CN101334381A - Vector phased array ultrasound checking parameter optimization method - Google Patents

Abstract

The invention relates to ultrasonic detection with a vector phased array which is the further development and improvement of conventional ultrasonic detection with a phased array. The selection of frequency and phase position of vector pulse actuating signals have great influence to the detecting resolution, so the optimization of vector parameters is a required step in the implementation of the ultrasonic detection with the vector phased array. The invention aims at providing a new parameter optimization method of the ultrasonic detection with the vector phased array. The ultrasonic detecting technique with the vector phased array implements focusing and deflecting by utilizing the incoherent addition of vector pulse ultrasonic waves with different frequencies and phase positions in space. According to a preset deflecting direction and a preset focusing point, the ultrasonic detecting technique with the vector phased array uses the strength of focused acoustic pressure as an optimization objective function and implements the optimization of the vector phased array parameters including the frequency and the phase position by combining the method of steepest descent and the Armijo line search method according to the K-T condition.

Description

Vector phased array ultrasound checking parameter optimization method

Technical field

The present invention relates to ultrasonic detection technology, especially the phased array ultrasonic detection method.

Background technology

Often need during Ultrasonic Detection imaging is carried out in a certain zone in the object, for this reason, must carry out acoustic beam scanning.Conventional phased array ultrasonic detection is the time delay by each array element excitation (or reception) pulse in the control transducer array, phase relation when change arrives certain point in (or from) object by each array element emission (or reception) sound wave, realize the variation in focus point and acoustic beam orientation, thereby it is synthetic to finish phased wave beam, be formed into the picture scan-line technique, principle as shown in Figure 1.

The resolution of phased array ultrasonic detection imaging is the important indicator that is detected as picture, is the important evidence of measurement system detectability, therefore also is the target that domestic and international phased array researcher's unremitting effort is pursued.

The contrast resolution characterizes and to be detected as defective and the minimum difference of background on color in the picture, be can detected echo amplitude on the image minimum differentiation, this index is good more, image is fine and smooth more soft, detailed information is abundant more.Axial resolution characterizes spatial axes to the ability of distinguishing two targets.We can be interpreted as axial resolution in shape in echoed signal: under the impulse response condition in system, the actual ghosts signal through signal (waveform envelope) on the time domain after the HILBERT conversion-3dB or-the 6dB width.

Main lobe height in the focusing acoustic field directly affects the contrast resolution of phased imaging.So we are optimized phase place, frequency in the vector phased array driving pulse as objective function with the main lobe height.

Summary of the invention

Deal with problems: the vector phased array Ultrasonic Detection be to conventional phased array ultrasonic detection further develop and perfect.But the selection of the frequency of vector pulse excitation signal and phase place has material impact to detection resolution in the testing process, so the optimization of vector parameters becomes the steps necessary that the vector phased array Ultrasonic Detection realizes.Purpose of the present invention just provides a kind of new method of vector phased array ultrasound checking parameter optimization.

Technical scheme: for realizing above purpose, the following technical scheme of the special proposition of the present invention:

The vector phased array ultrasonic detection technology utilizes the non-coherent addition of vector pulse ultrasonic wave in the space of different frequency, phase place to realize focusing on and deflection exactly.

According to yawing moment and the focus point set, focusing on sound pressure as the objective function of optimizing, to the vector phased array parameter: frequency and phase place are carried out optimizing with method of steepest descent in conjunction with the Armijo line search method according to the K-T condition.

Technique effect: owing to have fluctuation characteristic in the objective function, so it is a little bigger to have a lot of local pole, practice according to algorithm, provide an initial point preferably according to simulation result and engineering experience, what can rapid solving obtain generally is two dimension (frequency and the phase place) vector of overall maximal point correspondence.

For the algorithm of stochastic patterns such as heredity, simulated annealing, present algorithm belongs to the algorithm of determining type, and promptly each iteration all can produce definite slippage, reliable results, and also computing velocity is fast.

Embodiment

Consideration is focused on by the array point on the scene place of the arbitrary shape that N dot matrix unit forms, as shown in Figure 2.For focus point, the acoustic pressure formula of i array element is as follows:

In the formula: P _iI array element is at the acoustic pressure of focus point, P _ImSound pressure amplitude, ρ density of material, the c velocity of sound, f _iFrequency of sound wave, r _iArray element is to focal length, u _iThe array element amplitude, α _iAttenuation coefficient, α ₀Scattering attenuation coefficient, α ₁The attenuation by absorption coefficient, k _iWave number,

Phase place, Δ A array element area

At first determine the position r of i array element and focus point _iSecondly calculate under this locality condition by following formula (a) and (b) draw the relation of sound pressure amplitude and frequency; Therefrom determine the frequency f of correspondence when acoustic pressure is maximum _iCalculate initial phase by following formula (d) then

So,, then can obtain bigger array and focus on acoustic pressure if we make it satisfy top condition the frequency and the phase place of each array element in the array of controls in ultrasonic phase array, thus the contrast resolution who improves the signal to noise ratio (S/N ratio) of this point and improve imaging.Vector phased array can mathematical description be:

Because the transducer of Any shape, size, its effective vibration source surface can regard that many point source arraies form as.The ultrasonic transducer of each small size can be similar to regards the piston vibration source that is set on the hard baffle as, so arbitrfary point in the sound field (x, y, acoustic pressure p z) (x, y, z) can be by trying to achieve with lower integral:

So distribute for actual sound field, also can study vector phased array, but will notice that this moment, parameter object was each physics array element with top mathematical model formula, not each equivalent point source; The frequency and the initial phase in the equivalent lattice source on the just same physics array element should be consistent.

We are that the main lobe height carries out vector optimization as objective function to focus on acoustic pressure, are each point source sound radiation pressure sum in the focusing acoustic pressure of spatial point F.

$P=P_1+P_2+L{P}_n=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{P}_i$

Obtain by the decomposition of point source radiation formula:

$P_i=\frac{\mathrm{j\ρc\ΔA}}{{\mathrm{\λ}}_i{r}_i}{u}_i{e}^{{-\mathrm{\α}}_i{r}_i}{e}^{-j(k_i{r}_i-{\mathrm{\φ}}_i)}$

$=\frac{\mathrm{j\ρc}{u}_i\mathrm{\ΔA}}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i}(\cos (k_i{r}_i-{\mathrm{\φ}}_i)-j\sin (k_i{r}_i-{\mathrm{\φ}}_i))$

The focus place focuses on the sound pressure amplitude maximum.Concerning single source, maximum amplitude promptly: $\left|P_i\right|=\frac{\mathrm{\ρc}{u}_i\mathrm{\ΔA}}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i};$ And superpose any point (x, y, z) ∈ R for the sound field of N point source ³The place has:

$P/\mathrm{\ΔA}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{\mathrm{\ρ}{\mathrm{cu}}_i}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i}\sin (k_i{r}_i-{\mathrm{\φ}}_i)+j\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{\mathrm{\ρ}{\mathrm{cu}}_i}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i}\cos (k_i{r}_i-{\mathrm{\φ}}_i)$

It is maximum that vector phase-control focusing focal point F place sound pressure amplitude reaches, so as long as find the solution | and P/ Δ A| ²Maximal value get final product.

${|P/\mathrm{\ΔA}|}^2=[{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{\mathrm{\ρ}{\mathrm{cu}}_i}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i}\sin (k_i{r}_i-{\mathrm{\φ}}_i)\right)}^2+{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{\mathrm{\ρ}{\mathrm{cu}}_i}{{\mathrm{\λ}}_i{r}_i}{e}^{-{\mathrm{\α}}_i{r}_i}\cos (k_i{r}_i-{\mathrm{\φ}}_i)\right)}^2]$

In the formula above noting:

$\left\{\begin{array}{c}{\mathrm{\λ}}_i=c{T}_i=c/f_i\\ {\mathrm{\α}}_i=\mathrm{\α}\left(f_i\right)={\mathrm{\α}}_0+{\mathrm{\α}}_1{f}_i^2\\ k_i=2\mathrm{\π}{f}_i/c\end{array}\right.$

Former problem can be described with following nonlinear optimal problem:

max f(x)

s.t. x≥0

Wherein:

$f\left(x\right)={\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{\mathrm{\ρ}{u}_i{f}_i}{r_i}{e}^{-({\mathrm{\α}}_0+{\mathrm{\α}}_1{f_i}^2)r_i}\sin (2\mathrm{\π}{f}_i{r}_i/c-{\mathrm{\φ}}_i)\right)}^2$

$+{\left(\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\mathrm{\ρu}}_i{f}_i}{r_i}{e}^{-({\mathrm{\α}}_0+{\mathrm{\α}}_1{f}_i^2)r}\cos (2\mathrm{\π}{f}_i{r}_i/c-{\mathrm{\φ}}_i)\right)}^2$

Independent variable is x=(f ₁, f ₂, Λ f _n, φ ₁, φ ₂, Λ φ _n) the 2n n dimensional vector n.

According to the K-T condition, can be as if x ^*Be optimum solution, necessarily satisfy following optimality condition:

$\left\{\begin{array}{c}{x}^{*}\▿f\left(x^{*}\right)=0\\ \▿f\left(x^{*}\right)\≥0\\ x^{*\≥0}\end{array}\right.$

Promptly find the solution a nonlinear complementarity problem:

$\left\{\begin{array}{ccccc}\frac{\∂f\left(x^{*}\right)}{\∂x^i}=0& \mathrm{if}& x^{*i}>0& i=\mathrm{1,2}L& n\\ \frac{\∂f\left(x^{*}\right)}{\∂x^i}\≥0& \mathrm{if}& x^{*i}=0& i=\mathrm{1,2}L& n\end{array}\right.$

Promptly $x^{*}={[x^{*}-\mathrm{\α}\▿f\left(x^{*}\right)]}^{+}$ , wherein α is a positive constant, [] ⁺Representative is in the projection of positive quadrant.If x ^*〉=0 satisfies optimality condition, claims x ^*One stable point.In view of the complicacy of objective function, consider to find the solution in conjunction with the Armijo line search method with method of steepest descent.The iterative formula in concrete k step is:

$x_{k+1}={[x_k{-\mathrm{\α}}_k\▿f\left(x_k\right)]}^{+}k=\mathrm{0,1},\mathrm{Ln}$

Wherein ${\mathrm{\α}}_k={\mathrm{\β}}^{m_k}s,$ S＞0, β ∈ (0,1), σ ∈ (0,1/2) is given constant.m _kIt is first nonnegative integer that satisfies following formula.

$f\left(x_k\right)-f(x_k-{\mathrm{\β}}^{m}s\▿f\left(x_k\right))\≤\mathrm{\σ}{\mathrm{\β}}^{m}s\▿f{\left(x_k\right)}^T\▿f\left(x_k\right)$

Specific algorithm is as follows:

Beg in ε=10 ^-8, s=1, k=0, β=0.5, σ=10 ^-3, x _k=x ⁰, x ⁰Be given initial value.

Step $d_k=-\▿f\left(x_k\right)$

m＝1

do?while

$f\left(x_k\right)-f(x_k+{\mathrm{\β}}^{m}s{d}_k)\≥\mathrm{\σ}{\mathrm{\β}}^{m}s\▿f{\left(x_k\right)}^T{d}_k$ m＝m+1

end?do

α _k＝β ^ms

x _k+1＝[x _k+α _kd _k] ⁺

if||x _k+1-x _k||＜ε then stop

else?k＝k+1 go?to?Step

End

Description of drawings

Fig. 1 phased array ultrasonic detection focuses on and deflection

On the scene some F place stack of the array of the arbitrary shape that Fig. 2 dot matrix unit forms focuses on

Claims (2)

1, a kind of phased-array ultrasonic detection technique is characterized in that: utilize the non-coherent addition of vector pulse ultrasonic wave in the space of different frequency, phase place to realize focusing on and deflection.

2, phased-array ultrasonic detection technique as claimed in claim 1, it is characterized in that: according to yawing moment and the focus point set, focusing on sound pressure as the objective function of optimizing, to the vector phased array parameter: frequency and phase place are carried out optimizing with method of steepest descent in conjunction with the Armijo line search method according to the K-T condition.

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