CN102967189B - Explosive blast overpressure space-time field reconstruction method - Google Patents

Abstract

An explosive blast overpressure space-time field reconstruction method adopts an overpressure sensor array in a blast test system to acquire blast signals, and utilizes a blast overpressure space-time field reconstruction module to reconstruct an explosive blast overpressure space-time field; during reconstruction, a tested area is first meshed, sensor array elements are arranged, an explosion point is then located, a blast velocity field and a blast peak overpressure field are reconstructed, and thereby therefore a blast peak overpressure field reconstruction result is obtained; in combination with the blast peak overpressure field reconstruction result of the point, each parameter of a 'modified Friedlander equation' is solved, so that blast overpressure space-time data are obtained; finally, the reconstructed data are converted into an image file, and thereby therefore the blast overpressure space-time field is visualized. The method provides a basis for the evaluation of the damage effectiveness of blast and the structure and performance of explosive; and meanwhile, the method also is an important means for evaluating the safety of personnel, the shock resistance of equipment and the affection of blast on the surrounding environment.

Description

Explosion wave superpressure time space field method for reconstructing

Technical field

The invention belongs to Array Signal Processing and reconstruction field, be specifically related to a kind of explosion wave superpressure time space field method for reconstructing.

Background technology

Along with society and scientific and technological progress, and the needs of the national economic development, explosion technique is applied to traffic, water conservancy and hydropower Facilities Construction, the every field such as process of moving mountains and fill seas more and more.In explosion technique widespread use, impact and harm thereof that blast operation brings surrounding environment and Architectural Equipment become the emphasis that people pay close attention to.How assessing the power of blast, the harm of control blast, reduce the impact of blast operation on surrounding environment, is the important content of explosion safety technical research.

Powder charge is explosion time in air, forms high temperature and high pressure gas, and this gas promotes static air fiercely around, produces a series of wave of compression simultaneously and propagates to surrounding, finally forms air-shock wave.Air-shock wave wave front surge pressure surpasses the quantity of air normal pressure, is called positive pressure of shock wave.Shock wave arrives moment, air pressure rises to peak overpressure by original pressure hop, and because detonation product expansion is slack-off gradually, gases at high pressure movement velocity reduces subsequently, the pressure that makes shock wave hop increase is constantly decayed, so that excess pressure drop has occurred again the pressure lower than ambient gas after being as low as zero.Positive pressure of shock wave is to produce the principal element of killing and wounding with destruction, is the important component part of injuring target energy.Shock wave is positive pressure of shock wave field coefficient result on room and time to injuring of target.As long as know positive pressure of shock wave, with the attenuation law of locus and time, just can determine the execution of diverse location different time shock wave.Positive pressure of shock wave is to weigh the key character amount of shock wave to people, thing damage, for the personnel that are engaged in production, use ammunition, must take into full account this destruction of shock wave, especially utilizing explosion wave to carry out operation, must fully estimate positive pressure of shock wave size while destroying a large amount of ammunition, to determine the safe distance of not causing danger.At present for the not accomplished case of blast, procuratorate often requires power that public security organ produces blast and destruction to make to identify to using as the foundation to suspect's measurement of penalty.Therefore, be necessary explosion wave superpressure time space field to rebuild, obtain Overpressure Field distribution and positive pressure of shock wave with the attenuation law of room and time, with the needs that meet safety in production and use.

At present, although relevant scholar has summed up some and has calculated the formula of positive pressure of shock wave both at home and abroad, but these formula are all some experimental formulas, due to when carrying out actual tests research, test environment, test condition, charger shape and test data result are also incomplete same, therefore, are directly utilized these data and achievement in research to bring difficulty.

Explosive charge is to complete within the extremely short time, the shock wave producing is to all the winds propagated, symmetrical explosive is as spherical explosive, the air-shock wave that blast produces is outwards propagated with the form of spherical wave, and be erratic for impacting wavelength-division cloth after asymmetric explosive charge, therefore will assess the shock wave situation of injuring just needs shock wave superpressure transmission rule and distribution thereof to study.The number of sensors that experimental test is used is limited, and the locus that sensor is laid is also limited, quiet when quick-fried, if sensor distance bombing site is very near, can make sensor damage; When moving quick-fried, because bombing site is unknown, sensor is laid and is also subject to certain restrictions; So can only record the shock wave parameter of limited space position, these measured values are injured situation and analyzed ammunition performance for assessment shock wave is far from being enough.

Summary of the invention

The object of the invention is can not fully understand the deficiency of shock motion process for layout test and the strength test of existing part, a kind of explosion wave superpressure time space field method for reconstructing is provided, the fragmentary data reconstruction technique of the method utilization based on chromatographic technique obtains the distribution of certain area implode peak value of shock wave overpressure field and positive pressure of shock wave with the attenuation law apart from discrete time, having realized the time space field of explosion wave superpressure rebuilds, and the positive pressure of shock wave that blast is produced shows by clear picture with spatial variations process in time, realized the visual of positive pressure of shock wave time space field.

Technical scheme of the present invention is:

A kind of explosion wave superpressure time space field method for reconstructing, adopt shock wave test macro to realize the reconstruction of explosion wave superpressure time space field, shock wave test macro is by impulse wave overpressure sensor array, signal condition module, synchronous A/D modular converter, high speed data transfer module, data preprocessing module, positive pressure of shock wave time space field rebuilds module and computing machine forms, wherein, impulse wave overpressure sensor array is converted to electric signal by positive pressure of shock wave signal, by signal condition module, nurse one's health into standard voltage signal and be converted to digital signal with synchronous A/D modular converter, and then digital signal is transferred to computing machine by high speed data transfer module, data preprocessing module and superpressure time space field are rebuild module and are installed on computers, positive pressure of shock wave signal input data preprocessing module after A/D conversion, after data pre-service, input positive pressure of shock wave time space field and rebuild module, by positive pressure of shock wave time space field, rebuild module and complete the reconstruction to explosion wave superpressure time space field, it is characterized in that, this time space field method for reconstructing is: first test zone is carried out to grid division, and lay sensor array element, next adopts in passive positioning algorithm time difference method and in conjunction with iterative algorithm, fried point is positioned, then when walking and the relation of raypath and the relation of shock velocity and peak overpressure carry out the reconstruction of peak value of shock wave overpressure field, then study fixed position, space positive pressure of shock wave attenuation law and feature in time, in conjunction with this peak value of shock wave overpressure, " the Freedlander equation of correction " each parameter is asked for, obtain positive pressure of shock wave space-time data, finally, data reconstruction is changed into image file, be presented on the display of computing machine, realize the visual of positive pressure of shock wave time space field, wherein: described peak value of shock wave overpressure field rebuilds by velocity field reconstruction and peak overpressure's field reconstruction two parts and forms.

The concrete grammar that described peak value of shock wave overpressure field rebuilds: when extracting shock wave and surveying away, optimize slowness initial model, calculate raypath, the highest iterations be set, the theory of computation while walking, slowness field Inversion Calculation and peak value of shock wave overpressure conversion, obtain peak value of shock wave overpressure field reconstructed results p _m(x, y).

The concrete steps of this time space field method for reconstructing are:

(1) when the division of test zone grid and sensor array element are laid, measured zone is divided into the grid cell of some rules, sensor array element is used number to be distributed in the node at grid edge and grid on indivedual nodes according to test, and demolition point occupy the center of test zone;

(2) according to signal time delay, signal speed and relation obtain path length difference, combined sensor position coordinates, sets up an equation to each sensor, and then adopts iterative algorithm to calculate the locus of fried point; The time and the raypath relation that by measuring shock waves, arrive sensor array element are finally inversed by each grid cell impact wave propagation velocity, according to the relation of shock velocity and peak overpressure, obtain peak value of shock wave overpressure field reconstructed results, i.e. the peak value of shock wave overpressure p of optional position _m(x, y);

(3) the time dependent curve of certain point of fixity positive pressure of shock wave that during according to test, testing sensor obtains, select superpressure-time tranfer model of suitable shock wave, by matching comparison, select " the Freedlander equation of correction " and in conjunction with peak value of shock wave overpressure field reconstructed results p _m(x, y), obtain positive pressure of shock wave in time with the variation relation in space, and obtain positive pressure of shock wave time space field reconstructed results, i.e. the shock wave overpressure p (x, y, t) of optional position and time;

(4) set up the mapping between superpressure data reconstruction and color or geometrical body, complete application data to the conversion of the geometric element data such as point, line, surface, body; Geometric data is become to view data, by view data synthetic image file, again the image generating is carried out to smoothing processing to eliminate the abnormity point that does not meet individually shock wave transmission rule, the positive pressure of shock wave finally blast being produced dynamically shows with the change procedure of locus in time.

Outstanding feature of the present invention and remarkable result are:

By adopting various Time And Space Parameters in the positive pressure of shock wave time space field reconstruction module reconstructs blast process in shock wave test macro (locus of point as fried in ammunition, shock wave transmission speed, positive pressure of shock wave distribution, positive pressure of shock wave spatial attenuation rule in time etc.), for the injure usefulness and ammunition structure and performance of assessment shock wave provides foundation; Meanwhile, be also appraiser security, equipment impact resistance, evaluates the important means of shock wave to surrounding environment influence, also can be research water shooting Overpressure Field reconstruction and power assessment, tunnel blast Overpressure Field reconstruction and power assessment technical foundation is provided.

Accompanying drawing explanation

Fig. 1 is shock wave test macro schematic diagram of the present invention;

Fig. 2 explosion wave superpressure time space field is rebuild process flow diagram;

Fig. 3 is that cell of the present invention is divided schematic diagram;

Fig. 4 is that sensor of the present invention is laid schematic diagram;

Fig. 5 is that velocity field of the present invention is rebuild process flow diagram;

Fig. 6 is shock wave pressure-time curve of the present invention;

Fig. 7 is air burst positive pressure of shock wave field reconstructed results 3-D display figure.

Embodiment

The air burst positive pressure of shock wave field 2-d reconstruction of take is below example, by reference to the accompanying drawings the present invention is described in further detail.

As shown in Figure 1, shock wave test macro is by impulse wave overpressure sensor array, signal condition module, synchronous A/D modular converter, high speed data transfer module, data preprocessing module, positive pressure of shock wave time space field rebuilds module and computing machine forms, wherein, impulse wave overpressure sensor array is converted to electric signal by positive pressure of shock wave signal, by signal condition module, nurse one's health into standard voltage signal and be converted to digital signal with synchronous A/D modular converter, and then digital signal is transferred to computing machine by high speed data transfer module, data preprocessing module and superpressure time space field are rebuild module and are installed on computers, positive pressure of shock wave signal input data preprocessing module after A/D conversion, after data pre-service, input positive pressure of shock wave time space field and rebuild module, positive pressure of shock wave time space field is rebuild module and is completed the reconstruction to explosion wave superpressure time space field.

As shown in Figure 2, first air burst positive pressure of shock wave field 2-d reconstruction carries out grid division to test zone, and lay sensor array element, then adopt in passive positioning algorithm time difference method and in conjunction with iterative algorithm, fried point positioned, then when walking and the relation of raypath and be related to shock wave velocity field and the peak value of shock wave overpressure field of shock velocity and peak overpressure rebuild; Research positive pressure of shock wave is attenuation law and feature in time, in conjunction with this peak value of shock wave overpressure reconstructed results, " the Freedlander equation of correction " each parameter is asked for, and obtains positive pressure of shock wave space-time data; Finally, data reconstruction is changed into image file, realize the visual of positive pressure of shock wave time space field.

1) test zone grid is divided and the laying of sensor array element

During to air burst positive pressure of shock wave field 2-d reconstruction, demolition point occupy the center of test zone, sensor array element and fried point are all laid in same plane, in order to guarantee the validity of data reconstruction, on the grid node at each edge of reconstruction regions, lay as far as possible testing sensor, so that the tested region of the multi-faceted as far as possible covering of the layout of sensor.

Grid coordinate system as shown in Figure 3, is usingd first grid cell summit, lower left as the initial point O (0,0) of coordinate system, and establishing demolition point coordinate is K (x ₀, y ₀), the sensor coordinates that i bar ray is corresponding is s _i(x _i, y _i), during test, use 50KgTNT explosive charge, sensor is laid within the scope of 32m * 32m, demolition point occupy the center of test zone, 30 sensors have been used, according to the size of effective ray sum and search coverage and radiographic density, test zone is divided into each 64 * 64 grids that size is identical of length and width, sensor array element is distributed on the node and the interior indivedual nodes of grid at grid edge, as shown in Figure 4.

2) fried point location

It is to carry out in the certain area centered by exploding a little that positive pressure of shock wave time space field is rebuild, and instant of detonation bombing site can change, so first will accurately locate fried point.

The sensor array element of spatial arrangement is used for real-time receiving target information, because the residing position of sensor array element is different, when shock wave arrives different sensors array element, the path of process is also different, and sensor array element receives signal and just exists the regular hour poor, i.e. time delay.According to the signal time delay of laying sensor acquisition in Fig. 4, and the relation of sensor signal time delay and signal speed can obtain path length difference, combined sensor position coordinates, each sensor can be set up an equation, and then adopts iterative algorithm to calculate the locus of fried point.

3) peak value of shock wave overpressure field rebuilds

Peak value of shock wave overpressure field rebuilds by velocity field reconstruction and peak overpressure's field reconstruction two parts and forms.The time and the raypath relation that by measuring shock waves, arrive sensor array element can be finally inversed by each grid cell impact wave propagation velocity, according to the relation of shock velocity and peak overpressure, can obtain the distribution situation of peak value of shock wave overpressure field.

(1) velocity field is rebuild

Because shock wave is propagated in air, so propagation medium can be considered uniform dielectric, and shock motion speed is larger, so can be similar to, thinks that shock wave propagates along direct rays (wavefront normal family).Suppose that shock wave is not to propagate along the border of grid cell, and shock wave is similar to and thinks along certain rectilinear propagation, the corresponding ray of each sensor in each grid cell.The time that shock wave arrives sensor array element, shock wave, in the process of transmission, was the function of speed and geometric path when it is walked when walking, as the formula (1):

$t={\∫}_L\frac{1}{v}\·\mathrm{dr}={\∫}_{L}s\·\mathrm{dr}---\left(1\right)$

In formula, r is ray; V is speed; S is slowness; L is path of integration.

By above formula discretize, according to test zone grid dividing condition, for i bar ray, have:

$t_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{s}_j{d}_{\mathrm{ij}}$ (i=1,2,3,…,M;j=1,2,3，…,N) （2）

In formula, t _i: during the walking of i bar ray, shock wave wave front arrives the time of sensor;

D _ij: i bar ray is through the ray length of j grid;

S _j: the slowness in j grid;

M: number of rays;

N: grid number.

Being write above formula as matrix form is:

DS＝T （3）

Wherein, T=(t ₁, t ₂... t _m) ' be the M dimensional vector of each ray traveltime; S=(s ₁, s ₂s _n) ' for discrete unit slowness value to be asked, for N ties up unknown column vector; D is M * N rank sparse matrixes, and its element is d _ij.

In matrix equation group (3), because ray has only passed through a seldom part for grid cell, so matrix D is a Large Scale Sparse matrix, nonzero element accounts for seldom ratio; Not exclusively projection has determined less qualitative (nonuniqueness) of problem; The existence of measuring error has determined the incompatibility of problem.In addition, inaccurate due to noise and measurement, the exact solution of solving equation (3) is very difficult, therefore, direct solution equation not here, but poor during with theoretical walk while first asking observation to walk, and then utilize process of iteration to solve.

Velocity field is rebuild flow process as shown in Figure 5.

(shock wave arrives the time of sensor array element) data tc when a) extraction shock wave is surveyed away

By each sensor array element signal is analyzed and feature extraction, obtain the time that shock wave arrives sensor array element.

B) optimize initial slowness model

According to the initial slowness model of peak value of shock wave overpressure experimental formula optimization:

Charge density is 1.6 gram per centimeters ³spherical TNT cartridge bag explosion time in infinite medium, the p of air-shock wave peak overpressure _mcan calculate according to following experimental formula:

$p_m=0.84\frac{\sqrt[3]{W}}{r}+2.7{\left(\frac{\sqrt[3]{W}}{r}\right)}^2+7{\left(\frac{\sqrt[3]{W}}{r}\right)}^3$ (be applicable to $1\≤\stackrel{\‾}{r}\≤10~15$ ） （4）

In formula, W: weight of charge (kilogram);

R: measuring point is to the distance (rice) at cartridge bag center;

scaled distance (rice/kilogram ^1/3);

$p_m=\frac{20.06}{\stackrel{\‾}{r}}+\frac{1.94}{{\stackrel{\‾}{r}}^2}-\frac{0.04}{{\stackrel{\‾}{r}}^3}$ (be applicable to $0.05\≤\stackrel{\‾}{r}\≤0.50$ ） （5）

$p_m=\frac{0.67}{\stackrel{\‾}{r}}+\frac{3.01}{{\stackrel{\‾}{r}}^2}+\frac{4.31}{{\stackrel{\‾}{r}}^3}$ (be applicable to $0.50\≤\stackrel{\‾}{r}\≤70.9$ ） （6）

While using other explosive or charge density different, can powder charge be converted into equivalent TNT equivalent according to the energy principle of similitude and by formula (4)～(6), calculate again.

Equivalence TNT equivalent computing formula is as follows:

$W_T=W_i\frac{Q_i}{Q_T}---\left(7\right)$

In formula, W _i: the weight of explosive used (kilogram);

Q _i: the quick-fried heat (kcal/kg) of explosive used;

W _t: W _ithe TNT equivalent of conversion (kilogram);

Q _t: the quick-fried heat of TNT (kcal/kg);

The pass of shock velocity and peak overpressure is:

$c^2=C_0^2(\frac{6p_m}{7p_0}+1)---\left(8\right)$

In formula, p _mfor peak value of shock wave overpressure, c is shock velocity, p ₀for intact air original pressure, C ₀for the intact air velocity of sound, for different temperature, have: (meter per second), T ₀for intact air initial temperature (K).

According to above experimental formula, calculate peak value of shock wave overpressure initial value in each grid of test zone, then be converted to slowness initial value according to formula (8).

C) calculate raypath d _ij

Because the path of direct rays is all identical in the iterative process of each modification raypath, difference while just changing because of velocity of wave walking of causing, so only need calculating once in actual iterative process.

Using first grid cell summit, lower left as the initial point O (0,0) of coordinate system, and establishing demolition point coordinate is K (x ₀, y ₀), the sensor coordinates that i bar ray is corresponding is s _i(x _i, y _i), length, the height of establishing test rectangle region are respectively Length, Height, and grid is divided into the capable L row of H, and the length of each grid cell, height are respectively Length/L, Height/H, i bar ray equation is:

$\frac{y-y_0}{y_i-y_0}=\frac{x-x_0}{x_i-x_0}---\left(9\right)$

Horizontal partition line equation is: y=mHeight/H(m is integer, and 0≤m≤H),

Longitudinally cut-off rule equation is: x=nLength/L(n is integer, and 0≤n≤L),

Distinguish simultaneous ray equation and horizontal partition line equation, ray equation and longitudinal cut-off rule equation, can obtain the intersection point of direct rays and horizontal partition line and longitudinal cut-off rule.To i bar ray, according to from demolition point to sensor s _iin this raypath, the abscissa value of intersection point progressively reduces all intersection point sortings.

Which grid cell what according to adjacent two intersection point transverse and longitudinal coordinate figure sizes, determine raypath process is: establish arbitrary neighborhood two intersection points and be distributed as (x _d, y _d) and (x _d+1, y _d+1), wherein point coordinate is: $b_1=\frac{y_d+y_{d+1}}{2},$ Get $a_2=\mathrm{INT}\left(\frac{a_1}{\mathrm{Length}/L}\right),$ $b_2=\mathrm{INT}\left(\frac{b_1}{\mathrm{Height}/H}\right),$ There is grid cell sequence number G=b ₂l+a ₂+ 1.Wherein INT represents rounding operation.Then the air line distance of calculating successively adjacent two intersection points can way to acquire length d _ij.

D) the highest iterations Maxq is set, in this calculating, iterations is set to 100.

When the theory of e) calculating successively each ray according to following formula is walked

$t_{\mathrm{il}}^{\left(q\right)}=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{s}_j^{(q-1)}$ (i=1,2,3,…,M;j=1,2,3，…,N,q=1,2,3,…,Maxq) （10）

In formula, q be iterations (q=1,2,3 ..., Maxq), when while being the q time iteration, the theory of i bar ray is walked, (i=1,2,3 ..., M; J=1,2,3 ..., N); be the q-1 time iterative computation gained slowness value.When q=1, slowness value according to b) in initial model select to obtain.

Poor when f) calculating successively each ray and survey away according to following formula and when theory walks.

$\mathrm{\δ}{t}_i^{\left(q\right)}=t_{\mathrm{ic}}-t_{\mathrm{il}}^{\left(q\right)}$ (i=1,2,3,…,M,q=1,2,3,…,Maxq) （11）

G) adopt Joint iteration reconstruction algorithm (SIRT) to calculate successively the average modified value of slowness in each grid cell

Suppose total K in j grid cell _jbar ray passes through:

$\mathrm{\δ}{s}_j^{\left(q\right)}=\frac{1}{K_j}\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\mathrm{\δ}{t}_i^{\left(q\right)}\·d_{\mathrm{ij}}/\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}^2$ (i=1,2,3,…,M;j=1,2,3，…,N,q=1,2,3,…,Maxq) （12）

H) revise the slowness value s of each grid cell _j

$s_j^{\left(q\right)}=s_j^{(q-1)}+\mathrm{\δ}{s}_j^{\left(q\right)}$ (j=1,2,3…N,q=1,2,3,…,Maxq) （13）

I) according to shock wave actual measurement speed, provide constraint condition.

$s_{\min }\≤s_j^{\left(q\right)}\≤s_{\max }---\left(14\right)$

In formula, s _min, s _maxvalue according to experimental test gained velocity amplitude, determine, if if $s_j^{\left(q\right)}<s_{\min },$ $s_j^{\left(q\right)}=s_{\min }.$

J) establish e=0.00001m/s, as q≤Maxq, while meeting formula (15), stop iteration, when q≤Maxq does not meet formula (15), enter next round iteration, repeat e) to i) step.Work as q>Maxq, but also do not meet formula (15), stop iteration.

$|s_j^{\left(q\right)}-s_j^{(q-1)}|\&le;e,$ (j=1,2,3…N,q=1,2,3,…,Maxq) （15）

Wherein, c) and e) be forward simulation process.F)-h) be slowness refutation process.

(2) peak overpressure field rebuilds

Peak overpressure's value that the shock velocity that test is recorded and sensor obtain compares matching, obtains the relation of test point peak value of shock wave overpressure and shock velocity:

$p_m=\frac{7p_0}{6}(\frac{c^2}{C_0^2}-1)---\left(16\right)$

In formula, p _mfor peak value of shock wave overpressure, c is shock velocity, p ₀for intact air original pressure; C ₀for the intact air velocity of sound, for different temperature, have: (meter per second) (T ₀for intact air initial temperature (K)).

By reconstructed results slewing rate field, slowness field, then be converted into peak value of shock wave overpressure field reconstructed results p according to formula (16) _m(x, y), this result is the peak value of shock wave overpressure value of optional position, space (x, y), the spatial field of having described positive pressure of shock wave distributes.

4) positive pressure of shock wave time space field is rebuild

Certain that during according to test, testing sensor obtains is put the time dependent curve of positive pressure of shock wave, selects superpressure-time tranfer model of suitable shock wave, by matching comparison, in conjunction with above-mentioned peak value of shock wave overpressure field reconstructed results p _m(x, y), select " the Freedlander equation of correction " obtain positive pressure of shock wave in time with the variation relation in space:

$p(x,y,t)=p_0+p_m(x,y)(1-t/T^{+})e^{-\mathrm{ct}/T^{+}}---\left(17\right)$

In formula, p (x, y, t) is that shock wave is located at t superpressure value constantly, p in locus (x, y) ₀for environmental pressure; p _m(x, y) is the peak overpressure of (x, y) point; T ⁺for positive phase duration; C is attenuation parameter.

(1) p ₀before experiment, can record;

(2) p _m(x, y) rebuild and calculated acquisition by peak value of shock wave overpressure field;

(3) T ⁺apart from demolition point distance R, can set up following relational model with test dose W, testing sensor:

$\frac{T^{+}}{\sqrt[3]{W}}=a{\left(\frac{R}{\sqrt[3]{W}}\right)}^n---\left(18\right)$

Above formula can be converted into:

n(lnR-lnB)+lna=lnT ⁺-lnB （19）

Wherein regard n and lna as unknown quantity x, y,

This formula just can be converted into linear equation

z ₁x+y＝z ₂ （20）

Z wherein ₁=lnR-lnB, z ²=lnT ⁺-lnB.

I testing sensor is R apart from demolition point distance _i(i=1,2,3 ..., M), dose is W, can obtain z _1i=lnR _i-lnB (i=1,2,3 ..., M); In the time of testing, test each sensor test shock wave curve positive duration T of gained _i ⁺bring z into ₂, can obtain z _2i=lnT _i ⁺-lnB (i=1,2,3 ..., M), set up system of linear equations z _1ix+y=z _2i(i=1,2,3 ..., M), and use least square fitting, can obtain parameter x, y, obtains parameter n, a.Bring formula (18) into and obtain parameter T ⁺funtcional relationship with distance R and dose W; According to formula (17) spatial location (x, y), determine that test point is apart from demolition point distance R, and can determine positive duration T in formula (17) in conjunction with dose W ⁺.

(4) parameter c is determined

Parameter c is a constant not, but shows complicated character.By the analysis to measured signal, find, in fact parameter c has more than only relevant with peak overpressure, it is actually multivariate function, and this function is not only relevant with time t but also relevant with the distance r of quick-fried source and measuring point, and can the retrodict expression formula of parameter c of utilization formula (17) is:

$c=\left(\frac{T^{+}}{t}\right)[\ln \left(p_m(x,y)(T^{+}-t)\right)-\ln \left(T^{+}(p(x,y,t)-p_0)\right)]---\left(21\right)$

P in formula (x, y, t) is surveyed superpressure value corresponding to different time t different spatial (x, y) on shock wave curve by testing sensor, obtains, by p (x, y, t) and corresponding T from testing sensor output data ⁺bring the time history curve that formula (21) can obtain parameter c into.

By the time history CURVE STUDY to the parameter c of measured signal, analyze, the logarithm (lnlnc) of the logarithm of discovery c linear with the time:

kt+m=lnlnc(0≤t≤T ⁺) （22）

Wherein k and m are undetermined parameter.

If matrix $A={\left[\begin{array}{cc}1& 1\\ 2& 1\\ 3& 1\\ ...& ...\\ \mathrm{data}& 1\end{array}\right]}_{\mathrm{data}\&times;2},$ $X=\left(\begin{array}{c}k\\ m\end{array}\right),$ $B={\left[\begin{array}{c}\ln \ln c_1\\ \ln \ln c_2\\ \ln \ln c_3\\ ...\\ \ln \ln c_{\mathrm{data}}\end{array}\right]}_{\mathrm{data}\&times;1}$

Wherein the first row of matrix A represents that testing sensor surveys the different time t that sample point on shock wave curve (getting data sample point) is corresponding, and matrix B represents the lnlnc value in the corresponding moment of sample point, and the logarithm of being taken the logarithm by formula (21) obtains.Formula (22) is the linear equation about k and m, brings measured signal data into and sets up system of linear equations and be:

AX=B (23)

Through transform (23), become:

A ^TAX=A ^TB （24）

A wherein ^ttransposed matrix for matrix A.

X＝(A ^TA) ^-1A ^TB (25)

Solving equation (25) can be determined parameter k and m, by formula (22), can determine parameter c.

5) positive pressure of shock wave time space field is visual

Superpressure data reconstruction is transformed to the geometric element data of point, line, surface, body etc.; Geometric data is converted into view data, and is transferred to display device, synthetic image file; The image generating is carried out to smoothing processing, and the shock wave finally blast being produced dynamically shows with the change procedure of locus in time.

6) reconstructed results

Adopt this patent method to carry out 2-d reconstruction to 32m * 32m scope implode shock-wave field, and superpressure sensor test result compares when peak overpressure's reconstructed results is with test when shock wave is arrived, minimal difference is 0.000961Mp, and two-dimentional explosive field superpressure reconstructed results is carried out to result after three-dimensional visualization as shown in Figure 7.

Claims (3)

1. an explosion wave superpressure time space field method for reconstructing, adopt shock wave test macro to realize the reconstruction of explosion wave superpressure time space field, shock wave test macro is by impulse wave overpressure sensor array, signal condition module, synchronous A/D modular converter, high speed data transfer module, data preprocessing module, positive pressure of shock wave time space field rebuilds module and computing machine forms, wherein, impulse wave overpressure sensor array is converted to electric signal by positive pressure of shock wave signal, by signal condition module, nurse one's health into standard voltage signal and be converted to digital signal with synchronous A/D modular converter, and then digital signal is transferred to computing machine by high speed data transfer module, data preprocessing module and superpressure time space field are rebuild module and are installed on computers, positive pressure of shock wave signal input data preprocessing module after A/D conversion, after data pre-service, input positive pressure of shock wave time space field and rebuild module, by positive pressure of shock wave time space field, rebuild module and complete the reconstruction to explosion wave superpressure time space field, it is characterized in that, this time space field method for reconstructing is: first test zone is carried out to grid division, and lay sensor array element, next adopts in passive positioning algorithm time difference method and in conjunction with iterative algorithm, fried point is positioned, then when walking and the relation of raypath and the relation of shock velocity and peak overpressure carry out the reconstruction of peak value of shock wave overpressure field, then study positive pressure of shock wave attenuation law and feature in time, in conjunction with grid cell peak value of shock wave overpressure, " the Freedlander equation of correction " each parameter is asked for, obtain positive pressure of shock wave space-time data, finally, data reconstruction is changed into image file, be presented on the display of computing machine, realize the visual of positive pressure of shock wave time space field, wherein: described peak value of shock wave overpressure field rebuilds by velocity field reconstruction and peak overpressure's field reconstruction two parts and forms.

2. a kind of explosion wave superpressure time space field method for reconstructing according to claim 1, it is characterized in that: the concrete grammar that described peak value of shock wave overpressure field rebuilds: when extracting shock wave and surveying away, optimize slowness initial model, calculate raypath, the highest iterations be set, the theory of computation while walking, slowness field Inversion Calculation and peak value of shock wave overpressure conversion, obtain peak value of shock wave overpressure field reconstructed results p _m(x, y).

3. a kind of explosion wave superpressure time space field method for reconstructing according to claim 1, is characterized in that: the concrete steps of this time space field method for reconstructing are:

(1) when the division of test zone grid and sensor array element are laid, measured zone is divided into the grid cell of some rules, sensor array element is used number to be distributed in the node at grid edge and grid on indivedual nodes according to test, and demolition point occupy the center of test zone;

(2) according to signal time delay, signal speed and relation obtain path length difference, combined sensor position coordinates, sets up an equation to each sensor, and then adopts iterative algorithm to calculate the locus of fried point; The time and the raypath relation that by measuring shock waves, arrive sensor array element are finally inversed by each grid cell impact wave propagation velocity, according to the relation of shock velocity and peak overpressure, obtain peak value of shock wave overpressure field reconstructed results, i.e. the peak value of shock wave overpressure p of optional position _m(x, y);

(3) the time dependent curve of certain point of fixity positive pressure of shock wave that during according to test, testing sensor obtains, select superpressure-time tranfer model of suitable shock wave, by matching comparison, select " the Freedlander equation of correction " and in conjunction with peak value of shock wave overpressure field reconstructed results p _m(x, y), obtain positive pressure of shock wave in time with the variation relation in space, and obtain positive pressure of shock wave time space field reconstructed results, i.e. the shock wave overpressure p (x, y, t) of optional position and time;

(4) set up the mapping between superpressure data reconstruction and color or geometrical body, complete application data to the conversion of point, line, surface, body geometric element data; Geometric data is become to view data, by view data synthetic image file, again the image generating is carried out to smoothing processing to eliminate the abnormity point that does not meet individually shock wave transmission rule, the positive pressure of shock wave finally blast being produced dynamically shows with the change procedure of locus in time.