Management methods and management systems

Abstract

This management method includes: measuring inclination angle information at respective measuring points using a plurality of sensors arranged on a ceiling, and carrying out a prescribed calculation that includes function fitting using at least some of the measured information from the plurality of sensors to derive ceiling shape information (step S116); deriving information pertaining to a change in the shape of the ceiling from a shape in the initial state, on the basis of the derived ceiling shape information and information pertaining to the ceiling shape in the initial state (step S118); and assessing whether ceiling maintenance is needed, on the basis of the information pertaining to the change in the shape of the ceiling from the shape in the initial state (steps S120-S122).

Description

[Technical Field]

[0001] The present invention relates to a management method and management system for maintaining and managing the ceilings (including roofs) of indoor and outdoor facilities. This application claims priority based on Japanese Patent Application No. 2022-211931, filed on December 28, 2022, and the contents of that application are incorporated herein by reference. [Background technology]

[0002] Patent Document 1 discloses an invention relating to a ceiling collapse warning mechanism, which aims to directly assess the damage to the ceiling and warn occupants that the ceiling may collapse. Furthermore, when constructing roofs for outdoor facilities, there is a risk that part of the roof may fall during construction, so there is a need for a system that can predict and warn of this risk during construction.

[0003] However, the invention described in Patent Document 1 uses a magnetic switch and / or an acceleration sensor to detect the movement of at least one of the multiple ceiling components that make up the ceiling. Therefore, it is difficult to detect gradual changes in the shape of the ceiling surface, and for this reason, it was not possible to determine the appropriate timing for maintenance. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2017-84105 [Overview of the project] [Means for solving the problem]

[0005] First aspect of the present invention This is a management method for maintaining and managing the ceiling of a facility, comprising: measuring information on the inclination angle at each measurement point using a plurality of sensors arranged in a predetermined positional relationship on the ceiling; obtaining information on the shape of the ceiling by performing a predetermined calculation including function fitting using at least a portion of the measurement information from the plurality of sensors; determining the distribution of deformation of the ceiling shape based on the obtained shape information and the ceiling shape determined based on the ceiling design information; and identifying a position or region on the ceiling where the deformation exceeds a threshold based on the distribution of deformation. .

[0006] A second aspect of the present invention is: A management method for maintaining the ceiling of a facility, comprising: obtaining the shape of the ceiling, which is determined based on the ceiling's design information, as a first function expressed by an orthogonal polynomial; measuring information on the inclination angle at each measurement point using a plurality of sensors arranged on the ceiling in a predetermined positional relationship; performing a predetermined calculation including function fitting using at least a portion of the measurement information from the plurality of sensors to obtain information on the ceiling's shape as a second function expressed by an orthogonal polynomial of the same type as the first function; representing information on changes in the ceiling's shape using a function expressed by an orthogonal polynomial of the same type as the first function, based on the first function and the second function; and determining whether the change in the ceiling's shape exceeds a threshold based on the information on the change. .

[0007] Third aspect of the present invention The management system for maintaining and managing the ceiling of a facility comprises a plurality of sensor devices arranged in a predetermined positional relationship on the ceiling and measuring information on the inclination angle at each measurement point with the ceiling as the measurement target, and an analysis device and a terminal device respectively connected to the plurality of sensor devices via a network, wherein the analysis device has the function of measuring information on the inclination angle of the ceiling at each measurement point using the plurality of sensor devices, the function of obtaining information on the shape of the ceiling by performing a predetermined calculation including function fitting using at least a part of the measurement information of the plurality of sensor devices, the function of determining the distribution of deformation of the shape of the ceiling based on the shape information obtained by the predetermined calculation and the shape of the ceiling obtained based on the design information of the ceiling, the function of identifying a position or region on the ceiling where the deformation amount exceeds a threshold based on the distribution of deformation, and the function of transmitting specific information regarding the identified position or region where the deformation amount exceeds a threshold to the terminal device.

[0008] A fourth aspect of the present invention is: A management system for maintaining and managing the ceiling of a facility, comprising: a plurality of sensor devices arranged in a predetermined positional relationship on the ceiling and measuring information on the inclination angle at each measurement point with the ceiling as the measurement target; an analysis device and a terminal device connected to the plurality of sensor devices via a network, wherein the analysis device has the following functions: a function to acquire the shape of the ceiling, determined based on the ceiling design information, as a first function expressed by an orthogonal polynomial; a function to measure information on the inclination angle of the ceiling at each measurement point using the plurality of sensor devices; a function to obtain information on the shape of the ceiling as a second function expressed by an orthogonal polynomial of the same type as the first function by performing a predetermined calculation including function fitting using at least a portion of the measurement information of the plurality of sensor devices; a function to represent information on changes in the shape of the ceiling as a function expressed by an orthogonal polynomial of the same type as the first function, based on the first function and the second function; a function to determine whether the change in the shape of the ceiling exceeds a threshold based on the change information; and a function to transmit information related to the determination to the terminal device. . [Brief explanation of the drawing]

[0009] [Figure 1] This diagram schematically shows the overall configuration of the management system according to the first embodiment. [Figure 2] This block diagram shows an example of the configuration of the sensor device shown in Figure 1. [Figure 3] This diagram shows a perspective view of the interior of a gymnasium, an example of an indoor facility, and also illustrates an example of the placement of sensor devices. [Figure 4] Figure 4(A) is a diagram illustrating the measurement surface W in a three-dimensional Cartesian coordinate system (x,y,z), and Figure 4(B) is a diagram illustrating the measurement surface W in a polar coordinate system (x=ρcosθ,y=ρsinθ). [Figure 5] This figure shows a portion of the Czernike mode map, which displays each term (component) of the Czernike polynomial in equation (1) as a grayscale pattern within the unit circle of the polar coordinate system (ρ,θ). [Figure 6] This diagram illustrates the setting of a polar coordinate system (ρ,θ) with the center of the rectangular ceiling where the sensor device is placed as the origin, and a virtual unit circle, which are used when measuring an actual ceiling. [Figure 7] This figure shows a portion of a flowchart illustrating the flow of the management method according to the first embodiment. [Figure 8] This figure shows the remaining portion of the flowchart illustrating the flow of the management method according to the first embodiment. [Figure 9] This diagram schematically shows the overall configuration of the management system according to the second embodiment. [Modes for carrying out the invention]

[0010] The first embodiment will be described below with reference to Figures 1 to 8. Figure 1 schematically shows the overall configuration of the management system 10 used to implement the management method according to the first embodiment. The management system 10 includes a server 12 that also functions as an analysis device connected to each other via a wide-area network 13 such as the Internet, a field computer 14, a mobile terminal 16, and a plurality of sensor devices 18. ij (i=1, 2, 3, ...I, j=1, 2, 3, ...J), and multiple sensor devices 18 ij It is composed of different measuring devices, such as a 3D surveying instrument 30. Sensor device 18 ij Let the total number be I × J = N. Multiple sensor devices 18 ij The device is connected to the wide-area network 13 via a communication line, such as a wireless LAN. Similarly, the 3D surveying equipment 30 is connected to the wide-area network 13 via a communication line, such as a wireless LAN.

[0011] Furthermore, since communication lines can be considered as part of the network including the wide-area network 13, this network will be referred to as network (also called communication network) 13 below, using the same notation as the wide-area network. Note that all communication lines may be wireless, but at least some may be wired.

[0012] The field computer 14 can be a typical desktop PC (personal computer), a notebook PC, or a tablet PC, but it is not limited to these; a mobile PC or smartphone may also be used as the field computer 14.

[0013] The mobile device 16 is carried by the workers on site. The mobile device 16 is a commonly used portable computer, such as a tablet PC. The mobile device 16 may also be a smartphone.

[0014] Note that there are multiple sensor devices 18 ijThe output may be provided to the network 13 via the on-site computer 14 and further to the server 12 via the network 13, or the on-site computer 14 may not be provided. The mobile terminal 16 may also serve as the on-site computer. Or, the outputs of the plurality of sensor devices 18 ij may be provided to the server 12 via the network 13 without passing through a PC or the like.

[0015] In this embodiment, the plurality of sensor devices 18 ij are arranged on one surface of the ceiling that constitutes a gymnasium as an indoor facility. The arrangement of the sensor device 18 ij will be further described later.

[0016] As the server 12, in this embodiment, a generally used server computer is used, but a cloud (computer) may also be used. The server 12 includes a CPU, ROM, RAM, HDD, etc. (storage) not shown. The CPU uses, for example, the RAM as a work area and executes various processing algorithms defined by various programs stored in the ROM, HDD, etc. Note that the configuration of the analysis device is not limited to this embodiment, and it may have at least a configuration (or function) capable of obtaining, by calculation, the state of the measurement target (ceiling), such as shape information, based on the outputs of the plurality of sensor devices 18 ij The analysis device is not limited to hardware as in this embodiment, and may be, for example, software capable of at least executing an arithmetic function.

[0017] As an example of a 3D surveying instrument 30, a 3D laser scanner is used to perform a surveying method (3D laser scanner surveying) in which a laser beam is shone onto the object to be measured, and the 3D coordinates of the object are obtained from the time it takes for the reflected light to return and the angle of the laser beam's irradiation. The laser beam emitted by the 3D laser scanner is, for example, approximately tens of thousands of times per second, and it instantly scans every point on the object to be measured and obtains coordinate values. The measurement time is determined according to the density and range to be observed. Hereinafter, the 3D surveying instrument 30 will also be referred to as the 3D laser scanner 30 as appropriate. In this embodiment, measurement instructions for the 3D laser scanner 30 are given from the server 12 via the network 13, and output data from the 3D laser scanner 30 is provided to the server 12 via the network 13. In addition, necessary calculation processing using the output data from the 3D laser scanner 30 is performed by the server 12, and necessary information is provided from the server 12 to the mobile terminal 16 in response to inquiries from the mobile terminal 16 or according to a predetermined program. Other surveying equipment besides laser scanners may be used as the 3D surveying equipment 30.

[0018] Sensor device 18 ij Each of these comprises, as shown in Figure 2, an angle sensor 181, a processing unit 182, a communication unit 183, a display operation unit 187, and a power supply unit 184 consisting of, for example, a battery, and a waterproof housing 185 that houses these inside. Sensor device 18 from power supply unit 184 ij The power supply to each part can be turned on and off by operating the power switch 186 provided on the housing 185. In this embodiment, the communication unit 183 is composed of a wireless communication unit that performs wireless communication, but the communication unit 183 is not limited to wireless and may be at least partially wired. Also, the sensor device 18 ij It is not necessary to have a power switch 186; the configuration may allow the power to be turned on and off by external operation (such as a server 12 or mobile terminal 16). Furthermore, a configuration without power on / off is also acceptable. Also, the sensor device 18 ijThe configuration is not limited to this embodiment, and the angle sensor 181, communication unit 183, etc. do not need to be integrated, and at least the angle sensor 181, i.e., the sensor device 18 ij The sensor device 181 only needs to have the function of measuring the angle information of the installation location. For example, the angle sensor 181 and other parts (including the arithmetic processing unit 182, etc.) may be connected by a wireless or wired communication line, and the device may be configured to output measurement data from the angle sensor 181 and supply power to the angle sensor 181 via the communication line. In this case, it is not necessary to provide another part for each angle sensor 181, and multiple angle sensors 181 may be connected to the same other part via the communication line. Alternatively, the functions of this other part may be given to other terminals connected to the network 13. Sensor device 18 ij For example, it may consist only of an angle sensor 181, a communication unit 183, and a power supply unit 184. In this case, the calculation processing unit 182 may be provided in another device, such as a field-side computer 14.

[0019] In this embodiment, as an example of the angle sensor 181, a 2DMEMS (2-dimensional microelectromechanical system) tilt angle sensor is used. The power required by the 2DMEMS tilt angle sensor is extremely low, with power consumption in the microampere range, making it suitable for wireless applications. As an example of the angle sensor 181, a sensor is used that has two pairs of electrodes consisting of a fixed electrode and a movable electrode, and measures the change in capacitance between the electrodes due to the change in positional relationship caused by tilting, using the positional relationship between the electrodes in the horizontal position as a reference, and converts this into an angle. For example, it outputs information on the tilt angles (α, β) in two directions (θx direction and θy direction). Here, the θx direction and θy direction are the tilt directions around the X axis and Y axis of the orthogonal 3D coordinate system shown in Figure 3. The angle sensor 181 may also have an ASIC built in.

[0020] As an angle sensor, it is not limited to a 2D MEMS tilt angle sensor; other types of 2D tilt angle sensors may also be used. Furthermore, the angle sensor is not limited to a 2D tilt angle sensor; a 3D tilt angle sensor is also acceptable, and depending on the object being measured, a 1D tilt angle sensor may also be used. In this case, multiple 1D tilt angle sensors may be used in combination. As an example of a 3D tilt angle sensor, a 3D MEMS tilt angle sensor can be used. As an example of a 3D MEMS tilt angle sensor, one can use a sensor that incorporates two MEMS accelerometers with symmetrical output characteristics and an ASIC.

[0021] The arithmetic processing unit 182 consists of, for example, a microcontroller (MCU) and includes a CPU (not shown), memory devices (RAM, ROM), input / output circuits, and timer circuits. The arithmetic processing unit 182 executes a processing algorithm defined by a program stored in ROM. Alternatively, the functions of the arithmetic processing unit 182 may be integrated into the ASIC built into the angle sensor 181 instead of providing a separate arithmetic processing unit 182.

[0022] Here, sensor device 18 ij Various means can be used to attach the sensor device 18 to the object, depending on the type of object. For example, if the object is a material that can be fastened with screws to obtain sufficient strength, such as metal, screws (including bolts) can be used to fasten the sensor device 18. ij The sensor device 18 can be fixed to the object. In addition, depending on the type of object and the method of use, the magnetic force of a magnet can be used instead of or in conjunction with screws and adhesive. ij It may be fixed to the object.

[0023] The surface of the housing 185 is treated with an anti-reflective coating against laser light to prevent light reflected from the 3D laser scanner 30 from returning to the scanner when the laser light emitted by the scanner is shone upon it.

[0024] In the following explanation, the sensor device 18 will be referred to as appropriate. ij to "Sensor 18 ijIt is also referred to as "Sensor 18" as a general term.

[0025] Figure 3 shows a perspective view of the interior of a gymnasium as an example of an indoor facility. The gymnasium shown in Figure 3 has a suspended ceiling and a flat ceiling parallel to the floor (floor surface) 20a. In Figure 3, one surface of the ceiling (ceiling surface) is indicated by the reference numeral 20b. Both the floor 20a and the ceiling surface 20b are rectangular in plan view (viewed from above or below). In this embodiment, as shown in Figure 3, the vertical direction (direction of gravity) is defined as the Z-axis direction, and within a plane perpendicular to the Z-axis, the directions parallel to mutually orthogonal sides of the ceiling surface 20b and their adjacent sides are defined as the X-axis direction and the Y-axis direction, respectively, and the inclination directions around the X-axis and Y-axis are defined as the θx and θy directions, respectively.

[0026] The ceiling surface 20b is a surface consisting of one side (bottom surface) of each of the multiple ceiling boards, which are finishing materials that make up the lowest layer of the ceiling. Multiple sensors 18 ij The sensors are fixed in a matrix arrangement, with the Y-axis direction being the column direction (the direction in which the row number changes) and the X-axis direction being the row direction (the direction in which the column number changes). Here, for the sake of illustration, Figure 3 shows 5 × 5 = 25 sensors 18 ij The diagram shows a configuration where (i=1~5, j=1~5) sensors are arranged, but in reality, there are I × J = N sensors 18 ij These are located on the ceiling surface 20b. In reality, lighting fixtures and other items are also placed on the ceiling surface 20b, but they are omitted from the illustration in Figure 3.

[0027] Multiple sensors 18 ij Each mounting position is predetermined by the server 12 based on design data. In this embodiment, for identification purposes, the sensor 18 located in the i-th row and j-th column is designated as sensor 18 ij This is how it is written. In Figure 3, only some of the sensors located in the first row and some of the sensors located in the first column are labeled with a symbol.

[0028] Note that the multiple sensors 18 shown in Figure 3 ij The arrangement is just one example, and multiple sensors 18 ijThe arrangement is not limited to this; the mounting position can be predetermined based on the design data of the object to be mounted. A two-dimensional arrangement is sufficient (in other words, the positions can be different in at least one of the X-axis and Y-axis directions). For example, the sensors 18 could be placed at each vertex of a figure formed by arranging many equilateral triangles of the same size but with different orientations without gaps. ij It would also be acceptable to arrange them in that way.

[0029] The management method according to this embodiment involves multiple sensors 18 ij Since the purpose is to monitor changes in the state (shape, etc.) of one surface of the object to which the device is attached, in this case the ceiling surface 20b, the following section will explain how to obtain the shape of this ceiling surface 20b.

[0030] First, we will explain how to obtain the shape of the ceiling surface 20b using a 3D laser scanner 30. First, a 3D laser scanner 30 is used to perform a 3D laser scan of the ceiling surface 20b and acquire 3D coordinate data at multiple points. Ideally, these multiple points should be evenly distributed across the entire surface of the ceiling surface 20b. Next, the shape of the ceiling surface 20b is calculated using the acquired 3D coordinate data from multiple points, including a function fitting operation. The ceiling surface 20b is equipped with a 3D laser scanner 30 and a sensor 18 ij Since this is the surface being measured, in the following explanation, it will also be referred to as the measurement surface W as appropriate.

[0031] The measurement surface W corresponds to the set of points with height z at point P(x,y) on the XY plane in a three-dimensional Cartesian coordinate system defined by the X, Y, and Z axes as shown in Figure 4(A), and can be expressed by the function z=f(x,y). The shape of the measurement surface W can also be described as the distribution of the deviation of each point on the measurement surface from the reference plane (XY plane) (i.e., height z with respect to the reference plane, hereafter referred to as height z as appropriate).

[0032] Furthermore, as shown in Figure 4(B), any point P in the polar coordinate system (x=ρcosθ, y=ρsinθ) can be expressed as P(ρ,θ). Therefore, the measurement surface W can be expressed as z=W(ρ,θ) in the polar coordinate system (x=ρcosθ, y=ρsinθ).

[0033] However, although positional information (3D coordinate values ​​(x,y,z)) at multiple points on the measurement surface W is acquired using the 3D laser scanner 30, this is discrete positional information, not information about the measurement surface W. In this embodiment, the measurement surface W, i.e., the ceiling surface, is covered by sensors 18 ij Since it is positioned, sensor 18 ij Reflected light from the point where the sensor is placed cannot be received. Therefore, it is difficult to obtain non-discrete positional information (3D coordinates) of the measurement surface.

[0034] Therefore, in this embodiment, discrete positional information is fitted to a function to obtain a function that represents W. In the function fitting, it is possible to use a function of any orthogonal polynomial. By using an orthogonal polynomial, it becomes possible to uniquely determine the amount of deformation and the deformation position.

[0035] In this embodiment, we will use Zernike polynomials as orthogonal polynomials. Zernike polynomials are orthogonal polynomials defined on the unit circle.

[0036] The following describes a function fitting method using the Zernike polynomial to find a function representing the measurement surface W (hereinafter referred to as the first method).

[0037] The Czernike polynomial is defined by the following equation:

number

[0038] The Czernike polynomial is |Z n m The range (ρ,θ)|≦1 is taken. Here, the radial polynomial R n m (ρ) is defined by equation (2) below when nm is an even number.

number

[0039] Here, we will adopt fringe notation to combine the two exponents n and m into a single exponent i. In other words, in the Fringitzernike polynomial, the exponent i is defined as follows:

number

[0040] Table 1 shows the relationship between the exponents n, m and i of the first few terms of the Fringitzernike polynomial obtained according to equation (3) above. [Table 1]

[0041] In this specification, each term of the Fringitzernike polynomial is appropriately represented as Z i It is denoted as (ρ,θ). Therefore, the measurement surface W(ρ,θ) can be expressed as follows:

number

[0042] Z i Let's consider (ρ,θ) up to the 37th term, and the coefficient k i This is shown in Table 2. [Table 2] Here, equation (4) can be obtained only for the number of points (number of measurement points) whose positional information was measured by the 3D laser scanner 30. Therefore, the second to q terms (for example, the 37th term) of the Czernike polynomial are used for fitting, and the number of measurement points (or some of them) whose positional information was measured is M (M>q-1). The z obtained at each of the M measurement points is then function-fitted. That is, by solving the M observation equations, the coefficients k of each term in equation (4) are obtained. i Find (i=2,3,……q). Here, z includes the error, so the coefficient k i To minimize the error included in the calculation, the least squares method will be used.

[0043] In this first method, the coefficients k of each term of the function W(ρ,θ) are determined by the method described above. i Find the coefficient k i The finalized function z=W(ρ,θ) is determined as a function representing the shape of the measurement surface, i.e., the distribution of the deviation.

[0044] Next, multiple sensor devices 18 ij This section describes how to obtain the shape of the ceiling surface 20b (measurement surface W) using [a specific method / tool].

[0045] First, multiple sensors 18 are placed on the ceiling surface 20b (measurement surface W). ij Each of these can be used to measure multiple points (each sensor 18) ij Information on the angle of inclination at each point where the object is placed is obtained.

[0046] Next, the shape of the measurement surface W is calculated by a calculation that includes function fitting using the discrete distribution of the acquired tilt angle information.

[0047] Multiple sensors 18 ij Each measurement data is provided by each sensor 18 ijThe inclination angles α and β in two directions (θx direction and θy direction) at the mounting position (measurement point) on the measurement surface W are obtained, and these are nothing other than the inclination angles of the normal vector of the measurement surface W at each measurement point. The inclination angles α and β in the θx and θy directions of the normal vector of the measurement surface at each measurement point are nothing other than the gradient of the tangent plane at each measurement point of the measurement surface represented by the function z=W(ρ,θ), and can also be expressed as gradient α=∂W / ∂x and β=∂W / ∂y. Here, ∂W / ∂x and ∂W / ∂y are the derivatives of the function W.

[0048] Therefore, discrete sensor 18 ij By fitting the measured values ​​to a function obtained by differentiating the Zernike polynomial (also referred to as the differential Zernike polynomial in this specification), a function dW(ρ,θ) representing the distribution of the measured values ​​of sensor 18 can be obtained. By integrating the obtained dW(ρ,θ), the function W(ρ,θ) can be obtained.

[0049] Below, we will briefly explain the function fitting method using differential Zernike polynomials to find a function representing the measurement surface W (hereinafter referred to as the second method).

[0050] The distribution of the measured values ​​dW(ρ,θ) is given by the differential Zernike polynomial Z i Using (ρ,θ), it can be expressed as in equation (5).

number

[0051] The x-part derivative ∂Z / ∂x of equation (1) can be expressed as follows:

number

[0052]

number

[0053]

number

[0054] In this embodiment, the Czernike polynomial, the differential Czernike polynomial, and the formulas for each of these terms are determined in advance and stored in the storage of the server 12.

[0055] Discrete sensor 18 ij The measured values ​​(∂W / ∂x, ∂W / ∂y) are functionally fitted to the polynomial in equation (5) above, and the coefficients k of each term are determined using the least squares method. i We will determine this. At this time, sensor 18 ij If we let N be the number of observation equations, then the number of observation equations is 2N. This allows us to determine the coefficient k of each term in polynomial (5). i It is possible to find this.

[0056] Then, the coefficients of each term obtained are the definite coefficients k of the corresponding terms in equation (5). i Then, we integrate the polynomial in equation (5) after determining the coefficients to find the function W(ρ,θ).

number

[0057] According to this second method, sensor 18ij The height z of points other than the point where the object is placed can also be obtained from the function z=W(ρ,θ) without performing proportional calculations.

[0058] In this embodiment, the determination of whether maintenance is necessary, or in other words, whether the time for maintenance has come, is made based on the results of the component decomposition of the Czernike polynomial. Here, the component decomposition of the Czernike polynomial will be explained. In Figure 5, for ease of understanding, the first few terms (components) of the Czernike polynomial in equation (1) are shown as a shading pattern within a unit circle in polar coordinate system (ρ,θ) (the density of each coordinate point (ρ,θ) corresponds to the magnitude of the z position at that point (which can also be called the degree of deformation)). Note that Figure 5 is a part of the Czernike mode map showing each term of the Czernike polynomial.

[0059] The definite coefficient k of each term in equation (4) or equation (9) mentioned above. i The value of indicates the extent to which each term's component is present, and furthermore, the component diagram in Figure 5 shows the degree of deformation of each part within the circle. For example, k4, k9, k 16 When these are larger than the others, Z4, Z9, Z have these as coefficients. 16 It can be seen that this component is present in greater quantities than others. The Fringitzernike order of 4, 9, and 16 are formed by combining two indices (2,0), (4,0), and (6,0) into a single indice, respectively, so from Figure 5, it can be visually understood that the central part within the circle is the most prominent. However, Figure 5 shows Z 16 This is not shown. In practice, by decomposing the Zernike polynomial, which represents the shape of the measurement surface, i.e., the in-plane distribution of the deformation (deviation), into its individual components, the most protruding position (ρ,θ), for example, can be numerically determined.

[0060] In measurements targeting the actual ceiling surface 20b, as shown in Figure 6, the XY coordinate system, with the origin O at the center of the rectangular ceiling surface 20b, is transformed into a polar coordinate system (ρ,θ), and a virtual unit circle (0≦ρ≦1) is set up on this polar coordinate system, circumscribing the four corner vertices of the ceiling surface 20b. This unit circle corresponds to a virtual circle with radius Ra centered at the origin O in the XY coordinate system. In other words, the unit circle in the polar coordinate system is a circle with radius Ra in the XY coordinate system, which shares a common origin, scaled down by a factor of 1 / Ra. Note that in the polar coordinate system, the angle from the axis corresponding to the X axis is the deflection angle θ.

[0061] Sensor 18 ij If the actual position coordinates of a certain measurement point in the XY coordinate system are (a,b), then various calculations such as function fitting are performed assuming that the position coordinates of the calculated measurement point are (a / Ra,b / Ra).

[0062] Figures 7 and 8 show flowcharts corresponding to the processing algorithms executed by the CPU of server 12 according to the program when implementing the management method according to this embodiment. The management method will be described below based on the flowcharts in Figures 7 and 8, and with reference to other figures as appropriate.

[0063] As a prerequisite, the ceiling surface 20b has multiple sensors 18 as described above. ij However, they are arranged in a matrix-like structure, with the X-axis direction being the row direction (the direction in which the column number changes) and the Y-axis direction being the column direction (the direction in which the row number changes).

[0064] Also, each attached sensor 18 ij After the power is turned on by the on-site worker by turning on the switch 186, the necessary initial settings are performed in advance so that communication can be made via the network 13. Sensor 18 ij The initial settings are configured via the display operation unit 187, and the sensor 18 ij This includes inputting identification information for sensor 18 in the i-th row and j-th column. ij Identification information (01-ij) is individually input to each sensor 18ij The arithmetic processing unit 182 stores the input identification information in internal memory (RAM). Here, of the identification information, 01 is the identification number of the ceiling surface 20b that is the object of measurement, and "ij" is the identification number of each sensor 18 ij This is the identification number. For example, the three sensors 18 in the first row shown in Figures 3 and 6. 11 , 18 12 , 18 13 Each of these will have the identification information (01-11), (01-12), and (01-13) entered individually. The identification number ij is for each sensor 18 ij The placement location is indicated, and this placement location is recognized by the server 12. Upon completion of the initial setup, each sensor 18 ij It enters a standby state where it can measure at any time. After initial setup, each sensor 18 ij Switch 186 remains in the ON state. Note that each sensor 18 ij However, if the system is configured to allow the power to be turned on and off remotely, the power may be set to OFF after the initial setup.

[0065] Furthermore, the 3D laser scanner 30 will be installed in a location inside the gymnasium that allows for positional measurement of the ceiling surface 20b (measurement surface W).

[0066] Under these conditions, a command to start measurement is input to the server 12 from a terminal device connected to the network 13, such as a mobile terminal 16 (or a field computer 14). This starts the flowchart (corresponding algorithm).

[0067] First, in step S102, a 3D laser scanner survey of the ceiling surface 20b (measurement surface W) is performed using the 3D laser scanner 30. In this survey, the measurement surface (ceiling surface) is scanned with laser light by the 3D laser scanner 30, and 3D coordinate values ​​(x, y, z) are acquired at multiple points (distributed across the entire measurement surface) according to the observation density. At the start of the survey, multiple sensor devices 18 ijIt is fixed to the ceiling surface 20b. Therefore, the sensor device 18 ij The reflected laser light from each surface does not reach the 3D laser scanner 30. Therefore, the 3D coordinate values ​​(x,y,z) at multiple points corresponding to the observation density described above are obtained from multiple sensors 18. ij The 3D coordinate values ​​(x, y, z) at each placement location will not be included.

[0068] In the next step S104, the shape of the measurement surface W (the first function z=W(ρ,θ) representing the shape) is determined using the first method described above, with at least some of the acquired positional information (3D coordinate values) from multiple points. Specifically in this step S104, information about the shape of the measurement surface, that is, information about the first function z=W(ρ,θ), is obtained by the following procedure.

[0069] In other words, the server 12 applies the first method described above to the 3D coordinate values ​​of at least some of the M points (where M is a number to which the least squares method described above can be applied) among the 3D coordinates of multiple points obtained in step S102, and calculates the coefficients k of each term of the function W(ρ,θ). i Find the coefficient k i The first function z=W(ρ,θ), after determination, is obtained as a function representing the shape of the measurement surface (i.e., the distribution of deviation (deformation)). The information about the shape of the measurement surface obtained at this time, i.e., the information of the function z=W(ρ,θ), will be referred to below as the information about the shape of the measurement surface in the initial state. The information about the shape of the measurement surface in the initial state is stored in memory (RAM).

[0070] In the next step S106, based on the shape information obtained, multiple sensors 18 ij The inclination angle information of the normal to the measurement surface W at each placement position is obtained. Specifically, based on the differential Zernike polynomial stored in the storage of server 12 and the equations of each term therein, multiple sensors 18 ij The system calculates the inclination angle of the normal vector of the measurement surface (α1=∂Z / ∂x and β1=∂Z / θy) at each placement position (which substantially coincides with the measurement points (x,y) of each of the multiple sensors).

[0071] In the next step S108, a plurality of sensors 18 ij respectively measure information on the inclination angles α2 and β2 in two directions (here, the directions of θx and θy) at respective measurement points on the measurement surface W (ceiling surface 20b). Specifically, for the angle sensors 181 each of the sensors 18 ij is instructed to start measurement from the server 12 via the respective arithmetic processing units 182 of the sensors 18 ij respectively. In response to the measurement start instruction, measurement is performed by the angle sensors 181, and the measured inclination angle information is taken into the arithmetic processing units 182. Then, the arithmetic processing units 182 attach an ID (identification code) to the taken-in inclination angle information, and it is transmitted as one (a bundled set) of sensor data to the server 12 via the communication units 183 and the network 13. Here, as the ID, a number (code) created based on the identification information input by the operator at the time of initial setting and stored in the RAM is used. The server 12 sequentially stores the sent sensor data in a predetermined storage area of the RAM. When a plurality of sensor data are sent simultaneously, the server 12 stores the sensor data in the predetermined storage area of the RAM in parallel by time-division processing.

[0072] Here, the processing of the above steps S102 to S108 does not necessarily need to be performed in the order described above. After the processing of step S108, the processing of step S102 may be performed, or steps S102 and S108 may be performed at least partly in parallel. However, the processing of steps S104 and S106 is performed after the processing of step S102.

[0073] In the next step S110, based on the inclination angles (α1, β1) of the normal line of the measurement surface at points corresponding to the respective measurement points of the plurality of sensors 18 ij calculated using the measurement data (position information measured by the 3D laser scanner 30) of the 3D laser scanner 30 ijCalculate calibration information (δθx, δθy) for correcting or calibrating the measurement information (tilt angles (α2, β2)). The calibration information can also be referred to as correction information or offset information.

[0074] δθx = α2 - α1 δθy = β2 - β1 In the next step S112, perform an origin reset to reset each measurement origin using the calculated calibration information for the plurality of sensors 18 ij As a result of this origin reset, the measurement information of each of the plurality of sensors 18 ij substantially coincides with the information on the tilt angles (α1, β1) of the normal to the measurement plane at the points corresponding to the respective measurement points, which are calculated using the measurement data of the 3D laser scanner 30.

[0075] In the next step S114 (Fig. 8), wait for a certain time T to elapse since the end of the previous measurement by the plurality of sensors 18 ij The certain time T is the measurement interval by the plurality of sensors 18 ij and a time such as several days, several weeks, or several months is determined. When the certain time T elapses, proceed to step S116.

[0076] In step S116, measure the tilt angles (α, β) of the measurement plane at each measurement point using each of the plurality of sensors 18 ij and obtain the shape of the measurement plane, that is, the second function z = W(ρ, θ), using the sensor data of each of the plurality of sensors 18 ij by the second method described above. Here, the sensors 18 used for the measurement in this step S116 ij do not have to be all of the N sensors 18, but when obtaining the second function, it is necessary to be a number to which the above-mentioned least squares method is applicable.

[0077] In the next step, S118, information on the change in the shape of the measurement surface from its initial state (hereinafter referred to as "information on the change in shape from the initial state of the measurement surface") is obtained based on the information on the shape of the measurement surface at that point in time and the information on the shape of the measurement surface in its initial state obtained in step S104 (the information on the first function z=W(ρ,θ)). The information on the change in shape from the initial state of the measurement surface can be expressed using the Zernike polynomial as the function ΔZ=ΔW(ρ,θ).

[0078] Therefore, in the next step S120, the information on the shape change from the initial state of the measurement surface obtained in step S118, that is, the function ΔZ=ΔW(ρ,θ) expressed as a Zernike polynomial, is decomposed into its components, and the coefficients k of each term of the Zernike polynomial are decomposed. i After determining the distribution of deformation within the measurement surface W based on its size and the aforementioned Zernike mode map, the next step S122 is initiated.

[0079] In step S122, a determination is made as to whether maintenance is necessary. This determination is made, for example, by determining whether the amount of deformation exceeds a predetermined threshold in any region of the plane, based on the distribution of the amount of deformation obtained. If the determination in step S122 is negative, that is, if the amount of deformation is below the predetermined threshold in all regions of the plane and therefore maintenance is not necessary, the process returns to step S114, and the loop of steps S114 to S122 (including the determination) is repeated thereafter.

[0080] On the other hand, if the determination in step S122 is affirmed, that is, if it is determined that maintenance is necessary because the amount of deformation exceeds a predetermined threshold in any region of the surface, the process proceeds to step S124, where notification information (including specific information that identifies all locations (regions) where the amount of deformation exceeds the threshold) is sent to the on-site computer 14 and / or mobile terminal 16 indicating that maintenance of the ceiling of ○○ is necessary, and then the series of processes is terminated. In this embodiment, ○○ is information that identifies the ceiling surface 20b to be maintained.

[0081] Upon receiving the above notification information, the display screen of the on-site computer 14 and / or mobile terminal 16 will show something like, "Ceiling maintenance required for XX, especially maintenance required for XX." XX is the location (area) information specified in the specific information.

[0082] Furthermore, the notification information mentioned above may include, instead of specific information identifying all locations (regions) where the deformation exceeds the threshold, specific information identifying the location (region) where the deformation exceeds the threshold is greatest, or it may be omitted altogether. In other words, it may be sufficient to simply notify that maintenance is needed on the ceiling of XX. The threshold may be changed for each facility being measured, and the threshold may also be different for several sub-regions within the same measurement surface, for example, depending on the structure.

[0083] As explained in detail above, according to the management system 10 and its management method according to this embodiment, the necessity of ceiling maintenance is determined based on information (information on changes over time) of the change in shape of one surface (ceiling surface) 20b of the gymnasium (indoor facility) ceiling from its initial state (which can also be called the reference state). Therefore, if the amount of deformation of at least a part exceeds a predetermined threshold, a determination is made that maintenance of the gymnasium (indoor facility) ceiling is necessary. Furthermore, according to the management system 10, when the server 12 makes the determination that "maintenance of the gymnasium (indoor facility) ceiling is necessary," this notification information is transmitted to other terminals (on-site computer 14 and / or mobile terminal 16), and "maintenance of the gymnasium (indoor facility) ceiling is necessary" is displayed on the screen of the terminal's display. Therefore, those involved in ceiling maintenance management can accurately determine when maintenance of the ceiling of indoor facilities such as gymnasiums is necessary.

[0084] Furthermore, according to the management system 10 and its management method as described in this embodiment, information on changes in the shape of the ceiling surface 10b is expressed by a function represented by a Czernike polynomial, which is a type of orthogonal polynomial. The determination of whether maintenance is necessary is made based on a comparison between the in-plane distribution of the change in the shape of the ceiling surface 20b, which is obtained based on the magnitude of the coefficients of each term in the Czernike polynomial and the Czernike mode map, and a predetermined threshold. This makes it possible to determine whether maintenance of the shape of the ceiling surface 20b is necessary quickly and efficiently.

[0085] Furthermore, according to the management system 10 of this embodiment, the notification information includes specific information that identifies all locations (areas) where the amount of change in shape from the reference state exceeds a predetermined threshold, and information corresponding to the notification information containing this specific information is displayed on the screen of another terminal (field-side computer 14 and / or mobile terminal 16). This makes it possible for those involved in ceiling maintenance to easily know all locations (areas) where the amount of change in shape from the reference state exceeds a predetermined threshold, i.e., locations (areas) that require particular maintenance, and to perform ceiling surface maintenance while taking into account the locations where the amount of change in shape exceeds a predetermined threshold.

[0086] In the first embodiment described above, in step S112, a plurality of sensors 18 ij After each of them has been reset to its origin, in step S116 above, the multiple sensors 18 after the origin reset ij The inclination angle of the measurement surface at each measurement point is measured using the above method, and the shape of the measurement surface is determined using the sensor data from each of the multiple sensors. However, this method is not limited to this, and after calculating the calibration information of the measurement information of each of the multiple sensors in step S110, without performing an origin reset, each sensor 18 is measured each time. ij The inclination angle of the measurement surface at the measurement point, measured by the sensor 18, may be corrected using the calibration information described above, and the corrected inclination angle information may be used. In any case, after the calibration information is calculated, the sensor 18 ijBy measuring the inclination angle at the measurement point on the measurement surface, it is possible to obtain information on the inclination angle that is substantially equal to the inclination angle of the measurement surface at the measurement point that would have been measured by the 3D laser scanner 30.

[0087] Furthermore, in the first embodiment described above, in step S118, the reference state shape that serves as the basis for determining information on changes in the shape of the measurement surface is the initial state shape calculated using the measurement information of the 3D laser scanner 30. However, the invention is not limited to this, and information on changes in the shape of the measurement surface may also be determined based on the shape of the measurement surface (initial shape) obtained based on design information. The initial shape of the measurement surface can also be expressed by a Czernike polynomial. In this case, in step S118 (and step S120), the initial shape of the measurement surface is used instead of the shape of the measurement surface in the initial state. In this case, when the shape of the measurement surface in the initial state is determined in step S104, the necessity of ceiling maintenance at that initial state may be determined based on the information on the change in the shape of the measurement surface in this initial state from the initial shape of the measurement surface.

[0088] In the first embodiment described above, multiple sensors 18 are located on the ceiling surface 20b (measurement surface). ij After the sensors are positioned, measurements are taken using the 3D laser scanner 30, but this is not limited to this, and the sensors 18 ij Prior to placing the sensors on the ceiling surface 20b, measurements are taken using a 3D laser scanner 30 to determine the initial deformation distribution. The sensors may then be placed more densely in areas with large deformations or in areas with greater density than other areas.

[0089] Furthermore, in the first embodiment described above, since it was assumed that the ceiling of an already constructed facility would be used for maintenance and management, surveying equipment such as a 3D laser scanner was used in conjunction with it. However, if the aforementioned sensor device is used during the construction (new construction) of the facility, surveying equipment does not need to be used. During construction, the aforementioned sensor device is used to measure the ceiling, and this measurement value is used as the initial value. After that, the sensor device is used to measure the change from that initial value as needed.

[0090] Furthermore, although the first embodiment described above described the case where the ceiling surface 10b is rectangular, multiple sensors 18 are present on one surface. ij The ceiling to which the device is installed may be a ceiling of other polygonal shape, or a circular ceiling, etc. Furthermore, the ceiling to which the first embodiment described above can be applied may be a suspended ceiling with a slope or step in part, other than a flat ceiling, or a straight ceiling. Regardless of the type of ceiling, by applying the first embodiment described above, it becomes possible to accurately determine the timing of ceiling maintenance.

[0091] In the first embodiment described above, each sensor 18 ij In contrast, the example given was of inputting identification information via the display operation unit during the initial setup of each sensor 18 ij The timing and method of inputting identification information (or storing it in RAM (memory)) for each sensor are not particularly limited, but it is preferable that the sensor 18 used in the first embodiment outputs data including the identification code (ID) of the sensor 18. In the first embodiment, the identification code (ID) of each sensor 18 includes the identification code of the object to which each sensor 18 is attached and the identification code of the attachment position on that object, but the identification code of the object does not have to be included.

[0092] Furthermore, when monitoring changes over a long period of time, power supply (powering) to each sensor 18 will be necessary. Possible solutions in this case include power supply using MEMS vibration generation, wireless power supply (contactless power supply) that uses the induced magnetic flux generated between the transmitting and receiving sides of an electromagnetic induction system, solar power generation, or wired LAN power supply using a LAN cable.

[0093] Furthermore, the orthogonal polynomials that can be suitably used for the above function fitting are not limited to Czernike polynomials, but may also be Fourier series, Chebyshev polynomials, Legendre polynomials, and others.

[0094] Furthermore, while the first embodiment described above focused on managing the ceiling of a gymnasium, the management system and management method of the above embodiment can be applied to the maintenance and management of ceilings in other indoor facilities, not limited to gymnasiums. These facilities include martial arts halls, indoor skating rinks, indoor swimming pools, dome stadiums, judo and kendo halls, archery ranges, indoor shooting ranges, sports practice areas, sports gyms, tennis or basketball courts, bowling alleys, theaters, auditoriums, public halls, auditoriums, concert halls, traditional performing arts venues, entertainment venues, cinemas, international conference centers, cultural centers, civic halls, multipurpose halls, meeting halls, libraries, art museums, museums, archives, aquariums, and more. Moreover, the scope of maintenance and management is not limited to indoor facilities; it may also apply to outdoor facilities such as stadiums (including athletic fields, baseball fields, soccer fields, etc.). In outdoor facilities, the roofs covering the seating areas are the target of maintenance and management. Furthermore, similar to indoor facilities, maintenance and management of already constructed facilities (such as roofs) may be carried out using the aforementioned sensor devices in combination with surveying equipment. Alternatively, if sensor devices are used during construction, maintenance and management can be performed using only the sensor devices, as described above, without the need for surveying equipment.

[0095] 《Second Embodiment》 Next, a second embodiment will be described with reference to Figure 9. In this second embodiment, the roof of an outdoor facility is the target of maintenance management, and maintenance management is performed from the time the roof is under construction. Figure 9 schematically shows the overall configuration of the management system 1010 according to this second embodiment.

[0096] In outdoor facilities, for example, when constructing a roof, the roof is extended from the support columns, and at this time, the aforementioned sensor device 18 is attached to the roof or its support members. The management device 1010 has a configuration in which, in the management system 10 of Figure 1, an alarm device 130 that issues an alarm based on an alarm instruction from the server 12 is provided instead of a 3D surveying instrument. For the sake of simplicity, here we will assume that only one sensor device 18 is provided.

[0097] Immediately after installation, the power switch 186 of the sensor device 18 is turned on, and this power-on information is notified to the server 12. Upon receiving the power-on information, the server 12 starts the measurement algorithm defined in the measurement program and instructs the sensor device 18 to start measurement. As a result, the sensor device 18 starts measuring the roof's inclination angle at the measurement point. The server 12 sets an initial value for the inclination angle based on the measured value of the inclination angle included in the first sensor data from the sensor device 18. After setting the initial value, the server 12 sequentially acquires sensor data from the sensor device 18 at predetermined sampling intervals, sequentially calculates the difference between the measured value of the inclination angle included in the sensor data and the initial value, and monitors the change in the difference over time by repeatedly determining the magnitude relationship between this calculated difference and a predetermined threshold. When the difference exceeds the threshold, the server 12 issues an alarm command to the alarm device 130. As a result, the alarm device 130 sounds an alarm. The alarm device 130 emits, for example, a loud sound (such as a siren), or an audio message such as "Roof is in danger of collapsing, run away," or a light (such as flashing). The server 12 may, along with or in lieu of the alarm instruction, notify one or more terminal devices (which may include other mobile terminals) connected to the network 13, such as mobile terminals 16, of the occurrence of the emergency.

[0098] Furthermore, if multiple sensor devices 18 are arranged on one side of the roof of an outdoor facility, and these multiple sensor devices are connected to a server 12, an alarm device 130, etc. via a network 13, the server 12 may sample sensor data from each of the multiple sensor devices 18, and use the measured values ​​of the inclination angle obtained at multiple measurement points for each sampling time to determine the shape of the surface (an approximation function representing the shape, such as the Czernike polynomial mentioned above) for each sampling time using the same method as in the first embodiment described above, and when the amount of change in that shape (the coefficient of a predetermined term of the approximation function) exceeds a threshold, the server 12 may instruct the alarm device 130 to issue an alarm.

[0099] Furthermore, the warning system for outdoor facilities is not limited to roofs. In addition, if the ceiling is affected by external disturbances (such as vibrations), the time-varying waveform data of the angle data included in the sensor data may be frequency-decomposed (frequency analysis), and the time-varying change in the tilt angle may be monitored based on the waveform data of frequency components other than the disturbance component (vibration component) (for example, its amplitude), that is, it may be determined whether the amount of change in the tilt angle exceeds a threshold. [Explanation of symbols]

[0100] 10...Management system, 13...Network, 12...Server, 14...Field computer, 16...Mobile terminal, 18 ij ...sensor devices, 30...3D surveying equipment.

Claims

1. A management method for maintaining and managing the ceiling of a facility, Multiple sensors arranged in a predetermined positional relationship on the ceiling measure information about the inclination angle at each measurement point. The process involves performing a predetermined calculation, including function fitting, using at least a portion of the measurement information from the aforementioned multiple sensors, to obtain information about the shape of the ceiling. Based on the obtained shape information and the ceiling shape determined from the ceiling design information, the distribution of deformation of the ceiling shape is determined, A management method comprising identifying a location or region in the ceiling where the amount of deformation exceeds a threshold, based on the distribution of the amount of deformation.

2. In the management method described in Claim 1, A management method further comprising transmitting information to a terminal device regarding the location or region where the identified deformation amount exceeds a threshold.

3. In the management method according to claim 1 or 2, The aforementioned threshold is different depending on the portion of the ceiling, according to the management method.

4. In the management method described in claim 1, The shape of the ceiling, determined based on the aforementioned design information, is represented by a first function expressed as an orthogonal polynomial. The shape of the ceiling obtained by performing the predetermined calculation is represented by a second function which is expressed by an orthogonal polynomial of the same type as the first function. The distribution of the deformation is represented by a function expressed by an orthogonal polynomial of the same type as the first function, as a management method.

5. A management method for maintaining and managing the ceiling of a facility, The shape of the ceiling, determined based on the ceiling design information, is obtained as a first function expressed by an orthogonal polynomial, Multiple sensors arranged in a predetermined positional relationship on the ceiling measure information about the inclination angle at each measurement point. A predetermined calculation including function fitting using at least a portion of the measurement information from the plurality of sensors is performed to obtain information about the shape of the ceiling as a second function expressed by an orthogonal polynomial of the same type as the first function, Based on the first function and the second function, the information regarding the change in the shape of the ceiling is expressed by a function that is expressed by an orthogonal polynomial of the same type as the first function, A management method that includes determining whether the change in the shape of the ceiling exceeds a threshold based on the information of the aforementioned change.

6. In the management method described in claim 4 or 5, The aforementioned orthogonal polynomials are managed as Czernike polynomials.

7. In the management method described in claim 4, The aforementioned orthogonal polynomial is a Czernike polynomial, Identifying the position or region where the amount of deformation exceeds the threshold is a management method performed based on a comparison between the in-plane distribution of the change in the shape of the ceiling, which is determined based on the magnitude of the coefficients of each term in the Zernike polynomial and the Zernike mode map, and the threshold.

8. In the management method described in Claim 5, The aforementioned orthogonal polynomial is a Czernike polynomial, A management method is used to determine whether the change in the shape of the ceiling exceeds a threshold, based on a comparison between the in-plane distribution of the change in the shape of the ceiling, which is obtained based on the magnitude of the coefficients of each term in the Zernike polynomial and the Zernike mode map, and the threshold.

9. A management system for maintaining and managing the ceiling of a facility, Multiple sensor devices are arranged on the ceiling in a predetermined positional relationship and measure information on the inclination angle at each measurement point, with the ceiling as the measurement target. The system comprises an analysis device and a terminal device, each connected to the aforementioned plurality of sensor devices via a network, The aforementioned analysis device is The function includes measuring information on the inclination angle of the ceiling at each measurement point using the aforementioned plurality of sensor devices, A function to obtain information about the shape of the ceiling by performing a predetermined calculation including function fitting using at least a portion of the measurement information of the plurality of sensor devices, A function to determine the distribution of deformation of the ceiling shape based on the shape information obtained by performing the predetermined calculation and the ceiling shape obtained based on the ceiling design information, Based on the distribution of the deformation amount, a function is provided to identify a position or region in the ceiling where the deformation amount exceeds a threshold, A management system having a function to transmit specific information relating to a position or region where the identified deformation amount exceeds a threshold to the terminal device.

10. In the management system according to claim 9, The terminal device is a management system that, upon receiving the specified information, displays information corresponding to the specified information on a display screen.

11. In the management system according to claim 9, The shape of the ceiling, determined based on the aforementioned design information, is represented by a first function expressed as an orthogonal polynomial. The shape of the ceiling obtained by performing the predetermined calculation is represented by a second function which is expressed by an orthogonal polynomial of the same type as the first function. The distribution of the deformation amount is represented by a management system that is expressed by a function that is an orthogonal polynomial of the same type as the first function.

12. A management system for maintaining and managing the ceiling of a facility, Multiple sensor devices are arranged on the ceiling in a predetermined positional relationship and measure information on the inclination angle at each measurement point, with the ceiling as the measurement target. The system comprises an analysis device and a terminal device, each connected to the aforementioned plurality of sensor devices via a network, The aforementioned analysis device is A function to obtain the shape of the ceiling, which is determined based on the ceiling design information, as a first function expressed by an orthogonal polynomial, The function includes measuring information on the inclination angle of the ceiling at each measurement point using the aforementioned plurality of sensor devices, A function that performs a predetermined calculation including function fitting using at least a portion of the measurement information of the plurality of sensor devices to obtain information about the shape of the ceiling as a second function expressed by an orthogonal polynomial of the same type as the first function, A function that expresses information about the change in the shape of the ceiling using a function that is expressed by the same type of orthogonal polynomial as the first function, based on the first function and the second function. Based on the information on the aforementioned changes, a function is provided to determine whether or not the change in the shape of the ceiling exceeds a threshold. A management system having a function to transmit information relating to the aforementioned determination to the terminal device.

13. In the management system according to claim 11 or 12, The aforementioned orthogonal polynomial is a Czernike polynomial in the management system.

14. In the management system according to claim 11, The aforementioned orthogonal polynomial is a Czernike polynomial, The analysis device is a management system that identifies a position or region where the amount of deformation exceeds a threshold, based on a comparison between the in-plane distribution of the change in the shape of the ceiling, which is determined based on the magnitude of the coefficients of each term in the Zernike polynomial and the Zernike mode map, and the threshold.

15. In the management system according to claim 12, The aforementioned orthogonal polynomial is a Czernike polynomial, The analysis device is a management system that determines whether or not the change in the shape of the ceiling exceeds a threshold, based on a comparison between the in-plane distribution of the change in the shape of the ceiling, which is obtained based on the magnitude of the coefficients of each term of the Zernike polynomial and the Zernike mode map, and the threshold.

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