CN104376213A - Inverse algorithm for ultrasonic chromatography - Google Patents
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- 238000004587 chromatography analysis Methods 0.000 title claims abstract description 11
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- 238000004364 calculation method Methods 0.000 claims description 46
- 238000003325 tomography Methods 0.000 claims description 19
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- 238000002604 ultrasonography Methods 0.000 claims description 4
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- 238000009659 non-destructive testing Methods 0.000 description 2
- 238000002922 simulated annealing Methods 0.000 description 2
- 238000012614 Monte-Carlo sampling Methods 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
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Abstract
The invention discloses an inverse algorithm for ultrasonic chromatography. According to the inverse algorithm, an adjoint state variable is introduced to establish a new objective functional, the relation between the adjoint state variable and a gradient of a traditional objective functional to speed model parameters is subjected to theoretical derivation, the gradient is solved indirectly, and the variation trend of speed within a computational domain can be obtained through the gradient, so that the speed model is subjected to iteration updating, and computation of a Frechet derivative is avoided. The inverse algorithm has the advantages that the algorithm is simple, computation of the Frechet derivative of a large sparse matrix is avoided, and operation efficiency is high; the computer memory consumed in the computational process is only related to the size of the computational domain and unrelated to the number of ultrasonic probes, so that stable, efficient and rapid computation for ultrasonic chromatography is guaranteed.
Description
Technical Field
The invention belongs to the technical field of ultrasonic chromatography, and particularly relates to an inversion algorithm for ultrasonic chromatography.
Background
In the building engineering, the pile and the underground continuous wall are very important foundation forms, and the concrete of the pile foundation and the underground continuous wall is easy to generate quality defects such as cavities, mud inclusion, segregation, cracks and the like in the pouring process, thereby bringing great hidden danger to engineering safety. In order to eliminate the potential safety hazard, an effective nondestructive testing means is required to accurately find the scale, the property and the spatial position of the defect. At present, the ultrasonic tomography method is an efficient detection means for detecting the defects of the concrete structure.
The ultrasonic tomography method adopts a transmitter to transmit ultrasonic signals outside a tested concrete member, a receiver to receive the signals which pass through the concrete and carry the internal information of the concrete, and a computer image processing technology to reproduce a two-dimensional or three-dimensional clear image inside the concrete member.
The implementation process of the ultrasonic tomography detection system can be divided into four steps: data acquisition, forward modeling, establishment of a Jacobian matrix (namely a Frechet derivative) and inversion solving. The inversion solution is the key of the ultrasonic tomography technology, and the imaging accuracy and resolution are directly determined.
The currently commonly used ultrasonic tomography inversion methods include a least square method, a genetic algorithm, a simulated annealing method and the like.
The least square method is a linear iterative method, and has the advantages that the formula is simple, the physical significance is clear, but the difficulty is that the Jacobian matrix (namely the Frechet derivative) is recalculated according to the modified model in each step of iteration in the inversion process, the calculation is very complicated, and the local extremum is easy to fall into in the iteration process.
The genetic algorithm is a random global optimization search nonlinear inversion algorithm for simulating the evolution rule of 'survival of suitable persons' in the biological field, has better control capability on the inversion iterative convergence process, and can always converge to more optimal solution estimation as long as the hybridization probability and the variation probability are selected properly although the iterative convergence to the global optimal solution of the objective function cannot be guaranteed. However, the genetic algorithm needs to perform multiple iterations to achieve more optimal solution estimation, and is not suitable for processing large-batch data.
The simulated annealing method is a global optimization nonlinear inversion technology based on Monte Carlo sampling, simulates the characteristics that a heated substance is rapidly cooled at a high temperature and slowly annealed at a low temperature, gives consideration to the search of global and local optimal solutions, avoids the problem that local extremum is trapped in iteration, but has the problems of slow search and more iteration times as with a genetic algorithm.
Disclosure of Invention
The invention aims to provide an inversion algorithm for ultrasonic tomography according to the defects of the prior art, the inversion algorithm introduces a state variable to construct a new target functional, indirectly solves a gradient, and can obtain the change trend of the speed in a calculation region through the gradient, thereby performing iterative update on a speed model and improving the calculation speed.
The purpose of the invention is realized by the following technical scheme:
an inversion algorithm for ultrasound tomography, characterized in that the inversion algorithm comprises the steps of:
the method comprises the following steps: collecting ultrasonic detection data in a member to be detected, and establishing an initial velocity model C by using the background velocity in the detection area of the member to be detected as the initial velocityn；
Step two: establishing a target functional of ultrasonic chromatography, wherein the expression is as follows:
wherein,
j is a target functional;
t (r) represents the theoretical travel time at the ultrasonic receiving point obtained by forward calculation;
t (r) represents the actual travel time at the ultrasound receiving point acquired on site;
λ (x) represents an accompanying state variable within the calculation region;
representing the boundary of the calculation region;
means for graduating t (x);
c (x) is the velocity in the calculation region;
step three: solving for the accompanying state variable λ (x) inside the calculation region, the calculation formula is as follows:
wherein,represents the partial derivative of t to x; represents the partial derivative of t to z;
step four: determining a target functional of the ultrasonic tomography with respect to the initial velocity model CnGradient of internal velocity parameterThe calculation formula is as follows:
step five: using the obtained gradientFor the initial velocity model CnAnd performing iterative updating, wherein the calculation formula is as follows:
wherein alpha is an iteration step length;representing the updated velocity model.
The method for acquiring the ultrasonic detection data comprises the following steps: the two sides of the component to be detected are provided with acoustic pipes, an ultrasonic transmitting probe and an ultrasonic receiving probe are respectively arranged in the acoustic pipes at the two sides, and the sampling measuring point of the ultrasonic receiving probe is the ultrasonic receiving point; and acquiring ultrasonic data transmitted by the ultrasonic transmitting probe through the ultrasonic receiving probe.
The calculation formula of the iteration step length alpha is as follows:
wherein J is a target functional.
The method has the advantages that the algorithm is simple, the calculation of the large sparse matrix Frechet derivative is avoided, and the operation efficiency is high; the computer memory consumed in the calculation process is only related to the size of the calculation area and is not related to the number of the ultrasonic probes, so that stable, efficient and rapid calculation of the ultrasonic chromatography is guaranteed.
Drawings
FIG. 1 is a schematic view of a concrete member according to the present invention;
FIG. 2 is a diagram of accompanying state variables over a computation region in accordance with the present invention;
FIG. 3 is a schematic diagram of the gradient over a calculation region in the present invention;
FIG. 4 is a diagram showing the result of ultrasonic tomography by the satellite state method in the present invention.
Detailed Description
The features of the present invention and other related features are described in further detail below by way of example in conjunction with the following drawings to facilitate understanding by those skilled in the art:
referring to fig. 1-4, the labels 1-2 in the figures are: concrete element 1, defect 2.
Example (b): the embodiment particularly relates to an inversion algorithm for ultrasonic tomography, which introduces an accompanying state variable to construct a new target functional, theoretically deduces the relation between the accompanying state variable and the gradient of the traditional target functional to a velocity model parameter, indirectly solves the gradient, and can obtain the change trend of the velocity in a calculation region through the gradient, so that the velocity model is iteratively updated, and the calculation of the Frechet derivative is avoided. The calculated amount of the inversion algorithm is only equivalent to two forward operations, the memory occupation amount in the calculation process is only related to the size of a calculation area and is not related to the number of the ultrasonic probes, so that the method is stable and efficient, the memory occupation amount is small, the ultrasonic data can be accurately and efficiently processed, and the ultrasonic tomography can be better applied to the nondestructive testing of the pile foundation concrete.
As shown in fig. 1-4, the inversion algorithm in the present embodiment specifically includes the following steps:
step one, as shown in fig. 1, a rectangular defect 2 is preset in a concrete member 1 with the abscissa (x direction) as a distance and the ordinate (z direction) as a depth, the width of the concrete member 1 is 1m, and the length of the concrete member 1 is 4 m; the length of the defect 2 is 0.64m, the width of the defect 2 is 0.1m, and the buried depth of the defect 2 from the top is 0.75 m;
PVC sounding pipes are arranged on two sides of the concrete member 1, and the distance between the defect 2 and the left sounding pipe is 0.43 m, and the distance between the defect 2 and the right sounding pipe is 0.47 m; respectively placing an ultrasonic transmitting probe and an ultrasonic receiving probe in the left and right sounding pipes, wherein the ultrasonic receiving probe is used for receiving ultrasonic data transmitted from the ultrasonic transmitting probe, and the position of the ultrasonic receiving probe for receiving the ultrasonic data is a receiving point; establishing an initial velocity model C by using background velocity in a detection area of a member to be detected as an initial velocityn(ii) a Establishing a 101 multiplied by 401 grid model (namely a calculation area) according to the arrangement condition of the sounding pipes in the detection area, wherein the grid distance is 0.01m multiplied by 0.01 m;
step two, introducing accompanying state variables based on an accompanying state method of a perturbation theory, and establishing a new target functional of ultrasonic chromatography, wherein the expression is as follows:
wherein,
j is a target functional;
t (r) represents the theoretical travel time at the receiving point obtained by forward calculation;
t (r) represents the actual travel time at the receiving point from the field acquisition;
λ (x) represents an accompanying state variable within the calculation region;
representing a calculation regionThe boundary of (2);
means for graduating t (x);
c (x) is the velocity in the calculation region;
step three, determining a gradient expression of the ultrasonic tomography target functional about a speed model parameter (namely, speed), wherein the gradient is a partial derivative of the target functional J to the model speed c and can be expressed as follows:
deducing solution equations of the accompanying state variables at the boundary of the calculation region and in the calculation region, and further obtaining the gradient of the target functional to the model parameters;
according to the formula in the third step, the gradient of the target functional to the velocity model velocity can be indirectly obtained by solving the accompanying state variable lambda (x) in the calculation region；
Because t (x) and c (x), λ (x) and c (x) are independent of each other in the optimization process, the target generic J satisfies the following formula:
then at the receiving point, the accompanying state variable λ satisfies the following equation:
inside the calculation region, the accompanying state variable λ (x) satisfies the following calculation formula:
where Δ t (r) is the time-of-flight residual at the receiving point;means for gradient of t (r); λ (r) is the accompanying state variable at the point of reception;nthe external normal vector of the measuring line of the receiving point; λ (x) is an accompanying state variable inside the calculation region;represents the partial derivative of t to x;represents the partial derivative of t to z;
according to the two formulas, the accompanying state variable λ in the whole calculation area can be obtained, and fig. 2 is a schematic diagram showing the variation of the accompanying state variable; then obtaining the gradient of the target functional to the velocity model parameter according to the formula in the step threeAs shown in fig. 3, the gradient approximately reflects the trend of the velocity in the calculation region;
step five utilizing the obtained gradientUsing linear search algorithm to model C of initial velocitynAnd performing iterative updating, wherein the calculation formula is as follows:
wherein alpha is an iteration step length;representing an initial velocity model;representing the updated velocity model;
in this embodiment, the iteration step α is calculated by using the following formula:
j is a target functional and meets the formula in the second step;the gradient solved in the step four is obtained;
the iteratively updated velocity model is shown in FIG. 4, which can determine the size and type of the defect.
By analysis, ultrasonic tomography using a state inversion algorithm can better determine the type of the defect and better identify the velocity in the defect. The reliability of interpretation and evaluation of the ultrasonic chromatography result in the later period is ensured by accurate positioning and better speed identification capability.
In the adjoint state inversion algorithm in the embodiment, the gradient is indirectly solved by deducing the relation between the adjoint state variable and the gradient of the traditional objective function to the model parameter, so that the calculation of the Frechet derivative is avoided, the calculation speed is improved, and the memory occupation amount is reduced; the method is applied to the ultrasonic time-lapse tomography technology, so that the calculation efficiency of tomography is improved to a great extent, and the technology can better serve for actual production.
Claims (3)
1. An inversion algorithm for ultrasound tomography, characterized in that the inversion algorithm comprises the steps of:
the method comprises the following steps: collecting ultrasonic detection data in a member to be detected, and establishing an initial velocity model C by using the background velocity in the detection area of the member to be detected as the initial velocityn；
Step two: establishing a target functional of ultrasonic chromatography, wherein the expression is as follows:
wherein,
j is a target functional;
t (r) represents the theoretical travel time at the ultrasonic receiving point obtained by forward calculation;
t (r) represents the actual travel time at the ultrasound receiving point acquired on site;
λ (x) represents an accompanying state variable within the calculation region;
representing the boundary of the calculation region;
means for graduating t (x);
c (x) is the velocity in the calculation region;
step three: solving for the accompanying state variable λ (x) inside the calculation region, the calculation formula is as follows:
wherein,represents the partial derivative of t to x;represents the partial derivative of t to z;
step four: determining a target functional of the ultrasonic tomography with respect to the initial velocity model CnGradient of internal velocity parameterThe calculation formula is as follows:
step five: using the obtained gradientFor the initial velocity model CnAnd performing iterative updating, wherein the calculation formula is as follows:
wherein alpha is an iteration step length;representing the updated velocity model.
2. An inversion algorithm for ultrasonic tomography according to claim 1, wherein the method of acquiring ultrasonic test data comprises: the two sides of the component to be detected are provided with acoustic pipes, an ultrasonic transmitting probe and an ultrasonic receiving probe are respectively arranged in the acoustic pipes at the two sides, and the sampling measuring point of the ultrasonic receiving probe is the ultrasonic receiving point; and acquiring ultrasonic data transmitted by the ultrasonic transmitting probe through the ultrasonic receiving probe.
3. An inversion algorithm for ultrasonic tomography according to claim 1, characterized in that the iterative step size α is calculated by the formula:
wherein J is a target functional.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111077227A (en) * | 2019-12-18 | 2020-04-28 | 华南理工大学 | Ultrasonic array scanning inversion method, system, storage medium and equipment |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102590347A (en) * | 2012-03-07 | 2012-07-18 | 重庆交通大学 | Ultrasonic mortar grouting fullness detection device and method for prestress anchoring structure system |
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| CN102590347A (en) * | 2012-03-07 | 2012-07-18 | 重庆交通大学 | Ultrasonic mortar grouting fullness detection device and method for prestress anchoring structure system |
Non-Patent Citations (2)
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| 宋焕生等: "混凝土超声CT层析成像算法的改进", 《长安大学学报（自然科学版）》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111077227A (en) * | 2019-12-18 | 2020-04-28 | 华南理工大学 | Ultrasonic array scanning inversion method, system, storage medium and equipment |
| CN111077227B (en) * | 2019-12-18 | 2021-11-02 | 华南理工大学 | Ultrasonic array scanning inversion method, system, storage medium and equipment |
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Application publication date: 20150225 |