CN104376213A - Inverse algorithm for ultrasonic chromatography - Google Patents
Inverse algorithm for ultrasonic chromatography Download PDFInfo
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- CN104376213A CN104376213A CN201410656651.6A CN201410656651A CN104376213A CN 104376213 A CN104376213 A CN 104376213A CN 201410656651 A CN201410656651 A CN 201410656651A CN 104376213 A CN104376213 A CN 104376213A
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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 ultrasound wave chromatographic technique field, be specifically related to a kind of inversion algorithm for ultrasound wave chromatography.
Background technology
In construction work, stake and diaphram wall are a kind of very important base forms, and the concrete of pile foundation and diaphram wall easily produces the mass defect such as cavity, folder mud, segregation, crack in casting process, brings great hidden danger to engineering safety.In order to eliminate safe hidden trouble, effective nondestructiving detecting means must be adopted, accurately ascertain the scale of defect, character and locus.At present, ultrasonic tomography method is a kind of detection means of efficient Detection of Concrete defect.
Ultrasonic tomography method adopts transmitter to launch ultrasonic signal at detected concrete member exterior, receiver receives and wore long concrete and carried the signal of inside concrete information, recycling computer image processing technology, reappear the method for the inner two dimension of concrete component or three-dimensional picture rich in detail, the position of defect and shape in the method energy Accurate Diagnosis concrete component, can be used to detect concrete quality.
The realization flow of ultrasonic tomography detection system can be divided into four steps: data acquisition, forward simulation, set up Jacobian matrix (i.e. Fr é chet derivative), inverting solves.Wherein inverting is solved to the key of Ultrasonic CT technique, directly determines imaging accuracy and resolution.
Ultrasound wave tomographic inversion solution conventional at present has least square method, genetic algorithm, simulated annealing etc.
Wherein least square method is a kind of linear iterative method, its advantage is that formula is comparatively simple, explicit physical meaning, but difficulty is that often walking iteration in refutation process all will recalculate Jacobian matrix (i.e. Fr é chet derivative) according to amended model, its calculating is very numerous and diverse, and is easily absorbed in local extremum in iterative process.
Genetic algorithm is the one random global optimization search non-linear inversion algorithm of simulation organic sphere " survival of the fittest " Evolution, to inversion iterates convergence process, there is good control ability, although it can not ensure the globally optimal solution of iteration convergence to objective function, as long as but probability of crossover and mutation probability are selected suitable, genetic algorithm can converge to the solution comparatively optimized and estimate.But genetic algorithm will reach the solution comparatively optimized and estimate to need to carry out successive ignition, is unwell to the process of data in enormous quantities.
Simulated annealing is the global optimization non-linear inversion technology based on Monte Carlo sampling, the imitation material that is heated cools rapidly when high temperature, to anneal during low temperature feature slowly, take into account the search to the overall situation and locally optimal solution, avoid in iteration the problem being absorbed in local extremum, but the same with genetic algorithm, it also also exists searches for slow, that iterations is more problem.
Summary of the invention
The object of the invention is according to above-mentioned the deficiencies in the prior art part, a kind of inversion algorithm for ultrasound wave chromatography is provided, this inversion algorithm is introduced and is built new cost functional with state variable, indirectly solve gradient, the variation tendency of speed in zoning can be obtained by this gradient, thus iteration renewal is carried out to rate pattern, improve computing velocity.
The object of the invention realizes being completed by following technical scheme:
For an inversion algorithm for ultrasound wave chromatography, it is characterized in that described inversion algorithm comprises the steps:
Step one: gather ultrasonic test data in component to be checked, adopts the background velocity in described component surveyed area to be checked to set up initial velocity model C as initial velocity
n;
Step 2: the cost functional setting up ultrasound wave chromatography, expression formula is:
Wherein,
J is cost functional;
When t (r) represents that the theory at the ultrasound wave acceptance point place that forward modelling obtains is walked;
T* (r) represent that collection in worksite obtains ultrasound wave acceptance point place actual walk time;
λ (x) represents the adjoint state variable in zoning;
represent the border of zoning;
represent and gradient is asked to t (x);
C (x) is the speed in zoning;
Step 3: the adjoint state variable λ (x) solving inside, zoning, computing formula is as follows:
Wherein,
represent that t is to the local derviation of x; Represent that t is to the local derviation of z;
Step 4: determine that the cost functional of described ultrasound wave chromatography is about described initial velocity model C
nthe gradient of interior speed parameter
, computing formula is:
Step 5: utilize the gradient obtained
, to described initial velocity model C
ncarry out iteration renewal, computing formula is as follows:
Wherein, α is iteration step length;
represent the rate pattern after upgrading.
In the method for described collection ultrasonic test data be: the both sides of described component to be checked arrange sound detecting pipe, in sound detecting pipe described in both sides, arrange ultrasound wave transmitting probe and ultrasound wave receiving transducer respectively, described ultrasound wave receiving transducer sampling measuring point place is described ultrasound wave acceptance point; By the ultrasound data that the collection of described ultrasound wave receiving transducer is launched from described ultrasound wave transmitting probe.
The computing formula of described iteration step length α is:
Wherein, J is cost functional.
Advantage of the present invention is, algorithm is simple, and avoid the calculating of Large sparse matrix Fr é chet derivative, operation efficiency is high; The calculator memory consumed in computation process is only relevant with the size of zoning, and has nothing to do with the number of ultrasonic probe, ensure that ultrasound wave chromatography is stable, efficiently, fast calculates.
Accompanying drawing explanation
Fig. 1 is concrete component schematic diagram in the present invention;
Fig. 2 is the adjoint state variable schematic diagram in the present invention on zoning;
Fig. 3 is the gradient schematic diagram in the present invention on zoning;
Fig. 4 is Adjoint State Method ultrasonic tomography result schematic diagram in the present invention.
Embodiment
Feature of the present invention and other correlated characteristic are described in further detail by embodiment below in conjunction with accompanying drawing, so that the understanding of technician of the same trade:
Be respectively as marked 1-2 in Fig. 1-4, figure: concrete component 1, defect 2.
Embodiment: the present embodiment is specifically related to a kind of inversion algorithm for ultrasound wave chromatography, this inversion algorithm introduces one with state variable to build new cost functional, theory deduction this with state variable and conventional target functional to the relation between the gradient of rate pattern parameter, indirectly solve gradient, the variation tendency of speed in zoning can be obtained by this gradient, thus iteration renewal is carried out to rate pattern, avoid the calculating of Fr é chet derivative.The calculated amount of this inversion algorithm is only equivalent to just drill for twice, EMS memory occupation amount in computation process is only relevant with the size of zoning, and have nothing to do with the number of ultrasonic probe, this just makes, and the method is stable, efficient, EMS memory occupation amount is few, accurately can process ultrasound data efficiently, ultrasonic tomography can be better applied in pile foundation concrete nondestructive testing.
As Figure 1-4, the inversion algorithm in the present embodiment specifically comprises the steps:
[step one] as shown in Figure 1, horizontal ordinate (x direction) is distance, and ordinate (z direction) is the degree of depth, pre-sets a rectangle defect 2 in concrete component 1, and concrete component 1 is wide is 1m, and long is 4m; Defect 2 is long is 0.64m, and wide is 0.1m, and defect 2 is 0.75m apart from top buried depth;
Arrange PVC sound detecting pipe in the both sides of concrete component 1, defect 2 and left side sound detecting pipe at a distance of 0.43 meter, with right side sound detecting pipe at a distance of 0.47 meter; Ultrasound wave transmitting probe and ultrasound wave receiving transducer are placed in the sound detecting pipe of the left and right sides respectively, ultrasound wave receiving transducer is for receiving the ultrasound data from the bottom of ultrasound wave transmitting probe, and the position that ultrasound wave receiving transducer receives ultrasound data is acceptance point; The background velocity in component surveyed area to be checked is adopted to set up initial velocity model C as initial velocity
n; According to the deployment scenarios of sound detecting pipe in search coverage, set up the grid model (i.e. zoning) of one 101 × 401, mesh spacing is 0.01m × 0.01m;
[step 2], based on the Adjoint State Method of perturbation theory, is introduced with state variable, and set up the cost functional of a new ultrasound wave chromatography, its expression formula is:
Wherein,
J is cost functional;
When t (r) represents that the theory at the acceptance point place that forward modelling obtains is walked;
T* (r) represent that collection in worksite obtains acceptance point place actual walk time;
λ (x) represents the adjoint state variable in zoning;
represent zoning
border;
Represent and gradient is asked to t (x);
C (x) is the speed in zoning;
[step 3] determines the gradient expression formula of ultrasound wave chromatography cost functional about rate pattern parameter (i.e. speed), and this gradient is the local derviation of cost functional J to model velocity c, can be expressed as following form:
[step 4] derives with the solving equation of state variable in border, zoning and inside, zoning, and then obtains cost functional to the gradient of model parameter;
From the formula in step 3, the gradient of cost functional to rate pattern speed indirectly can be obtained by the adjoint state variable λ (x) solved in zoning
;
Because in optimization procedure, t (x) and c (x), λ (x) are separate with c (x), and namely the general J of target meets following formula:
Then at acceptance point place, meet following formula with state variable λ:
Inner in zoning, meet following computing formula with state variable λ (x):
Wherein, △ t (r) is the travel time residual at acceptance point place;
represent and gradient is asked to t (r); The adjoint state variable that λ (r) is acceptance point place;
nfor the outer normal vector of acceptance point survey line; The adjoint state variable that λ (x) is inside, zoning;
represent that t is to the local derviation of x;
represent that t is to the local derviation of z;
Just can obtain the adjoint state variable λ on whole zoning according to above-mentioned two formula, be illustrated in figure 2 the change schematic diagram with state variable; Then the gradient of cost functional to rate pattern parameter can just be obtained according to the formula in step 3
, as shown in Figure 3, this gradient roughly reflects the variation tendency of speed in zoning;
[step 5] utilizes the gradient obtained
, adopt linear search algorithm to initial velocity model C
ncarry out iteration renewal, computing formula is as follows:
Wherein, α is iteration step length;
represent initial velocity model;
represent the rate pattern after upgrading;
In the present embodiment, iteration step length α adopts following formulae discovery:
Wherein, J is cost functional, meets the formula in step 2;
for the gradient solved in step 4;
As shown in Figure 4, this figure can determine size and the type of defect to rate pattern after iteration upgrades.
Known by analyzing, adopt and can determine defect type preferably with the ultrasound wave chromatography of state inversion algorithm, can speed preferably in defect recognition body.Accurately location and preferably speed recognition capability ensure that the reliability of later stage ultrasound wave tomographic results interpretation and evaluation.
Adjoint state inversion algorithm in the present embodiment, by deriving with state variable and traditional objective function to the relation between the gradient of model parameter, indirectly solving gradient, avoiding the calculating of Fr é chet derivative, improve computing velocity, decrease EMS memory occupation amount; Be applied in ultrasound wave Zoumaling tunnel technology, greatly enhanced the counting yield of tomography, make this technology to be actual production service better.
Claims (3)
1., for an inversion algorithm for ultrasound wave chromatography, it is characterized in that described inversion algorithm comprises the steps:
Step one: gather ultrasonic test data in component to be checked, adopts the background velocity in described component surveyed area to be checked to set up initial velocity model C as initial velocity
n;
Step 2: the cost functional setting up ultrasound wave chromatography, expression formula is:
Wherein,
J is cost functional;
When t (r) represents that the theory at the ultrasound wave acceptance point place that forward modelling obtains is walked;
T* (r) represent that collection in worksite obtains ultrasound wave acceptance point place actual walk time;
λ (x) represents the adjoint state variable in zoning;
represent the border of zoning;
represent and gradient is asked to t (x);
C (x) is the speed in zoning;
Step 3: the adjoint state variable λ (x) solving inside, zoning, computing formula is as follows:
Wherein,
represent that t is to the local derviation of x;
represent that t is to the local derviation of z;
Step 4: determine that the cost functional of described ultrasound wave chromatography is about described initial velocity model C
nthe gradient of interior speed parameter
, computing formula is:
Step 5: utilize the gradient obtained
, to described initial velocity model C
ncarry out iteration renewal, computing formula is as follows:
Wherein, α is iteration step length;
represent the rate pattern after upgrading.
2. a kind of inversion algorithm for ultrasound wave chromatography according to claim 1, it is characterized in that in the method for described collection ultrasonic test data be: the both sides of described component to be checked arrange sound detecting pipe, in sound detecting pipe described in both sides, arrange ultrasound wave transmitting probe and ultrasound wave receiving transducer respectively, described ultrasound wave receiving transducer sampling measuring point place is described ultrasound wave acceptance point; By the ultrasound data that the collection of described ultrasound wave receiving transducer is launched from described ultrasound wave transmitting probe.
3. a kind of inversion algorithm for ultrasound wave chromatography according to claim 1, is characterized in that the computing formula of described iteration step length α is:
Wherein, J is cost functional.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111077227A (en) * | 2019-12-18 | 2020-04-28 | 华南理工大学 | Ultrasonic array scanning inversion method, system, storage medium and equipment |
Citations (1)
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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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| 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 |
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）》 * |
| 谢春等: "伴随状态法初至波走时层析", 《石油地球物理勘探》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |