JP4815607B2 - Non-destructive measuring device and non-destructive measuring method of reinforcing bar diameter in reinforced concrete structure by electromagnetic wave radar - Google Patents

Description

  The present invention relates to a non-destructive measuring device and a non-destructive measuring method of a reinforcing bar diameter in a reinforced concrete structure in which a reinforcing bar is embedded.

In recent years, interests such as the presence of reinforcing bars in reinforced concrete structures as well as the measurement of the diameter of reinforcing bars have increased due to the occurrence of social problems such as seismic camouflage problems.
However, it is extremely difficult to measure the diameter of a reinforcing bar in a reinforced concrete structure, and no useful method has been developed so far.

Patent Document 1 includes a transmission antenna and a reception antenna, and transmits electromagnetic waves from the transmission antenna toward the medium while moving the transmission antenna and the reception antenna along the medium surface, and is obtained from an invisible object in the medium. Using a device that receives the reflected wave by the receiving antenna and displays it on the screen, run the antenna along the main rebar, obtain the first, second, and third images of the crescent-shaped reflected wave, The half-wavelength time t ₁ is obtained from the vertex of the second image and the vertex of the third image, the time t ₂ from the top side of the band-like image and the vertex of the second image is obtained, and estimated from the time t ₂ -t ₁ A method for estimating the diameter of a reinforcing bar is disclosed in which the round-trip propagation time T of the reinforcing bar diameter is obtained and the diameter of the reinforcing bar is estimated from V × T / 2, where V is the electromagnetic wave propagation speed obtained from the relative dielectric constant in the medium. ing.

Patent Document 2 discloses a predicted received signal waveform based on physical characteristics of an electromagnetic wave radar developed by the present inventor and propagation characteristics including reflection and refraction at the medium interface of the electromagnetic wave, and an actual received signal measured by the electromagnetic wave radar. And a method for measuring the position of the reinforcing bar in the concrete and the shape of the reinforcing bar by pattern matching.
JP-A-5-323026 Japanese Patent Application No. 2006-132996

  The object of the present invention is that the reinforcing bars in the reinforced concrete structure are (1) deformed reinforcing bars, and nodes are periodically provided along the reinforcing bars so that the reinforcing bars are easily fixed in the concrete. 2) Focusing on the fact that the distance between the nodes is determined by the diameter of the reinforcing bar, and providing a non-destructive measurement method for simply measuring the diameter of the reinforcing bar.

In order to achieve these objects, the present invention is configured as follows.
The invention according to claim 1 is a non-destructive measuring method of a reinforcing bar diameter of a deformed reinforcing bar disposed in a reinforced concrete structure, wherein an electromagnetic wave radar including a transmitting antenna and a receiving antenna is provided along the deformed reinforcing bar. Scanning the surface of a reinforced concrete structure and repeating transmission / reception of electromagnetic waves at a predetermined pitch, storing a propagation time of electromagnetic waves reflected from the deformed rebar in a time series, and storing the time series of the stored propagation times Analyzing the frequency of the data; determining an average interval between the deformed reinforcing bars based on the maximum peak value obtained by the frequency analysis; and determining a reinforcing bar diameter based on a predetermined correspondence table according to the average interval. The non-destructive measuring method of the reinforcing bar diameter characterized by comprising.
The invention according to claim 2 is the non-destructive measurement method for reinforcing bar diameter according to claim 1, wherein the frequency analysis is performed by a maximum likelihood method.
The invention according to claim 3 is the non-destructive measuring method for reinforcing bar diameter according to claim 1, wherein the frequency analysis is performed by fast Fourier transform.
The invention according to claim 4 is the non-destructive measuring method for reinforcing bar diameter according to claim 1, wherein the frequency analysis is performed by a maximum entropy method.
Further, the invention according to claim 5 is a nondestructive measuring device for reinforcing bar diameter of deformed reinforcing bars arranged in a reinforced concrete structure, wherein the nondestructive measuring device for reinforcing bar diameter includes a transmitting antenna and a receiving antenna. The electromagnetic wave radar provided, and the electromagnetic wave radar scans the surface of the reinforced concrete structure along the deformed reinforcing bar and repeats transmission / reception of the electromagnetic wave at a predetermined pitch, so that the propagation time of the electromagnetic wave reflected from the deformed reinforcing bar is time-sequentially Storing means for storing the data, analyzing means for analyzing the frequency of the time series data of the propagation time stored in the storing means, and obtaining an average interval of the nodes of the deformed reinforcing bars based on the maximum peak value obtained by the frequency analysis Non-destructive reinforcing bar diameter, comprising control means and determining means for determining a reinforcing bar diameter based on a predetermined correspondence table according to the average interval It is a measuring apparatus.
The invention according to claim 6 is the non-destructive measuring apparatus for reinforcing bar diameter according to claim 5, wherein the frequency analysis is performed by a maximum likelihood method.
The invention according to claim 7 is the non-destructive measuring apparatus for reinforcing bar diameter according to claim 5, wherein the frequency analysis is performed by fast Fourier transform.
The invention according to claim 8 is the non-destructive measuring apparatus for reinforcing bar diameter according to claim 5, wherein the frequency analysis is performed by a maximum entropy method.

  The non-destructive inspection can easily and accurately measure and judge the diameter of a reinforcing bar in a reinforced concrete structure in which reinforcing bars are embedded.

  Reinforced concrete is concrete in which reinforcing bars are arranged to reinforce concrete that is weak against tension. In order to prevent the reinforcing bars from being pulled out even if a tensile force acts on them, reinforcing bars called deformed reinforcing bars having periodic nodes as shown in FIGS. 1 and 2 are usually used.

表１によると、節の間隔に対しては、各径に対し少し自由度があり、節間隔がとるべき最大値が定められている。例えば、径が１２．７ｍｍの鉄筋に対しては節間隔の平均値の最大値は８．９ｍｍであり、間隔平均値は、強度上の観点からはこれより小さいものは幾らでも小さくて良いが、コストの観点からはこの径よりも１規格低い異形鉄筋である径が９．５３ｍｍの異形鉄筋の平均間隔の最大値６．７ｍｍより大きくするのが合理的であり、実際このように製造されていると考えられる。 This deformed reinforcing bar has different node intervals and heights depending on the diameter of the reinforcing bar, and has standards as shown in Table 1 (JIS-G3112-75).

According to Table 1, there is a slight degree of freedom for each diameter with respect to the knot spacing, and the maximum value that the knot spacing should take is determined. For example, for a reinforcing bar with a diameter of 12.7 mm, the maximum value of the average value of the node interval is 8.9 mm, and the average value of the interval may be as small as possible from the viewpoint of strength. From the viewpoint of cost, it is reasonable to make the diameter of the deformed reinforcing bar 1 standard lower than this diameter larger than the maximum value of the average interval of the deformed reinforcing bar of 9.53 mm, which is actually 6.7 mm. It is thought that.

  Therefore, as shown in FIG. 1, the electromagnetic wave radar scans the concrete surface along the reinforcing bars in the concrete.

  When electromagnetic waves are emitted from the transmission antenna of the electromagnetic wave radar, a part is first reflected by the concrete surface and received by the receiving antenna (path AFE in FIG. 1). The remaining electromagnetic waves pass through the surface, reach the rebar inside the concrete and are reflected there. The reflected wave at this time passes through the concrete surface again and is received by the receiving antenna (path ABCDE in FIG. 1).

  Now, in FIG. 1, when the reflection point in the reinforcing bar of the electromagnetic wave is in the main axis part between the nodes and the path in the case where the reflection point is in the node part, the case where it is reflected in the node part is reflected in the main axis part. Since the propagation path is shorter than in the case of the electromagnetic wave, the round-trip propagation time of the electromagnetic wave is shortened.

  The present invention utilizes this fact to measure the average distance between nodes and calculates the diameter from the correlation between the diameter of the reinforcing bar and the distance between the nodes as shown in Table 1.

  As shown in FIG. 3, when the radar is run along the reinforcing bar and the transmission / reception of the electromagnetic wave is repeated at a certain pitch, the propagation time of the electromagnetic wave from the reinforcing bar periodically changes because the nodes are provided at certain intervals. The propagation time time series data is stored in the storage means, and the stored propagation time time series data is subjected to frequency analysis by the analysis means, whereby the average interval of the nodes is obtained. For this frequency analysis, for example, well-known FFT (Fast Fourier Transform) or MEM (Maximum Entropy Method) can be used. In addition, a maximum likelihood method using a physical model that uses the periodic arrangement of nodes is also conceivable.

ここで、z₀＝a₀
,z₁＝a₁sin(ωx＋ψ)である。また、ω＝２πｆで、ｆは節の繰り返し周波数である。つまり、節の平均間隔がＬであればｆ＝１/Ｌで与えられる。 Hereinafter, this maximum likelihood method will be described.
Now, the average value of the time series data of the round-trip propagation time is obtained, and this average value is subtracted from each propagation time. As a result, a periodic time-series signal whose value varies positively or negatively is obtained. In addition, since the bias of the time series signal subtracted at this time does not become zero completely, this time series signal is modeled as follows in continuous time.

Where z ₀ = a ₀
, z ₁ = a ₁ sin (ωx + ψ). Also, ω = 2πf, and f is the node repetition frequency. That is, if the average interval between nodes is L, f = 1 / L.

を定義すれば、z(x)の従うダイナミックスは

となる。ここで、（２）式のドットはｘについての微分を表し、Ａは次式で定義される。

また、w(x)はw(x)＝(w₁,0,w₂)^Tなる遷移雑音であり、w₁(x)，w₂(x)は平均値がゼロ、分散がσ₁ ²,σ₂ ²の互いに独立な白色ガウス雑音とする。この雑音を導入したのは、計測に際してのデータウインドウ内での時系列信号の（（１）式による）モデル化誤差を補償するためである。（３）式をΔＬでサンプリングすれば、次のサンプル値系表現が得られる。

なお、z_k,w_kはそれぞれサンプリング地点k(ΔL)における状態ベクトル及び遷移雑音である。ここに、Fは次式で定義される遷移行列である。

ここに、£^−１［・］はラプラス逆変換を表わす。また、遷移雑音ベクトルw_ｋは平均値がゼロ、共分散行列が次式で与えられる白色ガウス雑音である。

なお、

なる対角行列である。 Now, state vector

, The dynamics obeyed by z (x) is

It becomes. Here, the dot in equation (2) represents the differentiation with respect to x, and A is defined by the following equation.

Further, w (x) is a transition noise of w (x) = (w ₁ , 0, w ₂ ) ^T , and w ₁ (x) and w ₂ (x) have an average value of zero and a variance of σ ₁ ² , σ ₂ ² mutually independent white Gaussian noise. The reason for introducing this noise is to compensate for the modeling error (according to the equation (1)) of the time series signal in the data window at the time of measurement. If the expression (3) is sampled with ΔL, the following sample value system expression can be obtained.

Z _k and w _k are a state vector and a transition noise at the sampling point k (ΔL), respectively. Here, F is a transition matrix defined by the following equation.

Here, £ ⁻¹ [·] represents Laplace inversion. The transition noise vector w _k is white Gaussian noise having an average value of zero and a covariance matrix given by the following equation.

In addition,

Is a diagonal matrix.

ここで、ＨはH=[1,1,0]である。なお、y_k及びv_kはサンプリング地点k(ΔL)における観測値（上記平均値を差し引いた時系列信号）及び観測雑音を表わす。 On the other hand, since this time series signal {y _k } is obtained by radar scanning, the following equation is given as an observation equation of the state vector z _k .

Here, H is H = [1,1,0]. Y _k and v _k represent the observed value (time series signal obtained by subtracting the average value) and the observed noise at the sampling point k (ΔL).

なお、Ｖは観測雑音v_kの分散である。 In this way, a dynamic model of the time series signal defined above was obtained. Therefore, z _k is estimated by the following Kalman filter.

V is the variance of the observation noise v _k .

などを用いればよい。ここにc₁, c₂は時系列信号の値の大きさをみて適切に与えればよい。また、ωは不明なため、P_0/−1の計算に当っては、予めＦＦＴなどで求めたωの概略値を使うなどすればよい。 The initial value of the Kalman filter is

Etc. may be used. Here, c ₁ and c ₂ may be appropriately given in view of the magnitude of the time series signal value. Further, since ω is unknown, an approximate value of ω obtained in advance by FFT or the like may be used for calculating P _{0 / −1} .

However, what is required by this measurement method is to obtain a truly accurate ω. However, since K and K of the Kalman filter are functions of ω and ω is unknown, the Kalman filter cannot be directly applied to the estimation of the state vector. However, once the candidate for ω is given, the Kalman filter can be applied, and the state vector can be estimated under the parameters.

ここに、

はそれぞれパラメータωの下でのカルマンフィルタにより求めた状態ベクトルの予測値

及びΛ_kを表す。従って、結局は、（１６）式をωについて最大化することにより、最適なω*を求めることができ、これにより節間隔Ｌ*(=2π/ω^＊)を計算することができる。 The probability of the parameter ω used at this time can be evaluated by the following likelihood function obtained under the observed value series Y ^K−1 = {y ₁ , y ₂ ,..., Y _K−1 }.

here,

Is the predicted value of the state vector obtained by the Kalman filter under each parameter ω

And Λ _k . Therefore, in the end, the optimum ω * can be obtained by maximizing the equation (16) with respect to ω, and thereby the node interval L * (= 2π / ω ^* ) can be calculated.

  Here, as a time-series signal model defined by subtracting the average value from the propagation time, one sine wave function with a bias applied is considered, but two or more sine wave functions can also be considered. . In addition, it should be noted that the smaller the pitch of the electromagnetic wave emission, the better the repetitive shape of the node, so it is desirable for the measurement of the interval between nodes. For this reason, if the radar pitch is rough, for example, the radar may be switched to time-based electromagnetic wave emission instead of distance-based and moved at a speed that realizes a sufficiently small electromagnetic wave emission pitch.

  In addition, if this maximum likelihood approach is adopted, the likelihood function obtained for each time series signal when the radar scan is performed a plurality of times is added, and this is maximized with respect to ω, thereby improving the reliability. It can be further increased.

  In addition, it is the diameter measurement when the deformed reinforcing bar in the reinforced concrete is rusted. By doing so, it is possible to measure the original node spacing of the reinforcing bars and thereby measure the diameter of the reinforcing bars.

Next, a method for measuring the propagation time will be described.
The received signal r (t) from the reinforcing bar is observed by overlapping the reflected wave r ₀ (t) from the reinforcing bar with the reflected wave r _s (t) from the concrete surface. Therefore, it is reasonable to subtract the reflected wave r _s (t) from the concrete surface from the received signal to obtain the electromagnetic wave round-trip propagation time to the reinforcing bar at each observation point (r _s (t) Is required).

から鉄筋までの電磁波伝播時間を求めるのであるが、何も正確な往復伝播時間を求める必要はない。つまり、往復伝播時間と連動する相対的な時間変化が重要なのである。 This difference signal

However, it is not necessary to obtain an accurate round-trip propagation time. In other words, the relative time change associated with the round-trip propagation time is important.

の最大ピーク値を与える時刻の時系列を観測値として代用することを考える。そして、この時系列信号の平均値を求め、この平均値を各時系列信号から差し引いたものを、前節の{y_k}とすればよい。 From this point of view, the difference signal is one of the simple ways to express the change in the round-trip propagation time.

Consider substituting the time series that gives the maximum peak value as the observed value. Then, an average value of the time series signals is obtained, and a value obtained by subtracting the average value from each time series signal may be set as {y _k } in the previous section.

のデータは所定のサンプリング周期ごとに与えられるため、より正確なピーク時刻を求めるには、例えば以下に示すパターンマッチングの方法がある。 In addition,

Since this data is given every predetermined sampling period, for example, there is a pattern matching method shown below to obtain a more accurate peak time.

（ここでΔTはサンプリング周期）が与えられたとする。このとき、事前に鉄筋からの基準となる反射波信号s(kΔT)(k＝0,1,…)を得ておき、より詳細な波形情報を与えるものとして、内挿法によりs(kΔT′)(k＝0,1,2,…)を作成しておく。但し、ΔT′はΔT′＝ΔT/N（Nは整数)。 Now

Assume that (where ΔT is a sampling period). At this time, the reflected wave signal s (kΔT) (k = 0, 1,...) Serving as a reference from the reinforcing bar is obtained in advance, and more detailed waveform information is given. ) (k = 0,1,2, ...) is created. However, ΔT ′ is ΔT ′ = ΔT / N (N is an integer).

のパターンマッチングがなされるよう｛s(kΔT′)｝を動かせ、これらの最適パターンマッチングが実現するときの｛s(kΔT′)｝の最大ピーク位置により

の最大ピーク位置を（ΔTのサンプリング時刻ではなく、ΔTのＮ分割点の正確さ）で求めようとするものである。従って、Ｎ＝１０とすれば、本来のサンプリング周期の（１/１０）きざみで正確な最大ピーク位置が求まる。

{S (kΔT ′)} can be moved so that the following pattern matching is performed, and the maximum peak position of {s (kΔT ′)} when these optimum pattern matching is realized

The maximum peak position is determined by (accuracy of N division points of ΔT, not sampling time of ΔT). Therefore, if N = 10, an accurate maximum peak position can be obtained in (1/10) increments of the original sampling period.

で評価することである。ここに、（・，・）及び‖・‖はユークリッド空間の内積及びノルム記号である。 It should be noted that the matching angle of both waveforms at time kΔT (k = 0, 1, 2, ...) as pattern matching

It is to evaluate with. Here, (·, ·) and ‖ · ‖ are inner products and norm symbols of Euclidean space.

Let's consider the measurement of the diameter of a deformed bar with a diameter of 19.1mm and a depth of 60mm (thus covering 50.45mm).
A time-series signal of the round-trip propagation time after subtracting the bias is shown in FIG. Electromagnetic wave emission was measured at a pitch of 1 mm using a Japan Radio Co., Ltd. NJJ-95A (central frequency 800 MHz) radar. This pitch is data when a radar that emits an electromagnetic wave every 0.05 s on a time base is run along the reinforcing bar at the same speed as possible.

  FIG. 5 to FIG. 7 show the frequency analysis results when (1) FFT, (2) MEM, and (3) maximum likelihood methods are used for this time series signal. The maximum spectrum peaks by FFT and MEM are given by f = 0.085 Hz and f = 0.069 Hz, respectively. Back-calculating the node spacing L (= 1 / f) gives 11.8 mm and 14.4 mm, respectively.

On the other hand, in the method based on the maximum likelihood method, the frequency f = 0.085 Hz giving the maximum likelihood value is obtained. In using the Kalman filter, σ ₁ = 0.06, σ ₂ = 0.1, c ₁ = 0.1, and c ₂ = 0.3 were used. Thus, the node interval L by the maximum likelihood method is L = 1 / f = 11.8 mm. These three node spacings are larger than the maximum rebar spacing of 11.1 mm for a diameter of 15.9 mm in the FFT and maximum likelihood method, and smaller than 13.4 mm of the maximum rebar spacing for a diameter of 19.1 mm. In the MEM, the diameter is 15.9 mm. The maximum distance between the reinforcing bars for mm is 11.1 mm, and the diameter is very close to the maximum distance of 13.4 mm for the reinforcing bars for 19.1 mm. It can be said with any method that the diameter of the reinforcing bars is 19.1 mm with high accuracy.

This is an electromagnetic wave propagation path of the electromagnetic wave radar. It is a figure which shows the external appearance of a deformed bar. It is a figure which shows the scanning of a reinforcing bar and a radar. It is a figure which shows an observation value series. It is a figure which shows the spectrum by FFT. It is a figure which shows the spectrum by MEM. It is a figure which shows the likelihood function by a maximum likelihood method.

Claims (8)

A non-destructive measurement method for the diameter of a deformed reinforcing bar arranged in a reinforced concrete structure,
Scanning the surface of the reinforced concrete structure along the deformed reinforcing bar with an electromagnetic wave radar including a transmitting antenna and a receiving antenna and repeating transmission and reception of electromagnetic waves at a predetermined pitch; and
Storing the propagation time of electromagnetic waves reflected from the deformed reinforcing bars in time series;
Frequency analyzing the stored time series data of the propagation time;
Obtaining an average interval between the nodes of the deformed reinforcing bars based on the maximum peak position by the frequency analysis;
Determining a rebar diameter based on a predetermined correspondence table according to the average interval;
A non-destructive measuring method for reinforcing bar diameter, comprising:   The non-destructive measurement method for reinforcing bar diameter according to claim 1, wherein the frequency analysis is performed by a maximum likelihood method.   The said frequency analysis is performed by a fast Fourier transform, The nondestructive measuring method of the reinforcing bar diameter of Claim 1 characterized by the above-mentioned.   The said frequency analysis is performed by the maximum entropy method, The non-destructive measuring method of the reinforcing bar diameter of Claim 1 characterized by the above-mentioned. A non-destructive measuring apparatus for reinforcing bar diameter of deformed reinforcing bars arranged in a reinforced concrete structure, wherein the non-destructive measuring apparatus for reinforcing bar diameter is
An electromagnetic wave radar having a transmitting antenna and a receiving antenna;
Storage means for storing the propagation time of the electromagnetic wave reflected from the deformed reinforcing bar in time series by scanning the surface of the reinforced concrete structure along the deformed reinforcing bar with the electromagnetic wave radar and repeating the transmission and reception of the electromagnetic wave at a predetermined pitch. When,
Analyzing means for frequency analysis of time series data of the propagation time stored in the storage means;
Control means for obtaining an average interval of the nodes of the deformed reinforcing bars based on the maximum peak position by the frequency analysis;
In accordance with the average interval, a determination means for determining a reinforcing bar diameter based on a predetermined correspondence table;
A non-destructive measuring apparatus for reinforcing bar diameter, comprising:   The said frequency analysis is performed by the maximum likelihood method, The reinforcing bar diameter nondestructive measuring apparatus of Claim 5 characterized by the above-mentioned.   The non-destructive measuring apparatus for reinforcing bar diameter according to claim 5, wherein the frequency analysis is performed by fast Fourier transform.   The said frequency analysis is performed by the maximum entropy method, The rebar diameter nondestructive measuring apparatus of Claim 5 characterized by the above-mentioned.

Images