Monitoring system, monitoring method, and computing device

Abstract

A monitoring system (1) comprises: a shaker (10) that vibrates a tubular structure (40) in each of a first axis direction and a second axis direction perpendicular to the first axis; one or more triaxial accelerometers (20) that are installed on the tubular structure (40) and measure acceleration each time the tubular structure (40) is vibrated in each of the first and second axis directions; and a computing device (30) that derives a vibration mode for each of the first and second axis directions on the basis of the measured values of the acceleration, and determines whether a U-bolt has fallen off or a supporting hardware has fallen off on the basis of the vibration mode.

Description

[Technical Field]

[0001] The present disclosure relates to a monitoring system, a monitoring method, and a computing device for remotely monitoring for failure of U-bolts and support hardware that secure tubular structures to fall off. [Background technology]

[0002] Traditionally, tubular structures have been fixed to various locations, including bridge girders, using U-bolts and support hardware. However, when a tubular structure vibrates, the U-bolts or support hardware that secure the tubular structure can loosen and fall off. For this reason, the condition of the U-bolts and support hardware that secure the tubular structure must be constantly monitored, and if any problems occur, they must be repaired promptly.

[0003] Non-Patent Document 1 describes the development and practical application of a bolt axial force measuring device that uses ultrasonic waves. According to Non-Patent Document 1, it is possible to detect loosening of hexagon bolts using an ultrasonic probe. However, there is no established method for detecting loosening of U-bolts using an ultrasonic probe. Furthermore, there is a cost issue in attaching a bolt axial force measuring device to each U-bolt.

[0004] Non-Patent Document 2 describes an experiment to detect vibration frequencies by hammering bridge suspension members. However, since tubular structures are installed in places with poor footing, such as bridge girders, it requires a lot of human effort to hit them by hammering. In addition, there is an issue of low reliability, as the logic for evaluating soundness has not been established. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Takayuki Makino and two others, "Development and Practical Application of a Bolt Axial Force Measuring Device Using Ultrasonic Waves," Japan Society for Precision Engineering, Precision Machinery, February 1977, Vol. 43, No. 506, pp. 223-232, Published [Non-patent document 2] Tetsuya Ito and two others, "Hammering Vibration Experiments of Hanging Members for the Purpose of Evaluating the Soundness of Bridge Components," Research Presentation Meeting of the Western Branch of the Japan Society of Civil Engineers (March 2009), pp. 75-76 (Published) Summary of the Invention [Problem to be solved by the invention]

[0006] When tubular structures are installed in places with poor footing, such as bridge girders, or in dangerous places such as the premises of nuclear power plants, constant monitoring of the tubular structures requires a great deal of human effort and time.

[0007] In consideration of the above circumstances, the object of the present invention is to provide a monitoring system, a monitoring method, and a computing device that monitors for failure to drop off U-bolts and support hardware by remotely receiving measurement values ​​from a three-axis accelerometer installed in a tubular structure via wired or wireless connection. [Means for solving the problem]

[0008] In order to solve the above problem, the monitoring system of this embodiment is a monitoring system that remotely monitors for failure to drop off U-bolts and support hardware that secure a tubular structure, and is equipped with a vibrator that vibrates the tubular structure in each of a first axial direction and a second axial direction perpendicular to the first axis, one or more triaxial accelerometers installed on the tubular structure that measure acceleration each time the tubular structure is vibrated in each of the first axial direction and the second axial direction, and a computing device that derives vibration modes in each of the first axial direction and the second axial direction based on the acceleration measurements, and determines whether the U-bolt or the support hardware has dropped off based on the vibration modes.

[0009] In order to solve the above problem, the monitoring method of this embodiment is a method for remotely monitoring for failure to drop off U-bolts and support hardware that secure a tubular structure, and includes the steps of: vibrating the tubular structure in each of a first axial direction and a second axial direction perpendicular to the first axis using a vibrator; measuring acceleration using one or more triaxial accelerometers each time the tubular structure is vibrated in each of the first axial direction and the second axial direction; deriving vibration modes in each of the first axial direction and the second axial direction based on the measured values ​​using a computing device; and determining, based on the vibration modes, whether the U-bolt or the support hardware has dropped off using the computing device.

[0010] In order to solve the above-mentioned problems, the calculation device according to this embodiment is a calculation device that determines whether a U-bolt or a support metal fastening a tubular structure has fallen off, and includes a receiving unit that receives acceleration measurement values ​​from one or more triaxial accelerometers each time the tubular structure is vibrated in each of a first axis direction and a second axis direction perpendicular to the first axis, a calculation unit that derives a vibration mode based on the measurement values ​​and determines whether the U-bolt or the support metal has fallen off based on the vibration mode, and a display unit that displays and visualizes the vibration mode. [Effects of the Invention]

[0011] According to the present disclosure, it is possible to constantly and remotely determine whether or not the U-bolt and support member have fallen off. [Brief explanation of the drawings]

[0012] [Figure 1] 1 is a block diagram illustrating a configuration example of a monitoring system according to an embodiment of the present disclosure. [Figure 2] 1 is a schematic diagram of a tubular structure in a healthy state. [Figure 3] FIG. 1 is a schematic diagram of a tubular structure with a U-bolt in a detached state. [Figure 4] This is a schematic diagram of a tubular structure in which the U-bolt and support hardware have fallen off. [Figure 5] FIG. 1 is a block diagram illustrating an example configuration of a computing device according to an embodiment of the present disclosure. [Figure 6] This is a diagram showing the vibration modes of a tubular structure when the U-bolts and supporting hardware are in a healthy state, based on ODS analysis. [Figure 7] FIG. 10 shows the vibration modes of a tubular structure with a U-bolt missing, as determined by ODS analysis. [Figure 8] FIG. 10 is a diagram showing the vibration mode of a tubular structure in a state where the U-bolt and the support metal fitting have fallen off, as determined by ODS analysis. [Figure 9] 1 is a graph of a frequency response function showing a characteristic vibration mode that detects a U-bolt falling out condition. [Figure 10] 1 is a graph of a frequency response function showing a characteristic vibration mode that detects a support hardware falling off. [Figure 11] 10 is a flowchart illustrating an example of a monitoring method executed by a monitoring system according to an embodiment of the present disclosure. [Figure 12] FIG. 1 is a block diagram showing a schematic configuration of a computer that functions as a computing device. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The present invention is not limited to the following embodiments, and various modifications can be made within the scope of the present invention.

[0014] <Monitoring system> Fig. 1 is a block diagram showing an example configuration of a monitoring system 1 according to an embodiment of the present disclosure. As shown in Fig. 1, the monitoring system 1 includes a vibrator 10, one or more triaxial accelerometers 20, and a computing device 30. The monitoring system 1 remotely monitors for failure of U-bolts 41 and support metal fittings 42 that secure a tubular structure 40 to fall off.

[0015] The tubular structure 40 is a pipe that supports social infrastructure and is laid at various locations, such as bridge girders, using U-bolts 41 and support metal fittings 42. FIG. 2 is a schematic diagram of the tubular structure 40 in a healthy state. In FIGS. 2 to 4, a horizontal direction (hereinafter referred to as the Y-axis direction) and a vertical direction (hereinafter referred to as the Z-axis direction) are defined. As shown in FIG. 2, the tubular structure 40 is fixed by the U-bolts 41 and support metal fittings 42. Here, the support metal fittings 42 include the support bases of the support metal fittings 42. One or more triaxial accelerometers 20 are installed on the tubular structure 40. The tubular structure 40 is vibrated by a vibrator 10. In FIGS. 2 to 4, as an example, the vibrator 10 vibrates the tubular structure 40 in the Z-axis direction. As will be described later, the vibrator 10 vibrates the tubular structure 40 in the Y-axis direction and then in the Z-axis direction. Figure 3 is a schematic diagram of a tubular structure 40 in which a U-bolt 41 has fallen off. As shown in Figure 3, the U-bolt 41 has come loose and fallen off at position a, which is surrounded by a dashed line in the center. One support metal fitting 42 is in a sound state. Figure 4 is a schematic diagram of a tubular structure 40 in which the U-bolt 41 and support metal fitting 42 have fallen off. As shown in Figure 4, the U-bolt 41 and support metal fitting 42 have come off the tubular structure 40 at position b, which is surrounded by a dashed line in the center.

[0016] The vibrator 10 vibrates the tubular structure 40 in each of a first axis direction and a second axis direction perpendicular to the first axis. The first axis direction is the horizontal direction (Y axis direction). The second axis direction is the vertical direction (Z axis direction). As shown in FIGS. 2 to 4, the Y axis and the Z axis are perpendicular to each other. In the example of FIGS. 2 to 4, the vibrator 10 vibrates the tubular structure 40 in the Z axis direction. Note that the vibrator 10 is not necessary when the tubular structure 40 is vibrating due to environmental vibrations.

[0017] One or more tri-axis accelerometers 20 are installed in the tubular structure 40. As shown in FIG. 1, the one or more tri-axis accelerometers 20 are composed of n tri-axis accelerometers 20-1 to 20-n. The tri-axis accelerometer 20-1 includes a measurement unit 21-1 that measures the acceleration of the tubular structure 40 and a transmission unit 22-1 that transmits the measurement value to a reception unit 31 of the calculation device 30. The tri-axis accelerometers 20-2 to 20-n also have the same configuration and function. The measurement units 21-1 to 21-n of the one or more tri-axis accelerometers 20 measure acceleration every time the tubular structure 40 is vibrated in each of a first axis direction (Y-axis direction) and a second axis direction (Z-axis direction) perpendicular to the first axis. The transmission units 22-1 to 22-n transmit the acceleration measurement values ​​to the reception unit 31 of the calculation device 30 via a wired connection or wirelessly via Wi-Fi or the like.

[0018] The computing device 30 derives the vibration mode in each of the first axis direction (Y axis direction) and the second axis direction (Z axis direction) based on the acceleration measurement values ​​measured by one or more three-axis accelerometers 20, and determines whether the U-bolt 41 or the support metal fitting 42 has fallen off based on the vibration mode. The computing device 30 will be described in detail below.

[0019] <Arithmetic device> Fig. 5 is a block diagram showing an example configuration of a calculation device according to an embodiment of the present disclosure. As shown in Fig. 5, the calculation device 30 includes a receiving unit 31, a calculation unit 32, and a display unit 33. The calculation device 30 determines whether or not U-bolts 41 and support metal fittings 42 that secure a tubular structure have fallen off. The calculation unit 32 constitutes a control calculation circuit (controller) 50. The control calculation circuit 50 may be constituted by dedicated hardware such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field-Programmable Gate Array), or may be constituted by a processor, or may be constituted by including both.

[0020] When the receiving unit 31 is vibrated in each of the first axial direction (Y direction) and the second axial direction (Z direction) orthogonal to the first axis of the tubular structure 40, the receiving unit 31 receives the measured values of the acceleration of the tubular structure 40 from the transmitting units 22-1 to 22-n of one or more triaxial accelerometers 20.

[0021] The calculation unit 32 derives the vibration mode based on the measured value of the acceleration, and determines whether the U-bolt 41 has fallen off or the support hardware 42 has fallen off based on the vibration mode.

[0022] We confirmed by experiments that there is a relationship between each dropout defect of the U-bolt 41 and the support hardware 42 for fixing the tubular structure 40 and the vibration direction when detecting the defect, as described in the following (i) to (iii). Refer to FIGS. 2 to 4 again.

[0023] (i) When the tubular structure 40 is vibrated in each of the first axial direction (Y direction) and the second axial direction (Z direction) orthogonal to the first axis, if it is stationary at the installation position of the U-bolt 41, the U-bolt 41 and the support hardware 42 are in a sound state. (Refer to FIG. 2)

[0024] (ii) When the tubular structure 40 is vibrated in the first axial direction (Y direction), if a specific vibration mode is detected at the installation position of the U-bolt 41, the U-bolt 41 is detached and in a dropped state. (Refer to FIG. 3)

[0025] (iii) When the tubular structure 40 is vibrated in the second axial direction (Z direction) orthogonal to the first axis, if a specific vibration mode is detected at the installation position of the U-bolt 41, the support hardware 42 is detached and in a dropped state. (Refer to FIG. 4)

[0026] <Vibration mode by ODS analysis> The calculation unit 32 may derive the vibration mode by ODS (Operating Deflection Shapes) analysis based on the measured values of one or more triaxial accelerometers 20.

[0027] The calculation unit 32 performs a fast Fourier transform (FFT) on the received measurement values. )) to calculate the amplitude and phase of the vibration, and by performing ODS analysis on the calculation results, the vibration mode of the tubular structure 40 is visualized and expressed. ODS analysis is a simulation technique that analyzes the vibration pattern of a structure under operating conditions and visualizes it using animation, etc. ODS analysis is also called operational analysis.

[0028] Fig. 6 is a diagram showing the vibration modes of a tubular structure in which U-bolt 41 and support metal fittings 42 are in a sound state (corresponding to Fig. 2) by ODS analysis. As shown in Fig. 6, calculation unit 32 determines that U-bolt 41 is in a sound state if the vibration mode in the first axial direction (Y-axis direction) does not fluctuate at the installation position of U-bolt 41 (position c surrounded by the dashed line in the center), and determines that support metal fittings 42 are in a sound state if the vibration mode in the second axial direction (Z-axis direction) does not fluctuate at the installation position of U-bolt 41 (position d surrounded by the dashed line in the center).

[0029] 7, when the vibration mode in the first axis direction (Y-axis direction) is displayed as a convex curve with an amplitude equal to or greater than the first threshold and with a maximum at the installation position of U-bolt 41 (position e surrounded by the dashed line in the center), calculation unit 32 determines that U-bolt 41 has fallen off. Since the vibration mode in the second axis direction (Z-axis direction) does not fluctuate at the installation position of U-bolt 41 (position f surrounded by the dashed line in the center), calculation unit 32 determines that support hardware 42 is in a sound state.

[0030] 8, the calculation unit 32 determines that the U-bolt 41 has also fallen off because the vibration mode in the first axis direction (Y-axis direction) is displayed as a convex curve having an amplitude equal to or greater than a first threshold value and having a maximum at the installation position of the U-bolt 41 (position g surrounded by the dashed line in the center). Furthermore, the calculation unit 32 determines that the support metal fitting 42 has fallen off when the vibration mode in the second axis direction (Z-axis direction) is displayed as a convex curve having an amplitude equal to or greater than a second threshold value and having a maximum at the installation position of the U-bolt 41 (position h surrounded by the dashed line in the center).

[0031] <Vibration modes based on frequency response functions> The calculation unit 32 may derive the vibration mode from the frequency response function based on the measurement values ​​of one or more three-axis accelerometers 20.

[0032] 9 is a graph of a frequency response function showing a specific vibration mode i that detects that the U-bolt 41 has fallen off. The calculation unit 32 determines that the U-bolt 41 has fallen off when the frequency response function derived based on the measured values ​​of the acceleration of the tubular structure 40 excited in the first axial direction (Y-axis direction) displays a vibration mode (vibration mode i surrounded by the dashed line in the center) having an amplitude equal to or greater than the third threshold in a specific frequency band. In FIG. 9, the specific frequency band is a frequency band around 70 Hz.

[0033] FIG. 10 is a graph of a frequency response function showing a specific vibration mode j that detects that the support metal has fallen off. When the frequency response function derived based on the measured acceleration of the tubular structure 40 excited in the second axial direction (Z-axis direction) displays a vibration mode (vibration mode j surrounded by a dashed line in the center) having an amplitude greater than a third threshold and equal to or greater than a fourth threshold in a specific frequency band, the calculation unit 32 determines that the support metal 42 has fallen off. In FIG. 10, the specific frequency band in which vibration mode j occurs is the same frequency band of around 70 Hz as vibration mode i. As shown in FIG. 10, vibration mode j has a larger amplitude than vibration mode i.

[0034] 9 and 10, if mode j specific to support hardware coming loose does not appear when the tubular structure 40 is vibrated in the Z-axis direction, and vibration mode i appears when the tubular structure 40 is vibrated in the Y-axis direction, it is determined that the detachment is due to loosening and coming loose of the U-bolt 41. On the other hand, if mode j specific to support hardware coming loose appears when the tubular structure 40 is vibrated in the Z-axis direction, it is determined that the detachment is due to the support hardware 42 coming loose.

[0035] The display unit 33 displays and visualizes the vibration modes in the Y-axis direction and the Z-axis direction based on the ODS analysis and the frequency response function. The display unit 33 is a display.

[0036] FIG. 11 is a flowchart illustrating an example of a monitoring method executed by a monitoring system according to an embodiment of the present disclosure.

[0037] In step S101, the vibrator 10 vibrates the tubular structure 40 in the Y-axis direction.

[0038] In step S102, the measuring units 21-1 to 21-n of one or more triaxial accelerometers 20 measure the acceleration of the tubular structure 40.

[0039] In step S103, the vibrator 10 vibrates the tubular structure 40 in the Z-axis direction.

[0040] In step S104, the measuring units 21-1 to 21-n of one or more triaxial accelerometers 20 measure the acceleration of the tubular structure 40.

[0041] In step S105, the transmitting units 22-1 to 22-n of one or more triaxial accelerometers 20 transmit the acceleration measurement values ​​measured in steps S102 and S104.

[0042] In step S106, the receiving unit 31 of the arithmetic device 30 receives the measurement value.

[0043] In step S107, the calculation unit 32 of the calculation device 30 derives the vibration modes in the Y-axis direction and the Z-axis direction.

[0044] In step S108, the display unit 33 of the computing device 30 displays the vibration modes in the Y-axis direction and the Z-axis direction.

[0045] In step S109, the calculation unit 32 of the calculation device 30 determines whether the U-bolt or the support metal fitting has fallen off.

[0046] As described above, there is a relationship between the direction in which vibration occurs and the defective state of U-bolt 41 and support metal fittings 42. According to monitoring system 1 of the present disclosure, by observing vibrations for each direction of vibration, it is possible to constantly and remotely determine whether U-bolt 41 and support metal fittings 42 have fallen off.

[0047] A computer capable of executing program instructions can be used to operate the arithmetic unit 30. Fig. 12 is a block diagram showing a schematic configuration of a computer that functions as the arithmetic unit 30. The computer that functions as the arithmetic unit 30 may be a general-purpose computer, a dedicated computer, a workstation, a PC (Personal Computer), It may be an electronic notepad, etc. The program instructions may be program code, code segments, etc. for performing the necessary tasks.

[0048] 12, the computer 100 includes a processor 110, a memory unit including a ROM (Read Only Memory) 120, a RAM (Random Access Memory) 130, and a storage 140, an input unit 150, an output unit 160, and a communication interface (I / F) 170. Each component is connected to each other via a bus 180 so as to be able to communicate with each other.

[0049] The ROM 120 stores various programs and various data. The RAM 130 temporarily stores programs or data as a working area. The storage 140 includes a hard disk drive (HDD). The ROM 120 or the storage 140 is configured with a ROM (Read Only Memory) or a Solid State Drive (SSD) and stores various programs including an operating system and various data. In the present disclosure, the program according to the present disclosure is stored in the ROM 120 or the storage 140.

[0050] The processor 110 specifically includes a CPU (Central Processing Unit), an MPU (Microprocessor Unit), and The processor 110 may be configured with multiple processors of the same or different types, such as a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), or a SoC (System on a Chip). The processor 110 reads a program from the ROM 120 or the storage 140, and executes the program using the RAM 130 as a work area, thereby controlling the above components and performing various arithmetic processing. Note that at least a part of the processing content may be realized by hardware.

[0051] The program may be recorded on a recording medium readable by the arithmetic device 30. Using such a recording medium, the program can be installed in the arithmetic device 30. Here, the recording medium on which the program is recorded may be a non-transitory recording medium. The non-transitory recording medium is not particularly limited, and may be, for example, a CD-ROM, a DVD-ROM, a USB (Universal Serial Bus) memory, or the like. Furthermore, the program may be downloaded from an external device via a network.

[0052] The following additional notes are provided regarding the above-described embodiments.

[0053] (Additional note 1) A monitoring system that remotely monitors for failure of U-bolts and support metal fittings that secure tubular structures, A monitoring system comprising: a vibrator that vibrates the tubular structure in each of a first axial direction and a second axial direction perpendicular to the first axis; one or more triaxial accelerometers installed on the tubular structure that measure acceleration each time the tubular structure is vibrated in each of the first axial direction and the second axial direction; and a computing device that derives vibration modes in each of the first axial direction and the second axial direction based on the acceleration measurements, and determines whether a U-bolt or a support hardware has fallen off based on the vibration modes. (Additional note 2) A computing device that determines whether a U-bolt and a support metal fitting that secures a tubular structure have fallen off, A computing device comprising: a receiver that receives acceleration measurement values ​​from one or more three-axis accelerometers each time the tubular structure is vibrated in each of a first axis direction and a second axis direction perpendicular to the first axis; a controller that derives a vibration mode based on the measurement values ​​and determines whether the U-bolt or the support hardware has fallen off based on the vibration mode; and a display that displays and visualizes the vibration mode. (Additional note 3) the controller determines that the U-bolt has fallen off when the vibration mode in the first axial direction is displayed as a convex curve having an amplitude equal to or greater than a first threshold value and having a maximum at an installation position of the U-bolt; The calculation device described in Appendix 2 determines that the support hardware has fallen off when the second axial vibration mode is displayed as a convex curve having an amplitude greater than or equal to a second threshold value, with the maximum at the installation position of the U-bolt. (Additional note 4) The controller determines that the U-bolt has fallen off when a frequency response function derived based on measured values ​​of acceleration of the tubular structure excited in the first axial direction indicates a vibration mode having an amplitude equal to or greater than a third threshold in a specific frequency band, and determines that the support hardware has fallen off when a frequency response function derived based on measured values ​​of acceleration of the tubular structure excited in the second axial direction indicates a vibration mode having an amplitude equal to or greater than a fourth threshold that is greater than the third threshold in the specific frequency band. (Additional note 5) A monitoring method for remotely monitoring for failure of U-bolts and support hardware that secure a tubular structure to fall off, comprising: a vibrator that vibrates the tubular structure in each of a first axial direction and a second axial direction that is perpendicular to the first axis; one or more triaxial accelerometers that measure acceleration each time the tubular structure is vibrated in each of the first axial direction and the second axial direction; a computing device that derives vibration modes in each of the first axial direction and the second axial direction based on the measured values; and a computing device that determines, based on the vibration modes, whether the U-bolt or the support hardware has fallen off.

[0054] Although the above-described embodiments have been described as typical examples, it will be apparent to those skilled in the art that many modifications and substitutions can be made within the spirit and scope of the present disclosure. Therefore, the present invention should not be interpreted as being limited by the above-described embodiments, and various modifications or alterations are possible without departing from the scope of the claims. For example, multiple building blocks shown in the block diagrams of the embodiments can be combined into one, or one building block can be divided. [Explanation of symbols]

[0055] 1. Surveillance System 10. Vibrator 20. 1 or more 3-axis accelerometer 20-1~20-n 3-axis accelerometer 21-1~21-n Measurement section 22-1 to 22-n Transmitting unit 30 Arithmetic unit 31 Receiver 32 Arithmetic section 33 Display unit (display) 40 Tubular structures (monitored objects) 41 U-bolt 42 Support hardware 50 Control operation circuit (controller) 100 computers 110 processors 120 ROM 130 RAM 140 Storage 150 Input section 160 Output section 170 Communication Interface (I / F) 180 Bus

Claims

1. A monitoring system for remotely monitoring for failure of U-bolts and support metal fittings that secure a tubular structure, a vibrator that vibrates the tubular structure in each of a first axis direction and a second axis direction perpendicular to the first axis; one or more triaxial accelerometers installed in the tubular structure, which measure acceleration each time the tubular structure is vibrated in each of the first axial direction and the second axial direction; a computing device that derives a vibration mode in each of the first axis direction and the second axis direction based on the measurement value of the acceleration, and determines whether a U-bolt or a support metal fitting has fallen off based on the vibration mode; A monitoring system comprising:

2. A computing device for determining whether a U-bolt or a support metal fitting that fixes a tubular structure has fallen off, a receiving unit that receives acceleration measurement values ​​from one or more triaxial accelerometers each time the tubular structure is vibrated in each of a first axis direction and a second axis direction perpendicular to the first axis; a calculation unit that derives a vibration mode based on the measurement value and determines whether the U-bolt or the support metal fitting has fallen off based on the vibration mode; a display unit that displays and visualizes the vibration mode; A computing device comprising:

3. The calculation unit If the vibration mode in the first axial direction is displayed as a convex curve having an amplitude equal to or greater than a first threshold value and having a maximum at the installation position of the U-bolt, it is determined that the U-bolt has fallen off, 3. The computing device according to claim 2, wherein when the second axial vibration mode is displayed as a convex curve having an amplitude equal to or greater than a second threshold value and having a maximum at the installation position of the U-bolt, it is determined that the support hardware has fallen off.

4. The calculation unit determining that the U-bolt has fallen off when a frequency response function derived based on a measurement value of the acceleration of the tubular structure excited in the first axial direction indicates a vibration mode having an amplitude equal to or greater than a third threshold value in a specific frequency band; 3. The computing device according to claim 2, wherein when a frequency response function derived based on the measured acceleration of the tubular structure excited in the second axial direction indicates a vibration mode having an amplitude equal to or greater than a fourth threshold value greater than the third threshold value in the specific frequency band, the computing device determines that the support hardware has fallen off.

5. A monitoring method for remotely monitoring for failure of U-bolts and support metal fittings that secure a tubular structure, comprising: vibrating the tubular structure in a first axial direction and a second axial direction perpendicular to the first axis by a vibrator; measuring accelerations by one or more three-axis accelerometers each time the tubular structure is vibrated in each of the first axis direction and the second axis direction; deriving, by a calculation device, vibration modes in each of the first axial direction and the second axial direction based on the measurement values; determining, by the computing device, whether the U-bolt or the support metal fitting has fallen off based on the vibration mode; Monitoring methods including:

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