JP6213859B2 - Estimating the average remaining thickness by estimating the average corrosion depth of the ground corrosion damage zone - Google Patents

Description

  The present invention relates to a method for estimating a residual average plate thickness by estimating an average corrosion depth of a subsurface corrosion damaged portion for estimating a residual plate thickness of a subsurface portion of a steel material embedded in concrete or ground using an eddy current flaw detection sensor. About.

Conventionally, as the structure of the ground part of steel material buried in concrete or ground, there is, for example, the base of a steel pier, etc. In this case, in order to evaluate the soundness of the boundary part of the steel material, nondestructive inspection is used. It is necessary to estimate the average corrosion depth.
Here, it is known that rainwater and an antifreezing agent stay for a long period of time as a ground part of the steel material, so that the paint film on the ground part deteriorates earlier than other parts. In this case, since there is a difference in the corrosive environment property between the exposed portion of the ground portion and the buried portion of concrete or the like, a large corrosion current is generated due to a potential difference between the two, thereby corroding the ground portion.

As an inspection for such corrosion of steel materials, investigations have been conducted to expose steel members through concrete. However, since it requires labor and cost, a non-destructive investigation method is desired. As this nondestructive inspection method, the use of ultrasonic flaw detection technology is being studied, but even if ultrasonic waves are incident on the steel material, the ultrasonic flaws have a large influence on the surface of the steel material where the ultrasonic waves are reflected. There is a limit to the detection accuracy of corrosion damage (see, for example, Patent Document 1).
On the other hand, there is eddy current inspection as a nondestructive inspection method. In eddy current flaw detection, eddy currents are generated in the specimen by the magnetic field generated when an alternating current is passed through the coil, and changes in the eddy current (voltage changes) that are disturbed due to volume reduction in areas where there is corrosion (scratches) are observed. This is a method for detecting a scratch (see, for example, Patent Document 2). By using eddy current flaw detection, non-contact continuous inspection becomes possible.

JP 2008-64540 A JP 2000-310618 A

Usually, the surface of the steel material which is the object of the flaw detection inspection is coated with rust prevention, but the coating bulges together with rust at the corroded portion of the steel material to form a coating film. Moreover, the caulking for water stop may be given to the ground part with the concrete of steel materials.
For this reason, when performing the above-described ultrasonic flaw detection inspection, in order to increase the inspection accuracy, measurement is performed after removing the blistering film and caulking in the ground portion in advance, but further excavating the ground. There are cases where work such as hanging concrete is also performed. For this reason, since the labor and time required for these removal processes increase, an inspection method with high work efficiency is required, and there is room for improvement in that respect.
Further, even in the eddy current flaw inspection described above, the conventional apparatus requires the sensor to pass above the corrosion, and is difficult to apply to the inspection of corrosion existing on the ground. Further, even if a signal change corresponding to the corrosion volume is obtained by eddy current flaw detection, there is no method for obtaining the average corrosion depth of the subsurface portion.

  The present invention has been made in view of the above-described problems, and can be measured by a simple operation without removing the swollen coating film or caulking, or removing the concrete or ground on the ground, and efficiently. It is an object of the present invention to provide a residual average plate thickness estimation method by estimating an average corrosion depth of a ground corrosion damaged portion capable of estimating a residual average plate thickness.

In order to achieve the above object, the residual average plate thickness estimation method based on the estimation of the average corrosion depth of the ground corrosion damage portion according to the present invention uses the eddy current flaw detection sensor to detect the ground of the steel material embedded in the concrete or the ground. A residual average plate thickness estimation method by estimating an average corrosion depth of a subsurface corrosion damaged portion for estimating a remaining plate thickness of a boundary portion, and extending the ground portion of the steel material on the ground by an eddy current flaw detection sensor A first step of obtaining a ½ flaw detection waveform that forms a symmetric one-side scanning waveform centered on the ground corrosion damage portion from eddy current flaw detection data measured non-destructively by scanning in a direction orthogonal to the direction And the first probability density function (1) approximated to the 1/2 flaw detection waveform is obtained using a Gaussian function, and the maximum is obtained by nonlinear regression analysis using the first probability density function (1). Voltage amplitude a, voltage amplitude The second step of estimating each parameter of the standard deviation b, the position c of the maximum amplitude, and the initial value d of the amplitude, the second probability density function (2) representing the probability density function of the normal distribution, and the first probability A third step of comparing the density function (1) and the deviation σ of the expression (3) representing the maximum voltage amplitude a as a calibration coefficient of the second probability density function, and the 1/2 flaw detection The accumulation of the first probability density function of the equation (1) that approximates the waveform is assumed to be a deficient cross-sectional area of the subsurface corrosion damaged portion, and is divided into a virtual corrosion width and an average corrosion depth using a normal distribution . step and said a fifth step of calculating, based virtual corrosion width standard deviation b of the voltage amplitude and the calibration factor, the average corrosion depth than deficient sectional area which is obtained the virtual corrosion width from the maximum voltage amplitude a have a, a sixth step of estimating, the fourth In the step, the first probability density function approximates the scanning waveform from the nearest to the subsurface corrosion damaged portion, and the signal component on one side of the symmetric scanning waveform corresponds to the missing cross-sectional area. Therefore, a step of obtaining a cross-sectional area having a symmetrical cross-sectional area centered on the peak value of the normal distribution and a cross-sectional area of the normal distribution being halved, and the vertical dimension without changing the cross-sectional area The method has a step of modeling a rectangular cross section having the peak value corresponding to the average corrosion depth, and a step of calculating a lateral dimension of the model of the rectangular cross section as the virtual corrosion width .

In the present invention, based on the fact that the flaw detection waveform obtained by the eddy current flaw measurement that scans in the direction perpendicular to the extending direction of the ground portion of the steel material is similar to the second probability density function of the normal distribution . The maximum voltage amplitude a, the standard deviation b of the voltage amplitude, the position c of the maximum amplitude, and the amplitude of the first probability density function obtained by using the Gaussian function approximating the flaw detection waveform in the second step Each parameter of the initial value d can be estimated, and the calibration coefficient of the second probability density function is compared by comparing the expression (1) with the expression (2) indicating the second probability density function of the normal distribution in the third step . Can be calculated .
Then, in the fourth step, the defect cross-sectional area of the scratch of the steel material is modeled by conversion, and the virtual corrosion width can be calculated from this simple model, and the average corrosion depth is calculated from the virtual corrosion width and the defect cross-sectional area. Can be estimated.

  As described above, according to the method for estimating the remaining average plate thickness based on the estimation of the average corrosion depth of the ground corrosion damage portion of the present invention, the eddy current flaw measurement of only the ground portion of the steel material is performed non-destructively with the eddy current flaw detection sensor. Thus, it is possible to estimate the corrosion width and corrosion depth of the scratch including the portion buried in the concrete or the ground. For this reason, it is not necessary to perform an operation for removing the blistering film and coking of the damaged portion of the steel material to be inspected for inspection, and the measurement can be easily performed, so that the efficiency of the inspection operation can be improved.

Moreover, as described above, by scanning in a direction orthogonal to the extending direction of the submarine portion, the flaw detection waveform obtained from the eddy current flaw detection data is similar to the second probability density function of the normal distribution . Since the corrosion depth is estimated based on this point, the soundness of the ground portion of the steel material can be evaluated.

In addition, according to the present invention, the method of calculating the virtual corrosion width obtained by using the rectangular model can be further simplified by assuming a rectangular model having a shape that allows easy calculation of the missing cross-sectional area. Work efficiency can be improved.
Furthermore, since the virtual corrosion width can be corrected by the calibration coefficient calculated based on the probability distribution curve of the normal distribution, the accuracy of the numerical value of the average corrosion depth estimated in the above-described sixth step can be improved. it can.

  Further, in the residual average plate thickness estimation method based on the estimation of the average corrosion depth of the ground corrosion damage portion according to the present invention, the missing cross section is obtained from the relationship between the estimated value indicating the maximum voltage amplitude a and the missing cross section. It is preferable to calculate from a characteristic straight line.

  In this case, by using the characteristic straight line indicating the correlation between the estimated value indicating the maximum voltage amplitude a and the missing sectional area, the missing sectional area can be given in the fourth step described above.

  According to the residual average plate thickness estimation method by estimating the average corrosion depth of the ground corrosion damage portion of the present invention, it is simple without removing the blistering coating film or caulking, or removing the concrete or ground on the ground portion. It can be measured by work, and there is an effect that the remaining average plate thickness can be estimated efficiently.

It is a perspective view which shows the outline | summary of the eddy current flaw measurement of the ground corrosion damage part by embodiment of this invention. It is a side view which shows the outline | summary of the eddy current flaw measurement shown in FIG. It is a longitudinal cross-section which shows the outline | summary of the eddy current flaw measurement shown in FIG. It is a figure which shows the test body of this Embodiment, Comprising: (a) is the top view, (b) is the side view. It is a figure which shows the ECT flaw detection waveform of the test body shown in FIG. It is a figure which shows correction | amendment of a probability density curve. (A)-(c) is a figure which shows the conversion state from the probability density curve of a normal distribution to a defect | deletion cross section.

  Hereinafter, a residual average plate thickness estimation method by estimating an average corrosion depth of a ground corrosion damaged portion according to an embodiment of the present invention will be described with reference to the drawings.

As shown in FIG. 1 to FIG. 3, the residual average plate thickness estimation method based on the estimation of the average corrosion depth of the ground corrosion damage portion according to the present embodiment is embedded in concrete or ground using an eddy current flaw detection sensor 3. It is a method for estimating the average corrosion depth of the ground part of the steel material 1 made. In the present embodiment, a method for estimating the average corrosion depth of the scratch 1a portion of the steel material 1 at the base portion of the steel pier embedded in the concrete 2 (the ground portion 1A with the concrete 2) will be described below. .
Here, the surface of the steel material 1 is painted, and a coking material for water stoppage (not shown) is provided at the ground portion 1A.

  First, in step S1 (first step), as shown in FIGS. 1 to 3, the ground portion 1A (1Aa) on the ground of the steel material 1 is moved in the extending direction X (in the present embodiment) by the eddy current flaw detection sensor 3. In this case, a flaw detection waveform (hereinafter referred to as an ECT flaw detection waveform) is obtained from eddy current flaw detection data measured in a non-destructive manner by scanning in a direction orthogonal to the horizontal direction (hereinafter referred to as a scanning direction Y).

  The measurement range is a range from the sound part (position above the ground part 1A) to the ground part 1A in the steel material 1 exposed on the concrete 2 in the scanning direction Y. Scanning is performed at a plurality of locations along the extending direction X at predetermined pitches. That is, the scanning range does not include the concrete embedded portion of the steel material 1.

  In addition, in the following description, it demonstrates using the test body 10 of the steel plate shown to Fig.4 (a), (b) instead of the steel material 1 of the pier mentioned above. On one surface of the test body 10, a linear slit 11 simulating a cross-sectional defect due to ground corrosion is provided. The linearly extending direction of the slit 11 is the extending direction X, and the direction orthogonal to the slit 11 in plan view is the scanning direction Y.

  The test body 10 is made of SM490, has a vertical dimension (length dimension in the scanning direction Y) of 400 mm, a horizontal dimension (length dimension in the extending direction X) of 200 mm, and a thickness dimension of 9 mm. Yes. The slit 11 is located 100 mm inside from one end in the vertical direction of the test body 10 (the left end in FIG. 4A), has a width W, a depth D, and a cross-sectional area A (see FIG. 7). ).

  Then, the scanning starting point of the scanning range measured by the eddy current flaw detection sensor 3 is set as the scanning origin P, and the position in the immediate vicinity of the slit 11 is set. 4A, the right edge of the slit 11 is the scanning origin P. At this time, the scanning distance Y is 0, and scanning is performed from the scanning origin P toward the right.

  As the eddy current flaw detection sensor 3 described above, a sensor having a function of detecting an eddy current change by generating an eddy current with respect to the test body 10 (flaw detection object) is used. The eddy current flaw detector used is used. As a scanning method, the eddy current flaw detection sensor is moved along the scanning direction Y within the scanning range while leaving a predetermined interval from the surface of the test body 10, and the eddy current flaw measurement is performed nondestructively.

  In step S1, the ECT flaw detection waveform scanned in the direction perpendicular to the cross-sectional defect part (ground part) of the specimen 10 shows the accumulation of the decrease in voltage amplitude due to the decrease in the cross-sectional defect volume (cross-sectional area).

Next, in step S2 (second step), the first probability density function approximated to the ECT flaw detection waveform is subjected to nonlinear regression analysis using a Gaussian function shown in equation (1), and each parameter (a, b, c, d) we estimate (see Fig. 5). As shown in FIG. 5, the ECT flaw detection waveform scanned in the direction perpendicular to the slit 11 of the specimen 10 of FIG. 4 (scanning direction Y) is indicated by a broken line. And the continuous line shown in FIG. 5 has shown the 1st probability density function mentioned above. Here, in equation (1), a is the maximum voltage amplitude (V), b is the standard deviation (mm) of the voltage amplitude, c is the position (mm) of the maximum amplitude, and d is the voltage amplitude. The initial value (V) is shown.

Next, in step S3 (third step), a calibration coefficient of the second probability density function is calculated based on a probability density curve of a normal distribution. That is, in the residual average plate thickness estimation method based on the estimation of the average corrosion depth of the subsurface corrosion damage portion according to the present embodiment, the ECT flaw detection waveform is almost similar to the second probability density function of the normal distribution . Based on this, nonlinear regression analysis using the Gaussian function shown in the first probability density function (1) is performed to estimate the parameters a, b, c, and d, and the flaw center position Yc, which will be described later, and the virtual This is a method of calculating the corrosion depth D by calculating the corrosion width W using the calibration coefficient of the second probability density function .

First, the second probability density function of the normal distribution N (μ, σ2) shown in FIG. 6 is expressed by the above equation (2). When the regression equation of nonlinear regression analysis using the Gaussian function shown in equation (1) is made to correspond to equation (2), the maximum voltage amplitude a can be expressed by equation (3).

  Here, as shown in FIG. 6, since σ is a probability density curve of a standard normal distribution multiplied by σ in the horizontal axis direction and multiplied by 1 / σ in the vertical axis direction, σ in equation (3) is corrected. When expressed using the coefficient α, equation (4) is obtained. Since the correction coefficient α in the equation (4) is determined by the maximum voltage amplitude a obtained from the flaw shape of the contrast specimen when the flaw detection sensitivity is set, the correction coefficient α is hereinafter referred to as a calibration coefficient.

Next, in step S4 (fourth process), it is assumed that the accumulation of the first probability density function of equation (1) is a missing cross section, and the missing cross section is calculated from the probability density curve of the normal distribution shown in FIG. By modeling to a rectangular cross section, the virtual corrosion width and the average corrosion depth are separated. In step S5 (fifth step), the modeled virtual corrosion width W (see FIG. 7) is calculated based on the standard deviation b of the voltage amplitude and is corrected by the calibration coefficient α.
That is, by assuming that the accumulation of the first probability density function is equal to the defect cross-sectional area, the virtual corrosion width W can be evaluated using the standard deviation b of the voltage amplitude of the Gaussian function. Note that the modeling of the missing cross-sectional area in this embodiment is a simple rectangular model having a rectangular cross section shown in FIG.

Note that the ECT flaw detection waveform by the eddy current flaw detection sensor when passing through the flaw (slit 11) of the test body 10 is a symmetric scanning waveform with the slit 11 as the center. However, since the probability density function approximating the scanning waveform from the position closest to the slit 11 corresponds to the signal component on one side and the missing sectional area A, the missing sectional area is halved as described above.
As shown in FIG. 7, the area of the probability density function of the normal distribution N (0,1) is 1, and when the area is 0.5, x of the normal distribution is 0.67. The position of 67σ is 1 / 2A of the missing cross-sectional area A. However, since it is necessary to integrate the second probability density function in order to calculate the area, here, the cumulative density of 0.5 A is simply modeled into a rectangular model as described above. . Therefore, the peak value × horizontal axis of the vertical axis of the normal distribution is expressed by the equation (5) based on the conversion as shown in FIGS.
Therefore, the virtual corrosion width W obtained from Gaussian regression is given by equation (6) using the calibration coefficient α of equation (4).

Next, in step S6 (sixth step), the corrosion depth D (see FIG. 7C) is estimated from the defect cross-sectional area obtained from the corrected virtual corrosion width W and the maximum voltage amplitude a.
Further, the center position Yc of the scratch (slit 11) is given by the equation (8) from the position c of the maximum amplitude.
Further, the corrosion depth D is expressed by the equation (9) using the defect cross-sectional area A.

  In order to calculate the corrosion depth D using the virtual corrosion width W, it is necessary to calculate the defect cross-sectional area A based on the maximum voltage amplitude a of the parameter. For this purpose, non-linear regression analysis of the ECT scan waveforms of specimens with known imaginary corrosion width W (slit width in FIG. 4) and corrosion depth D (slit depth in FIG. 4) and different defect cross-sectional areas A is performed. The values of the parameters a, b, c, and d are estimated, and a characteristic straight line indicating the relationship between the estimated value indicating the maximum voltage amplitude a and the missing cross-sectional area A is obtained. The missing cross-sectional area A can be calculated from this characteristic line.

Next, the effect | action of the residual average board thickness estimation method of the above-mentioned ground corrosion damage part is demonstrated in detail based on FIGS.
In the present embodiment, the ECT flaw detection waveform obtained by the eddy current flaw measurement that scans in the direction perpendicular to the extending direction in the ground portion of the steel material is similar to the probability density function of the normal distribution. based, the maximum voltage amplitude a of the non-linear regression analysis equation (1) of the Gaussian function approximating to the ECT inspection profile in step S 2 described above, the standard deviation b of the voltage amplitude, the position of the maximum amplitude c, and amplitude initial value of Each parameter of d is estimated, and in step S3, the calibration coefficient of the second probability density function is obtained by comparing with the above equation (2) indicating the second probability density function of the normal distribution . In step S4, the defect cross sectional area A of the steel material is modeled as a rectangular cross section, and the virtual corrosion width W can be calculated based on the standard deviation b of the voltage amplitude from this simple model. The corrosion depth D can be estimated from the deficient cross-sectional area A obtained from W and the maximum voltage amplitude a .

  Thus, in the present embodiment, the eddy current flaw measurement of only the ground portion 1A of the steel material 1 is performed non-destructively by the eddy current flaw sensor 3, so that the corrosion width W of the flaw including the portion embedded in the concrete is obtained. The corrosion depth D can be estimated. For this reason, it is not necessary to perform an operation for removing the blistering film and coking of the damaged portion of the steel material to be inspected for inspection, and the measurement can be easily performed, so that the efficiency of the inspection operation can be improved.

Moreover, as described above, the ECT flaw detection waveform obtained from the eddy current flaw detection data and the second probability density function of the normal distribution are obtained by scanning in the scanning direction Y orthogonal to the extending direction X of the ground portion 1A. Since it becomes similar and the average corrosion depth is estimated based on this point, the soundness of the ground portion 1A of the steel material 1 can be evaluated.

  In addition, according to the present embodiment, the method of calculating the virtual corrosion width W obtained by using the rectangular model can be further simplified by using the rectangular model having a shape that allows easy calculation of the missing cross-sectional area A. Thus, the work efficiency for estimation can be improved.

  Further, by using the characteristic straight line indicating the correlation between the estimated value indicating the maximum voltage amplitude a and the missing sectional area A, the missing sectional area A can be given in step S4 described above.

Furthermore, in this embodiment, since the virtual corrosion width W can be corrected by the calibration coefficient α calculated based on the probability density curve of the normal distribution , the corrosion depth D estimated in step S6 described above can be corrected. The accuracy of numerical values can be improved.

  As described above, in the residual average plate thickness estimation method based on the estimation of the average corrosion depth of the subsurface corrosion damaged portion according to the present embodiment, removal of the blistering film and caulking, and removal of concrete and ground at the subsurface portion are performed. It is possible to measure by a simple operation without any problem, and there is an effect that the remaining average plate thickness can be estimated efficiently.

(Example)
Here, in order to confirm the effect of the method for estimating the remaining average thickness of the subsurface corrosion damage portion according to the present embodiment, the signal of the cross-sectional defect of the corroded surface in the actual structure (ECT flaw detection waveform by the eddy current flaw detection sensor) is implemented. It was confirmed that the reaction similar to the defect signal by the test body 10 simulating the defect of the form was generated. As a scanning method, the eddy current flaw detection sensor is moved along the scanning direction Y in the scanning range while the measurement part of the eddy current flaw detection sensor is spaced a predetermined distance from the surface of the steel material at the end of the pier material as a flaw detection object. Measure. Therefore, the measurement according to the present embodiment is performed nondestructively.

  By performing nonlinear regression analysis of eddy current flaw detection data using a Gaussian function in this way, although there is some error, corrosion damage can be detected without removing the sealing, and the ground in the concrete part of the concrete of the actual structure can be detected. It was possible to estimate the average corrosion depth and the location of ground corrosion.

  As mentioned above, although embodiment of the residual average board thickness estimation method of the ground corrosion damage part by this invention was described, this invention is not limited to said embodiment, In the range which does not deviate from the meaning, it is appropriate. It can be changed.

For example, in the present embodiment, an example in which the steel material of the pier is embedded in concrete is shown, but the present invention is not limited to concrete and may be ground. The target material may be any material that conducts electricity, such as aluminum, titanium, and copper.
In other words, the remaining average plate thickness estimation method based on the estimation of the average corrosion depth of the subsurface corrosion damage part of the present embodiment includes the lower truss bridge, the vertical material of the arch bridge, the diagonal material of the composite truss bridge, the waveform Steel plate web PC abdominal plate, footbridge base, guard fence post, high-voltage tower base, guardrail base, etc. It is possible to target piping of plant equipment.

  In the present embodiment, in step S4 (fourth process), the missing cross-sectional area is modeled as a rectangular model, but the shape is not limited to the rectangular model. In short, it is preferable that the model of the missing cross-sectional area has a simple shape that can be easily calculated.

Further, in the present embodiment, the correction coefficient (calibration coefficient α) of the second probability density function is calculated based on the probability density curve of the normal distribution , and the virtual corrosion width W obtained from the modeled rectangular cross section is calculated as follows: Although correction is performed using the calibration coefficient α, the correction is not limited to such correction, and may be omitted.

  In addition, it is possible to appropriately replace the components in the above-described embodiments with known components without departing from the spirit of the present invention.

DESCRIPTION OF SYMBOLS 1 Steel material 1A Ground part 1a Scratch 2 Concrete 3 Eddy current test sensor 10 Specimen X Extension direction Y Scanning method

Claims (2)

This is a residual average plate thickness estimation method based on the estimation of the average corrosion depth of the subsurface corrosion damage part to estimate the residual plate thickness of the subsurface portion of steel materials embedded in concrete or ground using an eddy current flaw detection sensor. And
From the eddy current flaw detection data measured nondestructively by scanning the ground surface portion of the steel material in the direction perpendicular to the extending direction by the eddy current flaw detection sensor, it is symmetrical about the ground corrosion damage portion. A first step for obtaining a ½ flaw detection waveform forming a scanning waveform on one side ;
The first probability density function (1) approximated to the 1/2 flaw detection waveform is obtained using a Gaussian function, and the maximum voltage amplitude is obtained by nonlinear regression analysis using the first probability density function (1). a second step of estimating parameters of a, standard deviation b of voltage amplitude, position c of maximum amplitude, and initial value d of amplitude;
The deviation σ of the equation (3) representing the maximum voltage amplitude a by comparing the equation (2) of the second probability density function indicating the probability density function of the normal distribution with the equation (1) of the first probability density function. A third step of calculating as a calibration coefficient of the second probability density function;
Assuming that the accumulation of the first probability density function of the equation (1) approximating the 1/2 flaw detection waveform is a deficient cross-sectional area of the subsurface corrosion damaged portion, using the normal distribution, the virtual corrosion width and the average corrosion depth A fourth step of separating into
A fifth step of calculating the virtual corrosion width based on the calibration coefficient and the standard deviation b of the voltage amplitude;
A sixth step of estimating an average corrosion depth from a cross-sectional area obtained from the virtual corrosion width and the maximum voltage amplitude a;
I have a,
In the fourth step,
The first probability density function approximates a scanning waveform from the nearest of the ground corrosion damaged portion, and since the signal component on one side of the left-right symmetric scanning waveform corresponds to the missing cross-sectional area, Obtaining a cross-sectional area having a symmetrical cross-sectional area around the peak value of the normal distribution and a cross-sectional area of the normal distribution being halved; and
Modeling a rectangular cross-section with the vertical dimension corresponding to the average corrosion depth without changing the cross-sectional area;
And a step of calculating a lateral dimension of the model of the rectangular cross section as the virtual corrosion width, and a method for estimating a remaining average plate thickness by estimating an average corrosion depth of a ground corrosion damage portion.

  2. The average corrosion depth of a subsurface corrosion damaged portion according to claim 1, wherein the deficient cross-sectional area is calculated from a characteristic line obtained from a relationship between an estimated value indicating a maximum voltage amplitude a and a deficient cross-sectional area. Remaining average plate thickness estimation method by estimating the thickness.

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