CN106168942A - A kind of fluctuation types dynamic data reconstructing method based on singular boundary method - Google Patents

Abstract

The invention discloses a kind of fluctuation types dynamic data reconstructing method based on singular boundary method, directly application wave equation time basic solution is as kernel function, source point singular term is replaced with source point intensity factor, without numerical integration, singular integral, mesh free divides, directly application wave equation time basic solution is as kernel function, without complicated mathematic(al) manipulation, its simple efficient feature suit the reconstruct of fluctuation types dynamic data need data reconstruction technology quickly, stable, accurate feature request；Experimental comparison shows, applies technology proposed by the invention, processes fluctuation types dynamic data reconstruction, under the conditions of obtaining similarity precision, typically time-consumingly only need about the 10% of conventional linear boundary element algorithm, there is precision high, calculate fast, mathematics is simple, the feature that program is easy, can be applicable to sound wave noise abatement, wave energy dissipating, the Wave type data reconstructions such as earthquake prediction, the field of engineering technology such as image procossing.

Description

A kind of fluctuation types dynamic data reconstructing method based on singular boundary method

Technical field

The present invention relates to a kind of fluctuation types dynamic data reconstructing method, be specifically related to the fluctuation class of a kind of singular boundary method Type dynamic data reconstructing method.

Background technology

Wave phenomenon is as one of modal natural phenomena of nature, and in engineer applied field, tool is widely used and shadow Ring, such as scientific research engineering fields such as sound wave noise abatement, wave energy dissipating, seismic wave predictions, be both needed to process a large amount of fluctuation types dynamic data. Due to the uniqueness of wave phenomenon governing equation, such as the hysteresis quality of ripple propagation, three-dimensional markov property etc., make wave equation base This solution has has obvious multi-form with diffusion equation, Laplace's equation basic solution, and this makes fluctuation types dynamic data Reconstruct extremely difficult.

Process the reconstruct of fluctuation types dynamic data traditionally, typically have Finite Element Method, Element BEM, finite difference calculus Deng.But as traditional area type grid method, finite element is processing such as a series of infinite domains such as sound scattering, acoustic irradiations Data reconstruction time, often occur stress and strain model difficulty, calculate that speed is slow, problem that to calculate load big etc. is difficult to overcome.And Element BEM is as Boundary-Type grid method, although overcoming Finite Element Method to a certain extent needs zoning grid Shortcoming, improve computational efficiency, but owing to needing to process the unusualst and Nearly singular integral during calculating, have a strong impact on The reconstructed velocity of data.Fundamental solution method overcomes conventional mesh class algorithm to a certain extent as a kind of non-mesh method and needs Want the defect of grid division, but due in fundamental solution method for overcoming singularity to introduce false border so that the method exists When processing the data reconstruction problem under some complex working conditions, the phenomenon of numerical value instability often occurs (see document 1.Young D L,Gu M H,Fan C M.The time-marching method of fundamental solutions for wave equations[J].Engineering Analysis with Boundary Elements,2009,33(12):1411- 1425.)。

Summary of the invention

Goal of the invention: the fluctuation types dynamic data reconfiguration technique process that present invention aims to prior art is multiple Miscellaneous, calculate the defect of load matter of fundamental importance evaluation time length, it is provided that a kind of simple, efficiently, without integration, mesh free based on singular boundary method Fluctuation types dynamic data reconstructing method, thus reach save reconstitution time, improve reconstruct efficiency purpose.

Technical scheme: the invention provides a kind of fluctuation types dynamic data reconstructing method based on singular boundary method, bag Include following steps:

(1) configure some test points on the inside of investigated material and border, it is thus achieved that the primary data of these test points and Data boundary；

(2) directly use the time basic solution of three-dimensional wave equation as kernel function, set up the corresponding interpolation of wave propagation problem Matrix；

(3) empirical equation calculating is utilized to process the source point intensity factor of fluctuation data reconstruction；

(4) source point intensity factor is substituted into interpolating matrix, calculate the unknowm coefficient of interpolating matrix；

(5) the fluctuation data value of any time arbitrarily interior point is calculated.

Further, in step (1), initial time configures N in the inside of investigated material₁Individual test point, it is thus achieved that time initial Carve the fluctuation data value u of these test points_i, i=1 ..., N₁；Surface configuration N at investigated material₂Individual test point, along with ripple Dynamic carrying out, it is thus achieved that the fluctuation data value u of these points the most in the same time_i, i=N₁+1,...,N₁+N₂。

Further, the fluctuation problem governing equation used in step (2) is:

$u=\left\{\begin{array}{c}\mathrm{\Δ}u-\frac{1}{c^2}\frac{{\∂}^{2}u}{\∂t^2}=0,(x,y,z)\∈\mathrm{\Ω},t>0\\ u{|}_{\mathrm{\Γ}}=\stackrel{\‾}{u}\\ u{|}_{t=0}=u_0,\frac{\∂u}{\∂t}{|}_{t=0}={\mathrm{\υ}}_1\end{array}\right.---\left(1\right)$

Wherein, Ω represents the region of investigated material, (x, y, z) be space coordinates, t be (x, y, z) corresponding to moment, C represents velocity of wave, and u represents potential function,Represent boundary condition, u₀And υ₁Representing initial condition, Δ represents Laplace operator, at sound Ripple represents sound pressure level in propagating；

Three-dimensional wave propagation problem correspondence basic solution is:

$G(r,t)=\frac{1}{4\mathrm{\π}r}\mathrm{\δ}\[(t-\mathrm{\τ})-r/c\]---\left(2\right)$

Wherein δ represents that Dirac function, c represent that velocity of wave, t and τ represent and join a little and the moment of source point, and r represents distance；Due to The propagation of ripple requires time for, and basic solution G only just can represent current time by the correlation combiner of the corresponding sound pressure level postponing the moment Sound pressure level, postponing the moment depends on the spread speed of the distance between source point and tested point and ripple；Therefore, for fc-specific test FC Point, only requires about source point { s_jPostpone the moment unknowm coefficient { α_j, then the sound pressure level in moment required by test point can be asked Go out；

Full scale equation u can be counted as an initial boundary problems, applies principle of stacking, is split as u₁And u₂, such as formula (3) With formula (4) Suo Shi, i.e.Wherein u₁A boundary value problem, u can be counted as₂Can be counted as an initial-value problem:

$u_1^{*}=\left\{\begin{array}{c}{\mathrm{\Δu}}_1^{*}-\frac{1}{c^2}\frac{{\∂}^2{u}_1^{*}}{\∂t^2}=0,(x,y,z)\∈\mathrm{\Ω},t>0\\ u_1^{*}{|}_{\mathrm{\Γ}}=\stackrel{\‾}{u}-{\stackrel{\‾}{u}}_2^{*}={\stackrel{\‾}{u}}_1^{*}\\ u_1^{*}{|}_{t=0}=0,\frac{\∂u_1^{*}}{\∂t}{|}_{t=0}=0\end{array}\right.---\left(3\right)$

$u_2^{*}=\left\{\begin{array}{c}{\mathrm{\Δu}}_2^{*}-\frac{1}{c^2}\frac{{\∂}^2{u}_2^{*}}{\∂t^2}=0,(x,y,z)\∈\mathrm{\Ω},t>0\\ u_2^{*}{|}_{\mathrm{\Γ}}={\stackrel{\‾}{u}}_2^{*}\\ u_2^{*}{|}_{t=0}=0,\frac{\∂u_2^{*}}{\∂t}{|}_{t=0}=0,(x,y,z)\∉\mathrm{\Ω}\\ u_2^{*}{|}_{t=0}=u_0,\frac{\∂u_2^{*}}{\∂t}{|}_{t=0}={\mathrm{\υ}}_1,(x,y,z)\∈\mathrm{\Ω}\end{array}\right.---\left(4\right)$

Formula (4)Directly obtain with Solving Three-Dimensional poisson Equation:

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(5\right)$

WhereinRepresent that radius is the ct sphere with M as the center of circle；In formula (4), it is only necessary to obtain the test point M zone of influence TerritoryIn sound pressure level, so in the domain of influenceMiddle layout initial data acquisition point；

Thereafter, it is considered to equation (3)By Huygen's principle, " every bit arrived in ripple propagation can serve as one New secondary wave source, the enveloping surface that all these subwaves are formed constitutes the new corrugated of subsequent time ", it is assumed that having one on border is Arrange time dependent some wave sourceThe summation of the subwave that these wave sources are sent forms in computational fields Ω it The sound pressure level of rear any timeWhereinRepresent sound pressure, x_mRepresent boundary point, then in computational fields Ω Acoustic pressureCan be represented as

$u_1^{*}\left(x_i\right)=\underset{\mathrm{\Ω}}{\∫\∫\∫}\frac{\mathrm{\α}\left(r\right)}{4\mathrm{\π}r}\mathrm{\δ}(t-\frac{r}{c})dv,x_i\∈\mathrm{\Ω}---\left(6\right)$

Layout data collection point on the Γ of border, with Δ t as time interval, v representation space integration variable, t_n∈((n-1) Δ t, n Δ t), t represent calculating moment, the subscript n express time number of plies of t, acoustic pressureCan be by a series of lines of basic solution G Property combination approximate:

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\Σ}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,\mathrm{3......}---\left(7\right)$

Wherein, α_j(t_R) represent for source point s_jPostpone moment t_RUnknowm coefficient, G_ijRepresent and postponing moment t_R's Three-dimensional wave equation basic solution, Q_iRepresent and postponing moment t_RSource point intensity factor, x_iRepresent that i-th is joined a little, x_jRepresent jth Source point, N is data collection point sum；

In simple harmoinic wave motion, it is assumed that

${\mathrm{\α}}_j\left(t_R\right)={\mathrm{\α}}_j^{*}\left(t_R\right)e^{-{\mathrm{i\ωt}}_R}\≈{\mathrm{\α}}_j^{*}\left(t_{m\mathrm{\Δ}t}\right)e^{-{\mathrm{i\ωt}}_R}---\left(8\right)$

Wherein, 0≤t_mΔt-t_R＜ Δ t, α_j(t_R) represent delay moment unknowm coefficient,Represent disengaging time variable t After delay moment unknowm coefficient, m and the n express time number of plies, if m ＜ n, then unknowm coefficient α_j(t_R) obtained by front step, If t_RA ＜ 0, then it represents that at ripple does not reaches and joins,ω represents that the frequency of ripple, k=ω/c represent ripple Number；

Formula (5), formula (7) and formula (8) together constitute singular boundary method and process the matrix of differences of wave propagation problem.

Further, in step (3), the empirical equation calculating source point intensity factor is:

$Q_i=\frac{1}{4\mathrm{\π}}\[\frac{{\mathrm{\π}}^4}{25\sqrt{A_j}}+\frac{{\left(ln\mathrm{\π}\right)}^2}{S}\]+\frac{ik}{4\mathrm{\π}}---\left(9\right)$

Wherein A_jRepresent source point s_jInfluence area, S represents the surface area of whole zoning.

Further, being pushed away to obtain source point intensity factor according to step (3), unknowm coefficient is solved drawn by formula (7) and (8): logical Cross formula (7) and (8), obtain at the n-th time horizon, the unknowm coefficient of n Δ t secondAnd then tried to achieve the delay moment by formula (8) Unknowm coefficient α_j(t_R)。

Further, step (5) moment t arbitrarily in put x acoustic pressure u by trying to achieve without integral formulas:

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(10\right)$

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\Σ}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,3,\mathrm{......}---\left(11\right)$

$u=u_1^{*}+u_2^{*}---\left(12\right)$

Beneficial effect: the present invention only needs border to configure data boundary collection point, and subregion configures initial data acquisition point, Without numerical integration, singular integral, mesh free divides, and directly application wave equation time basic solution is as kernel function, without complexity Mathematic(al) manipulation, its simple efficient feature suits the reconstruct of fluctuation types dynamic data needs data reconstruction technology quick, stable, smart True feature request；Experimental comparison shows, applies technology proposed by the invention, processes the reconstruct of fluctuation types dynamic data and asks Topic, under the conditions of obtaining similarity precision, typically time-consumingly only needs about the 10% of conventional linear boundary element algorithm, has precision high, Calculating fast, mathematics is simple, and the feature that program is easy can be applicable to the Wave type data such as sound wave noise abatement, wave energy dissipating, earthquake prediction Reconstruct, the field of engineering technology such as image procossing.

Accompanying drawing explanation

Fig. 1 is fluctuation types dynamic data reconstructing method flow chart of the present invention；

Fig. 2 (a) is that schematic diagram is arranged in three-dimensional wave propagation problem data boundary collection point, and Fig. 2 (b) is area data collection point Arrange schematic diagram；

Fig. 3 is data boundary collection point s_jInfluence area schematic diagram；

Fig. 4 arranges schematic diagram for wheel the form of the foetus area data collection point；

Fig. 5 is singular boundary method data reconstruction result to count increase change convergence graph with border data collection point；

Fig. 6 is that singular boundary method data reconstruction result continues changing trend diagram in time；

Fig. 7 is that acoustic radiation dimensionless real part acoustic pressure reconstruct numerical result is with wave number variation diagram；

Fig. 8 is that acoustic radiation dimensionless imaginary part acoustic pressure reconstruct numerical result is with wave number variation diagram.

Detailed description of the invention

Below technical solution of the present invention is described in detail, but protection scope of the present invention is not limited to described enforcement Example.

Embodiment: as it is shown in figure 1, one reconstructs fluctuation types dynamic data based on mesh free singular boundary method, specifically walk Rapid as follows:

(1) initial time configures N in the inside of investigated material₁Individual test point, it is thus achieved that these test points of initial time Fluctuation data value u_i, i=1 ..., N₁；

Surface configuration N at investigated material₂Individual test point, along with the carrying out of fluctuation, it is thus achieved that these are put the most in the same time Fluctuation data value u_i, i=N₁+1,...,N₁+N₂。

(2) according to the basic thought of singular boundary method, directly the time basic solution of employing three-dimensional wave equation is as kernel function, Set up wave propagation problem corresponding singular boundary method interpolating matrix:

Application principle of stacking, former data u can be divided into primary data u₂With data boundary u₁, i.e.

Primary dataDirectly can obtain with Solving Three-Dimensional poisson Equation

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(S.1\right)$

WhereinRepresent that radius is the ct sphere with M as the center of circle.In formula (S.1), singular boundary method only needs to obtain survey Pilot M influence areaIn sound pressure level, so singular boundary method only needs in the domain of influenceMiddle layout initial number According to collection point, as shown in Figure 2.

Thereafter, it is considered to data boundarySingular boundary method arranges data boundary collection point on the Γ of border, as in figure 2 it is shown, With Δ t as time interval, the subscript express time number of plies of t.Acoustic pressuret_n((n-1) Δ t, n Δ t), can be by substantially for ∈ The a series of linear combinations solving G approximate, as shown in formula (S.2):

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\Σ}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,\mathrm{3......}---\left(S.2\right)$

Wherein α_j(t_R) represent for source point s_jPostpone moment t_RUnknowm coefficient, G_ijRepresent and postponing moment t_R's Three-dimensional wave equation basic solution, Q_iRepresent and postponing moment t_RSource point intensity factor.

In simple harmoinic wave motion, it is assumed that

${\mathrm{\α}}_j\left(t_R\right)={\mathrm{\α}}_j^{*}\left(t_R\right)e^{-{\mathrm{i\ωt}}_R}\≈{\mathrm{\α}}_j^{*}\left(t_{m\mathrm{\Δ}t}\right)e^{-{\mathrm{i\ωt}}_R}---\left(S.3\right)$

Wherein 0≤t_mΔt-t_R＜ Δ t, if m ＜ n, then unknowm coefficient α_j(t_R) obtained by front step, if t_R＜ 0, At then representing that ripple does not reaches and joins,ω represents that the frequency of ripple, k=ω/c represent wave number.

Formula (S.1), formula (S.2) and formula (S.3) together constitute singular boundary method and process the interpolating matrix of wave propagation problem.

(3) utilize empirical equation calculate singular boundary method source point intensity factor: the source point intensity of three dimension wave equation in wavelets because of Shown in sub-computing formula such as formula (S.4).

$Q_i=\frac{1}{4\mathrm{\π}}\[\frac{{\mathrm{\π}}^4}{25\sqrt{A_j}}+\frac{{\left(ln\mathrm{\π}\right)}^2}{S}\]+\frac{ik}{4\mathrm{\π}}---\left(S.4\right)$

Wherein A_jRepresent source point s_jInfluence area, as it is shown on figure 3, S represents the surface area of whole zoning.

(4) source point intensity factor is substituted into singular boundary interpolating matrix, calculate the unknown system of singular boundary method solving equation Number.Applying step (3) is pushed away to obtain source point intensity factor, in step (4) unknowm coefficient of singular boundary method can by formula (S.2) and (S.3) solve and draw.By formula (S.2) and (S.3), obtain at the n-th time horizon, the unknowm coefficient of n Δ t secondAnd then Delay moment t is tried to achieve by formula (S.3)_RUnknowm coefficient α_j(t_R)。

(5) according to singular boundary method formula, the fluctuation data value of any time arbitrarily interior point is calculated.In step (5), pass through The unknowm coefficient that step (4) is tried to achieve, moment t arbitrarily in put x acoustic pressure u can be tried to achieve by following singular boundary method formula:

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(S.5\right)$

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\Σ}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,3......\left(S.6\right)$

$u=u_1^{*}+u_2^{*}---\left(S.7\right)$

Embodiment 1: considering wheel the form of the foetus region fluctuation data reconstruction as shown in Figure 4, area equation is

Wherein R=0.8, r=0.2, data boundary collection point is as shown in Figure 3.

Fluctuation data governing equation and accurately solution be:

$\left\{\begin{array}{c}{u}_{tt}=c^2(u_{xx}+u_{yy}+u_{zz}),(x,y,z)\∈\mathrm{\Ω}\\ u{|}_{t=0}=0\\ u_t{|}_{t=0}=ck\left(\cos \right(kx)+cos(ky)+\cos (kz\left)\right)\\ u_t{|}_{t=0}=\left(\cos \right(kr)+\cos (ky)+\cos (kz\left)\right)\sin \left(ckt\right),(x,y,z)\∈\mathrm{\Γ}\end{array}\right.$

In this example, we apply time step Δ t=2 × 10^-1, velocity of wave c=10, to each test point layout area data Collection point N_f=1255, it is 0.8 that test point is disposed in radius, on the time horizon of t=1s, Fig. 5 give singular boundary method with Border gather data point count increase numerical precision convergence graph, wherein wave number be respectively (k₁=0.5, k₂=5, k₃=10).Can To find that singular boundary method quickly restrains with 2 rank convergence rates, as k=5, convergence rate has been even up to C=5.0.

Thereafter, application time step Δ t=2 × 10^-1, velocity of wave c=10, arranges data boundary collection point N_s=972, to often Individual test point layout area data collection point N_f=1255, Fig. 6 give (k in the case of different wave numbers₁=0.5, k₂=5, k₃ =10) singular boundary method data reconstruction maximum absolute error changes over situation, it can be seen that continue in time, singular boundary Method maximum relative error still keeps consistent with accurately solving, and does not change over and discrete case occurs.

Embodiment 2: consider to reconstruct at unit ball acoustic pressure radiation data, wherein radius a=1, velocity of wave c=v₀, accurate solution can To be represented as:

$u(r,\mathrm{\θ},t)=\frac{a}{r}\left(\frac{{\mathrm{ikaz}}_0}{ika-1}\right)v_0{e}^{ik(r-a)+iwt},$

Wherein z₀=ρ₀C, represents Medium impedence, ρ₀For Media density, c is velocity of wave, and ω=kc is ripple frequency.Fig. 7 and Fig. 8 gives Go out dimensionless acoustic pressure real part solutionWith imaginary part solutionAt data boundary collection point N_s=400, Numerical value knot reconstruction result under the conditions of time step Δ t=0.5s.It appeared that singular boundary method reconstruction result and accurately solve essence Really matching, by contrast as empty border d=0.5, fundamental solution method reconstruction result and accurately solution matching are good, but when empty limit When boundary is taken as d=0.9, data reconstruction result there occurs the most discrete.Meanwhile, it should be pointed out that for acoustic radiation, sound scattering Deng the fluctuation data reconstruction of exterior domain, the inventive method fluctuates data without pickup area, substantially increases fluctuation types number According to reconstruct efficiency.

To sum up, fluctuation types dynamic data reconstructing method of the present invention, based on singular boundary method, directly applies fluctuation side Journey time basic solution as kernel function, replaces source point singular term with source point intensity factor, it is to avoid numerical integration and grid, it is only necessary to Layout in border, mesh free, without numerical integration and mathematic(al) manipulation, improves data reconstruction efficiency.Compared to prior art, it is not necessary to do Complicated fast Fourier transform or loaded down with trivial details more waveforms iterative, directly use time-dependent basic solution to make in time domain For Interpolation-Radix-Function, by application source point intensity factor reconstruct fluctuation types data, its simple efficient feature suits fluctuation class The reconstruct of type dynamic data need calculating instrument quickly, stable, accurate feature request, it is adaptable to sound wave, ripples, the mark such as seismic wave Amount ripple propagates the reconstruction of dynamic data.

Experimental comparison shows, application the inventive method processes fluctuation types dynamic data reconstruction, is obtaining similar essence Under the conditions of degree, typically time-consumingly only needing about the 10% of conventional linear boundary element algorithm, have precision high, calculate fast, mathematics is simple, The feature that program is easy.This technology is that the reconstruct of Wave type dynamic data provides new, simple efficient technology path.

Claims (6)

1. a fluctuation types dynamic data reconstructing method based on singular boundary method, it is characterised in that: comprise the following steps:

(1) some test points are configured in the inside of investigated material and border, it is thus achieved that the fluctuation data value of these test points；

(2) directly use the time basic solution of three-dimensional wave equation as kernel function, set up the corresponding interpolating matrix of wave propagation problem；

(3) empirical equation calculating is utilized to process the source point intensity factor of fluctuation data reconstruction；

(4) source point intensity factor is substituted into interpolating matrix, calculate the unknowm coefficient of interpolating matrix；

(5) the fluctuation data value of any time arbitrarily interior point is calculated.

Fluctuation types dynamic data reconstructing method based on singular boundary method the most according to claim 1, it is characterised in that: In step (1), initial time configures N in the inside of investigated material₁Individual test point, it is thus achieved that the ripple of these test points of initial time Dynamic data value u_i, i=1 ..., N₁；Surface configuration N at investigated material₂Individual test point, along with the carrying out of fluctuation, it is thus achieved that no The fluctuation data value u of these points in the same time_i, i=N₁+1,...,N₁+N₂。

Fluctuation types dynamic data reconstructing method based on singular boundary method the most according to claim 1, it is characterised in that: The fluctuation problem governing equation used in step (2) is:

$u=\left\{\begin{array}{c}\mathrm{\Δ}u-\frac{1}{c^2}\frac{{\∂}^{2}u}{\∂t^2}=0,(x,y,z)\∈\mathrm{\Ω},t>0\\ u{|}_{\mathrm{\Γ}}=\stackrel{\‾}{u}\\ u{|}_{t=0}=u_0,\frac{\∂u}{\∂t}{|}_{t=0}={\mathrm{\υ}}_1\end{array}\right.---\left(1\right)$

Wherein, Ω represents the region of investigated material, (x, y, z) be space coordinates, t be (x, y, z) corresponding to moment, c generation Table velocity of wave, u represents potential function,Represent boundary condition, u₀And υ₁Representing initial condition, Δ represents Laplace operator, at sound wave Propagation represents sound pressure level；

Three-dimensional wave propagation problem correspondence basic solution is:

$G(r,t)=\frac{1}{4\mathrm{\π}r}\mathrm{\δ}\[(t-\mathrm{\τ})-r/c\]---\left(2\right)$

Wherein δ represents that Dirac function, c represent that velocity of wave, t and τ represent and join a little and the moment of source point, and r represents distance；Due to ripple Propagation requires time for, and basic solution G only just can represent the sound of current time by the correlation combiner of the corresponding sound pressure level postponing the moment Pressure value, postponing the moment depends on the spread speed of the distance between source point and tested point and ripple；Therefore, for fc-specific test FC point, Only require about source point { s_jPostpone the moment unknowm coefficient { α_j, then the sound pressure level in moment required by test point can be obtained；

Full scale equation u can be counted as an initial boundary problems, applies principle of stacking, is split as u₁And u₂, such as formula (3) and formula (4) shown in, i.e.Wherein u₁A boundary value problem, u can be counted as₂Can be counted as an initial-value problem:

$u_1^{*}=\left\{\begin{array}{c}{\mathrm{\Δu}}_1^{*}-\frac{1}{c^2}\frac{{\∂}^2{u}_1^{*}}{\∂t^2}=0,(x,y,z)\∈\mathrm{\Ω},t>0\\ u_1^{*}{|}_{\mathrm{\Γ}}=\stackrel{\‾}{u}-{\stackrel{\‾}{u}}_2^{*}={\stackrel{\‾}{u}}_1^{*}\\ u_1^{*}{|}_{t=0}=0,\frac{\∂u_1^{*}}{\∂t}{|}_{t=0}=0\end{array}\right.---\left(3\right)$

$u_2^{*}=\left\{\begin{array}{cc}{\mathrm{\Δu}}_2^{*}-\frac{1}{c^2}\frac{{\∂}^2{u}_2^{*}}{\∂t^2}=0,& (x,y,z)\∈\mathrm{\Ω},t>0\\ u_2^{*}{|}_{\mathrm{\Γ}}={\stackrel{\‾}{u}}_2^{*}& \\ u_2^{*}{|}_{t=0}=0,\frac{\∂u_2^{*}}{\∂t}{|}_{t=0}=0& (x,y,z)\∉\mathrm{\Ω}\\ u_2^{*}{|}_{t=0}=u_0,\frac{\∂u_2^{*}}{\∂t}{|}_{t=0}={\mathrm{\υ}}_1& (x,y,z)\∈\mathrm{\Ω}\end{array}\right.---\left(4\right)$

Formula (4)Directly obtain with Solving Three-Dimensional poisson Equation:

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(5\right)$

WhereinRepresent that radius is the ct sphere with M as the center of circle；In formula (4), it is only necessary to obtain test point M influence areaIn sound pressure level, so in the domain of influenceMiddle layout initial data acquisition point；

Thereafter, it is considered to equation (3)By Huygen's principle " ripple propagate in the every bit that arrived can serve as one new Secondary wave source, enveloping surface that all these subwaves are formed constitutes the new corrugated of subsequent time ", it is assumed that exist on border a series of with The point wave source of time changeThe summation of the subwave that these wave sources are sent forms its successor in computational fields Ω The sound pressure level in meaning momentWhereinRepresent sound pressure, x_mRepresent boundary point, the then acoustic pressure in computational fields ΩCan be represented as

$u_1^{*}\left(x_i\right)=\underset{\mathrm{\Ω}}{\∫\∫\∫}\frac{\mathrm{\α}\left(r\right)}{4\mathrm{\π}r}\mathrm{\δ}\left(t-\frac{r}{c}\right)dv,x_i\∈\mathrm{\Ω}---\left(6\right)$

Layout data collection point on the Γ of border, with Δ t as time interval, v representation space integration variable, t_n∈((n-1)Δt,n Δ t), t represent calculating moment, the subscript n express time number of plies of t, acoustic pressureCan be by a series of linear group of basic solution G Incompatible approximation:

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,3......\left(7\right)$

Wherein, α_j(t_R) represent for source point s_jPostpone moment t_RUnknowm coefficient, G_ijRepresent and postponing moment t_RThree-dimensional Wave equation basic solution, Q_iRepresent and postponing moment t_RSource point intensity factor, x_iRepresent that i-th is joined a little, x_jRepresent jth source point, N is data collection point sum；

In simple harmoinic wave motion, it is assumed that

${\mathrm{\α}}_j\left(t_R\right)={\mathrm{\α}}_j^{*}\left(t_R\right)e^{-{\mathrm{i\ωt}}_R}\≈{\mathrm{\α}}_j^{*}\left(t_{m\mathrm{\Δ}t}\right)e^{-{\mathrm{i\ωt}}_R}---\left(8\right)$

Wherein, 0≤t_mΔt-t_R＜ Δ t, α_j(t_R) represent delay moment unknowm coefficient,After representing disengaging time variable t Delay moment unknowm coefficient, m and the n express time number of plies, if m ＜ n, then unknowm coefficient α_j(t_R) obtained by front step, if t_RA ＜ 0, then it represents that at ripple does not reaches and joins,ω represents that the frequency of ripple, k=ω/c represent wave number；

Formula (5), formula (7) and formula (8) together constitute singular boundary method and process the matrix of differences of wave propagation problem.

Fluctuation types dynamic data reconstructing method based on singular boundary method the most according to claim 3, it is characterised in that: In step (3), the empirical equation calculating source point intensity factor is:

$Q_i=\frac{1}{4\mathrm{\π}}\[\frac{{\mathrm{\π}}^4}{25\sqrt{A_j}}+\frac{{\left(ln\mathrm{\π}\right)}^2}{S}\]+\frac{ik}{4\mathrm{\π}}---\left(9\right)$

Wherein A_jRepresent source point s_jInfluence area, S represents the surface area of whole zoning.

Fluctuation types dynamic data reconstructing method based on singular boundary method the most according to claim 4, it is characterised in that: Being pushed away to obtain source point intensity factor according to step (3), unknowm coefficient is solved drawn by formula (7) and (8): by formula (7) and (8), ask Go out at the n-th time horizon, the unknowm coefficient of n Δ t secondAnd then the unknowm coefficient α in delay moment is tried to achieve by formula (8)_j(t_R)。

Fluctuation types dynamic data reconstructing method based on singular boundary method the most according to claim 5, it is characterised in that: Step (5) moment t arbitrarily in put x acoustic pressure u by trying to achieve without integral formulas:

$u_2^{*}\left(x_i\right)=\frac{1}{4\mathrm{\π}}\frac{\∂}{\∂r}\underset{S_{ct}^M}{\∫\∫}\frac{u_0}{r}ds+\frac{1}{4c\mathrm{\π}}\underset{S_{ct}^M}{\∫\∫}\frac{{\mathrm{\υ}}_1}{r}ds,x_i\∈\mathrm{\Ω}---\left(\mathrm{10}\right)$

$u_1^{*}\left(x_i\right)=u\left(x_i\right)-u_2^{*}\left(x_i\right)=\underset{j=1,j\≠i}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_j\left(t_R\right)G_{ij}+{\mathrm{\α}}_i\left(t_R\right)Q_i,t_R=t_n-\frac{r}{c}>0,i=1,2,3......\left(\mathrm{11}\right)$

$u=u_1^{*}+u_2^{*}---\left(12\right).$