CN116879404A - Reinforced concrete internal structure inversion imaging method based on density value - Google Patents
Reinforced concrete internal structure inversion imaging method based on density value Download PDFInfo
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
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Abstract
The invention discloses a reinforced concrete internal structure inversion imaging method based on a density value, which comprises three subroutines of ultrasonic data acquisition, ultrasonic data inversion analysis and inversion density value imaging; the ultrasonic data acquisition procedure comprises two steps of acquisition grid point division, ultrasonic signal transmission and acquisition; the ultrasonic data inversion analysis program comprises six steps of ultrasonic source prediction, initial model selection, forward modeling, objective function selection, optimization algorithm selection and prediction model updating; the inversion density value imaging program comprises three steps of density value three-dimensional imaging, rendering threshold analysis and image rendering. According to the invention, SH ultrasonic signal scanning is carried out on the reinforced concrete structure, the whole density value of the reinforced concrete is accurately obtained by using a full waveform inversion method, the image construction of the internal structure is realized by means of a density value imaging and rendering method, and based on the image construction, the internal steel bar and defect space information can be intuitively and accurately observed.
Description
Technical Field
The invention relates to a reinforced concrete internal structure inversion imaging method, in particular to a reinforced concrete internal structure inversion imaging method based on a density value.
Background
Reinforced concrete is the most used artificial material and is widely applied to various infrastructure constructions. The problems of micro cracks, steel bar corrosion, concrete layering, steel bar protection layer stripping and the like of the internal structure of the reinforced concrete affect the safety and durability of the whole structure, further threaten the service performance of the structure and cause malignant safety accidents when serious. The accurate assessment of the internal structure of reinforced concrete is an effective means for judging the service health status of the structure.
The existing nondestructive testing method of the concrete structure mostly focuses on the abnormal signal data intensity, so that the internal defect degree in the concrete structure is distinguished, imaging observation is absent, the internal structural space distribution state cannot be intuitively evaluated, and therefore the key damage index of the internal defect and the accurate evaluation of the deterioration development trend are realized. The defect damage in the reinforced concrete structure has diversity, and the durability and the safety of the structure have larger influence difference. There is a need for a method that can accurately grasp the spatial distribution of defects within a reinforced concrete structure.
SH ultrasonic wave has higher sensitivity to the density value of the reinforced concrete structure, inversion of the reinforced concrete density value is realized by means of SH ultrasonic wave, and accurate imaging of the internal structure can be realized by establishing a functional relation between key damage indexes (type, size and space position) of the internal defects of the concrete and the reinforced concrete density value, so that the reinforcement spreading rule and the concrete damage condition are evaluated in a direct hanging manner.
Disclosure of Invention
The invention aims to: the invention aims to provide a reinforced concrete internal structure inversion imaging method based on a density value, which can accurately identify the internal structure of a reinforced concrete structure.
The technical scheme is as follows: the invention relates to a reinforced concrete internal structure inversion imaging method based on a density value, which comprises the following three subprograms:
subroutine one: the ultrasonic data acquisition comprises two steps of data acquisition grid point division, ultrasonic signal transmission and acquisition;
subroutine II: the ultrasonic data inversion analysis comprises six steps of ultrasonic source signal prediction, inversion initial model selection, forward modeling analysis, objective function selection, optimization algorithm selection and prediction model updating;
and a third sub-program: the density value imaging comprises three steps of density value three-dimensional imaging, density rendering threshold analysis and image rendering.
Further, the data acquisition grid points are divided, the longitudinal spacing is 1-2 cm, the transverse spacing is 5-10 cm, and the higher the inversion accuracy is required, the smaller the grid point dividing spacing is.
Further, the ultrasonic waves are SH waves, and the number of ultrasonic probes is not less than 32.
Further, the ultrasonic source signal prediction method comprises green equation calculation and source signal prediction calculation;
the calculation method of the green equation comprises the following steps:
wherein, f-when collecting data, the ultrasonic frequency is in Hz; x-calculating the position function of the grid points; m-the density value of the calculated lattice points; g (f, x, m) -calculating a wave field green's function; d (f, x, m) -predicting the wavefield; w (f) -rake wavelet signal;
the method for calculating the seismic source signal comprises the following steps:
wherein, f-when collecting data, the ultrasonic test frequency, hz; x-calculating the position function of the grid points; m-the density value of the calculated lattice points; w (W) est (f) -calculating a source signal with a centre frequency f; d (f, x, m) -predicting the wavefield; g (f, x, m) -calculating the wavelength Green function.
Further, in the step of selecting the inversion initial model, the initial value of the density model adopted by inversion is determined according to actual measurement of the mixing ratio of the concrete materials.
Further, in the forward modeling analysis step, a time domain two-dimensional SH elastic wave equation is adopted to model the forward propagation process of SH waves in concrete:
wherein, the coordinates of the grid points in the x-forward model in the transverse direction, the coordinates of the grid points in the z-forward model in the longitudinal direction and the y-direction perpendicular to the xy plane; ρ (x, z) -the density value of the lattice point in the forward model, μ (x, z) -the shear modulus value of the lattice point in the forward model; v y -the velocity of the shear transverse wave particles in the y-direction; sigma (sigma) xy Shear stress in the xy plane, sigma yz -shear stress in the yz plane; f (f) y -source stress in a direction perpendicular to the xz plane;
the forward model adopts a mirror stress method on the boundary of the simulated concrete structure surface to simulate strong reflection waves generated by SH elastic waves on the concrete surface; on the remaining boundaries except the concrete structure surface, a perfect matching layer (Perfect Match Layers, PML) is used to absorb the boundary reflection waves.
Further, in the step of selecting the objective function, a least square method is selected as a model inversion objective function, the calculation process comprises wave field residual calculation and least square method calculation,
the wave field residual error calculation method comprises the following steps:
Δd t,r ＝D t,r (m)-d t,r
wherein, t is the serial number of the sensor; r-data channel number; m-medium density value; Δd t,r -wave field residuals; d (D) t,r (m) -predicting wavefield data; d, d t,r -actual wave field data;
the least square method comprises the following steps:
wherein m is the medium density value; e (m) -least squares; Δd—wavefield residual.
Further, in the optimization algorithm selection step, a Gaussian-Newton method is adopted to calculate the gradient direction of the density model, and the calculation method comprises the following steps:
in the method, in the process of the invention,-density model gradient direction; f (F) x -transversal virtual stresses in the forward wave field; r is R x -transverse virtual stresses in the post-transfer field; f (F) z -longitudinal virtual stresses in the forward wavefield; r is R z -longitudinal virtual stresses in the post-transfer field.
Further, in the step of updating the prediction model, a density model is updated by adopting a steepest gradient method, and the calculation method comprises the following steps:
in the formula, n-nth iterative inversion is carried out; n+1-n+1th iterative inversion; ρ -a medium density value; ρ n+1 -density values of the medium at n+1 iterative inversions; ρ n -density values of the medium at n iterative inversions; beta n -updating the step size; s-source; r-receiver;-a density model gradient direction matrix; />-density model gradientA transposed matrix of directions; lambda (lambda) 1 -laplace matrix diagonal value correction constants, typically taken as 0.1; P-Laplace equation matrix; p (P) t -transposed matrix of the laplace equation; lambda (lambda) 2 -a diagonal value correction constant of the identity matrix, typically taken to be 0.05; i-a matrix of unit equations; i t -transpose of the unit equation; Δd—wave field residual least squares value.
Further, in the density value two-dimensional imaging step, a MATLAB software programming program is adopted for inversion imaging based on the density value obtained by inversion.
Further, in the image rendering step, rendering processing is carried out on the image obtained in the step based on the numerical range of the inversion density value, the concrete body is processed in a transparentizing mode, and the internal structure of the concrete is emphasized;
concrete transparent rendering value V 1 The range selection method comprises the following steps:
0.8*V C <V 1 <1.2*V C
wherein V is C -according to the initial value of the density model selected in the inversion initial model, the unit is kg/m 3 ；V 1 Transparent rendering density value range in kg/m 3 ；
Crack defect rendering value V 2 In a range of not more than 500kg/m 3 ；
Reinforcing steel bar reinforcement rendering value V 3 In a range of not less than 7000kg/m 3 。
The beneficial effects are that: compared with the prior art, the invention has the following remarkable advantages: (1) The method for inverting the internal structure of the reinforced concrete based on the density value is provided, and the problem that the distribution of the internal density value cannot be provided in the current concrete nondestructive testing field is solved; (2) Based on the Gaussian-Newton optimization algorithm, compared with a conventional full waveform inversion method, the method can provide density value distribution with higher accuracy, and further has higher imaging accuracy; (3) The imaging method based on the density value can accurately identify the internal structure of the concrete; (4) The reinforcement spreading rule in the concrete can be judged through the analysis of the inversion density value matrix value; (5) The key damage parameters of the internal defects of the concrete, such as the geometrical characteristic parameters (width, length, shape and space position) of the internal cracks, can be displayed by rendering the image area with low inversion density value; (6) The method has the advantages that the defect problem inside the concrete can be intuitively and clearly identified by staff in the non-professional technical field through accurate and intuitive rendering imaging effect; (7) The method has stable and clear inversion analysis steps based on the algorithm analysis of physical properties, is suitable for nondestructive testing and identification of the interior of various concrete structures, and has higher stability and applicability.
Drawings
FIG. 1 is a flow chart of an inversion imaging method of reinforced concrete internal structure based on density values;
FIG. 2 is a schematic diagram of a two-dimensional cross-section of a horizontal crack detection within a concrete structure;
FIG. 3 is a graph of a density profile of horizontal cracks within a concrete imaged based on inversion density values;
fig. 4 is a schematic view of a two-dimensional cross section of a steel bar inspection in a concrete structure;
FIG. 5 is a graph of density profile of a concrete internal rebar imaged based on inversion density values;
FIG. 6 is a schematic diagram of a two-dimensional cross-section of a circular void detection within a concrete structure;
FIG. 7 is a graph of the density profile of circular voids within a concrete imaged based on inversion density values.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the inversion imaging method of the reinforced concrete internal structure based on the density value comprises three subroutines. Subroutine one: ultrasonic data acquisition 1; subroutine II: inverting and analyzing the ultrasonic data 2; and a third sub-program: inversion density value imaging 3.
The ultrasonic data acquisition program 1 comprises data acquisition grid point division 1-01 and signal transmission and acquisition 1-02. The data acquisition grid point division 1-01 is used for determining the data acquisition position so as to determine a single scanning inversion point, and an ultrasonic instrument is needed for signal emission and acquisition 1-02. The ultrasonic data inversion analysis program 2 comprises 2-01 of ultrasonic source signal prediction, 2-02 of inversion initial model selection, 2-03 of forward modeling analysis, 2-04 of objective function selection, 2-05 of optimization algorithm selection and 2-06 of prediction model update. The ultrasonic source signal prediction 2-01 is used for simulating a simulated source signal adopted during inversion analysis, the inversion initial model selection 2-02 is used for selecting an initial value which is required during inversion and is close to a detected concrete structure density value, the forward modeling analysis 2-03 is used for generating prediction wave field data to be compared with actual wavelength data, an objective function is calculated, the optimization algorithm selection 2-05 is used for optimally calculating the objective function by adopting a Gaussian-Newton optimization method, a gradient updating direction of a density value model is obtained, and therefore a model updating direction is provided for the density value model updating, and the density value model updating is carried out by combining calculated updating step length. The inversion density value imaging program 3 comprises a density value imaging method 3-01, a density rendering threshold value analysis 3-02 and a density distribution image rendering 3-03, wherein the density value imaging method 3-01 uses MATLAB programming program to image a density value matrix obtained by inversion, analyzes the density value matrix according to physical value characteristics of internal structures of concrete to obtain a density rendering threshold value, and performs rendering analysis on the density value image, so that the structural distribution condition of the internal structures of the concrete, in particular key damage parameters (size, shape and space position) of defects are identified.
The analysis steps of the full waveform inversion imaging method by utilizing the reinforced concrete internal structure are as follows:
(1) Analyzing the detected concrete structure, and determining division of data acquisition grid points;
(2) Based on the divided data acquisition grid points, utilizing an ultrasonic array instrument to acquire data;
(3) Predicting an ultrasonic source signal when data inversion analysis starts;
(4) Determining an inversion initial density value model;
(5) Starting from the inversion initial density value model, forward modeling analysis is carried out;
(6) Comparing the predicted wavelength data generated by the forward model with the actual wavelength data, and calculating an objective function equation;
(7) Selecting a Gaussian-Newton optimization algorithm, reducing an objective function equation, and calculating a model update gradient direction;
(8) Updating the density value model by using a steepest descent method;
(9) Imaging the inversion density value through MATLAB programming;
(10) Determining a density value rendering threshold according to analysis of the inversion density value;
(11) Rendering and imaging the inversion imaging result, and analyzing the key index parameters (size, shape and space position) of the structure and the defect in the concrete structure;
the data acquisition grid point division is determined based on inversion imaging precision, the transverse interval of the acquisition points is 5-10 cm, and the longitudinal interval is 1-2 cm. The ultrasonic wave is SH wave. The number of ultrasonic probes is not less than 32.
The seismic source prediction method comprises green equation calculation and seismic source signal prediction calculation. The calculation method of the green equation comprises the following steps:
wherein, f-ultrasonic instrument A1040 MIRA 3D collects the frequency used when the data, hz; x-calculate the position function of the lattice points, m-calculate the density values of the lattice points, G (f, x, m) -calculate the wave field green function, D (f, x, m) -predict the wave field, W (f) -rake wavelet signal.
The method for calculating the seismic source signal comprises the following steps:
wherein, f-ultrasonic instrument A1040 MIRA 3D collects the frequency used when the data, hz; x-calculating the position function of the lattice points, m-calculating the density value of the lattice points, W est (f) -computing the source signal, D (f, x, m), -predicting the wave field, G (f, x, m), -computing the wavelength green function.
The initial value V of the density model C And actually measuring according to the concrete mixing ratio.
The forward modeling analysis adopts a two-dimensional SH elastic wave equation of a time domain to model the forward propagation process of SH waves in a concrete medium:
wherein, the coordinates of grid points in the x-forward model in the transverse direction; y-coordinates of grid points in the forward model in the longitudinal direction; ρ (x, z) -density value of the lattice point in forward model, v y -SH transverse wave particle velocity in the y-direction; sigma (sigma) xy Shear stress in the xy plane, sigma yz Shear stress in the yz plane.
The forward model adopts a mirror stress method on the boundary of the simulated concrete structure surface to simulate strong reflection waves generated by SH elastic waves on the concrete surface; and absorbing boundary reflection waves by adopting a perfect matching layer on the rest boundaries except the surface of the concrete structure.
The method is characterized in that the least square method is used as an objective function of model inversion, and the calculation process of the objective function is divided into wave field residual calculation and least square method calculation.
The wave field residual error calculation method comprises the following steps:
Δd t,r ＝D t,r (m)-d t,r
wherein, t is the serial number of the sensor; r-data channel number; m-medium density value; Δd t,r -wave field residuals; d (D) t,r (m) -predicting wavefield data; d, d t,r -actual wave field data.
The least square method comprises the following steps:
wherein m is the medium density value; e (m) -least squares; Δd—wavefield residual.
Further, the optimization algorithm calculates the gradient direction of the density model by adopting a Gaussian-Newton method, and the calculation method comprises the following steps:
in the method, in the process of the invention,-density model gradient direction; f (f) x -transversal virtual stresses in the forward wave field; r is R x -transverse virtual stresses in the post-transfer field; f (F) z -longitudinal virtual stresses in the forward wavefield; r is R z -longitudinal virtual stresses in the post-transfer field.
In the step of updating the prediction model, a density model is updated by adopting a fastest gradient method, and the calculation method comprises the following steps:
in the formula, n-nth iterative inversion is carried out; n+1-n+1th iterative inversion; ρ -a medium density value; ρ n+1 -density values of the medium at n+1 iterative inversions; ρ n -density values of the medium at n iterative inversions; beta n -updating the step size; s-source; r-receiver;-a density model gradient direction matrix; />Rotation of gradient direction of density modelPlacing a matrix; lambda (lambda) 1 -laplace matrix diagonal value correction constants, typically taken as 0.1; P-Laplace equation matrix; p (P) t -transposed matrix of the laplace equation; lambda (lambda) 2 -a diagonal value correction constant of the identity matrix, typically taken to be 0.05; i-a matrix of unit equations; i t -transpose of the unit equation; Δd—the wavefield residual least squares value;
the density value two-dimensional imaging is realized, and MATLAB software is utilized to compile an image based on inversion physical values so as to identify physical value distribution conditions in a concrete structure;
the image rendering is carried out on the image in the steps based on the numerical range of the inversion physical value, and comprises a transparentizing treatment concrete body, so that the crack defect in the protruding concrete structure is emphasized, and the reinforcing steel bar structure in the protruding concrete is emphasized. Concrete transparent rendering value V 1 The range selection method comprises the following steps:
0.8*V C <V 1 <1.2*V C
wherein V is C Kg/m based on the initial value of the density model selected in the inversion initial model 3 ；V 1 Transparent rendering density value range, kg/m 3 ；
Crack defect rendering value V 2 In a range of not more than 500kg/m 3 ；
Reinforcing steel bar reinforcement rendering value V 3 In a range of not less than 7000kg/m 3 。
Example 1
Inversion imaging of cracks in concrete: reinforced concrete members were fabricated with dimensions of 50 cm. Times.50 cm. Times.19 cm. During pouring, the foam sheet is buried in advance to simulate horizontal cracks, and the density value of the sheet is about 100kg/m 3 The dimensions were 10cm by 1cm, embedded at a central position 10cm from the surface of the member. Meanwhile, 3 concrete test pieces of 10cm×10cm were prepared, and the concrete member and 3 test pieces were cured under standard conditions for 28d.
Dividing the surface of the formed concrete member into acquisition grid points, setting the transverse acquisition interval of the grid points to be 20cm, setting the longitudinal acquisition interval to be 1cm, and adopting an ultrasonic instrument to acquire ultrasonic data according to the points divided by the acquisition grid points. As shown in fig. 2, the ultrasonic instrument is placed right above the horizontal crack, and the area of the broken line in the figure is 20cm x 19cm of the area to be inverted, for testing the side view of the concrete member.
Based on the collected ultrasonic data, when inversion starts, an ultrasonic source signal is predicted first, as shown in fig. 3, for the calculated quasi-ultrasonic signal, it can be seen that the multi-channel quasi-ultrasonic signal is uniform in value and time phase, so that the ultrasonic source signal prediction method has reliability. Measuring the average density value of concrete used in pouring based on 3 concrete members, firstly measuring the volume and the weight of a single test piece, calculating the single density value, sequentially calculating the single density values of three test pieces, averaging to obtain the average density value, wherein the average density value of the concrete is 2405kg/m 3 Used as an initial model of the density values required for inversion.
Based on the initial model of the density value and the simulated ultrasonic source, forward modeling analysis is started, so that a predicted wave field signal is obtained, differential calculation is carried out on the predicted wave field signal and the actually collected ultrasonic wave field signal, a least square method calculation is carried out to obtain an objective function, analysis is carried out by using a Gaussian-Newton optimization algorithm, the gradient direction of the objective function is reduced, an update step length is calculated, the density value model is updated, and finally an inversion density value matrix is obtained.
The density value matrix obtained by inversion is programmed by MATLAB software to realize numerical imaging, as shown in FIG. 4, the density value-based two-dimensional concrete inversion image is obtained, the right side of the image is the correspondence between the inverted density value and the color, the dark color area is a density high value area, the bright white color area is a density low value area, the middle of the color column is a transition area, and the density values correspond to different density value values. As can be seen from the graph, a low density value line with a length of about 10cm and a width of 1mm exists at a position with a depth range of 10cm, and the inversion density value is about 0-150 kg/m 3 . The density value of the foam board used for the simulated cracking was about 100kg/m 3 It can be inferred that the low density line is in the simulated concreteAnd (3) a part crack, wherein the inversion crack is completely matched with the simulated concrete crack in width, length, density value and space burial depth. Therefore, the full-wave inversion nondestructive testing method for the density value of the concrete structure has the nondestructive testing capability on the internal structure of the concrete structure, particularly the key damage index aiming at the crack defect, and can provide information such as the width, the length and the space position of the crack through inversion, so that the full-wave inversion nondestructive testing method is fully proved in the embodiment.
Example 2
Inversion imaging of the steel bars in the concrete: reinforced concrete members were fabricated with dimensions of 50 cm. Times.50 cm. Times.19 cm. The test block is pre-embedded with reinforcing steel bar with the number 16 and the diameter of 16mm, and the density value of the reinforcing steel bar is about 7850kg/m 3 . The distance between the steel bar and the upper top end is 7cm. At the same time, 3 concrete test pieces of 10cm×10cm were prepared. The concrete member and the 3 concrete test piece were cured under standard conditions for 28d.
Dividing the surface of the formed concrete member into acquisition grid points, setting the transverse acquisition interval of the grid points to be 20cm, setting the longitudinal acquisition interval to be 1cm, and adopting an ultrasonic instrument to acquire ultrasonic data according to the points divided by the acquisition grid points. Fig. 4 shows a side view of the ultrasonic instrument and the concrete member during data acquisition, and the ultrasonic instrument is placed right above the steel bar, and the size of the ultrasonic instrument is 20cm multiplied by 19cm in the broken line area in the figure.
Based on the acquired ultrasonic data, an ultrasonic source signal is predicted first at the beginning of inversion. Determining average density value of concrete based on 3 concrete test blocks, firstly determining volume and weight of a single test block, calculating single density value, averaging to obtain average density value, and determining average density value to be 2410kg/m 3 Used as an initial model of the density values required for inversion.
Based on the initial model of the density value and the simulated ultrasonic source, forward modeling analysis is started, so that a predicted wave field signal is obtained, differential calculation is carried out on the predicted wave field signal and the actually collected ultrasonic wave field signal, a least square method calculation is carried out to obtain an objective function, analysis is carried out by using a Gaussian-Newton optimization algorithm, the gradient direction of the objective function is reduced, an update step length is calculated, the density value model is updated, and finally an inversion density value matrix is obtained.
The density value matrix obtained by inversion is programmed by MATLAB software to realize numerical imaging, as shown in FIG. 5, the inversion image is a two-dimensional concrete structure inversion image based on density values, the right side of the image is the correspondence between the inverted density values and colors, the dark color area is a density high value area, the bright white color area is a density low value area, the middle of a color column is a transition area, and the numerical values of different density values are corresponding. As can be seen from the graph, the density value of the whole concrete is 2410kg/m 3 At a depth of 7cm, there is a circular region with a high density value of about 16mm in diameter, and the inversion density value is about 6000-7500 kg/m 3 . Due to the fact that the actual density value of the steel bar is about 7800kg/m 3 It can be inferred that the high density circular region is a buried rebar within the concrete, and that the inverted rebar is exactly identical in shape, size and burial depth to the actual buried rebar. Therefore, the full-wave inversion nondestructive testing method for the density value of the concrete structure has the nondestructive testing capability on the steel bar structure in the concrete structure, and the shape, the size, the space position and other information of the steel bar can be provided through inversion, so that the full-wave inversion nondestructive testing method is fully verified in the embodiment.
Example 3
Inversion imaging of the cavity in the concrete: reinforced concrete members were fabricated with dimensions of 50 cm. Times.50 cm. Times.19 cm. Meanwhile, 3 small concrete test pieces of 10cm multiplied by 10cm are manufactured, and the concrete member and the test pieces are cured for 28 days under standard conditions. After curing and molding, drilling and molding a circular cavity at the center position with the side depth of 6cm, wherein the radius of the circular cavity is 2cm, the distance from the upper top end of the cavity to the upper surface of the concrete member is 4cm, and the distance from the lower end to the upper surface of the concrete member is 8cm.
Dividing the surface of the formed concrete member into acquisition grid points, setting the transverse acquisition interval of the grid points to be 20cm, setting the longitudinal acquisition interval to be 1cm, and adopting an ultrasonic instrument to acquire ultrasonic data according to the points divided by the acquisition grid points. Fig. 6 shows a side view of the ultrasonic instrument and the concrete member during data acquisition, and it can be seen from the figure that the ultrasonic instrument is placed right above the circular cavity, and the area of the broken line in the figure is an inversion-planned area, and the dimensions are 20cm×19cm.
Based on the acquired ultrasonic data, when inversion starts, an ultrasonic source signal is predicted first, as shown in fig. 3, in order to calculate a pseudo-ultrasonic signal, it can be seen that the pseudo-ultrasonic signal of multiple channels is uniform in value and time phase, so that the ultrasonic source signal prediction method has reliability. The average density value of the concrete was determined based on 3 small-sized concrete test pieces, and the average density value of the determined concrete was 2421kg/m 3 Used as an initial model of the density values required for inversion.
Based on the initial model of the density value and the simulated ultrasonic source, forward modeling analysis is started, so that a predicted wave field signal is obtained, differential calculation is carried out on the predicted wave field signal and the actually collected ultrasonic wave field signal, a least square method calculation is carried out to obtain an objective function, analysis is carried out by using a Gaussian-Newton optimization algorithm, the gradient direction of the objective function is reduced, an update step length is calculated, the density value model is updated, and finally an inversion density value matrix is obtained.
The density value matrix obtained by inversion is programmed by MATLAB software to realize numerical imaging, as shown in FIG. 7, the density value-based two-dimensional concrete inversion image is obtained, the right side of the image is the correspondence between the inverted density value and the color, the dark color area is a density high value area, the bright white color area is a density low value area, the middle of the color column is a transition area, and the density values correspond to different density value values. As can be seen from the figure, there is a circular region with a diameter of about 4cm and a low density value at a depth ranging from about 4cm to about 8cm, and the inversion density value is about 0kg/m to about 100kg/m 3 . Because the density value of the real cavity is 0, the low-density circular area can be deduced to be a circular cavity formed by drilling in concrete, and the inversion cavity is basically matched with the real cavity of the concrete in shape, size, density value and space burial depth. Therefore, the full-wave inversion nondestructive testing method for the density value of the concrete structure has the advantages that the circular cavity in the concrete structure is providedThe non-destructive testing capabilities of the construction can be provided by inversion with information such as the shape, size, spatial location, etc. of the voids, which is well documented in this embodiment.
Claims (10)
1. The inversion imaging method for the reinforced concrete internal structure based on the density value is characterized by comprising the following three subroutines:
subroutine one: the ultrasonic data acquisition comprises two steps of data acquisition grid point division, ultrasonic signal transmission and acquisition;
subroutine II: the ultrasonic data inversion analysis comprises six steps of ultrasonic source signal prediction, inversion initial model selection, forward modeling analysis, objective function selection, optimization algorithm selection and prediction model updating;
and a third sub-program: the density value imaging comprises three steps of density value three-dimensional imaging, density rendering threshold analysis and image rendering.
2. The inversion imaging method of the reinforced concrete internal structure based on the density value according to claim 1, wherein the data acquisition grid points are divided, the longitudinal distance is 1-2 cm, the transverse distance is 5-10 cm, the ultrasonic waves are SH waves, and the number of ultrasonic probes is not less than 32.
3. The reinforced concrete internal structure inversion imaging method according to claim 1, wherein the ultrasonic source signal prediction method comprises green's equation calculation and source signal prediction calculation,
the calculation method of the green equation comprises the following steps:
wherein, f-when collecting data, the ultrasonic frequency is in Hz; x-calculating the position function of the grid points; m-the density value of the calculated lattice points; g (f, x, m) -calculating a wave field green's function; d (f, x, m) -predicting the wavefield; w (f) -rake wavelet signal;
the method for calculating the seismic source signal comprises the following steps:
wherein, f-when collecting data, the ultrasonic test frequency, hz; x-calculating the position function of the grid points; m-the density value of the calculated lattice points; w (W) est (f) -calculating a source signal with a centre frequency f; d (f, x, m) -predicting the wavefield; g (f, x, m) -calculating the wavelength Green function.
4. The inversion imaging method of reinforced concrete internal structure based on density values according to claim 1, wherein in the inversion initial model selection step, an initial value of a density model used for inversion is determined according to actual measurement of a concrete material mix ratio.
5. The inversion imaging method of reinforced concrete internal structure based on density values according to claim 1, wherein in the forward modeling analysis step, a time domain two-dimensional SH elastic wave equation is adopted to model forward propagation process of SH waves in concrete:
wherein, the coordinates of the grid points in the x-forward model in the transverse direction, the coordinates of the grid points in the z-forward model in the longitudinal direction and the y-direction perpendicular to the xy plane; ρ%x, z) -the density value of the lattice point in the forward model, μ (x, z) -the shear modulus value of the lattice point in the forward model; v y -the velocity of the shear transverse wave particles in the y-direction; sigma (sigma) xy Shear stress in xy plane, sigma yz -shear stress in the yz plane; f (f) y -source stress in a direction perpendicular to the xz plane;
the forward model adopts a mirror stress method on the boundary of the simulated concrete structure surface to simulate strong reflection waves generated by SH elastic waves on the concrete surface; and absorbing boundary reflection waves by adopting a perfect matching layer on the rest boundaries except the surface of the concrete structure.
6. The method for inverse imaging of reinforced concrete internal structure based on density values according to claim 1, wherein in the step of selecting an objective function, a least square method is selected as a model inversion objective function, and the calculation process comprises wave field residual calculation and least square method calculation,
the wave field residual error calculation method comprises the following steps:
Δd t，r ＝D t，r (m)-d t，r
wherein, t is the serial number of the sensor; r-data channel number; m-medium density value; Δd t，r -a wave field residual; d (D) t，r (m) -predicting wavefield data; d, d t，r -actual wave field data;
the least square method comprises the following steps:
wherein m is the medium density value; e (m) -least squares; Δd-wavefield residual.
7. The inversion imaging method of reinforced concrete internal structure based on density values according to claim 1, wherein in the optimization algorithm selecting step, a gaussian-newton method is adopted to calculate a gradient direction of a density model, and the calculation method comprises the following steps:
in the method, in the process of the invention,-density model gradient direction; f (F) x -transversal virtual stresses in the forward wave field; r is R x -transverse virtual stresses in the post-transfer field; f (F) z -longitudinal virtual stresses in the forward wavefield; r is R z -longitudinal virtual stresses in the post-transfer field.
8. The inversion imaging method of reinforced concrete internal structure based on density values according to claim 1, wherein in the prediction model updating step, a density model is updated by a steepest gradient method, and the calculation method is as follows:
in the formula, n-nth iterative inversion is carried out; n+1-n+1th iterative inversion; ρ -medium density values; ρ n+1 -a density value of the medium at n+1 iterations of inversion; ρ n -a density value of the medium at n iterations of inversion; beta n -updating the step size; s-source; r-receiver;-a density model gradient direction matrix; />-transposed matrix of density model gradient directions; lambda (lambda) 1 -laplace matrix diagonal value correction constants, typically taken as 0.1; P-Laplace equation matrix; p (P) t -transposed matrix of the laplace equation; lambda (lambda) 2 -a diagonal value correction constant of the identity matrix, typically taken to be 0.05; i-a matrix of unit equations; i t -unitary equation transpose matrixThe method comprises the steps of carrying out a first treatment on the surface of the Δd—wave field residual least squares value.
9. The inversion imaging method of reinforced concrete internal structure based on the density value according to claim 1, wherein in the two-dimensional imaging step of the density value, the imaging is inverted by adopting MATLAB software programming based on the density value obtained by inversion.
10. The inversion imaging method of reinforced concrete internal structure based on density values according to claim 9, wherein in the image rendering step, the image obtained in claim 9 is rendered based on the numerical range of inversion density values, the concrete body is transparentized, and the internal structure of the concrete is emphasized;
concrete transparent rendering value V 1 The range selection method comprises the following steps:
0.8*V C <V 1 <1.2*V C
wherein V is C -inverting the initial value of the density model selected in the initial model in kg/m 3 ；V 1 Transparent rendering density value range in kg/m 3 ；
Crack defect rendering value V 2 In a range of not more than 500kg/m 3 ；
Reinforcing steel bar reinforcement rendering value V 3 In a range of not less than 7000kg/m 3 。
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