CN115420186A - Steel bar diameter pulse eddy current detection method and device based on parameter inversion - Google Patents

Steel bar diameter pulse eddy current detection method and device based on parameter inversion Download PDF

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CN115420186A
CN115420186A CN202210980238.XA CN202210980238A CN115420186A CN 115420186 A CN115420186 A CN 115420186A CN 202210980238 A CN202210980238 A CN 202210980238A CN 115420186 A CN115420186 A CN 115420186A
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steel bar
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induced voltage
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diameter
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陈兴乐
侯费隐
肖春燕
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G01B7/12—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring diameters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
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    • G01N27/04—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance
    • G01N27/041—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance of a solid body
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/72—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating magnetic variables
    • G01N27/82—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating magnetic variables for investigating the presence of flaws
    • G01N27/90—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating magnetic variables for investigating the presence of flaws using eddy currents

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Abstract

The invention discloses a method and a device for detecting the diameter of a steel bar by pulse eddy current based on parameter inversion. And when the sum of the relative errors of the measurement curve of the induction voltage and the theoretical calculation curve is minimum, the diameter, the relative permeability and the conductivity of the steel bar to be detected can be obtained, wherein the steel bar diameter obtained by inversion is a detection result, and the dimension specification of the steel bar to be detected is obtained. The method and the device do not need to calibrate a standard test block, can implement more accurate nondestructive testing on the parameters of the steel bar to be tested, and eliminate the influence of the electromagnetic parameters of the steel bar on the detection result.

Description

Steel bar diameter pulse eddy current detection method and device based on parameter inversion
Technical Field
The invention belongs to the technical field of electromagnetic nondestructive testing, and relates to a steel bar diameter pulse eddy current testing method and device based on parameter inversion.
Background
In the building field, reinforced concrete is widely applied due to excellent compressive strength and tensile strength, and parameters such as nominal diameter, position and protective layer thickness of steel bars in concrete have important influence on structural stability and mechanical property of buildings, so that the detection and evaluation of the parameters of reinforced concrete are very important in the fields of engineering project acceptance, old building overhaul and the like.
At present, in the field of buildings, an electromagnetic induction method is commonly used for detecting parameters of steel bars in concrete, the electromagnetic induction method can be used for detecting the steel bars and generating a magnetic field in a target area by adopting excitation modes such as direct current, alternating current and pulse, so that the steel bars are magnetized, eddy current is generated in the steel bars, a secondary magnetic field is further generated, and the parameters of the steel bars are estimated by detecting disturbance of the magnetic field through a sensor. At present, common detection equipment can measure the position of the steel bar and the thickness of a protective layer, but the diameter of the steel bar cannot be accurately detected due to the lack of direct electromagnetic field theoretical research.
The pulse eddy current method is a non-contact electromagnetic nondestructive testing method. The exciting coil is connected with pulse exciting current to generate a pulse strong magnetic field, the changing magnetic field induces a transient eddy current field in the reinforcing steel bar, and the eddy current field induces voltage signals at two ends of the detecting coil. The position of the steel bar is determined by measuring the attenuation process of the induced voltage, and the diameter of the steel bar is detected. The pulse eddy current method applies pulse excitation, can generate a transient strong magnetic field, and has the greatest advantages of strong penetration capability and higher sensitivity for detecting the change of parameters such as the diameter of the steel bar, the thickness of concrete outside the steel bar and the like. And the concrete is non-conductive and non-magnetic conductive material, and the distribution and detection signals of the pulse eddy current field can not be interfered.
Disclosure of Invention
Aiming at the problems, the invention provides a steel bar diameter pulse eddy current detection method and device based on parameter inversion.
A steel bar diameter pulse eddy current detection method based on parameter inversion is characterized in that: the steps are designed as follows:
step 1: determining buried reinforcement position
Step 2: the method comprises the following steps of performing parameter inversion by using an induced voltage time domain signal right above a steel bar so as to obtain the diameter of the steel bar to be detected, and specifically comprises the following steps:
firstly, the diameter D and the relative permeability mu of the steel bar to be detected are measured r Conductivity sigma is set as an unknown parameter, and the parameter vector x to be inverted is (D, mu) r ,σ) T (ii) a The induction voltage measurement data acquired at the position above the steel bar to be detected is (t) 1 ,u 1 ),(t 2 ,u 2 ),…,(t m ,u m ). Wherein t and u are induced voltage time domain signal curves u m And (t) comparing the induced voltage corresponding to the time point and the time point with an induced voltage theoretical value u (x, t), inverting a parameter x by the minimum sum of squares of relative errors between an induced voltage signal measurement value and a theoretical calculation value obtained by an induced voltage time domain expression, and establishing a least square problem:
Figure BDA0003800106170000021
the percentage residual function is:
Figure BDA0003800106170000022
and the residual function vector is recorded as:
r(x)＝(r 1 (x),r 2 (x),...,r m (x)) T 。
then, an iterative algorithm is utilized to solve the optimal solution x of the minimum two problems * The iterative algorithm comprises the following calculation steps:
(1) Given initial point
Figure BDA0003800106170000023
(wherein D (1) ＝5～40mm，
Figure BDA0003800106170000024
σ (1) =1 to 10 MS/m), and the allowable error ∈ > 0 (generally ∈ = 10) -3 ) Set k =1。
(2) The parameter vector of the k step
Figure BDA0003800106170000025
In the formula (1), each time point t is calculated i Induced voltage theoretical value u (x) of (k) ,t i ) Then with the measured value u of the induced voltage i Making difference, calculating residual quantity percentage function value
Figure BDA0003800106170000026
And obtaining a residual function vector r (k) (ii) a Then, the first partial derivative of the induced voltage theoretical curve to the diameter D is further calculated by the formula (1)
Figure BDA0003800106170000027
And induced voltage theory curve versus relative permeability mu r First partial derivative of
Figure BDA0003800106170000028
And the first partial derivative of the induced voltage theoretical curve to the conductivity sigma
Figure BDA0003800106170000029
Obtain a matrix A of m × 3 k ＝(a ij ) m×3 ，j＝1、2、3。
(3) Solving a system of equations
Figure BDA00038001061700000210
Finding the direction vector b (k) ；
(4) From a parameter vector x (k) Starting along b (k) One-dimensional search is carried out to obtain step length alpha k So that
Figure BDA0003800106170000031
And order
x (k+1) ＝x (k) +α k b (k) ；
(5) If | | | x (k+1) -x (k) If | | < epsilon, stopping the calculation to obtain the optimal solution of the least square problem
Figure BDA0003800106170000032
Otherwise, setting k = k +1, and returning to the step (2).
Solving the optimal solution of the least square problem by the iterative algorithm
Figure BDA0003800106170000033
Then, the inversion result of the diameter of the steel bar to be detected is obtained
Figure BDA0003800106170000034
Inversion result of relative permeability
Figure BDA0003800106170000035
Inversion results of conductivity
Figure BDA0003800106170000036
The invention has the advantages that:
1. the steel bar diameter pulse eddy current detection method and device based on parameter inversion can implement more accurate nondestructive detection on the parameters of the steel bar to be detected.
The method utilizes the time domain analytic solution of the induced voltage of the steel bar pulse eddy current detection model and the induced voltage measurement curve to establish the least square problem between the measured value and the calculated value of the induced voltage signal, and the relative error square sum between the measured value and the calculated value is minimized to invert the parameters of the detected steel bar. Compared with the traditional electromagnetic detection method for extracting the detection characteristic quantity from the detection signal, the method not only extracts a plurality of special points on the signal curve, but also fully utilizes the information on the whole induced voltage signal curve, can more effectively evaluate the whole attenuation process of the pulse eddy current electromagnetic field, and can implement more accurate eddy current detection on the parameters of the steel bar to be detected.
2. The invention discloses a steel bar diameter pulse eddy current detection method and device based on parameter inversion, which eliminates the influence of steel bar electromagnetic parameters on a detection result.
The electromagnetic parameters such as the magnetic conductivity and the electric conductivity of the steel bar can be changed due to the influence of the production process and the environmental factors such as temperature, stress and the like, so that the magnetic conductivity and the electric conductivity of the steel bar can not be accurately determined when the electromagnetic detection is carried out on the steel bar, and the measurement result of the diameter of the steel bar is influenced. In the invention, the magnetic conductivity and the electric conductivity of the steel bar to be detected are set as unknown parameters, and the values of the magnetic conductivity and the electric conductivity of each steel bar in each detection are determined by the parameter inversion method, so that the influence of the electromagnetic parameter change on the detection result is eliminated, and the detection precision and the reliability of the diameter of the steel bar are improved.
3. The invention relates to a steel bar diameter pulse eddy current detection method and device based on parameter inversion, which do not need to calibrate a standard test block.
Old buildings often lack relevant information such as reinforcing bar trade mark, size, can't mark its electromagnetic parameter through the standard reinforcing bar, and the degree of difficulty that carries out accurate detection to the reinforcing bar diameter under the condition that lacks reinforcing bar priori information is great. The method of the invention does not need to calibrate the steel bar, can simultaneously determine the diameter and the electromagnetic parameter of the steel bar to be detected through the parameter inversion of the induced voltage signals at the two ends of the detection coil, realizes the nondestructive detection of the diameter of the steel bar buried in the concrete, and can adapt to more application scenes.
Drawings
FIG. 1 is a block diagram of a buried steel bar pulsed eddy current electromagnetic nondestructive testing system.
Fig. 2 is a sectional structural view of a cylindrical coil probe.
Fig. 3 is a flow chart of the steel bar diameter pulse eddy current testing.
Fig. 4 is a graph comparing experimental measurement results of induced voltage with theoretical calculation results.
Fig. 5 is a graph of the difference of the induced voltages.
FIG. 6 is a graph of pulsed eddy current test signals for different probe eccentricity distances.
Fig. 7 is a comparison graph of the experimental measurement curve of the induced voltage collected by the reinforcing steel bars with different diameters and the theoretical calculation curve.
In the figure:
1-coil probe 2-computer 3-DA digital-to-analog converter 4-power amplifying circuit
5-data acquisition card 101-coil framework 102-exciting coil 103-detection coil
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention relates to a steel bar diameter pulse eddy current detection method based on parameter inversion. The detected steel bars can be common round steel or threaded steel bars and are buried in concrete, and as shown in fig. 3, the concrete detection steps are as follows:
step 1: and continuously scanning the buried steel bar by a pulse eddy current electromagnetic nondestructive testing device.
The pulsed eddy current electromagnetic nondestructive testing device, as shown in fig. 1, includes a coil probe 1, a computer 2, a DA digital-to-analog converter 3, a power amplification circuit 4 and a data acquisition card 5. The cylindrical coil probe 1 is used for acquiring an induced voltage time domain signal during continuous scanning and sending the induced voltage time domain signal to the computer 2 for storage. As shown in fig. 2, the coil probe 1 is composed of a coil bobbin 101, an excitation coil 102, and a detection coil 103. The coil framework 101 is arranged at the central part of the excitation coil 102, and the detection coil 103 is arranged outside the excitation coil 102; alternatively, the coil bobbin 101 is disposed at the center of the detection coil 103, and the excitation coil 102 is disposed outside the detection coil 103. The computer 2 is used for realizing the functions of signal acquisition, processing, result display, data storage and the like, processing the received discrete signal data and obtaining the information of the position, the diameter and the like of the steel bar in the concrete. The power amplifier is used for realizing signal amplification. The data acquisition card 5 is used for acquiring time domain signals of the induced voltage at two ends of the detection coil 103. The DA digital-to-analog converter 3 is used to convert the excitation digital signal output by the computer 2 into an analog signal.
By adopting the detection device, the coil probe 1 is placed close to the outer layer of the concrete, the radius r of the circular coil probe 1 is taken as the step length, and continuous scanning is carried out towards one direction along the vertical direction of the buried steel bar.
And 2, step: and carrying out pulse eddy current detection signal acquisition once on each detection point to obtain an induction voltage time-domain signal of each detection point.
The method comprises the following steps of collecting induced voltage time domain signals by using a pulse eddy current detection system, namely a pulse eddy current detection Signal collection step, a Signal Acquisition process, SAP, and the specific steps are as follows:
SAP-1: two ends of an exciting coil 102 in the coil probe 1 are connected with the output end of the power amplifying circuit, and two ends of a detecting coil 103 are connected with the input end of an AD (analog-to-digital) converter in the data acquisition card 5.
SAP-2: the computer 2 outputs an excitation digital signal with the continuous pulse width of 10-1000 ms and the amplitude of 0.1-1V; after passing through the DA digital-to-analog converter 3, the excitation analog signal is changed into an excitation analog signal with the continuous pulse width of 10-1000 ms and the amplitude of 0.1-1V, and is output to the power amplifying circuit 4; after the power is amplified by the power amplifying circuit 4, the pulse exciting current with the continuous pulse width of 10-1000 ms and the amplitude of 0.1-10A is output to the exciting coil 102;
SAP-3: and acquiring the induced voltage time domain signals u (t) at the two ends of the detection coil 103 and the unit V by using a data acquisition card 5, and storing the acquired induced voltage time domain signals u (t) into a computer.
In the above process, in the steel bar diameter pulse eddy current testing model, when pulse excitation current i (t) is introduced into the excitation coil 102, the induced voltage time domain expression at the two ends of the detection coil 103 is:
Figure BDA0003800106170000051
in the formula (1), pi is 3.14; e is the base of the natural logarithm, and the value is 2.72; sigma is the conductivity of the steel bar to be detected, and the unit is S/m; d is the diameter of the steel bar to be detected, and the unit is m; mu.s 0 The value is 4 pi x 10 for vacuum magnetic permeability -7 H/m；μ r The relative magnetic permeability of the steel bar to be detected; i (t) is pulse excitation current with unit of A; i' (t) represents the derivative of the pulsed excitation current with respect to time; "+" indicates the convolution operation over time; I.C. A m (x) And K m (x) Respectively carrying out class 1 and class 2 m-order modified Bessel functions; λ is an integral variable.
Coefficients in formula (1):
Figure BDA0003800106170000052
Figure BDA0003800106170000053
Figure BDA0003800106170000054
F(ξ,m)＝mJ m (ξ)-ξJ m+1 (ξ)；
wherein ξ t Is denominator expression Y m (xi) = t th true root of 0, and in the formula (1), Y' m (xi) denotes denominator Y m (xi) a derivative of the variable xi; c p (λ, m) is a coil coefficient of the detection coil, and the expression is as follows:
Figure BDA0003800106170000055
h is the thickness of the concrete layer on the surface of the steel bar; s is a variable after the laplace transform is performed; h is a total of p Is the height of the detection coil; r is pi And r po To detectThe inner and outer radii of the coil; r is an integral variable, and the integral interval is the inner radius and the outer radius of the detection coil; l 0 The eccentric distance of the probe (the distance of the central axis of the coil probe deviating from the axis of the steel bar);
Figure BDA0003800106170000061
N p the number of turns of the detection coil is;
Figure BDA0003800106170000062
C d (λ, m) is the coil coefficient of the exciting coil, and its expression is C p (lambda, m) are the same, and the variable with subscript p is the relevant parameter of the detection coil, which is related to the parameter of the coil itself, and only the parameter needs to be replaced by the relevant parameter of the excitation coil.
And 3, step 3: and judging the induction voltage time domain signals of the three adjacent detection points to determine the position of the steel bar.
Firstly, setting an induction voltage time-domain signal u collected by a middle detection point in three adjacent detection points within a time period t as m (t), the time domain signal of the induced voltage at the previous detection point is u m-1 (t), the time domain signal of the induced voltage at the next detection point is u m+1 (t) of (d). Drawing a difference curve u of the induced voltage m (t)-u m-1 (t) and determining the peak instant t of the difference curve 0 As shown in fig. 5; then respectively extracting the induction voltage time domain signals of three adjacent detection points at t 0 Voltage amplitude at time V m-1 、V m And V m+1 And stored in the host as corresponding signal feature quantities, as shown in fig. 6. If the characteristic quantities simultaneously satisfy V m >V m-1 And V m >V m+1 If the intermediate detection point is located right above the steel bar to be detected, the induced voltage signal u is generated m (t) storing the position information of the current point in the computer, and marking the detecting point right above the steel bar to be detected as Q j Then, step 4 is carried out to detect the diameter of the steel bar; otherwise, the step 1 is repeated, and continuous pulse eddy current scanning detection is carried out at other positions outside the concrete.
And 4, step 4: and (5) inverting the parameters of the steel bar to be detected, and determining the diameter of the steel bar to be detected.
After obtaining time domain signals of the induced voltages at two ends of the detection coil at the detection point right above the detected steel bar in the step 3, how to invert the diameter of the detected steel bar is the key of signal processing in the steel bar diameter pulse eddy current detection, therefore, in the invention, the least square problem is established after obtaining the time domain signals of the induced voltages at two ends of the detection coil at the detection point right above the detected steel bar in the step 3, and the diameter, the relative magnetic conductivity and the electric conductivity of the detected steel bar at the detection point are inverted, the process is called as a parameter Inversion step, parameters Inversion Procedure, PIP, and the specific steps are as follows:
step PIP-1: the diameter D and the relative permeability mu of the steel bar to be detected r Conductivity σ is set as unknown parameter, i.e. the parameter vector to be inverted x = (D, μ) r ,σ) T ；
Step PIP-2: according to the SAP step, the time domain induction voltage measuring data of two ends of the detection coil 3, which are acquired by the data acquisition card 11 at the position above the detected steel bar, are (t) 1 ,u 1 ),(t 2 ,u 2 ),…,(t m ,u m ) Where t and u are time domain signal curves u of the induced voltage m The induced voltage at the time point and the time point on (t) is compared with the theoretical value u (x, t) of the induced voltage calculated by the formula (1) as shown by the solid line in fig. 4, and the parameter x is inverted by the least square sum of the relative errors between the measured value of the induced voltage signal and the theoretical calculated value, that is, the least square problem is established:
Figure BDA0003800106170000063
wherein R is a real number domain;
the percentage residual function is:
Figure BDA0003800106170000071
and the residual function vector is recorded as:
r(x)＝(r 1 (x),r 2 (x),...,r m (x)) T 。
step PIP-3: in the computer 2, an optimal solution x of the least two problem (equation (2)) is solved by using an iterative algorithm * The iterative algorithm comprises the following calculation steps:
(1) Given initial point
Figure BDA0003800106170000072
(wherein D (1) ＝5～40mm，
Figure BDA0003800106170000073
σ (1) =1 to 10 MS/m), and the allowable error ∈ > 0 (generally ∈ = 10) -3 ) K =1;
(2) The parameter vector of the k step
Figure BDA0003800106170000074
In the formula (1), each time point t is calculated i Induced voltage theoretical value u (x) (k) ,t i ) Then with the measured value u of the induced voltage i Making difference, calculating residual quantity percentage function value
Figure BDA0003800106170000075
And obtaining a residual function vector r (k) (ii) a Then, the first partial derivative of the induced voltage theoretical curve to the diameter D is further calculated by the formula (1)
Figure BDA0003800106170000076
And induced voltage theoretical curve vs. relative permeability mu r First partial derivative of
Figure BDA0003800106170000077
And the first partial derivative of the induced voltage theoretical curve to the conductivity sigma
Figure BDA0003800106170000078
Obtain a matrix A of m × 3 k ＝(a ij ) m×3 ，j＝1、2、3。
(3) Solving a system of equations
Figure BDA0003800106170000079
Finding the direction vector b (k) ；
(4) From a parameter vector x (k) Starting along b (k) One-dimensional search is carried out to obtain step length alpha k So that
Figure BDA00038001061700000710
And make an order
x (k+1) ＝x (k) +α k b (k) ；
(5) If | | | x (k+1) -x (k) If | | < epsilon, stopping the calculation to obtain the optimal solution of the least square problem (2)
Figure BDA00038001061700000711
Otherwise, setting k = k +1, and returning to the step (2).
Solving the optimal solution of the least square problem (2) by the iterative algorithm
Figure BDA00038001061700000712
Then, the inversion result of the diameter of the detected steel bar is obtained
Figure BDA0003800106170000081
Inversion result of relative permeability
Figure BDA0003800106170000082
Inversion results of conductivity
Figure BDA0003800106170000083
Optimal solution of parameters
Figure BDA0003800106170000084
The theoretical calculation result of calculating the induced voltage in the formula (1) is shown as a solid point in fig. 4. And finally, corresponding the inversion result with the position information of the steel bar to be detected, and storing the inversion result in a computer.
Example 1
An example of the pulsed eddy current inspection of the diameter of the steel bar by parametric inversion in the present invention is given below.
4 twisted steel bars with inner diameters of 24.4mm, 21.7mm, 19.4mm and 17.4mm are available. Recording the detection points right above the 4 steel bars as Q 0 、Q 1 、Q 2 And Q 3 . The lifting distance between the lower edge of the coil probe and the surface of the steel bar to be detected is 25.0mm, and the eccentric distance of the probe is 0.
The pulse eddy current detection is carried out on 4 steel bars according to the SAP step provided by the invention, and the obtained induced voltage signal detection signal is shown as a solid line in figure 7, and the sampling rate is 50kS/s. And then according to the PIP step, performing parametric inversion on the induced voltage time domain signals of the 4 detection points, and finally obtaining the parametric inversion results of the 4 steel bars as shown in Table 1. The parameter inversion result is substituted into the formula (1), the theoretical calculation result of the induced voltage corresponding to the steel bars with different diameters is calculated, and is shown as a real point in fig. 7, and the experimental measurement result of the induced voltage is well matched with the theoretical calculation result. And comparing the diameter inversion results of the 4 steel bars with the actual diameter value, calculating that the relative error of the steel bar diameter detection result is not more than 3%, meeting the precision requirement in the actual engineering, and verifying the feasibility and reliability of the pulse eddy current method for detecting the diameter of the steel bar.
TABLE 1 results of parametric inversion of different rebars
Figure BDA0003800106170000085

Claims (4)

1. A steel bar diameter pulse eddy current detection method based on parameter inversion is characterized in that: the steps are designed as follows:
step 1: determining the position of a buried steel bar;
and 2, step: the method comprises the following steps of performing parameter inversion by using an induced voltage time domain signal right above a steel bar to obtain the diameter of the detected steel bar, and specifically comprises the following steps:
firstly, the diameter D and the relative permeability mu of the steel bar to be detected are measured r Conductivity sigma is set as unknown parameter, and parameter vector x to be inverted is (D, mu) r ,σ) T (ii) a The induction voltage measurement data acquired at the position above the steel bar to be detected is (t) 1 ,u 1 ),(t 2 ,u 2 ),…,(t m ,u m ) Where t and u are time domain signal curves u of the induced voltage m (t) comparing the induced voltage corresponding to the time point and the time point with a theoretical value u (x, t) of the induced voltage, inverting a parameter x by minimizing the sum of squares of relative errors between a measured value of an induced voltage signal and a theoretical calculation value obtained by an induced voltage time domain expression, and establishing a least square problem:
Figure FDA0003800106160000011
the percentage residue function is:
Figure FDA0003800106160000012
and the residual function vector is recorded as:
r(x)＝(r 1 (x),r 2 (x),...,r m (x)) T ；
then, an iterative algorithm is utilized to solve the optimal solution x of the minimum two problems * The iterative algorithm comprises the following calculation steps:
(1) Given initial point
Figure FDA0003800106160000013
(it isIn D (1) ＝5～40mm，
Figure FDA0003800106160000014
σ (1) =1 to 10 MS/m), and the allowable error ∈ > 0 (generally ∈ = 10) -3 ) K =1;
(2) The parameter vector of the k step
Figure FDA0003800106160000015
In the formula (1), each time point t is calculated i Induced voltage theoretical value u (x) (k) ,t i ) Then with the measured value u of the induced voltage i Making difference, calculating residual quantity percentage function value
Figure FDA0003800106160000016
And obtaining a residual function vector r (k) (ii) a Then, the first partial derivative of the induced voltage theoretical curve to the diameter D is further calculated by the formula (1)
Figure FDA0003800106160000021
And induced voltage theory curve versus relative permeability mu r First partial derivative of
Figure FDA0003800106160000022
And the first partial derivative of the induced voltage theoretical curve to the conductivity sigma
Figure FDA0003800106160000023
Obtain a matrix A of m × 3 k ＝(a ij ) m×3 ，j＝1、2、3。
(3) Solving a system of equations
Figure FDA0003800106160000024
Finding the direction vector b (k) ；
(4) From a parameter vector x (k) Starting along b (k) One-dimensional search is carried out to obtain the step length alpha k So that
Figure FDA0003800106160000025
And order
x (k+1) ＝x (k) +α k b (k) ；
(5) If | | | x (k+1) -x (k) If | | < epsilon, stopping the calculation to obtain the optimal solution of the least square problem
Figure FDA0003800106160000026
Otherwise, setting k = k +1, and returning to the step (2).
Solving the optimal solution of the least square problem by the iterative algorithm
Figure FDA0003800106160000027
Then, the inversion result of the diameter of the detected steel bar is obtained
Figure FDA0003800106160000028
Inversion result of relative permeability
Figure FDA0003800106160000029
Inversion results of conductivity
Figure FDA00038001061600000210
2. The pulsed eddy current inspection method for steel bar diameter based on parametric inversion according to claim 1, characterized in that: in the step 1, the actual position of the embedded steel bar is determined by continuously scanning detection signals through the pulse vortex, and the method comprises the following steps:
a. placing a circular coil probe close to the outer layer of the concrete, and continuously scanning towards one direction along the vertical direction of the embedded steel bar by taking the radius r of the coil probe as a step length;
b. acquiring a pulse eddy current detection signal of each detection point to obtain an induction voltage time domain signal of each detection point;
c. judging the induction voltage time domain signals of the three adjacent detection points to determine the position of the steel bar;
firstly, setting an induction voltage time-domain signal u collected from a middle detection point among three adjacent detection points in a time period t as m (t), the time domain signal of the induced voltage of the previous detection point is u m-1 (t), the time domain signal of the induced voltage at the next detection point is u m+1 (t); drawing a difference curve u of the induced voltage m (t)-u m-1 (t) and determining the peak instant t of the difference curve 0 (ii) a Then respectively extracting the induction voltage time domain signals of three adjacent detection points at t 0 Voltage amplitude at time V m-1 、V m And V m+1 As corresponding signal characteristic quantities; if the characteristic quantities simultaneously satisfy V m >V m-1 And V m >V m+1 If the detected steel bar is the middle detection point, the middle detection point is positioned right above the detected steel bar; otherwise, returning to the step a to be repeatedly executed, and carrying out continuous pulse eddy current scanning detection at other positions outside the concrete.
3. The pulsed eddy current inspection method for steel bar diameter based on parametric inversion, according to claim 2, characterized in that: the acquisition method of the pulse eddy current detection signal comprises the following steps:
1) Connecting two ends of an exciting coil in a coil probe with the output end of a power amplifying circuit, and connecting two ends of a detection coil with the input end of an AD (analog-to-digital) converter in a data acquisition card;
2) Outputting an excitation digital signal with a continuous pulse width of 10-1000 ms and an amplitude of 0.1-1V by a computer; after passing through the DA digital-to-analog converter, the signal is converted into an excitation analog signal with the continuous pulse width of 10-1000 ms and the amplitude of 0.1-1V, and the excitation analog signal is output to a power amplifying circuit; after the power is amplified by the power amplifying circuit, the pulse exciting current with the continuous pulse width of 10-1000 ms and the amplitude of 0.1-10A is output to the exciting coil;
3) And acquiring the induction voltage time domain signals u (t) at the two ends of the detection coil through a data acquisition card, and storing the acquired induction voltage time domain signals u (t) into a computer.
4. The pulsed eddy current inspection method for the diameter of the steel bar based on the parametric inversion, according to claim 1, is characterized in that: the induction voltage time domain expression is as follows:
Figure FDA0003800106160000031
in the formula (1), pi is 3.14; e is the base of the natural logarithm, and the value is 2.72; sigma is the conductivity of the steel bar to be detected, and the unit is S/m; d is the diameter of the steel bar to be detected, and the unit is m; mu.s 0 The value is 4 pi x 10 for vacuum magnetic permeability -7 H/m；μ r The relative permeability of the steel bar to be detected is obtained; i (t) is pulse excitation current with unit of A; i' (t) represents the derivative of the pulsed excitation current with respect to time; "+" indicates the convolution operation over time; I.C. A m (x) And K m (x) Respectively carrying out class 1 and class 2 m-order modified Bessel functions; λ is an integral variable;
coefficients in formula (1):
Figure FDA0003800106160000032
Figure FDA0003800106160000033
Figure FDA0003800106160000034
F(ξ,m)＝mJ m (ξ)-ξJ m+1 (ξ)；
wherein ξ t Is denominator expression Y m (xi) = t th true root of 0, and in the formula (1), Y' m (xi) denotes denominator Y m (xi) a derivative of the variable xi; c p (λ, m) is a coil coefficient of the detection coil, and the expression is as follows:
Figure FDA0003800106160000041
wherein h is the thickness of the concrete layer on the surface of the steel bar; s is a variable after the laplace transform is performed; h is p Is the height of the detection coil; r is pi And r po The inner radius and the outer radius of the detection coil are set; r is an integral variable, and the integral interval of the integral variable is the inner radius and the outer radius of the detection coil; l 0 The probe eccentric distance;
Figure FDA0003800106160000042
N p detecting the number of turns of the coil;
Figure FDA0003800106160000043
C d (λ, m) is the coil coefficient of the exciting coil, and its expression is equal to C p (λ, m) are the same, and the variable denoted by the subscript p is the relevant parameter of the detection coil.
CN202210980238.XA 2022-08-16 2022-08-16 Steel bar diameter pulse eddy current detection method and device based on parameter inversion Pending CN115420186A (en)

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