JP2011122859A - Method and system for diagnosis of defect - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method and system for diagnosis of defects, capable of accurately detecting the shape and depth of the defects of a structure in a short period of time. <P>SOLUTION: The system 1 for diagnosis of the defects includes an infrared camera 5 and a computer 10. The system detects the defects inside of the object structure 2. The infrared camera 5 photographs at least part of the imaging area 4 of the object structure 2 at predetermined time intervals to obtain a plurality of thermal images. The image analysis device 12 of the computer 10 produces a plurality of infinite thermal images for the obtained respective thermal images by expanding the mirror image period, and estimates the shape and the depth from the surface of the defects by an inverse analysis based on the plurality of infinite thermal images. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a defect diagnosis method and a defect diagnosis system for detecting defects such as peeling and voids inside a structure.

  Conventionally, as a method of detecting defects such as peeling of the structure surface layer and cavities that cause a peeling accident in a concrete structure, a hammering sound that determines the presence or absence of defects by the sound of hitting the structure with a hammer etc. An inspection was being conducted. However, since the hammering test requires a great deal of labor, an infrared thermography method that can perform a wide range of inspections in a non-contact manner is widely used as an effective alternative method.

  The infrared thermography method detects these defects by capturing changes in the surface temperature field that occur when heat transfer is hindered by the heat insulation of defects such as exfoliation inside the structure and cavities. is there. Infrared thermography requires heating or cooling in order to cause heat to move inside the structure. Depending on the heating / cooling method, active methods such as heaters, flash lamps, and low-temperature gas blowing, as well as sunshine and natural air cooling are used. Can be divided into passive methods.

  However, in the conventional infrared thermography method, a thermal image obtained by imaging a part including a defect is generally low in readability, and the defect detection sensitivity largely depends on the skill of the inspector. Therefore, quantitative evaluation of the shape and depth of the defect is performed. There was a problem that was difficult. Therefore, as a new method for detecting defects, there is a method for taking the difference from the forward analysis result based on the detailed heat balance model, a method for performing reverse analysis based on the detailed heat balance model, and a lock-in thermography based on active heating. Have been proposed (for example, Patent Documents 1 to 4 and Non-Patent Documents 1 and 2).

Japanese Patent No. 3407000 (registered on March 14, 2003) Japanese Patent No. 3834749 (Registered on August 4, 2006) JP 5-108796 A (published April 30, 1993) JP 11-258188 A (published on September 24, 1999)

Takahide Sakagami and five others, “Non-destructive inspection of concrete structures by lock-in infrared thermography”, Proceedings of the 76th Regular Meeting of the Japan Society of Mechanical Engineers Kansai Branch, 2001, No. 014-1, p. 6-15-6-16 Shin Masuda and three others, “Detection of Defects and Depth Estimation of Concrete Structures by Inverse Analysis of Thermal Images”, Transactions of the Japan Society of Mechanical Engineers (C), 2008, 74, 740, p. 789-797

  The invention described in Patent Document 1 is a technique that enables detection of defects and quantification of depth and three-dimensional shape from a single thermal image taken in an outdoor environment. The problem is solved by paying attention. However, in the present invention, in order to derive a regression equation for estimating the depth and thickness of the air gap, a precise forward analysis with respect to the heat balance model as a reference is required. For this reason, in the said invention, there exists a problem that the detailed prior knowledge regarding the three-dimensional shape of a target structure, the heat balance characteristic in surfaces other than an imaging surface, and a thermal load (sunlight conditions etc.) is required, and it is practical. It is doubtful.

  The invention described in Patent Document 2 is intended for RC or SRC concrete structures, and identifies defect positions based on thermal conduction inverse analysis. However, it presupposes active heating of the reinforcing bars or steel frames, and the specific contents of the heat conduction inverse analysis are not described.

  The inventions described in Patent Literature 3 and Patent Literature 4 extract a defective portion in an image from a difference between a forward analysis result of a heat balance analysis model representing a healthy state and an acquired thermal image. Therefore, in the present invention, the depth of the defect cannot be known, and in order to perform forward analysis, details regarding the three-dimensional shape of the target structure, heat balance characteristics and heat load (such as solar radiation conditions) on surfaces other than the imaging surface There is a problem of requiring prior knowledge.

  As described above, since the inventions described in Patent Documents 1 to 4 are based on a detailed heat balance model, detailed advance information on the structure of the target structure, environment, heat balance characteristics of the entire surface, and heat load (such as solar radiation conditions). There is a problem of needing knowledge, and practicality is difficult.

  Further, Non-Patent Documents 1 and 2 have a problem that the inspection time takes a long time (tens of minutes to several hours).

  Specifically, in the invention described in Non-Patent Document 1, the object is periodically heated by a lamp heater that is turned on / off at a certain cycle, and this is locked in, thereby causing a phase delay in the temperature response to the heat load input. And the depth to the defect is calculated from the relationship of the change in the phase lag to the change in the heating cycle. Although the SN ratio can be improved by performing periodic heating, there is a problem that a long measurement time is required in the case of a concrete structure.

  In the invention described in Non-Patent Document 2, it is possible to clarify the defect shape and estimate the defect depth by inverse analysis of the surface thermal image, but it is essential that the target structure is in a thermally steady state. It is a condition. For this reason, the passive heating method has a problem that the feasibility greatly depends on the natural conditions because the change in the heat load condition such as the solar radiation condition is small. In the active heating method, the target structure must be heated until it reaches a steady state, and a heating time of several hours is required, so a wide range can be inspected in a short time at a low cost. There is a problem that the inherent advantage of the infrared thermography method is offset.

  The present invention has been made to solve the above problems, and an object thereof is to realize a defect diagnosis method and a defect diagnosis system capable of accurately detecting the shape and depth of a defect in a structure in a short time. It is in.

  In order to solve the above problems, a defect diagnosis method according to the present invention is a defect diagnosis method for detecting a defect inside a target structure, and at least a part of the surface of the target structure at a predetermined time interval. A thermal image acquisition step of acquiring a plurality of thermal images, and for each acquired thermal image, the image and the mirror image of the image are connected to each other, and the mirror image and the mirror image of the mirror image By repeating the process of joining together, a mirror image period expansion process for creating a plurality of infinite thermal images, and estimating the shape of the defect and the depth from the surface by inverse analysis based on the plurality of infinite thermal images And a reverse analysis step.

  According to the above configuration, the plurality of thermal images acquired in the thermal image acquisition step are converted into a plurality of infinite thermal images that are infinite plate regions having infinite extent in the x and y axis directions in the mirror image period extension step. Convert. This makes it possible to perform a reverse heat analysis without using information outside the imaging region while avoiding the introduction of discontinuities that do not exist in the temperature distribution of the original thermal image. Furthermore, since the inverse analysis is performed based on a plurality of infinite thermal images at predetermined time intervals in the inverse analysis process, even if the temperature of the target structure is in an unsteady state, the shape of the defect and the depth from the surface can be accurately determined. Can be estimated. Further, since the target structure does not need to be in a steady state, the time required for diagnosis can be shortened. Therefore, it is possible to realize a defect diagnosis method capable of accurately detecting the shape and depth of the defect of the structure in a short time.

In the defect diagnosis method according to the present invention, in the thermal image acquisition step, M + 1 (M is an integer of 1 or more) thermal images are acquired, the imaging surface of the thermal image is rectangular, and the inverse analysis step includes From the thermal images at times t ₀ , t ₀ + Δt ₁ ,..., T ₀ + Δt _M of the thermal image acquisition step, the expansion coefficient of the temperature of the imaging surface is obtained by the following equation (A), A first calculation step for obtaining a power expansion coefficient of the heat flux in the depth direction of the imaging surface by the equation (B), and a second Fourier transform of the power expansion coefficient of the temperature and the power expansion coefficient of the heat flux. A second calculation step, and a third calculation step for obtaining the temperature and depth direction heat flux of the n (n is an integer of 1 or more) layer located at a specified depth by the following equation (C): Determine the depth at which the absolute value of the heat flux in the depth direction at each point on the imaging surface is minimized. It is preferable to have four calculation steps.

θ ^m : m-th order expansion coefficient of the imaging surface temperature q ^m : m-th order expansion coefficient of the heat flux in the depth direction of the imaging surface x: horizontal coordinate of the imaging surface y: vertical coordinate of the imaging surface z: Coordinates in the depth direction perpendicular to the imaging surface θ (x, y, z, t): Arbitrary point (x, y, z) Temperature at arbitrary time t q _z (x, y, z, t): Arbitrary (X, y, z) in the depth direction at an arbitrary time t a: thermal diffusivity a = κ / (cρ)
c: Specific heat ρ: Density κ: Thermal conductivity α ₀ : Total heat transfer coefficient on the imaging surface θ ₀ : Ambient temperature on the imaging surface q ₀ : Heat flux input to the imaging surface F _xy : Double Fourier transform for x and y IF _xy : Double inverse Fourier transform with respect to x and y k _x : Wave number in the x-axis direction k _y : Wave number in the y-axis direction In the defect diagnosis method according to the present invention, the estimated defect above It is preferable to have a defect visualization step of mapping the depth from the surface as color information.

  According to said structure, since the depth from the said surface of the estimated defect is mapped as color information, the state of a defect can be grasped | ascertained intuitively.

  In order to solve the above-described problem, a defect diagnosis system according to the present invention is a defect diagnosis system that includes a thermography device and a computer and detects a defect inside a target structure, and the thermography device includes the target At least a part of the surface of the structure is photographed at predetermined time intervals to obtain a plurality of thermal images, and the computer obtains an image and a mirror image of the image for each acquired thermal image. Mirror image period extending means for creating a plurality of infinite thermal images by repeating the process of connecting and further connecting the mirror symmetric image and a further mirror symmetric image of the mirror symmetric image, and based on the plurality of infinite thermal images And an inverse analysis means for estimating the shape of the defect and the depth from the surface by inverse analysis.

  According to said structure, a mirror image period expansion means converts the some thermal image acquired by the thermography apparatus into the some infinite thermal image which is an infinite flat area | region which has an infinite breadth in the x and y-axis directions. . This makes it possible to perform a reverse heat analysis without using information outside the imaging region while avoiding the introduction of discontinuities that do not exist in the temperature distribution of the original thermal image. Furthermore, since the inverse analysis means performs an inverse analysis based on a plurality of infinite thermal images at a predetermined time interval, even if the temperature of the target structure is in an unsteady state, the shape of the defect and the depth from the surface can be accurately determined. Can be estimated. Further, since the target structure does not need to be in a steady state, the time required for diagnosis can be shortened. Therefore, it is possible to realize a defect diagnosis system that can accurately detect the shape and depth of defects in a structure in a short time.

In the defect diagnosis system according to the present invention, the thermography apparatus acquires M + 1 (M is an integer of 1 or more) thermal images, the imaging surface of the thermal image is rectangular, and the inverse analysis means includes the thermography. From the thermal image acquired by the apparatus at times t ₀ , t ₀ + Δt ₁ ,..., T ₀ + Δt _M , the expansion coefficient of the temperature of the imaging surface is obtained by the following equation (A), and the following equation ( B), the power expansion coefficient of the heat flux in the depth direction of the imaging surface is obtained, the power expansion coefficient of the temperature and the power expansion coefficient of the heat flux are subjected to double Fourier transform, and the following equation (C): The depth at which the absolute value of the depth direction heat flux at each point on the imaging surface is minimized by obtaining the temperature and depth direction heat flux of the n layer (n is an integer of 1 or more) located at the specified depth. Is preferably obtained.

θ ^m : m-th order expansion coefficient of the imaging surface temperature q ^m : m-th order expansion coefficient of the heat flux in the depth direction of the imaging surface x: horizontal coordinate of the imaging surface y: vertical coordinate of the imaging surface z: Coordinates in the depth direction perpendicular to the imaging surface θ (x, y, z, t): Arbitrary point (x, y, z) Temperature at arbitrary time t q _z (x, y, z, t): Arbitrary (X, y, z) in the depth direction at an arbitrary time t a: thermal diffusivity a = κ / (cρ)
c: Specific heat ρ: Density κ: Thermal conductivity α ₀ : Total heat transfer coefficient on the imaging surface θ ₀ : Ambient temperature on the imaging surface q ₀ : Heat flux input to the imaging surface F _xy : Double Fourier transform for x and y IF _xy : Double inverse Fourier transform with respect to x and y k _x : Wave number in the x-axis direction k _y : Wave number in the y-axis direction In the defect diagnosis system according to the present invention, the computer calculates the estimated defect from the surface. It is preferable to have a defect visualization means for mapping the depth as color information.

  According to said structure, since the depth from the said surface of the estimated defect is mapped as color information, the state of a defect can be grasped | ascertained intuitively.

  As described above, the defect diagnosis method according to the present invention is a defect diagnosis method for detecting defects inside a target structure, and includes a plurality of heats on at least a part of the surface of the target structure at a predetermined time interval. For the thermal image acquisition step of acquiring an image, and for each acquired thermal image, the image and the mirror-symmetric image of the image are connected, and the mirror-symmetric image and a further mirror-symmetric image of the mirror-image symmetrical image are further connected. Mirror image period expansion step for creating a plurality of infinite thermal images by repeating processing, and an inverse analysis step for estimating the shape of the defect and the depth from the surface by reverse analysis based on the plurality of infinite thermal images It is the composition which has. A defect diagnosis system according to the present invention includes a thermography device and a computer, and detects a defect inside a target structure. The thermography device includes at least one surface of the target structure. The computer is photographed at predetermined time intervals to obtain a plurality of thermal images, and the computer connects the image and the mirror image of the image for each of the acquired thermal images, and the mirror image image And a mirror image period expanding means for creating a plurality of infinite thermal images by repeating the process of further joining the mirror symmetric image and a further mirror symmetric image of the mirror image symmetric image, and the defect by inverse analysis based on the plurality of infinite thermal images. And a reverse analysis means for estimating the depth from the surface. Therefore, there is an effect that it is possible to realize a defect diagnosis method and a defect diagnosis system capable of accurately detecting the shape and depth of the defect of the structure in a short time.

1 is a diagram showing a schematic configuration of a defect diagnosis system according to an embodiment of the present invention. It is sectional drawing which shows the inside of the target structure diagnosed by the said defect diagnostic system. (A)-(c) is a figure which shows the procedure of the mirror image period expansion of an area | region. It is a flowchart which shows the procedure of the reverse analysis which concerns on embodiment of this invention. It is a figure which shows an example of the depth image of the estimated defect. It is a figure which shows schematic structure of the experiment which concerns on Example 1 of this invention. (A) to (c) are surface temperature images after 26 minutes, 28 minutes and 30 minutes from the start of heating, respectively. It is a figure which shows the result of having performed the reverse analysis by the conventional reverse analysis method based on a steady model based on the surface temperature image shown in FIG. 7, and calculating the depth image. It is a figure which shows the result of having performed the reverse analysis by the reverse analysis method by this invention based on the surface temperature image shown in FIG. 7, and calculating the depth image. (A) is a top view which shows the rectangular parallelepiped model used in Example 2, (b) is sectional drawing of this rectangular parallelepiped model. It is a figure which shows the surface temperature distribution of the rectangular parallelepiped model calculated | required by the finite element analysis about the case of D = 0.02m, (a) The surface temperature distribution 20 minutes after a heating start is shown, (b) is heating The surface temperature distribution 60 minutes after the start is shown. It is the depth image created from the estimated internal heat flux distribution 20 minutes after the start of heating, (a) shows the case of the 0th order approximation, and (b) shows the case of the second order approximation. . It is a depth image created from the estimated internal heat flux distribution 60 minutes after the start of heating, (a) shows the case of the 0th order approximation, and (b) shows the case of the second order approximation. . It is the graph which plotted the depth direction distribution of the estimated value of the temperature and the heat flux in the center point of the rectangular parallelepiped model 20 minutes after a heating start with a true value. It is the graph which plotted the depth direction distribution of the estimated value of the temperature and heat flux in the center point of the rectangular parallelepiped model 60 minutes after a heating start with a true value. (A) is the graph which plotted the relationship between the imaging | photography time (elapsed time from a heating start) and the estimated value of defect depth in the case of defect depth D = 0.02m, (b) These are the graphs which plotted the relationship between the imaging | photography time (elapsed time from a heating start) of a thermal image, and the estimated value of a defect depth in case of the defect depth D = 0.04m.

  An embodiment of the present invention will be described below with reference to FIGS.

(Configuration of defect diagnosis system 1)
FIG. 1 is a diagram showing a schematic configuration of a defect diagnosis system 1 according to the present embodiment. The defect diagnosis system 1 is a system that detects a defect inside the target structure 2 and includes an infrared camera 5 and a computer 10.

  In the present embodiment, the target structure 2 is a concrete floor board of a bridge, and the upper surface of the target structure 2 is heated by solar radiation 3 that is an unsteady light source. The amount of heat incident on the upper surface (heating surface) and the boundary conditions of surfaces other than the imaging region are unknown. The infrared camera (thermographic apparatus) 5 images the lower surface (imaging surface) 4 of the target structure 2 at a predetermined time interval, and outputs a plurality of thermal image data to the computer 10. Reference numeral 4a denotes an imaging area of the infrared camera 5. The computer 10 includes an image storage device 11, an image analysis device 12, a display device 13, and a data input device 14. Based on the thermal image data output from the infrared camera 5, defects in the target structure 2 are detected. Estimate shape and depth.

  FIG. 2 is a cross-sectional view showing the inside of the target structure 2. As shown in the figure, the heat incident from the heating surface of the target structure 2 is conducted in the thickness direction of the target structure 2 to form a heat flux 6 inside the target structure 2. Here, it is assumed that there is a peeling defect 7 near the surface layer of the imaging surface 4 on the opposite side of the heating surface. Since the peeling defect 7 is a thin cavity layer, heat conduction is hindered. As a result, a low temperature portion 4 b is formed at a position corresponding to the peeling defect 7 on the imaging surface 4. Therefore, the shape of the peeling defect 7 and the depth from the imaging surface 4 can be estimated by inversely analyzing the surface temperature distribution of the imaging surface 4.

  In the defect diagnosis system 1, in order to grasp the surface temperature distribution on the imaging surface 4, the imaging surface 4 is imaged with the infrared camera 5 to obtain a thermal image (temperature image). At this time, the infrared camera 5 acquires a plurality of thermal images after a certain time and stores the thermal images in the image storage device 11. In the present embodiment, the imaging area 4a by the infrared camera 5 is rectangular, and when the image is distorted due to the geometric arrangement of the optical system of the infrared camera 5 and the imaging surface, the image is mapped to the rectangular area. Appropriate processing such as tilt correction is performed.

  The image analysis device 12 includes a CPU, performs reverse analysis on the thermal image data stored in the image storage device 11, and displays the result of the reverse analysis on the display device 13. Further, the inspector can input various parameters using the data input device 14 such as a keyboard or a mouse. Subsequently, processing contents in the image analysis device 12 will be described.

(Mirror image period extension)
In a rectangular parallelepiped region having a rectangular imaging region 4a as one surface and a surface obtained by translating the imaging region 4a by d in the depth direction, the x and y axes are set in the vertical and horizontal directions in the imaging surface 4, and the depth The z axis is set in the vertical direction, the imaging surface 4 is defined as z = 0, and the opposite facing surface is defined as z = d.

  Next, this rectangular parallelepiped region is periodically connected in the x and y axis directions, and is expanded into an infinite flat plate region having a thickness in the z axis direction and an infinite extent in the x and y axis directions. As a result, the target structure can be handled as an infinite flat plate, so that the inverse analysis is remarkably simplified, and the heat conduction inverse analysis can be performed without knowing information outside the imaging region.

  However, when regions are simply joined periodically, discontinuities that do not exist in the original temperature distribution are introduced at the joints of the regions. Therefore, in this embodiment, in order to avoid discontinuity, the rectangular parallelepiped region is expanded to the infinite flat plate region by the following operation. In the present embodiment, this operation is called mirror image period extension.

  FIGS. 3A to 3C are diagrams showing a procedure for extending the mirror image period of the region. First, the rectangular parallelepiped region shown in FIG. 3A and its mirror image in the x and y directions are joined together so that the temperature at the joint of the region is continuous, as shown in FIG. 3B. In the same manner, as shown in FIG. 3C, each region is expanded as a unit cell. In this way, it is possible to avoid introducing discontinuities that do not exist in the original temperature distribution by performing the mirror image expansion once after performing the mirror image symmetry expansion instead of the simple period expansion.

(Unsteady interlayer transmission matrix)
In an infinite flat plate region in which a rectangular parallelepiped region having the imaging region 4a as one surface is expanded in the x and y directions by the above method, the temperature at an arbitrary point (x, y, z) is θ (x, y, z, t), the three-dimensional unsteady heat conduction equation in the infinite flat plate region and the boundary condition of the imaging surface 4 are expressed by the following equations (1) and (2).

Where q _z is the heat flux in the depth direction,

Is defined. Further, a is the thermal diffusivity, c is the specific heat, ρ is the density, κ is the thermal conductivity, α ₀ is the total heat transfer coefficient on the imaging surface 4, θ ₀ is the ambient temperature on the imaging surface, and q ₀ is the temperature to the imaging surface. Heat flux input. All these parameters are known, and the inspector inputs them to the image analysis device 12 using the data input device 14.

The defect portion is a layered finite region having a thickness h parallel to the surface at a depth D from the flat plate surface, and assuming that the boundary Γ _defect is an internal heat insulation boundary, the heat flow in the depth direction on the upper and lower surfaces of the defect portion Bunch

It becomes.

An infinite flat plate region is virtually divided into layers in the z-axis direction. The n-th layer is defined as z∈ [z _n−1 , z _n ], and z ₀ = 0.

  Next, when the above governing equation (1) is subjected to double Fourier transform with respect to x and y, equation (5) is obtained.

Here, F _xy represents a double Fourier transform relating to x and y, and a hat represents a quantity in the double Fourier transform region. ^{_{Further, k (= √ (k x}} 2 + k y 2)), k x and _{k y} are, x, a wave number of y-axis direction.

  In order to solve equation (5), the temperature field and the depth heat flux field are approximated by power expansion with respect to time.

  When the first equation of Equation (6) is subjected to double Fourier transform with respect to x and y and substituted into Equation (5), and the coefficients of the same order with respect to time are equalized, Equation (7) is obtained.

Solving equation (7) as an initial value problem for z in the order of hat θ ^M , hat θ ^M−1 ,..., Hat θ ⁰ , the double of the temperature expansion coefficient of the n−1th layer and the nth layer. Equation (8) relating the double Fourier transform between the Fourier transform and the heat flux expansion coefficient is obtained.

Here, H _n is an interlayer transfer matrix, and maps the temperature and heat flux of the (n−1) th layer to the temperature and heat flux of the nth layer in the wave number region. When the specific contents of H _n ^m constituting H _n are shown from m = 0 to m = 2, equations (9) to (11) are obtained.

Since the estimation of the internal field by the equation (8) has instability, the equation (12) obtained by regularizing Tikhonov is actually used instead of the diagonal block H _n ⁰ .

  Here, λ is a regularization parameter.

(Inverse analysis procedure)
The procedure of the inverse analysis performed in the image analysis apparatus 12 using the equation derived as described above is as follows.

First, parameters necessary for the analysis (the boundary condition of the imaging surface, the thermal conductivity and thermal diffusivity of the object), and the power expansion approximation truncation order M are input from the data input device 14. Next, calculate the expansion coefficients q ^m to the expansion coefficient theta ^m and heat flux temperature to of the imaging area 4a (z = 0). The expansion coefficient of the temperature of the imaging region 4a is obtained by solving the following simultaneous linear equation (13) from the thermal image acquired by the infrared camera 5 at times t ₀ , t ₀ + Δt ₁ ,..., T ₀ + Δt _M. Sought by.

  Further, the expansion coefficient of the heat flux in the imaging region 4a is obtained by calculating the depth direction heat flux in the imaging region 4a from the known boundary condition equation (2) and then solving the following simultaneous equations (14). .

After the mirror image expansion as shown in FIG. 3B, the vector (hat u ₀ ) is obtained by performing high-speed double Fourier transform on the power expansion series of the temperature and the power expansion series of the heat flux. Using this vector (hat u ₀ ) as an initial value, the vector (hat u _n ) on the inner boundary surface is sequentially obtained by equation (8). The temperature distribution and the heat flux distribution in the depth direction at an arbitrary inner boundary surface can be obtained by performing high-speed double inverse Fourier transform on these and returning to the power expansion equation (6).

FIG. 4 is a flowchart showing the inverse analysis procedure according to the present embodiment. First, parameters necessary for inverse analysis such as thermal conductivity, thermal diffusivity, and surface boundary conditions are input by the data input device 14 (step S1). Subsequently, a temperature image of the surface of the target structure 2 is taken with the infrared camera 5 (step S2, thermal image acquisition step). Subsequently, the truncation order M of the power expansion approximation is set to 0 (step S3), necessary processing such as tilt correction is performed, and the surface temperature distribution is calculated (step S4). Next, the surface heat flux distribution is calculated using the boundary conditions (step S5), and the power expansion coefficient of the surface temperature and the power expansion coefficient of the heat flux are calculated by solving the equations (13) and (14). (Step S6, first calculation step). Subsequently, the power expansion series of the temperature and the power expansion series of the heat flux are subjected to high-speed double Fourier transform to obtain a vector (hat u ₀ ) (step S7, second calculation step).

Subsequently, using the vector (hat u ₀ ) as an initial value, the vector (hat u _n ) on the inner boundary surface is sequentially obtained by Expression (8). Specifically, first, n = 1 is set (step S8), and the temperature and heat flux of the nth layer are obtained from the Fourier transform of the power and the expansion coefficient of the n−1 layer temperature and heat flux according to the equation (8). A Fourier transform of the power expansion coefficient is obtained (step S9), the power expansion coefficient of the surface temperature of the nth layer and the power expansion coefficient of the heat flux are subjected to high-speed double inverse Fourier transform, The eye temperature and the heat flux in the depth direction are obtained (step S10, third calculation step). If the depth of the nth layer does not reach the prescribed depth (“NO” in step S11), n is increased by 1 (step S12), and steps S9 and S10 are performed again, and this cycle is repeated for the nth layer. Repeat until the depth reaches the specified depth.

  When the depth of the n-th layer reaches a prescribed depth (“YES” in step S11), a temperature image of the surface of the target structure 2 is taken with the infrared camera 5 after a certain time (step S13, heat Image acquisition process). Here, the surface temperature is predicted by the equation (13), and it is determined whether the error between the temperature image photographed in step S13 and the predicted temperature is within the specified range (step S14). If the error is not within the specified range (“NO” in step S14), the power expansion approximation truncation order M is incremented by 1 (step S15), and the processes in steps S4 to S14 are repeated again. When the error is within the specified range (“YES” in step S14), the depth direction heat flux at each point on the imaging surface is scanned in the depth direction, and the depth at which the absolute value of the depth direction heat flux is minimized. Is determined as the defect depth (step S16, fourth calculation step), and a depth image in which the defect depth at each point is imaged is created (step S17).

  As described above, the temperature of the inner layer and the distribution of the heat flux in the depth direction are sequentially obtained from the imaging region 4a in the depth direction, and the heat insulating layer (ie, the depth direction heat flux is zero at each point). It is determined that there is a defect.

  Subsequently, by displaying the depth image on the display device 13, the depth and shape of the defect can be visualized (step S18). FIG. 5 shows an example of an estimated defect depth image. In the depth image, the estimated depth of the defect from the imaging region 4a is mapped to each pixel as color information, and the correspondence between the depth and the color is indicated by a color bar. Therefore, it is possible to intuitively grasp the defect state.

  As described above, in the defect diagnosis system 1 according to the present embodiment, the stationary condition that has been an obstacle to the practical use in the conventional defect diagnosis system is removed, and the defect image is restored from the unsteady thermal image. Since the construction can be performed, the shape and depth of the defect can be accurately detected in a short time.

  In order to confirm that the defect shape and depth can be accurately detected in a short time by the defect diagnosis system according to the present invention, the following experiment was conducted.

  FIG. 6 is a diagram illustrating a schematic configuration of an experiment according to the present embodiment. As shown in the figure, a mortar test piece 22 was placed on a hot plate 20 with a thermally conductive silicon rubber sheet 21 interposed therebetween. The silicon rubber sheet 21 was used in order to eliminate the gap between the mortar test piece 22 and the hot plate 20 and to uniformly heat the back surface of the mortar test piece 22. The temperature of the hot plate was set to 50 ° C., the mortar test piece 22 was heated, an infrared camera was fixed immediately above the test piece, and a thermal image of the surface of the mortar test piece 22 was taken. Moreover, the side surface of the mortar test piece 22 was enclosed with styrofoam to reproduce the heat insulation boundary.

  The mortar test piece 22 is a rectangular parallelepiped having a side of 300 mm and a thickness of 60 mm. Inside the mortar test piece 22, a square styrofoam having a side of 100 mm and a thickness of 10 mm was embedded as an artificial defect at a position 20 mm deep from the imaging surface in the center of the imaging surface. With the above configuration, the depth of the defect was estimated based on the plurality of thermal image data photographed by the infrared camera.

  7A to 7C show surface temperature images after 26 minutes, 28 minutes and 30 minutes from the start of heating, respectively.

  8 and 9 are diagrams showing the results of performing a reverse analysis based on the surface temperature image shown in FIG. 7 and calculating the depth image. Here, FIG. 8 shows the result using the inverse analysis method based on the steady model (the method of Non-Patent Document 2), and FIG. 9 shows the result using the inverse analysis method (M = 2) according to the present invention. Is shown. In the method based on the steady model, the estimated defect depth (9 mm) is much shallower than the actual (20 mm). On the other hand, in the method according to the present invention, the estimated depth of the defect is 24 mm, and the depth of the defect is estimated almost accurately. From this result, it can be seen that the defect measurement method according to the present invention can accurately measure the depth of the defect even for a target structure in an unsteady state. Moreover, since the measurement time is as short as 4 minutes, it is highly practical.

  Further, in order to confirm that the defect shape and depth can be accurately detected in a short time by the defect diagnosis system according to the present invention, the following numerical experiment by simulation was performed.

  FIG. 10A is a plan view showing a rectangular parallelepiped model 30 used in the present embodiment, and FIG. 10B is a cross-sectional view of the rectangular parallelepiped model 30. The material of the rectangular parallelepiped model 30 is assumed to be mortar, and is 0.3 m in length, 0.3 m in width, and 0.06 m in height. The rectangular parallelepiped model 30 is assumed to have a square-shaped defect (cavity) 31 having a thickness of 0.01 m at a depth D from the surface (imaging surface) 30a as a defect. All the internal boundaries of the defect 31 are defined as heat insulation boundaries, all side surfaces are defined as heat insulation boundaries, and the surface is defined as a heat transfer boundary. The initial temperature is room temperature. Unsteady heat conduction analysis was performed by the finite element method with a constant temperature constraint on the back surface 30b from time zero, and the obtained internal temperature field and heat flux field were treated as true values for the inverse problem. Table 1 shows the parameter values used in the finite element analysis.

  FIG. 11 is a diagram showing the surface temperature distribution of the rectangular parallelepiped model 30 obtained by finite element analysis in the case of D = 0.02 m, (a) shows the surface temperature distribution 20 minutes after the start of heating, b) shows the surface temperature distribution 60 minutes after the start of heating. In FIG. 11, it can be seen that a low temperature portion appears at a position corresponding to the defect 31, but the outline of the low temperature portion is unclear and the defect shape cannot be determined, and information on the depth of the defect 31 cannot be obtained. .

  FIG. 12 is a depth image created from the estimated internal heat flux distribution 20 minutes after the start of heating. (A) shows the case of the 0th order approximation, and (b) shows the case of the second order approximation. Is shown. FIG. 13 is a depth image created from the estimated internal heat flux distribution 60 minutes after the start of heating. FIG. 13A shows the case of the zeroth order approximation, and FIG. 13B shows the second order approximation. Shows the case. 12 and 13, the bar on the right side of the image represents the estimated depth (unit m).

  As shown in FIG. 12A, in the case of the 0th order approximation, the defect image seems to be sharp at first glance, but the depth value is not accurate at all and is estimated as a value very close to the surface. ing. On the other hand, as shown in FIG. 12B, in the case of the quadratic approximation, the obtained depth image has a sharper outline although the defect image is reduced compared to the original temperature image. It can be clearly read that the defect is square and the depth is around 0.02 m. A similar tendency can be seen in FIG. 13, but the reduction of the defect image in the second-order approximation is relatively slight.

  In order to examine in detail the influence of the power expansion approximation order of the time dependence of the temperature field, FIG. 14 and FIG. As shown in FIG. In the heat flux graph, the zero level is indicated by a broken line, and the intersection of this and the heat flux curve is the defect depth at the center point.

  First, paying attention to the influence of the difference in approximation order, it can be seen that the second-order approximation can more appropriately express the dependency of the internal temperature and the heat flux field in the depth direction than the zero-order approximation. That is, increasing the time-dependent expressive power also increases the spatial-dependent expressive power. This can be explained using equation (7) above. The expression in which the wave number is zero in Expression (7) is an expression that gives an in-plane integral value of the temperature of each layer. Here, if M = 0 (0th order approximation), Equation (7) is

From this, it can be seen that the in-plane integral value of the temperature is estimated as a linear function in the depth direction. When M = 1 (first order approximation),

Thus, the in-plane integral value of the temperature becomes a cubic function in the depth direction. Similarly, when M = 2 (second-order approximation), it becomes a quintic function. In other words, if the degree of expansion of the power-dependent time dependence of the temperature is increased, the power of time-dependent expression can be improved, and it becomes possible to deal with data with stronger unsteadiness, while at the same time expressing spatial dependence. The force is also increased, resulting in improved depth estimation accuracy.

  Next, looking at the difference depending on the elapsed time after the start of heating, 20 minutes after the start of heating, the temperature rise that started from the heating surface (depth 0.06 m) hardly reached the downstream side of the defect. On the other hand, after 60 minutes from the start of heating, the temperature in the region downstream of the defect is sufficiently increased. As a result, the heat flux in the depth direction passing around the defect edge is increased, and the shape estimation accuracy of the defect edge in FIG. 13B is higher than that in FIG. 12B.

  Finally, in order to confirm the effectiveness of the inverse analysis method according to the present invention in consideration of unsteadiness, the relationship between the imaging time of the image to be used (elapsed time from the start of heating) and the estimated value of the defect depth FIG. 16A and FIG. 16B show plots for the case of the defect depth D = 0.02 m and D = 0.04 m, respectively. From the figure, it can be seen that as a general tendency, the estimation accuracy increases as time elapses from the start of heating. This is because the system approaches a steady state as time elapses from the start of heating.

  In particular, a solution that assumes a zero-order approximation, that is, a steady heat conduction field, has no reliability at all in a transient region (unsteady region) where the system reaches a steady state. On the other hand, the accuracy of the solution assuming a first-order approximate unsteady heat conduction field is remarkably improved, and the solution assuming a second-order approximation unsteady heat conduction field provides a good depth estimation for shallow defects. Accuracy is secured. For deep defects, a solution that assumes a higher-order approximate unsteady heat conduction field may be adopted.

(Summary of embodiment)
The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately modified within the scope of the claims are also included in the technical scope of the present invention.

  INDUSTRIAL APPLICABILITY The present invention can be used for a defect diagnosis system that detects defects such as peeling and cavities inside a structure.

DESCRIPTION OF SYMBOLS 1 Defect diagnosis system 2 Target structure 3 Solar radiation 4 Imaging surface 4a Imaging area 4b Low temperature part 5 Infrared camera (thermography apparatus)
6 Heat flux 7 Peeling defect (defect)
10 Computer 11 Image storage device 12 Image analysis device (mirror period expansion means, inverse analysis means, defect visualization means)
13 Display device (defect visualization means)
14 Data Input Device 20 Hot Plate 21 Silicon Rubber Sheet 22 Mortar Test Piece (Target Structure)
30 Cuboid model (target structure)
30a Front surface 30b Rear surface 31 Defect

Claims (6)

A defect diagnosis method for detecting defects inside a target structure,
A thermal image acquisition step of acquiring a plurality of thermal images of at least a part of the surface of the target structure at a predetermined time interval;
For each acquired thermal image, by repeating the process of connecting the image and the mirror-symmetric image of the image, and further connecting the mirror-image-symmetric image and the further mirror-symmetric image of the mirror-image symmetrical image, a plurality of infinite heat Mirror period expansion process to create an image,
Based on the plurality of infinite thermal images, an inverse analysis step of estimating the shape of the defect and the depth from the surface by inverse analysis;
A defect diagnosis method characterized by comprising: In the thermal image acquisition step, M + 1 (M is an integer of 1 or more) thermal images are acquired, and the imaging surface of the thermal image is rectangular,
The reverse analysis step is
From the thermal images at times t ₀ , t ₀ + Δt ₁ ,..., T ₀ + Δt _M of the thermal image acquisition step, the expansion coefficient of the temperature of the imaging surface is obtained by the following equation (A), A first calculation step of obtaining a power expansion coefficient of the heat flux in the depth direction of the imaging surface according to the formula (B);
A second calculation step of performing a double Fourier transform between the power expansion coefficient of the temperature and the power expansion coefficient of the heat flux;
A third calculation step for obtaining a temperature and a depth direction heat flux of an n (n is an integer of 1 or more) layer located at a specified depth by the following formula (C);
A fourth calculation step for obtaining a depth at which the absolute value of the heat flux in the depth direction at each point on the imaging surface is minimized;
The defect diagnosis method according to claim 1, further comprising:
θ ^m : m-th order expansion coefficient of the imaging surface temperature q ^m : m-th order expansion coefficient of the heat flux in the depth direction of the imaging surface x: horizontal coordinate of the imaging surface y: vertical coordinate of the imaging surface z: Coordinates in the depth direction perpendicular to the imaging surface θ (x, y, z, t): Arbitrary point (x, y, z) Temperature at arbitrary time t q _z (x, y, z, t): Arbitrary (X, y, z) in the depth direction at an arbitrary time t a: thermal diffusivity a = κ / (cρ)
c: Specific heat ρ: Density κ: Thermal conductivity α ₀ : Total heat transfer coefficient on the imaging surface θ ₀ : Ambient temperature on the imaging surface q ₀ : Heat flux input to the imaging surface F _xy : Double Fourier transform for x and y IF _xy : Double inverse Fourier transform for x and y k _x : Wave number in the x-axis direction k _y : Wave number in the y-axis direction After the reverse analysis step,
The defect diagnosis method according to claim 1, further comprising a defect visualization step of mapping a depth of the estimated defect from the surface as color information. A thermography device and a computer,
A defect diagnosis system for detecting defects inside a target structure,
The thermography device captures at least a part of the surface of the target structure at a predetermined time interval to obtain a plurality of thermal images,
The computer
For each acquired thermal image, by repeating the process of connecting the image and the mirror-symmetric image of the image, and further connecting the mirror-image-symmetric image and the further mirror-symmetric image of the mirror-image symmetrical image, a plurality of infinite heat Mirror image period expansion means for creating an image;
Inverse analysis means for estimating the shape of the defect and the depth from the surface by inverse analysis based on the plurality of infinite thermal images,
A defect diagnosis system comprising: The thermography apparatus acquires M + 1 (M is an integer of 1 or more) thermal images, and the imaging surface of the thermal image is rectangular,
The inverse analysis means is
From the thermal images acquired by the thermography device at times t ₀ , t ₀ + Δt ₁ ,..., T ₀ + Δt _M , a power expansion coefficient of the temperature of the imaging surface is obtained by the following equation (A):
The expansion coefficient of the heat flux of the imaging surface is obtained by the following equation (B),
Double Fourier transform the power expansion coefficient of the temperature and the power expansion coefficient of the heat flux,
According to the following formula (C), the temperature and the depth direction heat flux of the n layer (n is an integer of 1 or more) located at the specified depth are obtained,
The defect diagnosis system according to claim 4, wherein a depth at which an absolute value of the heat flux in the depth direction at each point on the imaging surface is minimized is obtained.
θ ^m : m-th order expansion coefficient of the imaging surface temperature q ^m : m-th order expansion coefficient of the heat flux in the depth direction of the imaging surface x: horizontal coordinate of the imaging surface y: vertical coordinate of the imaging surface z: Coordinates in the depth direction perpendicular to the imaging surface θ (x, y, z, t): Arbitrary point (x, y, z) Temperature at arbitrary time t q _z (x, y, z, t): Arbitrary (X, y, z) in the depth direction at an arbitrary time t a: thermal diffusivity a = κ / (cρ)
c: Specific heat ρ: Density κ: Thermal conductivity α ₀ : Total heat transfer coefficient on the imaging surface θ ₀ : Ambient temperature on the imaging surface q ₀ : Heat flux input to the imaging surface F _xy : Double Fourier transform for x and y IF _xy : Double inverse Fourier transform for x and y k _x : Wave number in the x-axis direction k _y : Wave number in the y-axis direction The computer
6. The defect diagnosis system according to claim 4, further comprising defect visualizing means for mapping a depth of the estimated defect from the surface as color information.