heat-resistant material, for example. The heat-resistant and adhesive material is mortar, for example.

[0037] The above configuration of the electric arc furnace is the configuration of a general electric arc furnace. The configuration of the electric arc furnace is not limited to the above configuration of the electric arc furnace. In the electric arc furnace 1 in this embodiment, the precast block 9 is installed in a partial region of the region where the permanent brick 8 is installed in such a general electric arc furnace. The precast block 9 is an example of a precast refractory block. As will be described later, this embodiment explains, by way of example, the case where the precast block 9 is manufactured from a monolithic refractory being precast with optical fibers included in optical fiber temperature sensors incorporated therein. Petition 870250088767, dated 09 / 30 / 2025, page 105 / 171 / 68

[0038] In the electric arc furnace 1 illustrated in Fig. 1 as an example, when the scrap, which is the raw material, melts, the portion of the side wall 6 becomes extremely hot locally due to radiant heat generated by the arc discharge or other reason. Therefore, the temperature distribution of the portion of the side wall 6 in a virtual plane parallel to the inner circumferential surface 6a has a maximum value (local maximum value) locally. In the following explanation, such a position where the temperature reaches a maximum locally is called a hot spot, as necessary. Incidentally, in the electric arc furnace (arc melting furnace), including the arc electrodes 3a to 3c, there are at least as many hot spots as there are arc electrodes in a virtual plane parallel to the inner circumferential surface 6a (in the example illustrated in Fig. 1, there are at least three hot spots).

[0039] This modality explains, by way of example, the case in which precast block 9 is installed in such a way as to satisfy all of the following (A) to (D).

[0040] (A) The position of the outer end of the precast block 9 is the same as the position of the outer end of the permanent brick 8, or is it an inner position relative to the outer end of the permanent brick 8.

[0041] (B) The position of the inner end of the precast block 9 is the same as the position of the inner end of the permanent brick 8, or is it an external position relative to the inner end of the permanent brick 8.

[0042] (C) The position of a region where a hot spot is expected to occur in the circumferential direction is included in the position of precast block 9 in the circumferential direction.

[0043] (D) The position of a region where a hot spot is expected to occur in the direction of height is included in the position of precast block 9 in the direction of height.

[0044] Precast block 9 is used to install a temperature sensor, which is intended to measure the temperature of the side wall portion. Petition 870250088767, dated 09 / 30 / 2025, pp. 106 / 171 / 68 6, in the side wall portion 6. This embodiment explains, as an example, the case where fiber optic temperature sensors are used as the temperature sensor that measures the temperature of the side wall portion 6. Fig. 1 illustrates, as an example, the case where fiber optic temperature sensors 111 to 112 include optical fibers 121 to 122 and measuring devices 131 to 132 in this embodiment. Measuring devices 131 to 132 emit light (e.g., infrared light) onto optical fibers 121 to 122. The light emitted from optical fibers 121 to 122 is scattered within optical fibers 121 to 122. Measuring devices 131 to 132 receive the scattered return light from optical fibers 121 to 122. Measuring devices 131 to 132 calculate the temperature at each position within optical fibers 121 to 122 based on the intensity, speed, and duration of the incoming and emitted light.Fiber optic temperature sensors 111 to 112 are manufactured using well-known techniques, and therefore a detailed explanation of fiber optic temperature sensors 111 to 112 is omitted here.

[0045] Optical fibers 121 to 122 are incorporated into pre-molded block 9. Optical fiber 121 is installed in a relatively internal position so that both the temperature distribution of the side wall portion 6 in the height direction and the temperature distribution of the side wall portion 6 in the circumferential direction can be measured. Optical fiber 122 is installed in a relatively external position so that both the temperature distribution of the side wall portion 6 in the height direction and the temperature distribution of the side wall portion 6 in the circumferential direction can be measured. In the following explanation, the optical fiber to be installed in a relatively internal position is referred to as the internal optical fiber, as necessary. Furthermore, the optical fiber to be installed in a relatively external position is referred to as the external optical fiber, as necessary.Furthermore, the height direction of side wall portion 6 and the circumferential direction of side wall portion 6 are... Petition 870250088767, dated 09 / 30 / 2025, page 107 / 171 / 68 abbreviated to a height direction and a circumferential direction, respectively, as needed.

[0046] Figure 2 is a cross-sectional view taken along line II in Figure 1. Incidentally, for convenience of notation and explanation, the hatching indicating cut surfaces is also omitted in Fig. 2. As illustrated in Fig. 2, this embodiment explains, as an example, the case where the electric arc furnace 1 includes a plurality of precast blocks 9a to 9r. The plural precast blocks 9a to 9r are arranged in the circumferential direction of the electric arc furnace 1. This embodiment explains, as an example, the case where the plural precast blocks 9a to 9r have the same configuration. However, at least one of the plural precast blocks 9a to 9r may be different in shape and size from the other precast blocks. The value of the physical property of at least one of the plural precast blocks 9a to 9r (i.e., the material that forms the precast block) may also be different from the other precast blocks.However, it is preferable that the values ​​of the physical properties of the plural precast blocks 9a to 9r be substantially the same, and it is even more preferable that they be the same. This is because there is no need to vary the value of the physical property of the precast block to be used when performing an inverse analysis of the three-dimensional non-steady-state heat transfer problem described later, depending on the position.

[0047] Of the precast blocks 9a to 9r, the circumferential ends of two precast blocks (for example, precast blocks 9a to 9b) adjacent to each other in the circumferential direction are connected (fixed) to each other by means of an adhesive and heat-resistant material, for example. Furthermore, the outer end of the wear-resistant brick 7 and the inner ends of the precast blocks 9a to 9r are also connected (fixed) to each other by means of an adhesive and heat-resistant material, for example. In addition, the inner end Petition 870250088767, dated 09 / 30 / 2025, page 108 / 171 / 68 of the furnace casing 10 and the outer ends of the precast blocks 9a to 9r are also connected (fixed) to each other by means of an adhesive and heat-resistant material, for example. The material (heat-resistant and adhesive material) used to connect (fix) the precast blocks 9a to 9r in the manner described above is mortar, for example.

[0048] As illustrated in Fig. 2, this embodiment explains, as an example, the case where internal optical fibers 121a to 121r and external optical fibers 122a to 122r are installed in pre-molded blocks 9a to 9r, respectively. Furthermore, this embodiment explains, as an example, the case where internal optical fibers 121a to 121r have the same configuration. Furthermore, this embodiment explains, as an example, the case where external optical fibers 122a to 122r have the same configuration. Furthermore, this embodiment explains, as an example, the case where the arrangement of internal optical fibers 121a to 121r and the arrangement of external optical fibers 122a to 122r are the same relative to pre-molded blocks 9a to 9r, respectively. As described earlier, this method explains, for example, the case where prefabricated blocks 9a to 9r have the same configuration.Therefore, in a relative coordinate system with a reference position (e.g., the center of gravity position) of each of the precast blocks 9a to 9r defined as the origin, the coordinates of the positions where the internal optical fibers 121a to 121r and the external optical fibers 122a to 122r are located are the same. That is, this embodiment explains, as an example, the case where the precast blocks 9a to 9r have the same configuration, including the internal optical fibers 121a to 121r and the external optical fibers 122a to 122r. Furthermore, this embodiment explains, as an example, the case where even if at least two of the precast blocks 9a to 9r are replaced, the state after the replacement is the same as before the replacement.

[0049] By the way, the precast block 9 illustrated in Fig. 1 is a Petition 870250088767, dated 09 / 30 / 2025, page 109 / 171 / 68 of precast blocks 9a to 9r. In the following explanation, when precast blocks 9a to 9r are explained without being limited to individual precast blocks 9a to 9r, 9 is used as the reference numeral for the precast blocks. Furthermore, the internal optical fiber 121 and the external optical fiber 122 illustrated in Fig. 1 are one of the internal optical fibers 121a to 121r and one of the external optical fibers 122a to 122r, respectively. When internal optical fibers 121a to 121r and external optical fibers 122a to 122r are explained without being limited to individual internal optical fibers 121a to 121r and individual external optical fibers 122a to 122r, 121 and 122 are used as reference numbers for internal optical fibers and external optical fibers, respectively.

[0050] Fig. 3 is a view illustrating an example of the configuration of the pre-molded block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated.

[0051] As described earlier, the internal optical fiber 121 is installed relatively inward. The external optical fiber 122 is installed relatively outward.

[0052] As illustrated in Fig. 3, this embodiment explains, by way of example, the case where the internal optical fiber 121 is installed in a virtual plane 31a to meander in the circumferential direction as its direction of travel. The virtual plane 31a is a plane parallel to the internal circumferential surface 6a of the side wall portion 6. By installing the internal optical fiber 121 in this manner, the internal optical fiber 121 is installed so that the position of the region where the hot spot described above is expected to occur in the direction of height is included within a strip of the region where the internal optical fiber 121 meanders in the direction of height.

[0053] Similarly, this modality explains, as an example, the case where the external optical fiber 122 is installed in a virtual plane 31b to meander in the circumferential direction as its direction of travel. Petition 870250088767, dated 09 / 30 / 2025, page 110 / 171 / 68 Virtual plane 31b is a plane parallel to the inner circumferential surface 6a of the side wall portion 6. By installing the external optical fiber 121 in this manner, the external optical fiber 122 is installed so that the position of the region where the previously described hot spot is expected to occur in the upward direction is included within a range of the region where the external optical fiber 122 meanders in the upward direction.

[0054] In the following explanation, the regions in virtual planes 31a and 31b where optical fibers 121 and 122 are installed respectively are referred to as optical fiber 121 and 122 installation regions, as needed.

[0055] Incidentally, to simplify the notation and explanation, Fig. 3 illustrates, as an example, the case where the shape of precast block 9 is a rectangular cylinder with a hollow fan-shaped bottom. However, the shape of precast block 9 is not limited to this shape. For example, the shape of precast block 9 can be a rectangular parallelepiped.

[0056] As illustrated in Fig. 3, both ends of the inner optical fiber 121 and the outer optical fiber 122 are pulled out of the pre-molded 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 internal optical fibers connected in series 121a to 121r is connected to the measuring device 131 illustrated in Fig. 1. The other end of the internal optical fibers connected in series 121a to 121r can be incorporated into the pre-molded block 9 or can also be pulled out of the pre-molded block 9. One end of the external optical fibers connected in series 122a to 122r is connected to the measuring device 132 illustrated in Fig. 1. Similarly, the other end of the external optical fibers connected in series 122a to 122r can be incorporated into the pre-molded block 9, or can also be pulled out of the pre-molded block 9.

[0057] An example of the method for connecting the remaining end Petition 870250088767, dated 09 / 30 / 2025, page 111 / 171 / 68 of the internal optical fiber 121 incorporated in the precast block 9 is as follows. In the explanation below, the right side and the left side in the circumferential direction when the side wall portion 6 (the precast block 9) is viewed from the central axis O of the electric arc furnace 1 with the upper direction of the electric arc furnace 1 in the height direction being the upward direction are referred to simply as a right side and a left side, respectively (see circumferential direction, right side and left side in Fig. 3).

[0058] From the two ends of the internal optical fiber 121 embedded in the pre-molded block 9, the end pulled out on the right side is mutually connected to the end pulled out on the left side of both ends of the internal optical fiber 121 embedded in the pre-molded block 9 adjacent to the right side of the pre-molded block 9. For example, in Fig. 2, from both ends of the internal optical fiber 121a embedded in the pre-molded block 9a, the end pulled out on the right side is mutually connected to the end pulled out on the left side of both ends of the internal optical fiber 121b embedded in the pre-molded block 9b adjacent to the right side of the pre-molded block 9a.

[0059] From the two ends of the internal optical fiber 121 embedded in the pre-molded block 9, the end pulled out on the left side is mutually connected to the end pulled out on the right side of both ends of the internal optical fiber 121 embedded in the pre-molded block 9 adjacent to the left side of the pre-molded block 9. For example, in Fig. 2, from both ends of the internal optical fiber 121a embedded in the pre-molded block 9a, the end pulled out on the left side is mutually connected to the end pulled out on the right side of both ends of the internal optical fiber 121r embedded in the pre-molded block 9r adjacent to the left side of the pre-molded block 9a.

[0060] When configuring and installing internal fiber optic cables 121a to 121r Petition 870250088767, dated 09 / 30 / 2025, page 112 / 171 / 68 as described above, the internal optical fibers 121a to 121r are installed so as to encircle the central axis O of the electric arc furnace 1 while meandering in the virtual plane 31a in the circumferential direction as their direction of travel.

[0061] Similarly, from both ends of the external optical fiber 122 embedded in the pre-molded block 9, the end pulled out on the right side is mutually connected to the end pulled out on the left side of both ends of the external optical fiber 122 embedded in the pre-molded block 9 adjacent to the right side of the pre-molded block 9. For example, in Fig. 2, from both ends of the external optical fiber 122a embedded in the pre-molded block 9a, the end pulled out on the right side is mutually connected to the end pulled out on the left side of both ends of the external optical fiber 122b embedded in the pre-molded block 9b adjacent to the right side of the pre-molded block 9a.

[0062] From the two ends of the external optical fiber 122 embedded in the pre-molded block 9, the end pulled out on the left side is mutually connected to the end pulled out on the right side of both ends of the external optical fiber 122 embedded in the pre-molded block 9 adjacent to the left side of the pre-molded block 9. For example, in Fig. 2, from both ends of the external optical fiber 122a embedded in the pre-molded block 9a, the end pulled out on the left side is mutually connected to the end pulled out on the right side of both ends of the external optical fiber 122r embedded in the pre-molded block 9r adjacent to the left side of the pre-molded block 9a.

[0063] When configuring and installing the external optical fibers 122a to 122r as described above, the external optical fibers 122a to 122r are installed so as to encircle the central axis O of the electric arc furnace 1 while meandering in the virtual plane 31b in the circumferential direction as their direction Petition 870250088767, dated 09 / 30 / 2025, page 113 / 171 / 68 regarding relocation.

[0064] Moreover, as above, this embodiment explains, by way of example, the case where the fiber optic temperature sensor 111, which measures the temperature in a relatively internal position, and the fiber optic temperature sensor 112, which measures the temperature in a relatively external position, are different temperature sensors. However, this embodiment does not necessarily have to be designed in this way. For example, both the temperature in a relatively internal position and the temperature in a relatively external position can be measured by a single fiber optic temperature sensor. In this case, a single fiber optic cable can be installed in the region where fiber optic cables 121 and 122 are installed.

[0065] The precast block 9 is manufactured as follows, for example.

[0066] A monolithic refractory is placed in a mold with a shape and size corresponding to the external 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 as to be incorporated into the positions described previously in 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 of the inner optical fiber 121 and the outer optical fiber 122 in the precast block 9 (coordinates in the relative coordinate system described previously) be identified even in a state where they are incorporated into the precast block 9.Therefore, for example, an unillustrated template is used that keeps the inner optical fiber 121 and the outer optical fiber 122 out of the mold, and therefore it is preferable to inhibit the change of positions of the inner optical fiber 121 and the outer optical fiber 122 (it is preferable not to change their positions) in the pre-molded block 9 from the moment the inner optical fiber 121 and the outer optical fiber 122 are placed in the mold. Petition 870250088767, dated 09 / 30 / 2025, p. 114 / 171 / 68 until the monolithic refractory hardens.

[0067] For example, a jig with a configuration that allows adjustment of the position of a target to be held in the mold can be used, so that the position of the target to be held in the mold can be identified. With this jig attached, the inner optical fiber 121 and the outer optical fiber 122 are placed in the mold. Then, the jig is adjusted to define the positions of the inner optical fiber 121 and the outer optical fiber 122 in predetermined positions in the mold. After that, the jig maintains the positions of the inner optical fiber 121 and the outer optical fiber 122 in the pre-molded block 9 until the monolithic refractory hardens.

[0068] By the way, after the inner optical fiber 121 and the outer optical fiber 122 are placed in the mold, the monolithic refractory can be placed in the mold.

[0069] Furthermore, as material for the monolithic refractory, a material is used that achieves the following: the precast block 9 has a mechanical strength required for the side wall portion 6, and the heat resistance of the precast block 9 satisfies the heat resistance required for the side wall portion 6.

[0070] Furthermore, the lengths of the inner optical fiber 121 and the outer optical fiber 122 taken from the pre-molded block 9 can be identified even when they are incorporated into the pre-molded block 9. Therefore, once each position on the inner optical fiber 121 and each position on the outer optical fiber 122 in the pre-molded block 9 has been identified, the lengths of the measuring devices 131 to 132 up to each position on the inner optical fiber 121 and each position on the outer optical fiber 122 are also identified.

[0071] Incidentally, this modality explains, as an example, the case where all of the following (E) to (G) are satisfied.

[0072] (E) The distances from the inner circumferential surface 6a of Petition 870250088767, dated 09 / 30 / 2025, page 115 / 171 / 68 portion of the side wall 6 up to the internal optical fibers 121a to 121r are constant.

[0073] (F) The distances from the inner circumferential surface 6a of the side wall portion 6 to the outer optical fibers 122a to 122r are constant.

[0074] (G) The spacing between the internal optical fibers 121a a 121r and the outer optical fibers 122a to 122r (the distance from the side wall portion 6 in the thickness direction) are constant.

[0075] This is preferable because it reduces the computational load of temperature interpolation calculations using temperatures measured by fiber optic temperature sensors 111 to 112 or other calculations, in the installation status monitoring device 100 described later. However, this embodiment does not necessarily need to be designed in this way, provided that the lengths of the measuring devices 131 to 132 to their respective positions on the internal fiber optic 121 and the external fiber optic 122 are identified.

[0076] Furthermore, when the inner optical fiber and the outer optical fiber (for example, inner optical fiber 121a and outer optical fiber 122a), whose positions in the circumferential direction are the same, are incorporated into the same pre-molded block 9, the installation of the inner optical fiber 121 and the outer optical fiber 122 is facilitated, which is preferable. However, this embodiment does not necessarily need to be designed in this way. For example, the inner optical fiber and the outer optical fiber whose positions in the circumferential direction are the same can be incorporated into different pre-molded blocks. Furthermore, since the positions of the inner optical fiber and the outer optical fiber (for example, inner optical fiber 121a and outer optical fiber 122a) in the circumferential direction are the same, the computational load when performing the inverse analysis of the described three-dimensional non-steady-state heat transfer problem Petition 870250088767, dated 09 / 30 / 2025, p. 116 / 171 / 68 may subsequently be reduced, which is preferable. However, the positions of the inner optical fiber and the outer optical fiber (e.g., inner optical fiber 121a and outer optical fiber 122a) in the direction of the circumference do not need to be the same.

[0077] Furthermore, a temperature sensor other than the fiber optic temperature sensor can be used instead of the fiber optic temperature sensor 112. The temperature sensor other than the fiber optic temperature sensor does not need to be incorporated into the side wall portion 6. The temperature sensor other than the fiber optic temperature sensor can be, for example, a temperature sensor that measures the temperature distribution on the outer surface of the oven enclosure 10. This temperature sensor can be a radiation thermometer or a thermocouple. Furthermore, such a temperature sensor is installed in an external position relative to the fiber optic temperature sensor (fiber optic) so as to be able to measure both the temperature distribution of the side wall portion 6 in the height direction and the temperature distribution of the side wall portion 6 in the circumferential direction.Furthermore, this temperature sensor is installed in a position that allows it to measure the temperature of a region where the previously described hot spot is expected to occur.

[0078] Furthermore, a permanent brick can be installed on the outside of the permanent brick 8. In this case, the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated is preferably installed in a partial region of the region where the permanent brick 8 closest to the furnace casing 10 is installed. For example, this is because the installation and maintenance of the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated are facilitated. However, the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated can Petition 870250088767, dated 09 / 30 / 2025, page 117 / 171 / 68 to be installed in a partial region of the area where a permanent brick different from the permanent brick closest to the furnace casing 10 is installed. Incidentally, the wear brick 7 forms the inner circumferential surface 6a of the side wall portion 6 of the electric arc furnace 1. For this reason, there is a risk that the thickness of the wear brick 7 may decrease due to erosion or something similar. Therefore, it is preferable that the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated does not form the internal circumferential surface 6a of the side wall portion 6 of the electric arc furnace 1. For example, it is preferable that the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated is not installed in the region where the wear brick 7 is installed.In this case, the precast block 9 in which the internal optical fiber 121 and the external optical fiber 122 are incorporated is installed, for example, in the region where the permanent brick, which is a refractory that does not form the internal circumferential surface 6a of the side wall portion 6 of the electric arc furnace 1, is installed. <Esboços do dispositivo de monitoramento do estado da instalação e do método de monitoramento do estado da instalação>

[0079] As will be described in detail later, the installation status monitoring device 100 in this embodiment calculates the temperature distribution of the sidewall portion 6 in the thickness direction, performing the inverse analysis of the three-dimensional non-steady-state heat transfer problem based on the measured values ​​of the optical fiber temperature sensors 111 to 112. Incidentally, the temperature distribution of the sidewall portion 6 in the thickness direction is information that indicates the relationship between the position of the sidewall portion 6 in the thickness direction and the temperature of the sidewall portion 6. Furthermore, the installation status monitoring device 100 can Petition 870250088767, dated 09 / 30 / 2025, page 118 / 171 / 68 further calculate the temperature distributions in other directions (e.g., the height direction and the circumferential direction). Incidentally, the temperature distribution of the side wall portion 6 in the thickness direction is calculated in a range considered to be the range where the inner circumferential surface 6a of the side wall portion 6 may be present. In other words, the temperature distribution of the side wall portion 6 in the thickness direction may include temperatures in the region inside the furnace, in addition to the region where the side wall portion 6 is actually present.

[0080] Next, the installation status monitoring device 100 calculates the position of the inner circumferential surface 6a based on the temperature distribution of the side wall portion 6 in the thickness direction. The position of the inner circumferential surface 6a calculated by the installation status monitoring device 100 includes the position of the side wall portion 6 in the thickness direction. Incidentally, the thickness direction of the side wall portion 6 is the direction in which a straight line connecting the inner circumferential surface 6a and the outer circumferential surface 6b extends the shortest distance (the radial direction of the electric arc furnace 1). The position of the side wall portion 6 in the thickness direction is represented, for example, by the value of a coordinate axis when the straight line is defined as the coordinate axis.In the explanation that follows, the thickness direction of side wall portion 6 is abbreviated to a thickness direction, as needed.

[0081] Here, the inverse problem of non-steady-state heat transfer, which is a problem based on a non-steady-state heat conduction equation that dominates an area of ​​calculus, refers to a problem of estimating at least one of the boundary conditions of physical quantities (such as temperature and heat flux) at an area boundary and initial conditions of the physical quantities at the boundary of Petition 870250088767, dated 09 / 30 / 2025, page 119 / 171 / 68 area, with temperature information within the area being known. In this mode, the inverse problem of non-steady-state heat transfer is a problem of estimating the temperature at the area boundary (the temperature of the inner circumferential surface 6a). Incidentally, a non-steady-state forward heat transfer problem refers to a problem of estimating temperature information within the area based on known boundary conditions.

[0082] As described above, Patent Literature 1 disclosed the solution to a one-dimensional non-steady-state inverse heat transfer problem. However, when the one-dimensional non-steady-state inverse heat transfer problem is used, it is not possible to sufficiently improve the accuracy of the temperature distribution estimate of the sidewall portion 6 in the thickness direction. This will be explained with reference to Fig. 4A, Fig. 4B, Fig. 5A, and Fig. 5B. Fig. 4A and Fig. 4B are views that explain an example of heat transfer that can be considered in the one-dimensional non-steady-state inverse heat transfer problem. Fig. 5A and Fig. 5B are views that explain an example of heat transfer that can be considered in a three-dimensional non-steady-state inverse heat transfer problem.

[0083] As will be described later, this embodiment explains, by way of example, the case where the inverse problem of non-steady-state heat transfer in three-dimensional systems is formulated in a three-dimensional orthogonal coordinate system (xyz coordinate system). Therefore, the xyz coordinates are illustrated in each of the drawings. However, the origin of the xyz coordinates illustrated in each of the drawings is not limited to the position illustrated in each of the drawings. Furthermore, in each of the drawings, the symbol with a black circle inside a white circle indicates an arrowhead from a distant side towards Petition 870250088767, dated 09 / 30 / 2025, page 120 / 171 / 68 a near side of the sheet of paper (the direction from a far side towards a near side of the sheet of paper indicates the coordinate axis in a positive direction).

[0084] 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. Moreover, in this embodiment, the inner circumferential surface 6a of the side wall portion 6 is not a planar surface. Therefore, this embodiment explains, as an example, the case where the circumferential direction and the height direction of the side wall portion 6, which appears as a planar surface when cutting and developing the side wall portion 6 along the height direction at a point in the circumferential direction, are defined as the y-axis direction and the z-axis direction, respectively, and the y-coordinate and z-coordinate of each position of the side wall portion 6 are determined.Similarly, this method explains, for example, the case where the y-coordinate and z-coordinate of each position of the portion of the side wall 6 are also determined in a plane parallel to the inner circumferential surface 6a (for example, the virtual planes 31a and 31b or similar) in the same way as the inner circumferential surface 6a.

[0085] In Fig. 4A and Fig. 4B, the heat flow is from the inner side, where the temperature is higher, to the outer side. In the case of using the inverse problem of non-steady-state one-dimensional heat transfer, the temperature distribution of the side wall portion 6 in the thickness direction is calculated assuming that heat is transferred only in the thickness direction (x-axis direction) of the side wall portion 6.

[0086] Therefore, when solving the inverse one-dimensional non-steady-state heat transfer problem to calculate the temperature distribution of the side wall portion 6 in the thickness direction, as illustrated in Fig. 4A and Fig. 4B, the measurement positions of Petition 870250088767, dated 09 / 30 / 2025, p. 121 / 171 / 68 temperature 41a to 41b, 41c to 41d, 41e to 41f, 41g to 41h, 41i to 41j and 41k to 41l are located so as to be aligned in the direction of the thickness of the side wall portion 6. In this case, the direction of heat transfer that can be considered in the inverse problem of non-steady-state heat transfer is limited to the direction in which the temperature measurement positions 41a to 41b, 41c to 41d, 41e to 41f, 41g to 41h, 41i to 41j and 41k to 41l are aligned (the direction along the arrow line illustrated in Fig. 4A and Fig. 4B). Moreover, in Fig. 4A and Fig. 4B, for convenience 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 illustrated in large, exaggerated sizes (the same is true for Fig. 5A and Fig. 5B).

[0087] However, the actual direction of heat transfer is not just the thickness direction (x-axis direction) of sidewall portion 6. When solving the inverse one-dimensional non-steady-state heat transfer problem to calculate the temperature distribution of sidewall portion 6 in the thickness direction, the direction of heat transfer is limited to the thickness direction of sidewall portion 6. For this reason, even if the number of temperature measurement positions is increased, there is a limit to the improvement in the accuracy of the estimate of the temperature distribution of sidewall portion 6 in the thickness direction.Furthermore, when solving a non-stationary two-dimensional inverse heat transfer problem to calculate the temperature distribution of side wall portion 6, the direction of heat transfer is limited to the direction of the thickness of side wall portion 6 and only one of the circumferential and height directions of side wall portion 6.

[0088] In contrast to this, when solving the inverse problem of non-stationary three-dimensional heat transfer to estimate the temperature of the inner circumferential surface 6a, it is possible to consider heat transfers from the temperature measurement positions 51a, 51c, 51e, Petition 870250088767, dated 09 / 30 / 2025, pages 122 / 171 / 68 51g, 51i, and 51k on the inner side for the temperature measurement positions 51b, 51d, 51f, 51h, 51j, and 51l on the outer side, respectively, as illustrated in Fig. 5A and Fig. 5B. Therefore, the direction of heat transfer that can be considered in the inverse problem of non-steady-state heat transfer is not limited to the directions in which the temperature measurement positions 51a to 51b, 51c to 51d, 51e to 51f, 51g to 51h, 51i to 51j, and 51k to 51l are aligned. In other words, the direction of heat transfer that can be considered in the inverse problem of non-steady-state heat transfer is each direction from any of the temperature measurement positions 51a, 51c, 51e, 51g, 51i and 51k on the inside to any of the temperature measurement positions 51b, 51d, 51f, 51h, 51j and 51l on the outside (directions along the arrow lines illustrated in Fig. 5A and Fig. 5B).As above, in the inverse problem of non-steady-state heat transfer, all directions—the thickness direction of sidewall portion 6, the circumferential direction of sidewall portion 6, and the height direction of sidewall portion 6—can be considered. Therefore, by solving the inverse problem of non-steady-state three-dimensional heat transfer and calculating the temperature distribution of sidewall portion 6 in the thickness direction, the accuracy of the estimate of the temperature distribution of sidewall portion 6 in the thickness direction can be improved. This makes it possible to improve the accuracy of the estimate of the position of the inner circumferential surface 6a in the thickness direction.

[0089] Thus, in this mode, the inverse analysis of the three-dimensional non-steady-state heat transfer problem is performed, in order to calculate the temperature distribution of the side wall portion 6 in the thickness direction.

[0090] Furthermore, to calculate the temperature distribution of the side wall portion 6 in the thickness direction over such a wide range Petition 870250088767, dated 09 / 30 / 2025, page 123 / 171 / 68 as far as possible, the temperature measurement positions also need to be present in as wide a range as possible. When using thermocouples as a temperature sensor, as described in Patent Literature 1, it is practically difficult to install a large number of thermocouples on the side wall portion 6 in precisely determined positions.

[0091] Thus, in this embodiment, fiber optic temperature sensors 111 to 112 are used as temperature sensors.

[0092] Furthermore, when the temperature measurement position is located between the wear brick 7 and the permanent brick 8, or between individual permanent bricks 8, there is a risk that the accuracy of the temperature measurement at the temperature measurement position may be lower than the accuracy of the temperature measurement at another temperature measurement position. This is because the temperature to be measured at the temperature measurement position is affected by the properties or voids around the temperature measurement position (temperature sensor). Therefore, the accuracy of the temperature to be measured by the temperature sensor may vary depending on the temperature measurement position. On the other hand, provided that the values ​​of the physical properties around the temperature sensor are substantially the same (preferably the same), such temperature variations can be inhibited.Furthermore, when the temperature sensor is embedded in bricks, the workload increases.

[0093] Thus, this embodiment explains, by way of example, the case where the temperature sensor is incorporated into the pre-molded block 9 having substantially the same values ​​of physical properties (preferably the same values ​​of physical properties). However, for example, provided that the values ​​of the physical properties around the temperature measurement position are substantially the same (preferably the same), the temperature sensor does not necessarily need to be incorporated into the pre-molded block 9. For example, the sensors of Petition 870250088767, dated 09 / 30 / 2025, page 124 / 171 / 68 optical fiber temperature 111 to 112 can be incorporated into permanent brick 8. In this case, it is preferable that only the positions within permanent brick 8 be defined as temperature measurement positions. Furthermore, in this case, precast block 9 does not need to be installed in electric arc furnace 1. <Dispositivo de monitoramento do estado da instalação 100>

[0094] The following explains an example of the 100 installation status monitoring device. Fig. 6 is a diagram illustrating an example of a functional configuration of the 100 installation status monitoring device. The 100 installation status monitoring device includes, as its hardware, one or more hardware processors, such as a CPU (Central Processing Unit), and one or more memories, such as RAM (Random Access Memory) and ROM (Read-Only Memory), for example. The 100 installation status monitoring device performs various arithmetic operations by executing one or more programs stored in memory using one or more hardware processors. In addition, the 100 installation status monitoring device includes an input device and an output device as hardware.At least one of the input and transmission devices may be provided outside of the facility status monitoring device 100. In this case, the facility status monitoring device 100 performs wired or radio communication with the input device and the transmission device.

[0095] This modality explains, by way of example, the case where the installation status monitoring device 100 includes a temperature acquisition part 61, an inverse problem analysis part 62, a refractory position calculation part 63 and an emission part 64. An example of the functions of the respective parts is explained below. Incidentally, Petition 870250088767, dated 09 / 30 / 2025, page 125 / 171 / 68, it is presumed that information that can be defined in advance in calculations described later has been stored in the installation status monitoring device 100 by means of the input device, for example. "Temperature acquisition part 61"

[0096] The temperature acquisition part 61 acquires the measured values ​​from the fiber optic temperature sensors 111 to 112. As described previously, this embodiment explains, as an example, the case where the temperatures at respective positions in the optical fibers 121 to 122 are calculated by the measuring devices 131 to 132. Therefore, this embodiment explains, as an example, the case where the temperature acquisition part 61 acquires the temperatures at the respective positions in the optical fibers 121 to 122 calculated by the measuring devices 131 to 132 as the measured values ​​from the fiber optic temperature sensors 111 to 112. The temperature acquisition part 61 can acquire the measured values ​​from the fiber optic temperature sensors 111 to 112 by performing wired or radio communication with the measuring devices 131 to 132.Furthermore, the temperature acquisition part 61 can acquire the measured values ​​from the fiber optic temperature sensors 111 to 112 by means of a device different from the measuring devices 131 to 132. Additionally, the temperature acquisition part 61 can have the functions of the measuring devices 131 to 132.

[0097] The positions at which the measured values ​​from the optical fiber temperature sensors 111 to 112 are obtained are defined in advance among the positions on optical fibers 121 to 122. It is preferable that the positions at which the measured values ​​from the optical fiber temperature sensors 111 to 112 are obtained be as wide as possible and have as many positions as possible. This is because the accuracy of the temperature calculation at temperature measurement points described later Petition 870250088767, dated 09 / 30 / 2025, pp. 126 / 171 / 68 (hot spot centroid positions, areas around the hot spot) improves. However, if there are many positions where measured values ​​from fiber optic temperature sensors 111 to 112 are obtained, there is a risk that the computational load will become too high. Therefore, it is preferable that the positions where measured values ​​from fiber optic temperature sensors 111 to 112 are obtained be defined in advance from the point of view of a balance between reducing the computational load and improving the calculation accuracy.

[0098] The temperature acquisition part 61 can acquire the measured values ​​during loading as well as the measured values ​​from the fiber optic temperature sensors 111 to 112. In this case, the installation status monitoring device 100 can calculate the position of the inner circumferential surface 6a in the thickness direction, even when it is not possible to measure the state of the inner circumferential surface 6a of the side wall portion 6 using a profile gauge or similar due to the presence of raw material in the furnace. However, the moment when the temperature acquisition part 61 acquires the measured values ​​from the fiber optic temperature sensors 111 to 112 is not limited to such a moment. For example, the temperature acquisition part 61 can acquire the measured values ​​in a period between loads as well as the measured values ​​from the fiber optic temperature sensors 111 to 112.The period between charges is, for example, the period from when the molten metal and molten slag are discharged from the furnace until the next raw material is added.

[0099] This embodiment explains, as an example, the case where the fiber optic temperature sensors 111 to 112 measure the temperatures at their respective positions in the optical fibers 121 to 122 at regular time intervals. Furthermore, this embodiment explains, as an example, the case where the temperature acquisition part 61 acquires the measured values ​​from Petition 870250088767, dated 09 / 30 / 2025, p. 127 / 171 / 68 fiber optic temperature sensors 111 to 112 in each time period. In the explanation below, the time period during which the temperature acquisition part 61 acquires the measured values ​​from the fiber optic temperature sensors 111 to 112 is called the temperature measurement period, as required. <<Parte da análise do problema inverso 62> >

[00100] Part 62 of the inverse problem analysis performs the three-dimensional analysis of the non-steady-state inverse heat transfer problem based on the measured values ​​from the fiber optic temperature sensors 111 to 112, thus calculating the temperature distribution of the sidewall portion 6 in the thickness direction (x-axis direction).

[00101] When performing the inverse problem analysis of three-dimensional non-steady-state heat transfer, N temperatures can be used per locus of the side wall portion 6 in the thickness direction as the temperature required to calculate a single position of the inner circumferential surface 6a in the thickness direction. The case where this embodiment is designed as above is explained by way of example. N is an integer of 2 or more. N is preferably an integer of 3 or more, and more preferably 5 (which will be explained later).

[00102] Furthermore, when performing the inverse analysis of the three-dimensional non-steady-state heat transfer problem, it is also considered that the accuracy of estimating a single position of the inner circumferential surface 6a in the thickness direction can be improved by using a larger number of temperatures as the temperature required to calculate a single position of the inner circumferential surface 6a in the thickness direction. However, this embodiment does not necessarily need to be designed in this way, and the present authors have found it preferable to use five temperatures per place of the side wall portion 6 in the thickness direction as the temperature required to calculate a single position. Petition 870250088767, dated 09 / 30 / 2025, page 128 / 171 / 68 position of the inner circumferential surface 6a in the thickness direction. That is, even if the number of temperatures (= N) needed to calculate a single position of the inner circumferential surface 6a in the thickness direction is no greater than five, the accuracy of the estimate of the position of the inner circumferential surface 6a in the thickness direction can satisfy the accuracy required in practical use (it can be approximated to a real measured value) (an example of calculation described later (see Fig. 11)).

[00103] Thus, this embodiment explains, as an example, the case where part 62 of the inverse problem analysis acquires five temperatures per location of the sidewall portion 6 in the thickness direction as the temperature required to calculate a single position of the inner circumferential surface 6a in the thickness direction based on the measured values ​​of the optical fiber temperature sensors 111 to 112, and performs the inverse problem analysis of the three-dimensional non-steady-state heat transfer based on the acquired temperatures. As described earlier with reference to Fig. 1 to Fig. 3, this embodiment explains, as an example, the case where there are two installation regions (regions in the virtual planes 31a and 31b) for optical fibers 121 and 122 in the thickness direction of the sidewall portion 6.Therefore, this method explains, as an example, the case where the analysis part of the inverse problem 62 acquires a total of 10 (= 5 χ 2) temperatures to calculate a single position of the inner circumferential surface 6a in the thickness direction.

[00104] The five temperatures acquired by part 62 of the inverse problem analysis at a location on the side wall portion 6 in the thickness direction may be measured values ​​from the optical fiber temperature sensors 111 to 112, or they may be temperatures calculated based on the measured values ​​from the optical fiber temperature sensors 111 to 112. As described above, it is preferable that the number of temperatures to be acquired by part 62 of the inverse problem analysis at a location on the side wall portion be 62. Petition 870250088767, dated 09 / 30 / 2025, page 129 / 171 / 68 lateral 6 in the thickness direction is five. However, the number of temperatures to be acquired by part 62 of the inverse problem analysis at a location on the lateral wall portion 6 in the thickness direction is not limited to five and may, for example, be a number greater than five. However, if the number of temperatures to be acquired by part 62 of the inverse problem analysis at a location on the lateral wall portion 6 in the thickness direction is very large, a large number of measured values ​​will be required as the measured temperature value. Furthermore, there is a risk that the accuracy of the calculation of a weighting coefficient wi,j,k,l in Equation (3) to be described later, which is calculated by performing the three-dimensional non-steady-state inverse heat transfer problem analysis, may decrease (specifically, overfitting may occur).Therefore, it is preferable to define the number of temperatures to be acquired by part 62 of the inverse problem analysis, considering these points. Furthermore, the ideal value for the number of temperatures (= N) needed to calculate a single position of the inner circumferential surface of the side wall portion in the thickness direction may vary depending on the installation, for example. In this case, the number of temperatures (= N) needed to calculate a single position of the inner circumferential surface of the side wall portion in the thickness direction may be greater than five or less than five.

[00105] Furthermore, the thickness of the side wall portion 6 (the wear brick 7) will likely decrease near the hot spot. Thus, this embodiment explains, as an example, the case where the positions of the five temperatures to be acquired by the analysis part of the inverse problem 62 at a location on the side wall portion 6 in the thickness direction are the following positions.

[00106] Fig. 7 is a view that explains an example of a hotspot region. As described earlier, a hotspot is a position in Petition 870250088767, dated 09 / 30 / 2025, p. 130 / 171 / 68 where the local temperature is maximum. The hot spot region is a region that includes the hot spot. This modality explains, as an example, the case where the hot spot region is determined at each of the x coordinates of the optical fiber installation regions 121 and 122 (regions in virtual planes 31a and 31b).

[00107] Fig. 7 illustrates the temperature distribution in the installation regions of optical fibers 121 and 122 (regions in virtual planes 31a and 31b) in the yz plane. The temperature distribution illustrated in Fig. 7 is calculated based on the values ​​measured by the optical fiber temperature sensors 111 to 112. For example, the temperature distribution illustrated in Fig. 7 is calculated by performing interpolation on the measured values ​​of the optical fiber temperature sensors 111 to 112. The interpolation method is not limited and can be any well-known method, such as linear approximation, spline interpolation, or polynomial interpolation, for example.

[00108] Since the position at which the local temperature is maximum can be clearly determined at a point from the measured values ​​of the fiber optic temperature sensors 111 to 112, the determined position can be defined as the position of the hot spot region. In this case, the temperature at the position can be defined as the temperature of the hot spot region. Furthermore, the search for the hot spot region can be performed in each of a plurality of temperature divisions obtained by dividing the temperature ranges measurable by the fiber optics 121 and 122 into a plurality of divisions. In this case, the region of the temperature division that represents the highest temperature among the plural temperature divisions can be defined as the hot spot region.In this case, a representative position of the hotspot region can be defined as the position of the hotspot region, and the temperature at that position can be defined as the temperature of the hotspot region. Fig. 7 illustrates, as an example, the case where the region corresponding to the division of... Petition 870250088767, dated 09 / 30 / 2025, page 131 / 171 / 68 temperature of 500°C to 525°C is a hotspot region 71. The representative position of the hotspot region 71 is, for example, the position of the center of gravity of the hotspot region 71.

[00109] This embodiment explains, as an example, the case where part 62 of the inverse problem analysis calculates the temperature of the hot spot region 71 based on the measured values ​​of the optical fiber temperature sensors 111 to 112, for all installation regions of optical fibers 121 and 122 (regions in virtual planes 31a and 31b). In this case, the temperature of the hot spot region 71 is one of the five temperatures described above. When there is a plurality of hot spot regions 71 in each of the installation regions of optical fibers 121 and 122 (regions in virtual planes 31a and 31b), the temperature of each of the hot spot regions 71 is one of the five temperatures described above.

[00110] Moreover, when the yz coordinates of the representative position of the hot spot region 71 in the installation region of the internal optical fiber 121 (region in the virtual plane 31a) do not coincide with the yz coordinates of the representative position of the hot spot region 71 in the installation region of the external optical fiber 122 (region in the virtual plane 31b), part 62 of the inverse problem analysis preferentially calculates the temperatures of the hot spot regions 71 in the installation regions of optical fibers 121 and 122 as follows. That is, in this case, part 62 of the inverse problem analysis preferentially makes the yz coordinates of the representative positions of the hot spot regions 71 in the installation regions of optical fibers 121 and 122 coincide with each other, and calculates the temperature of the corresponding yz coordinates as the temperatures of the hot spot regions 71 in the installation regions of optical fibers 121 and 122.For example, part 62 of the inverse problem analysis can determine an arithmetic mean value of the y-coordinates and an arithmetic mean value of the z-coordinates of the hot spot regions 71 in the optical fiber installation regions. Petition 870250088767, dated 09 / 30 / 2025, pp. 132 / 171 / 68 121 and 122 as the yea coordinate and z coordinate of each of the hotspot regions 71. Furthermore, part 62 of the inverse problem analysis can define a yea coordinate and a z coordinate of the yea coordinates and z coordinates of the hotspot regions 71 in the optical fiber installation regions 121 and 122 as the other yea coordinate and other z coordinate.

[00111] This embodiment explains, by way of example, the case where, of the five temperatures acquired by part 62 of the inverse problem analysis at a location on the side wall portion 6 in the thickness direction, the four different positions of the hot spot region 71 are located at positions distributed around the hot spot region 71. Distribution means that, for example, when four positions are projected onto the same plane, three or more of the four positions are not on the same straight line. Fig. 8A and Fig. 8B are shown, each illustrating an example of the temperature positions to be acquired when performing the three-dimensional non-steady-state inverse heat transfer problem analysis. In the following explanation, the position of the hot spot region 71 is referred to as the centroid position of the hot spot, as needed.

[00112] Fig. 8A is a view illustrating an example of positions 81a to 81e of five temperatures to be acquired in the installation region of the internal optical fiber 121 (region in the virtual plane 31a). Fig. 8B is a view illustrating an example of positions 82a to 82e of five temperatures to be acquired in the installation region of the external optical fiber 122 (region in the virtual plane 31b).

[00113] In Fig. 8A, a coordinate value for the centroid position of the hot spot 81a in the internal optical fiber installation region 121 is defined as (xA1, yA1, zA1). Incidentally, xA, yA and zA correspond to the symbols with an appendix above x, y and z, respectively, in mathematical equations described later. As illustrated in Fig. 8A, this modality Petition 870250088767, dated 09 / 30 / 2025, p. 133 / 171 / 68 explains, as an example, the case where the four positions 81b to 81e around the centroid position of the hotspot 81a are determined in the yz plane at a position where the x-coordinate is xi. The coordinate values ​​of positions 81b, 81c, 81d, and 81e are defined as (xAi, yAo, zAi), (xAi, yAi, zAo), (xA), yA2, zA1), and (xA1, yA1, za2), respectively.

[00114] In Fig. 8A, of the four positions 81b to 81e around the centroid position 81a of the hot spot, three or more positions are never located on the same straight line. Therefore, positions 81b to 81e are located in distributed positions around the centroid position 81a of the hot spot. Incidentally, Fig. 8A illustrates, as an example, the case where, of the four positions 81b to 81e around the centroid position 81a of the hot spot, only two positions (for example, positions 81b and 81d) are located on the same straight line.

[00115] Similarly, in Fig. 8B, a coordinate value for the centroid position of the hotspot 82a in the external optical fiber installation region 122 is defined as (xA2, yA1, zA1). As illustrated in Fig. 8B, this embodiment explains, as an example, the case where the four positions 82b to 82e around the centroid position of the hotspot 82a are determined in the yz plane at a position where the x-coordinate is x2. The coordinate values ​​for positions 82b, 82c, 82d, and 82e are defined as (xA2, yA0, za1), (xA2, yA1, ζΛ0), (xA2, yA2, ζΛ1), and (xA2, yA1, za2), respectively.

[00116] Distances Δy1, Δy2, Δζ1, and Δζ2 in the y-axis direction and in the ζ-axis direction from positions 81a and 82a of the hot spot centroid to the four positions 81b to 81e around the hot spot centroid position 81a and the four positions 82b to 82e around the hot spot centroid position 82a, respectively, are defined before performing the analysis of the inverse three-dimensional non-steady-state heat transfer problem. In the following explanation, the four positions around each of the hot spot centroid positions 81a and 82a are referred to as. Petition 870250088767, dated 09 / 30 / 2025, page 134 / 171 / 68 areas around the access point, as needed. Furthermore, the distances Δγ1, Δy2, Δζι, and Δζ2 in the y-axis direction and in the z-axis direction from the centroid position of hotspot 81a to the surrounding areas of hotspot 81b to 81e and from the centroid position of hotspot 82a to the surrounding areas of hotspot 82b to 82e are abbreviated to distances Δγ1, Δy2, Δζι, and Δζ2 respectively, as needed.

[00117] The distances Δγ1, Δy2, Δζι, and Δζ2 are not limited, provided they are determined in such a way that, for example, the accuracy of the calculation of the position of the inner circumferential surface 6a in the direction of the thickness, which is calculated as will be described later, satisfies the accuracy required for practical use.

[00118] For example, the distances Δγ1, Δυ2, Δζι, and Δζ2 where the accuracy of the calculation of the position of the inner circumferential surface 6a in the thickness direction satisfies the accuracy required for practical use can be found by trial and error. In this case, for example, the inverse analysis of the non-stationary three-dimensional heat transfer problem described later is performed in a test furnace simulating the electric arc furnace 1, in order to calculate the position of the inner circumferential surface 6a in the thickness direction, which is performed while varying the distances Δγ1, Δγ2, Δζι, and Δζ2. Then, the calculated value of the position of the inner circumferential surface 6a in the thickness direction is compared with the actual value measured in the test furnace at each of the distances Δγ1, Δγ2, Δζι, and Δζ2.Finally, based on the results of this comparison, the distances Δγ1, Δγ2, Δζι, and Δζ2 are found where the accuracy of the calculation of the position of the inner circumferential surface 6a in the thickness direction satisfies the accuracy required for practical use.

[00119] Furthermore, as in this embodiment, when the centroid position of the hot spot 81a, 82a is included in the five temperatures acquired by the analysis part of the inverse problem 62 at a location of Petition 870250088767, dated 09 / 30 / 2025, page 135 / 171 / 68 portion of the side wall 6 in the direction of the thickness of the wear brick 7, the wear brick 7 located in a position that intersects with a virtual line connecting the centroid positions of the hot spot 81a and 82a and the central axis O of the electric arc furnace 1 at the shortest distance sometimes becomes 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 lowered relative to other regions. In this case, it is preferable to determine the distances Δγ1, Δy2, Δζι, and Δζ2 based on the size of the lowered portion. In the following explanation, the portion of the inner circumferential surface 6a that is recessed due to wear of the wear block 7 is referred to as a worn portion, as necessary. Incidentally, wear of the wear block 7 occurs due to erosion, peeling, or other cause of wear of the brick 7.

[00120] Fig. 9A and Fig. 9B are views, each illustrating an example of the worn portion. Fig. 9A is a view illustrating an example of a region including the worn portion when the side wall portion 6 is viewed from above. Fig. 9B is a view illustrating an example of a region including the worn portion when the side wall portion 6 is viewed from the side of the central axis O of the electric arc furnace 1. Incidentally, Fig. 9A and Fig. 9B illustrate a state assumed to be the state in which the side wall portion 6 is cut along the height direction at a point in the circumferential direction and the side wall portion 6 is developed. Furthermore, Fig. 9A and Fig. 9B each illustrate only a portion of the side wall portion 6 (the region corresponding to a precast block 9). Furthermore, for convenience of notation and explanation, the hatching indicating cut surfaces is also omitted in Fig. 9A and Fig. 9B.

[00121] In Fig. 9A, assume that the wear brick 7 with a worn portion 92 formed on it is the wear brick 7 located at a position that intersects a virtual line 91 connecting the positions of Petition 870250088767, dated 09 / 30 / 2025, p. 136 / 171 / 68 centroid of hot spot 81a and 82a and the central axis O of the electric arc furnace 1 at the shortest distance.

[00122] The distances Δγ1 and Δy2 are determined based, for example, on a length WLy of the worn portion 92 in the circumferential direction (y-axis direction) (see Fig. 9A and Fig. 9B). Specifically, it is preferable that the distances Δy1 and Δy2 should be within a range of 1 / 2 or less (or less than 1 / 2) of the length WLy of the worn portion 92 in the circumferential direction. In this case, this is because the hot spot around areas 81b to 81e and 82b to 82e can be determined between both ends of the worn portion 92 in the y-axis direction. Furthermore, the present descriptors learned that when the distances Δy1 and Δy2 are defined for 1 / 4 of the length WLy of the worn portion 92 in the circumferential direction, the accuracy of the calculation of the position of the inner circumferential surface 6a in the thickness direction is further improved, which is preferable.

[00123] Furthermore, the distances Δζι and Δζ2 are determined based, for example, on a length WLz of the worn portion 92 in the height direction (z-axis direction) (see Fig. 9B). Specifically, it is preferable that the range that the distances Δζι and Δζ2 can assume should be a range of 1 / 2 or less (or less than 1 / 2) of the length WLz of the worn portion 92 in the height direction. In this case, this is because the hotspot around areas 81b to 81e and 82b to 82e can be determined between both ends of the worn portion 92 in the z-axis direction. Furthermore, the present descriptors learned that when the distances Δζι and Δζ2 are defined as 1 / 4 of the length WLz of the worn portion 92 in the height direction, the accuracy of the calculation of the position of the inner circumferential surface 6a in the thickness direction is further improved, which is preferable.

[00124] Furthermore, the distances Δy1, Δy2, Δζι, and Δζ2 can be adjusted according to a WLx depth of the worn part 92, by Petition 870250088767, dated 09 / 30 / 2025, p. 137 / 171 / 68 example. For example, as the depth WLx of the worn portion 92 increases, the distances Δγ1, Δy2, Δζι, and Δζ2 can be increased or decreased. By the way, the depth of the worn portion 92 is the length of the worn portion 92 in the thickness direction (x-axis direction).

[00125] Incidentally, to simplify the explanation and notation, Fig. 9A and Fig. 9B each illustrate, as an example, the case where the shape of a space that is the worn portion 92 is a right quadrangular prism. However, the shape of the actual worn portion 92 is more complex than that of the right quadrangular prism. In this case, the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions can be defined as, for example, representative lengths in the respective directions.

[00126] For example, the width WLy of the worn portion 92 and the height WLz of the worn portion 92 can be the length at an opening end 92a (a mouth portion) of the worn portion 92. Incidentally, the width of the worn portion 92 is the length in the circumferential direction (y-axis direction). Furthermore, the height of the worn portion 92 is the length in the height direction (z-axis direction).

[00127] Furthermore, for example, the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions may be, for example, the maximum lengths in the respective directions. Furthermore, for example, the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions may be the lengths of the worn portion 92 at the position of the center of gravity.

[00128] Here, the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions can be, for example, measured values ​​from a profile gauge, which are obtained by taking measurements over a period between loads, or they can be visually observed values, which are obtained by taking observations over a period between loads. Moreover, the Petition 870250088767, dated 09 / 30 / 2025, pp. 138 / 171 / 68. Measurement using a profile gauge is obtained by well-known techniques, such as those described in Japanese Open Patent Publication No. 2018185253 and similar publications, and therefore, its detailed explanation is omitted here. Furthermore, a test furnace simulating the electric arc furnace 1 can be used to investigate the relationship between the temperature of the hot spot region 71 and the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions. Then, based on the results of the relationship investigation, a mathematical equation or lookup table representing the relationship between the temperature of the hot spot region 71 and the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions can be created. In this case, part 62 of the inverse problem analysis reads the lengths WLx, WLy, and WLz of the worn portion 92 in the respective directions, which correspond to the temperature of the hot spot region 71.

[00129] Part 62 of the inverse problem analysis calculates the hotspot around areas 81b to 81e and 82b to 82e based on the distances Δγ1, Δγ2, Δζι, and Δζ2 determined as described above and the centroid positions of hotspot 81a and 82a, and acquires the temperatures in the areas surrounding hotspot 81b to 81e and 82b to 82e.

[00130] In this way, the analysis of the inverse problem part 62 acquires, as temperatures uAnas coordinates (xA1, yA1, zA1) and (xA2, yA1, zA1) of the centroid positions of the hot spot 81a and 82a, the temperature uA at each of the times t1 to tn of the time interval of the temperature measurement period. Similarly, part 62 of the inverse problem analysis acquires the temperature uA at each of the moments t1 to tn of the time interval of the temperature measurement period as the temperatures uA at the coordinates (xA1, yA0, zA1), (xA1, yA1, zA0), (xA1, yA2, zA1), (xA1, yA1, zA2), (xA2, yA0, zA1), (xA2, yA1, zaq), (xA2, yA2, zA1) and (xA2, yA1, ZA2) of the critical point around the areas 81b to 81e and 82b to 82e.

[00131] Next, part 62 of the inverse problem analysis solves Petition 870250088767, dated 09 / 30 / 2025, pp. 139 / 171 / 68, analysis of the inverse problem of heat transfer in a non-steady three-dimensional state.

[00132] Next, an example of the inverse problem of three-dimensional heat transfer in a non-steady state is explained. In the following explanation, the centroid positions of the hot spot 81a and 82a and the surrounding areas of the hot spot 81b to 81e and 82b to 82e are called temperature measurement points 81a to 81e and 82a to 82e, as needed.

[00133] First, the three-dimensional equation for non-steady-state heat conduction is represented by the following equation (1). [Mathematical equation 1]

[00134] Here, U represents the temperature. x, yez represent the x, yez coordinates in the xyz coordinate system, respectively. t represents the time. α represents the square root of a thermal diffusivity. Incidentally, thermal diffusivity is calculated using a thermal conductivity, a specific heat, and a density (specific gravity).

[00135] A basis function φ (x-xc, y-yc, z-zc, t-tc) is expressed by the following equation (2). The basis function φ (x-xc, y-yc, z-zc, t-tc) is a function expressed in the form of a fundamental solution that satisfies the non-steady-state heat conduction equation in Equation (1), and is a function when a central point c (a reference position xc and a reference time tc) is used as a reference. [Mathematical equation 2] Petition 870250088767, dated 09 / 30 / 2025, pp. 140 / 171 / 68

[00136] Here, T represents a constant (model parameter) that represents a variance of a spatial distribution of the fundamental solution of the non-steady-state heat conduction equation in equation (1), and is called the time shift. xc, yc, zc, and tc are a set of spatiotemporal coordinates called the source term and are defined values ​​(i.e., xc, yc, zc, and tc are not unknowns when solving the inverse problem of non-steady-state heat transfer). For example, information about the temperature measurement points 81a to 81e and 82a to 82e can be defined in xc, yc, zc, and tc. Incidentally, in this case, tc represents the time at which the values ​​measured by the fiber optic temperature sensors 111 to 112 used in acquiring the temperatures at the temperature measurement points 81a to 81e and 82a to 82e were obtained.In the explanation that follows, the time at which the measured values ​​from the fiber optic temperature sensors 111 to 112 were obtained is referred to as the measurement time, as needed.

[00137] Here, a variable that identifies the position in the x-axis direction (thickness direction) of the temperature measurement points 81a to 81e and 82a to 82e is defined as i (i = 1, 2). Additionally, a variable that identifies the position in the y-axis direction (circumferential direction) of the temperature measurement points 81a to 81e and 82a to 82e is defined as j (j = 0, 1, 2). A variable that identifies the position in the z-axis direction (height direction) of the temperature measurement points 81a to 81e and 82a to 82e is defined as k (k = 0, 1, 2). Furthermore, a variable that identifies the temperature measurement time is defined as l (= 1, ···, 2m).

[00138] An interpolation / extrapolation temperature u(x, y, z, t) required to calculate the temperature of side wall portion 6 is expressed as a linear sum of 10 xm basis functions 9(x-xi, y-yj, z-zk, t-tl). In this case, the interpolation / extrapolation temperature u(x, y, z, t) required to calculate the temperature of side wall portion 6 is expressed by the following Petition 870250088767, dated 09 / 30 / 2025, p. 141 / 171 / 68 equation (3). 10 in 10 χ m corresponds to the number of temperature measurement points 81a to 81e and 82a to 82e. m in 10 χ m corresponds to the temperature measurement time (1 am, m + 1 to 2m). The interpolation / extrapolation temperature u(x, y, z, t) is the temperature that satisfies the three-dimensional equation of heat conduction in non-steady state expressed by Equation (1). The interpolation / extrapolation temperature u(x, y, z, t) is an approximate solution of the temperature U(x, y, z, t). [Mathematical equation 3]

[00139] It is necessary to determine weighting coefficients of 10 χ m wij,k,l in Equation (3). For this purpose, a simultaneous equation is used which is composed of temperatures uA(xA, yAj, z%, tl) in 2 χ n times, which are the temperatures at the 10 temperature measurement points 81a to 81e and 82a to 82e. Here, n > m is established. n = m can be established. Furthermore, the value of the coordinate (xAi, yAj, z%, tl) of the time-space coordinates can be the same as the origin term (xi, yj, zk, tl). In this case, 20 χ n simultaneous equations are needed to determine the weighting coefficients of 10 χ m wij,k,l are expressed by the following equation (4). Incidentally, in Petition 870250088767, dated 09 / 30 / 2025, p. 142 / 171 / 68 equation (4), for convenience of notation, only two of the 20 xn simultaneous equations (the simultaneous equations in the case of l = 1, 2n) are illustrated. [Mathematical expression 4]

[00140] The matrix that stores the temperature uA in equation (4) is denoted as U(eR(2n x 5) x1). Furthermore, the matrix that stores the basis function φ in equation (4) is denoted as Φ(eR(2n x 5) x (2m x 5)). Additionally, the matrix (vector) that stores the weighting coefficient w in equation (4) is denoted as W(eR(2m x 5) x1). Furthermore, the matrix (vector) that stores an error term between a left-hand and right-hand side of equation (4) is denoted as e(e(2n x 5) x1). Therefore, equation (4) can be rewritten as the following equation (5). Incidentally, T represents a transpose matrix. To obtain a least squares solution for the matrix W, a cost function J: Petition 870250088767, dated 09 / 30 / 2025, pages 143 / 171 / 68 R(2n x 5) x 1^ R in equation (6) below for the matrix and is used. Here, y(gR) is a regularization coefficient needed to compensate for the stability of a 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(eZ(2m x 5) x (2m x 5)) is a unitary matrix. Incidentally, 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). [Mathematical equation 5]

[00141] The matrix W (weighting coefficient wij,k,l) ​​can be calculated from Equation (8). However, in an inverse problem, solving the inverse matrix on the right-hand side of equation (8) can cause the solution to be unstable due to error amplification. Thus, in this embodiment, the matrix Φ is subjected to singular value decomposition, as illustrated in Equation (9) below. Here, S(eR(2n x 5) x (2n x 5)) is a left-side singular value matrix. Σ(eR(2n x 5) x (2m x 5)) is a diagonal matrix in which singular values ​​are stored. V(eR(2m x 5) x (2m x 5)) is a right-side singular value matrix. Then, the matrix W is expressed by the following equation (10). This method explains, as an example, the case in which part 62 of the inverse problem analysis calculates the matrix W from Equation (10). Petition 870250088767, dated 09 / 30 / 2025, pp. 144 / 171 / 68 [Mathematical equation 6]

[00142] Part 62 of the inverse problem analysis performs the above processing, for example, every time part 61 of temperature acquisition acquires the measured values ​​from the fiber optic temperature sensors 111 to 112. Thus, the matrix W (weighting coefficient wij,k,l) ​​is calculated at each instant t (each measurement instant) of the time interval of the temperature measurement period.

[00143] Next, part 62 of the inverse problem analysis calculates the value of an interpolation / extrapolation temperature function u(x, y, z, t) by substituting the weighting coefficient wij,k,l, a thermal diffusivity α2 of the precast block 9, the time (reference time) tc (= tl) when the measured values ​​from the optical fiber temperature sensors 111 to 112 were acquired, and the coordinates (xAi, yAj, zAk) (= (xi, yj, zk)) of the temperature measurement points 81a to 81e and 82a to 82e into equation (3) and defines the calculated value as the temperature u(x, y, z, t).

[00144] Here, heat in the direction of the thickness of the region where the precast block 9 is present is transferred in the order of inside the furnace ^ adhesive substances on the inner circumferential surface 6a ^ the wear brick 7 ^ the precast block 9 ^ the furnace casing 10 ^ outside the furnace. Incidentally, it is possible that there are no adhesive substances present on the inner circumferential surface 6a. As described earlier, in the region between the wear brick 7 and the precast block 9, and in the region between the precast block 9 and the furnace casing 10, there is material necessary to connect (fix) them. In addition, voids may occur in these regions. Therefore, these regions result in regions that hinder heat transfer. Therefore, when performing a rigorous heat transfer calculation, it is Petition 870250088767, dated 09 / 30 / 2025, pp. 145 / 171 / 68, it is necessary to consider the values ​​of the physical properties of these regions. Thus, the inverse problem of three-dimensional heat transfer in a non-steady state can be formulated considering the values ​​of the physical properties of these regions. However, it is not easy to determine the values ​​of the physical properties of these regions. Furthermore, the values ​​of the physical properties differ depending on the type of adhering substances and, therefore, it is not easy to determine the values ​​of the physical properties of the adhering substances.

[00145] The present authors conducted a comprehensive investigation based on the above. As a result, the present authors verified that if the thermal diffusivity of precast block 9 is used as the thermal diffusivity (the square root of α) when calculating the weighting coefficient wi,j,k,l, the accuracy of the temperature calculated by the interpolation / extrapolation temperature function u(x, y, z, t) satisfies the accuracy required for practical use (it can be approximated to the actual measured value), even if no other thermal diffusivity is used when calculating the weighting coefficient wi,j,k,l (see an example calculation described later (Fig. 11)).

[00146] When the thermal diffusivity of precast block 9 is used as thermal diffusivity (the square root of α), the value of the interpolation / extrapolation temperature function u(x, y, z, t) basically becomes the temperature of precast block 9. In other words, when the thermal diffusivity of precast block 9 is used as thermal diffusivity (the square root of α), it is necessary to define the coordinate range (x, y, z) in the xyz coordinate system to which the interpolation / extrapolation temperature function u(x, y, z, t) is applied to the coordinates of the precast block 9 region. However, the present descriptors verified that even if the coordinates (x, y, z) are treated as coordinates of a region different from precast block 9, the accuracy of the function value remains. Petition 870250088767, dated 09 / 30 / 2025, page 146 / 171 / 68 The interpolation / extrapolation temperature function u(x, y, z, t) satisfies the precision required for practical use. Thus, this embodiment explains, as an example, the case where the thermal diffusivity of precast block 9 is used as the thermal diffusivity (the square root of α) included in the interpolation / extrapolation temperature function u(x, y, z, t), and the thermal diffusivities of other members are not used. For example, when optical fibers 121 to 122 are incorporated into permanent brick 8, the thermal diffusivity of permanent brick 8 is used, and the thermal diffusivities of other members are not used.

[00147] As above, this embodiment explains, as an example, the case where the temperature at each position of the electric arc furnace 1, including the side wall portion 6, is calculated based on the value of the interpolation / extrapolation temperature function u(x, y, z, t) in Equation (3). This embodiment explains, as an example, the case where the installation status monitoring device 100 calculates the position of the inner circumferential surface 6a in the thickness direction. Therefore, this embodiment explains, as an example, the case where part 62 of the inverse problem analysis calculates the temperature distribution of at least the side wall portion 6 in the thickness direction (x-axis direction) based on the value of the interpolation / extrapolation temperature function u(x, y, z, t) in Equation (3).

[00148] More specifically, this embodiment explains, as an example, the case where part 62 of the inverse problem analysis calculates the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) at the y- and z-coordinates of the hot spot centroid positions 81a and 82a. The position (y- and z-coordinates) at which the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) is calculated is preferably defined for the hot spot centroid positions 81a. Petition 870250088767, dated 09 / 30 / 2025, pp. 147 / 171 / 68 and 82a. This occurs because it is possible to calculate the temperature distribution of the sidewall portion 6 in the thickness direction (x-axis direction) at the position where wear is expected to have progressed the most.

[00149] However, the position (the y-coordinate and z-coordinate) at which the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) is calculated is not limited to the position of the centroid of the hot spot 81a or 82a.

[00150] For example, part 62 of the inverse problem analysis can calculate the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) at the hot spot around areas 81b to 81e and 82b to 82e, in addition to or instead of the hot spot centroid positions 81a and 82a.

[00151] Furthermore, for example, there may be a case where it is impossible to identify the hot spot region 71. In this case, part 62 of the inverse problem analysis does not need to identify the hot spot region 71. For example, part 62 of the inverse problem analysis can replace the position of the hot spot region 71 with a predefined position and calculate the temperature distribution of the sidewall portion 6 in the thickness direction (x-axis direction) at the replaced position, as described above. The position (the aforementioned predefined position) with which the position of the hot spot region 71 is replaced can be, for example, a position where the hot spot is expected to occur.Furthermore, the position with which the position of the hot spot region 71 is replaced may be a position that is scheduled to be repaired, or it may be another position (for example, a position defined to manage a time transition of the electric arc furnace state 1). <<Parte de cálculo da posição refratária 63> >

[00152] Part 63 of the refractory position calculation calculates the position of the inner circumferential surface 6a in the thickness direction based on Petition 870250088767, dated 09 / 30 / 2025, page 148 / 171 / 68 temperature distribution of the side wall portion 6 in the thickness direction calculated by part 62 of the inverse problem analysis. This embodiment explains, as an example, the case where part 62 of the inverse problem analysis calculates the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a. Therefore, this embodiment explains, as an example, the case where the refractory position calculation part 63 calculates the x-coordinate of the inner circumferential surface 6a in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a.

[00153] For example, part 63 of the refractory position calculation calculates, as the x-coordinate of the inner circumferential surface 6a, the position (x-coordinate) in the thickness direction where the temperature is the same as the molten metal temperature in the temperature distribution of the sidewall portion 6 in the thickness direction (x-axis direction). The molten metal temperature can be a measured value or an estimated value (a target value or a calculated value). Incidentally, when the temperature distribution of the sidewall portion 6 in the thickness direction (x-axis direction) is calculated at a y-coordinate different from the z-coordinate of the hot spot centroid positions 81a and 82a, for example, the temperature of the position in the furnace that has the same y-coordinate as the different z-coordinates of the hot spot centroid positions 81a and 82a can be used instead of the molten metal temperature.

[00154] Wearing brick 7 forms the inner circumferential surface 6a and therefore the state of wearing brick 7 can be identified by the x-coordinate of the inner circumferential surface 6a. For example, when the xyz coordinate system is determined as illustrated in Fig. 9A and Fig. 9B, a smaller value of the x-coordinate corresponds to the fact that Petition 870250088767, dated 09 / 30 / 2025, page 149 / 171 / 68, states that the depth WLx of the worn portion 92 becomes deep (i.e., it corresponds to the fact that the thickness of the wear brick 7 decreases). On the other hand, a larger value of the x coordinate corresponds to the fact that the adhering substances are on the inner circumferential surface 6a (the wear brick 7).

[00155] Here, the length in the thickness direction (x-axis direction) from the furnace shell 10 to the inner circumferential surface 6a is called the equivalent refractory length. This embodiment explains, as an example, the case where the equivalent refractory length is obtained by calculating the difference between the x-coordinate of the furnace shell 10 and the x-coordinate of the inner circumferential surface 6a at the y-coordinate and z-coordinate of the centroid positions of the hot spot 81a and 82a.

[00156] For example, part 63 of the refractory position calculation stores the equivalent refractory length in a new electric arc furnace 1 as a current value of the equivalent refractory length. The equivalent refractory length in the new electric arc furnace 1 is, for example, a design value. When the subsequently calculated equivalent refractory length is less than the current value of the equivalent refractory length, part 63 of the refractory position calculation determines that the thickness of the wear brick 7 has decreased. Then, part 63 of the refractory position calculation updates the current value of the equivalent refractory length to the calculated equivalent refractory length.On the other hand, when the calculated equivalent refractory length is greater than the actual value of the equivalent refractory length, part 63 of the refractory position calculation calculates the difference between the calculated equivalent refractory length and the actual value of the equivalent refractory length as the thickness of the adhering substances (length in the thickness direction (x-axis direction)). Incidentally, the method for managing the wear brick condition 7 uses the equivalent refractory length. Petition 870250088767, dated 09 / 30 / 2025, pp. 150 / 171 / 68 is not limited to the method described above. For example, part 63 of the refractory position calculation can calculate the increase or decrease in the equivalent refractory length from the previous value. <<Parte de emissão 64> >

[00157] Emission part 64 emits information about the state of the inner circumferential surface. The information about the state of the inner circumferential surface is information about the x-coordinate of the inner circumferential surface 6a (the position of the inner circumferential surface 6a in the thickness direction) calculated by the refractory position calculation part 63. The state information of the inner circumferential surface is not limited to the x-coordinate of the inner circumferential surface 6a. For example, the state information of the inner circumferential surface may be information calculated using the x-coordinate of the inner circumferential surface 6a. For example, emission part 64 emits at least one of the current values ​​of the x-coordinate of the inner circumferential surface 6a and the current value of the equivalent refractory length.The transmission of information by the transmission part 64 is carried out, for example, by at least one of the following: displaying it on a computer monitor, transmitting it to an external device, and storing it on a storage medium external to the installation status monitoring device 100.

[00158] When measured values ​​from the optical fiber temperature sensors 111 to 112 are acquired during loading, the emitting part 64 can transmit information about the state of the inner circumferential surface during loading. Therefore, with the information on the state of the inner circumferential surface, a repair portion of the inner circumferential surface 6a can be identified during loading. The repair portion of the inner circumferential surface 6a can be identified by an operator or by the installation status monitoring device 100. For example, the monitoring device of Petition 870250088767, dated 09 / 30 / 2025, page 151 / 171 / 68, installation status 100 may include a repair portion identification part that identifies the repair portion based on the current x-coordinate value of the inner circumferential surface 6a. In this case, the repair portion identification part determines whether or not the current equivalent refractory length value is less than a limit value, for example. As a result of this determination, when the current equivalent refractory length value is less than the limit value, the repair portion identification part identifies the position of the inner circumferential surface 6a used when calculating the equivalent refractory length as the repair portion. Furthermore, the limit value is determined based on the thickness (length in the x-axis direction) of the wear brick 7 whose function as a refractory is impaired.When the installation status monitoring device 100 calculates the repair part in this way, the emission part 64 can emit information indicating the repair part as the status information of the inner circumferential surface. Then, the repair part identified in the manner described above is repaired. The repair is carried out, for example, by filling the worn part 92 with a repair material. Incidentally, the refractory repair method can be achieved by a well-known technique, and therefore a detailed explanation of the method is omitted here.

[00159] Furthermore, with information on the state of the inner circumferential surface during loading, there is a risk that the contents inside the furnace (molten metal or similar) may be discharged from the side wall portion 6 to the outside of the furnace, and thus it is possible to determine whether or not the operation should be interrupted or stopped. This determination can be made by an operator or identified by the installation status monitoring device 100. For example, the installation status monitoring device 100 may include a continuation of operation determination section that determines whether or not the operation of the electric arc furnace 1 should be continued based on the current value of Petition 870250088767, dated 09 / 30 / 2025, page 152 / 171 / 68 coordinate x of the inner circumferential surface 6a. The part determining the continuation of the operation may determine whether or not to continue the operation (i.e., to interrupt or stop the operation) when the current value of the equivalent refractory length is less than a limit value, for example. The limit value is determined based on the thickness (length in the x-axis direction) of the wear brick 7 whose function as a refractory is impaired, for example. Incidentally, the limit value used to determine whether or not to continue the operation of the electric arc furnace 1 is preferably defined as a value less than the limit value used to calculate the repair part described above. In this case, the latter limit value is a length with a greater margin than the previous limit value for the thickness of the wear brick 7 whose function as a refractory is impaired.When the installation status monitoring device 100 determines whether or not to continue operating the electric arc furnace 1 in this manner, the emitting part 64 can emit information indicating the result of the determination, such as information on the condition of the inner circumferential surface. <fluxograma>

[00160] Next, an example of the installation status monitoring method to be performed using the installation status monitoring device 100 in this mode is explained with reference to a flowchart in Fig. 10. Moreover, information that can be defined in advance before the start of the flowchart in Fig. 10 has been stored in the installation status monitoring device 100 via the input device. Furthermore, the flowchart in Fig. 10 is obtained by a processor included in the installation status monitoring device 100 executing a program stored in memory, for example.

[00161] First, in Step S1001, the temperature acquisition part Petition 870250088767, dated 09 / 30 / 2025, pp. 153 / 171 / 68 acquires the measured values ​​from the optical fiber temperature sensors 111 to 112. This embodiment explains, as an example, the case in which the temperature acquisition part 61 acquires the temperature at each position in the optical fibers 121 to 122 at plural times t1, ..., tm.

[00162] Next, in Step S1002, part 62 of the inverse problem analysis calculates the temperatures uA(xAi, yAj, zAk, tl) at the temperature measurement points 81a to 81e and 82a to 82e based on the measured values ​​from the fiber optic temperature sensors 111 to 112. Then, the processing is performed in Step S1003.

[00163] Here, the temperature measurement points 81a to 81e and 82a to 82e include the centroid positions of hot spot 81a and 82a (positions of hot spot region 71). In Step S1002, when a plurality of positions are obtained as the centroid positions of hot spot 81a and 82a (positions of hot spot region 71), the surrounding areas of hot spot 81b to 81e are calculated for the centroid position of hot spot 81a and the surrounding areas of hot spot 82b to 82e are calculated for the centroid position of hot spot 82a.

[00164] Thus, Fig. 10 illustrates, as an example, the case in which, in single parts of the processing in Steps S1003 to S1106, the temperatures uA(xAi, yAj, zAk, tl) at the temperature measurement points 81a to 81e and 82a to 82e for a hot spot region 71 are used.

[00165] In step S1003, part 62 of the inverse problem analysis calculates the weighting coefficient wij,k,l of the interpolation / extrapolation temperature function u(x, y, z, t) in Equation (3) based on the temperatures irÉvj, yAj, zAk, tl) calculated in Step S1002.

[00166] Next, in Step S1004, part 62 of the inverse problem analysis calculates the value of the interpolation / extrapolation temperature function u(x, y, z, t) (i.e., the temperature u(x, y, z, t)) by substituting the weighting coefficient wij,k,l calculated in Step S1003, as Petition 870250088767, dated 09 / 30 / 2025, page 154 / 171 / 68 time coordinates (xAi, yAj, zAk, ti) (= (xi, yj, zk, ti)) of the temperature measurement points 81a to 81e and 82a to 82e, and the thermal diffusivity α2 of the precast block 9 in Equation (3).

[00167] Next, in Step S1005, part 62 of the inverse problem analysis calculates the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a based on the value of the interpolation / extrapolation temperature function u(x, y, z, t).

[00168] Next, in Step S1006, based on the temperature distribution of the side wall portion 6 in the thickness direction (x-axis direction) in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a calculated in Step S1005, the refractory position calculation part 63 calculates the position of the inner circumferential surface 6a in the thickness direction (x-coordinate) in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a.

[00169] Next, in Step S1007, the installation status monitoring device 100 determines whether or not processing has been performed in all hotspot regions 71. As a result of this determination, when processing has not been performed in all hotspot regions 71 (in the case of NO in Step S1007), processing in Step S1003 is performed. Then, in steps S1003 to S1006, the inverse problem analysis part 62 and the refractory position calculation part 63 calculate the position of the inner circumferential surface 6a in the thickness direction in the y-coordinate and z-coordinate of the hot spot centroid positions 81a and 82a of the hotspot region 71 in which processing has not been performed.

[00170] So, in Step S1007, when it is determined that processing has been performed in all access point regions 71 (in the case of SIM in Step S1007), processing in Step S1008 is executed. Petition 870250088767, dated 09 / 30 / 2025, pages 155 / 171 / 68 In Step S1008, emission part 64 emits the state information of the inner circumferential surface. When the plural hot spot regions 71 are obtained in Step S1002, in the repetitive processing in Steps S1003 to S1006, the same number of positions as the number of hot spot regions 71 is calculated as the position of the inner circumferential surface 6a in the thickness direction. Therefore, in this case, emission part 64 emits the state information of the inner circumferential surface for each of the plural positions of the inner circumferential surface 6a in the thickness direction. When the processing in Step S1008 is completed, the processing according to the flowchart in Fig. 10 will be completed. Example of calculation

[00171] The following is an example calculation. In this example calculation, the portion of the side wall 6 to be subjected to the analysis of the three-dimensional non-steady-state inverse heat transfer problem was defined as a portion of the side wall modeled as illustrated in Fig. 9A and Fig. 9B. In this example calculation, the x-coordinate of the inner circumferential surface 6a of the portion of the side wall 6 modeled in this way was calculated when the analysis of the three-dimensional non-steady-state inverse heat transfer problem was performed as explained in this embodiment and when the one-dimensional non-steady-state inverse heat transfer problem was performed.

[00172] The weathered portion 92 was assumed to be formed at the center of the yz plane of the model, and the lengths WLx, WLy, and WLz of the weathered portion 92 in the respective directions were defined as 0.14 m, 0.2 m, and 0.2 m (WLx = 0.14, WLy = WLz = 0.2), respectively. Furthermore, a height (length in the height direction (z-axis direction)) ZB, a width (length in the circumferential direction (y-axis direction)) YB, and a thickness (length in the thickness direction (x-axis direction)) XB of the modeled sidewall portion 6 were defined as 1 m, 1 m, and 0.46 m. Petition 870250088767, dated 09 / 30 / 2025, page 156 / 171 / 68 (ZB = YB = 1, XB = 0.46), respectively. Furthermore, a distance Δχ^ in the thickness direction (x-axis direction) from the outer circumferential surface 6b of the modeled sidewall portion 6 to the inner optical fiber 121 was defined as 0.14 m (Axm = 0.14), and, in addition, a distance Δxout in the thickness direction (x-axis direction) from the outer circumferential surface 6b of the modeled sidewall portion 6 to the outer optical fiber 122 was defined as 0.04 m (Axout = 0.04). Therefore, the distances Ay1 and Δy2 illustrated in Fig. 8A and Fig. 8B were defined as 0.05 m (Ay1 = Δy2 = 0.05). That is, the distances Ay1 and Δy2 were defined as 1 / 4 of the width WLy of the worn part 92. Furthermore, the distances Δζι and Δζ2 illustrated in Fig. 8A and Fig. 8B were defined as 0.05 m (Δζι = Δζ2 = 0.05). That is, the distances Δζι and Δζ2 were defined as 1 / 4 of the height WLz of the worn part 92.

[00173] Under the above conditions, the temperatures of the side wall portion 6 in the thickness direction (x-axis direction) in the y-coordinate and z-coordinate of the centroid positions of the hot spot 81a and 82a were calculated. In this case, the temperature measurement period was set to 0.01 h. Furthermore, the number of temperature measurements m was set to 50 (m = 50). Additionally, as a model parameter for the inverse problem of non-steady-state heat transfer, the time shift T (see Equation (1)) was set to 35 hr. Furthermore, the regularization coefficient γ (see Equation (6)) was set to 0.00000000001 (γ = 0.00000000001). Incidentally, the model parameter for the inverse problem of non-steady-state heat transfer can be determined according to the degree of instability.

[00174] Furthermore, the temperature of each part of the model was given as a true value. The actual values ​​(temperatures) at the temperature measurement points 81a to 81e and 82a to 82e were extracted and the inverse problem of non-steady-state heat transfer was Petition 870250088767, dated 09 / 30 / 2025, pp. 157 / 171 / 68 completed. Moreover, in the inverse problem of non-stationary one-dimensional heat transfer, the temperature measurement point is the two centroid positions of the hot spot 81a and 82a. The yea coordinate z coordinate at the center of gravity position of the worn part 92 were the yea coordinate z coordinate of the centroid positions of the hot spot 81a and 82a. Furthermore, a temperature TM of the inner circumferential surface 6a was 1665°C (TM = 1665).

[00175] Fig. 11A and Fig. 11B are shown, each illustrating an example of the relationship between a refractory temperature and a refractory thickness direction distance. The refractory temperature is the value (temperature) of the interpolation / extrapolation temperature function u(x, y, z, t) calculated by analyzing the inverse problem of non-steady-state heat transfer. The distance in the refractory thickness direction is the distance in the thickness direction (x-axis direction) of the outer circumferential surface 6b of the model.

[00176] Fig. 11A illustrates the results obtained by performing the analysis of the inverse problem of non-steady-state heat transfer in three dimensions, as explained in this embodiment. Fig. 11B illustrates the results obtained by performing the inverse problem of non-steady-state heat transfer in one dimension in the analysis of the inverse problem of non-steady-state heat transfer in three dimensions explained in this embodiment, where the direction of heat transfer is limited only to the thickness direction.

[00177] As described previously, the temperature TM of the inner circumferential surface 6a was 1665°C (TM = 1665). The distance from the direction of the refractory thickness at temperature TM (= 1665°C) of the inner circumferential surface 6a is the equivalent refractory length described previously.

[00178] As illustrated in Fig. 11A, the calculated value is close Petition 870250088767, dated 09 / 30 / 2025, page 158 / 171 / 68 to the actual value in the method explained in this modality. Furthermore, the distance of the refractory thickness direction at temperature Tm (= 1665°C) from the inner circumferential surface 6a was 0.323 m. In Fig. 9A and Fig. 9B, the thickness of the side wall portion 6 in the worn portion 92 (= XB - WLx) is 0.32 (= 0.46 - 0.14). It can be observed that as the refractory thickness advances in the direction of the distance (=0.323 m) at temperature Tm (=1665°C) from the inner circumferential surface 6a, a value close to the thickness (= 0.32 m) of the side wall portion 6 in the worn portion 92 is obtained.

[00179] In contrast to this, as illustrated in Fig. 11B, when the inverse problem analysis of one-dimensional non-steady-state heat transfer was performed, the calculated value was smaller than the actual value. Furthermore, the distance from the refractory thickness direction at temperature Tm (= 1665°C) to the inner circumferential surface 6a was 0.371 m, which was significantly different from the actual value (= 0.32 m).

[00180] As above, the results of the comparison between Fig. 11A and Fig. 11B reveal that, unless heat transfers in the y-axis direction and z-axis direction are considered, there is a risk that the accuracy of the calculation of the position of the inner circumferential surface in the thickness direction may decrease, whereas considering heat transfers in the y-axis direction and z-axis direction as in this embodiment makes it possible to improve the accuracy of the calculation of the position of the inner circumferential surface 6a in the thickness direction. Furthermore, Fig. 11A reveals that using the thermal diffusivity of the precast block 9 as the thermal diffusivity (the square root of α) included in the interpolation / extrapolation temperature function u(x, y, z, t) makes it possible to calculate the position of the inner circumferential surface 6a in the thickness direction with high accuracy without using the thermal diffusivities of other members. <hardware>

[00181] The following explains an example of the device's hardware. Petition 870250088767, dated 09 / 30 / 2025, page 159 / 171 / 68, concerning the installation status monitoring device 100. In Figure 12, the installation status monitoring device 100 includes a CPU 1201, a main memory 1202, an auxiliary memory 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.

[00182] CPU 1201 controls the entire installation status monitoring device 100. CPU 1201 uses main memory 1202 as a workspace to execute a program stored in auxiliary memory 1203. Main memory 1202 stores data temporarily. Auxiliary memory 1203 stores various data, in addition to programs to be executed by CPU 1201.

[00183] Communication circuit 1204 is a circuit intended to perform communication with the external part of the installation status monitoring device 100. Communication circuit 1204 can perform radio communication or wired communication with the exterior of the installation status monitoring device 100.

[00184] The signal processing circuit 1205 performs various signal processing fragments on signals received in the communication circuit 1204 and input signals according to the control by the CPU 1201.

[00185] The image processing circuit 1206 performs various image processing fragments on input signals according to the control by the CPU 1201. The signal that has undergone image processing is output to the monitor 1209, for example.

[00186] The user interface 1208 is a part through which an operator provides instructions to the installation status monitoring device 100. The user interface 1208 includes, for example, buttons, switches, displays, and so on. Furthermore, the interface of Petition 870250088767, dated 09 / 30 / 2025, page 160 / 171 / 68 user 1208 can also include a graphical user interface using monitor 1209.

[00187] Monitor 1209 displays an image based on the emission signal from the image processing circuit 1206. I / F circuit 1207 exchanges data with a device connected to I / F circuit 1207. Fig. 12 illustrates user interface 1208 and monitor 1209 as the device to be connected to I / F circuit 1207. However, the device to be connected to I / F circuit 1207 is not limited to these devices. For example, a portable storage medium can be connected to I / F circuit 1207. Furthermore, at least part of user interface 1208 and monitor 1209 can be provided for the external part of the installation status monitoring device 100.

[00188] Moreover, CPU 1201, main memory 1202, auxiliary memory 1203, signal processing circuit 1205, image processing circuit 1206, and I / F circuit 1207 are connected to bus 1210. Communication between these components is carried out via bus 1210. Furthermore, the hardware of the facility status monitoring device 100 is not limited to the hardware illustrated in Fig. 12, provided it can perform the functions of the facility status monitoring device 100. For example, a GPU can be used as a processor instead of or in addition to CPU 1201. Furthermore, the hardware of the facility status monitoring device 100 is also manufactured, for example, from the same hardware as the facility status monitoring device 100 illustrated in Fig. 12. Therefore, a detailed explanation of a specific example of the hardware of the facility status monitoring device 100 is omitted here. < Summary >

[00189] As above, in this mode, in the electric arc furnace 1, which is an example of the installation in which molten metal is present during the Petition 870250088767, dated 09 / 30 / 2025, pp. 161 / 171 / 68 operation, the inner circumferential surface 6a of the side wall portion 6 is formed of a refractory material. Furthermore, the optical fibers 121 to 122 included in the optical fiber temperature sensors 111 and 112 are incorporated into the member that forms the side wall portion 6. Therefore, as the temperature of the side wall portion 6, temperatures in a wider range can be measured.

[00190] Furthermore, in this embodiment, the precast block 9 is used as the member that forms the side wall portion 6. The precast block 9 is a fire-resistant block manufactured from a monolithic refractory material, precast with the optical fibers 121 to 122 incorporated therein. Therefore, this facilitates the installation of the optical fibers 121 to 122. In addition, it is possible to inhibit the occurrence of variations in temperature measurement errors caused by the optical fiber temperature sensors 111 to 112.

[00191] Furthermore, in this embodiment, the installation status monitoring device 100 calculates the temperature distribution of the sidewall portion 6 in the thickness direction, performing the inverse analysis of the three-dimensional non-steady-state heat transfer problem based on the measured values ​​of the optical fiber temperature sensors 111 to 112. Then, the installation status monitoring device 100 calculates, as the position of the inner circumferential surface 6a, the position, including the position of the sidewall portion 6 in the thickness direction, based on the temperature distribution of the sidewall portion 6 in the thickness direction. Therefore, the state of the inner circumferential surface 6a can be easily monitored with high precision. Moreover, even when molten metal or similar is present in the furnace, the state of the inner circumferential surface 6a can be monitored.

[00192] In addition, in this embodiment, the installation status monitoring device 100 acquires five temperatures per location of the sidewall portion 6 in the thickness direction as the temperature required for Petition 870250088767, dated 09 / 30 / 2025, pp. 162 / 171 / 68 calculate a single position of the inner circumferential surface 6a in the thickness direction. Therefore, the number of temperatures to be used when performing the inverse analysis of the three-dimensional non-steady-state heat transfer problem can be optimized.

[00193] Furthermore, in this mode, the installation status monitoring device 100 acquires the temperatures at positions 81a and 82a of the centroid of the hot spot. Therefore, it is possible to consider heat transfers in respective three-dimensional directions in the region that includes the hot spot.

[00194] Furthermore, in this mode, the installation status monitoring device 100 performs the inverse analysis of the three-dimensional non-steady-state heat transfer problem using only the physical property value (thermal diffusivity) of the precast block 9 among the physical property values ​​(thermal diffusivities) of the members forming the side wall portion 6. Therefore, it is possible to avoid the inverse non-steady-state heat transfer problem becoming a complicated problem. Additionally, it is possible to avoid a decrease in calculation accuracy caused by the introduction of assumptions about phenomena that are difficult to estimate in the inverse non-steady-state heat transfer problem.

[00195] Furthermore, in this embodiment, the fiber optic temperature sensor 111, which measures the temperature in a relatively internal position, and the fiber optic temperature sensor 112, which measures the temperature in a relatively external position, are designed to be separate temperature sensors. This facilitates the installation of fiber optic temperature sensors 111 and 112.

[00196] Furthermore, in this embodiment, the precast block 9 with the optical fibers 121 and 122 incorporated in it is installed in a partial region of the region where the permanent brick 8 is installed. This allows avoiding the Petition 870250088767, dated 09 / 30 / 2025, pp. 163 / 171 / 68 wear and tear of precast block 9. (Other modified examples)

[00197] Incidentally, the embodiment of the present description explained above can be implemented by having a computer execute a program. Furthermore, a computer-readable recording medium on which the aforementioned program is recorded and a computer program product such as the aforementioned program can also be applied as the embodiment of the present description. As a recording medium, it is possible to use a floppy disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM or similar, for example.

[00198] Furthermore, the embodiment of the present description explained above merely illustrates concrete examples of implementation of the present description, and the technical scope of the present description should not be interpreted restrictively by the embodiment. That is, the present description can be implemented in various ways without departing from its technical spirit or main characteristics. INDUSTRIAL APPLICABILITY

[00199] The present description can be used for an installation in which molten metal is present during operation, for example. Petition 870250088767, dated 09 / 30 / 2025, pages 164 / 171< / hardware> < / fluxograma>

Claims

1 / 6 CLAIMS 1. Installation (1) in which molten metal is present during operation, characterized in that an inner circumferential surface (6a) of a portion of the side wall (6) of the installation (1) is formed by a refractory (7) and an optical fiber (121, 122) included in an optical fiber temperature sensor (111, 112) is incorporated into a member that forms the portion of the side wall (6).

2. Installation (1) according to claim 1, characterized in that of the member forming the side wall portion (6), a member in which the optical fiber (121, 122) is incorporated is a fire-resistant block (9) manufactured from a monolithic refractory being pre-molded with the optical fiber (121, 122) incorporated therein.

3. Installation (1) according to claim 1 or 2, characterized in that it comprises: a temperature sensor that measures a temperature at a position of the side wall portion (6) on a side of the relatively inner circumferential surface; and a temperature sensor that measures a temperature at a position of the side wall portion (6) on a side of the relatively outer circumferential surface, wherein the temperature sensor that measures the temperature at the position of the side wall portion (6) on the side of the relatively inner circumferential surface is the fiber optic temperature sensor (111).

4. Installation (1) according to claim 3, characterized in that the temperature sensor that measures the temperature at the position of the side wall portion (6) on the side of the circumferential surface Petition 870250088767, dated 09 / 30 / 2025, page 165 / 171 2 / 6 relatively external is the fiber optic temperature sensor (112).

5. Installation (1) according to any one of claims 1 to 4, characterized in that: the member is present on the side of the outer circumferential surface of the side wall portion (6) in relation to the refractory (7) that forms the inner circumferential surface (6a) of the side wall portion (6).

6. Installation status monitoring device (100) that monitors an installation status (1) as defined in any one of claims 1 to 5, characterized in that the device comprises: an inverse problem analysis means (62) that calculates a temperature distribution of the sidewall portion (6) by performing a three-dimensional non-steady-state inverse heat transfer problem analysis based on a measured value from a temperature sensor that measures a temperature of the sidewall portion (6); and a refractory position calculation means (63) that calculates a position of the inner circumferential surface (6a) based on the temperature distribution calculated by the inverse problem analysis means (62), wherein the inverse problem analysis means (62) that calculates a temperature distribution of the sidewall portion (6) in a thickness direction,the position of the inner circumferential surface (6a) to be calculated by the means of calculating the refractory position (63) includes a position of the side wall portion (6) in the thickness direction, the temperature sensor measures a temperature at a position of the side wall portion (6) on a relatively inner side of the circumferential surface and a temperature at a position of the side wall portion (6) on a relatively outer side of the circumferential surface in a portion of the side wall portion (6) that is different from the inner circumferential surface (6a) of the side wall portion Petition 870250088767, dated 09 / 30 / 2025, page 166 / 171 3 / 6 (6),and the temperature sensor that measures at least the temperature at the position of the sidewall portion (6) on the relatively inner circumferential surface side between the temperature at the position of the sidewall portion (6) on the relatively inner circumferential surface side and the temperature at the position of the sidewall portion (6) on the relatively outer circumferential surface side is the fiber optic temperature sensor (111, 112).

7. Installation status monitoring device (100) according to claim 6, characterized in that of a member forming the side wall portion (6), a member in which the optical fiber (121, 122) is incorporated is a fire-resistant block (9) manufactured from a monolithic refractory being pre-molded with the optical fiber (121, 122) incorporated therein.

8. Installation status monitoring device (100) according to claim 6 or 7, characterized in that the temperature sensor that measures the temperature at the position of the side wall portion (6) on the relatively inner circumferential surface side and the temperature at the position of the side wall portion (6) on the relatively outer circumferential surface side is an optical fiber temperature sensor (111, 112) including an optical fiber (121, 122) incorporated in the member forming the side wall portion (6).

9. Installation status monitoring device (100) according to any one of claims 6 to 8, characterized in that the inverse problem analysis means (62) acquires N temperatures per place of the sidewall portion (6) in the thickness direction as temperatures needed to calculate a single position of the inner circumferential surface (6a) of the sidewall portion (6) in the thickness direction based on a measured value from the temperature sensor, and calculates a temperature distribution of the sidewall portion (6) in the thickness direction by performing a three-dimensional non-steady-state inverse heat transfer problem analysis based on the N temperatures, and N is an integer of two or more.

10. Installation status monitoring device (100) according to claim 9, characterized in that N is five.

11. Installation status monitoring device (100) according to any one of claims 6 to 10, characterized in that the inverse problem analysis means (62) acquires a temperature in a hot spot region, including a position where the temperature is locally maximum based on a measured value from the temperature sensor, and calculates a temperature distribution of the side wall portion (6) in the thickness direction, performing a three-dimensional non-steady-state inverse heat transfer problem analysis based on the acquired temperature.

12. Installation status monitoring device (100) according to any one of claims 6 to 11, characterized in that the inverse problem analysis means (62) performs the inverse problem analysis of heat transfer in a non-steady state in three-dimensional way using, from the physical property values ​​of the member forming the side wall portion (6), only the physical property value of the member in which the temperature sensor is embedded.

13. Installation state monitoring method that monitors an installation state (1) as defined in any of claims 1 to 5, characterized in that the method comprises: an inverse problem analysis step (S1003 to S1005) that calculates a temperature distribution of the sidewall portion (6) by performing a three-dimensional non-steady-state inverse heat transfer problem analysis based on a measured value from a temperature sensor measuring a temperature of the sidewall portion (6); and a refractory position calculation step (S1006) that calculates a position of the inner circumferential surface (6a) based on the temperature distribution calculated by the inverse problem analysis step (S1003 to S1005),wherein the inverse problem analysis step (S1003 to S1005) calculates a temperature distribution of the sidewall portion (6) in a thickness direction, the position of the inner circumferential surface (6a) to be calculated in the refractory position calculation step (S1006) includes a position of the sidewall portion (6) in the thickness direction, the temperature sensor measures a temperature at a position of the sidewall portion (6) on a relatively inner circumferential surface side and a temperature at a position of the sidewall portion on a relatively outer circumferential surface side in a portion of the sidewall portion (6) that is different from the inner circumferential surface (6a) of the sidewall portion (6),and the temperature sensor that measures at least the temperature at the position of the sidewall portion (6) on the relatively inner circumferential surface side between the temperature at the position of the sidewall portion (6) on the relatively inner circumferential surface side and the temperature at the position of the sidewall portion Petition 870250088767, dated 09 / 30 / 2025, page 169 / 171 6 / 6 (6) on the relatively outer circumferential surface side is the fiber optic temperature sensor (111, 112)., 14. Non-transient, computer-readable storage medium, characterized in that it stores instructions for the computer to perform the method as defined in claim 13. Petition 870250088767, dated 09 / 30 / 2025, pp. 170 / 171

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