CN103487786B - Structural impact wave-velocity-free positioning method based on two-dimensional linear arrays and spatial filters - Google Patents
Structural impact wave-velocity-free positioning method based on two-dimensional linear arrays and spatial filters Download PDFInfo
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Abstract
The invention discloses a structural impact wave-velocity-free positioning method based on two-dimensional linear arrays and spatial filters and belongs to the technical field of engineering structure health monitoring. Impact response signals of a two-dimensional linear piezoelectric sensor array collecting structure are adopted for the method, narrow-band Lamb wave complex signals in the impact response signals are extracted and constructed through Shannon continuous complex number wavelet transform, then, the spatial filter algorithm irrelevant to the wave velocity is utilized to obtain the angle of the structural impact relative to each linear piezoelectric sensor array, finally, the position coordinates of the structural impact is calculated through the impact wave-velocity-free positioning formula, and thus wave-velocity-free positioning of the structural impact is achieved through the spatial filter algorithm. The structural impact wave-velocity-free positioning method is simple, convenient to use and reliable, can be used for wave-velocity-free positioning of the structural impact, thus eliminates effects of material anisotropism and is particularly suitable for health monitoring of complex composite material structures.
Description
Technical field
The present invention relates to a kind of calm fast positioning method of structural impact based on two-dimentional linear array and spatial filter, belong to engineering structure health monitoring technical field.
Background technology
Compound substance has that specific strength is high, specific stiffness is large, specific modulus is high, designability is strong, and the performance that high temperature resistant, corrosion-resistant, antifatigue etc. is excellent, type aircraft is applied more and more wider.Composite material aircraft structure is in Service Environment complicated and changeable, be easy to suffer sandstone, hail, bird is hit, the grazing of ground service vehicle, instrument to drop etc. impact event, cause the interior laminate layer of composite structure, MATRIX CRACKING and fibre breakage etc., compromise performance and the integrality of structural member, weaken the intensity of structural member up to 65%, the safety of subsequent flights in serious threat.Therefore, carry out on-line monitoring to composite structure impact event, the status information of Real-time Obtaining structure is very necessary.Could implement after the ripe Dynamic Non-Destruction Measurement of conventional eddy-current method, supersonic testing method, radioscopy, Computer tomography detection method, microwave detection method etc. needs aircraft landing, can not real time on-line monitoring impact event.And the real time on-line monitoring that impacts can be realized based on the structural health monitoring technology of Lamb wave, be a focus of research both at home and abroad, concrete grammar mainly contains following three kinds on realizing:
(1) time-of-arrival loaction: utilize impact signal to arrive the time delay of different piezoelectric sensor, positions impact position based on signal velocity of propagation in the structure.But when structural anisotropy causes more greatly all directions velocity of wave to differ greatly, the error of im-pact location can become and even produce mistake comparatively greatly.
(2) System Modelling Method: by setting up the system optimization model of structure, transforms im-pact location problem in order to inversion problem is optimized in load inverting.Essentially a solution of inverse problems process from mathematics, the high-order nonlinear relation that the discomfort of indirect problem determines characteristic and impact position and response signal brings very large difficulty to solving, in addition unknown quantity huge amount and calculation task heavy, the real-time of location is also difficult to be guaranteed.Further, when complex structure, system modelling is more difficult, thus causes im-pact location error also to become large even mistake, and calculated amount also rolls up thereupon.
(3) artificial intelligence method: utilize artificial neural network technology, sets up the relation of impulse response signal characteristic parameter and impact position, thus realizes the location to structural impact.But the method needs to obtain the training sample of impulse test data a large amount of in structure as neural network in advance, this is difficult to realize in the middle of practical engineering application.
In recent years, spatial filter algorithm develops rapidly in the field such as Detection of Weak Signals and sonar detection.It by arrange filtering parameter make its formed wave number for [
k min,
k max] spatial filter, virtual rotation is carried out to linear piezoelectric transducer array, thus realizes 0 °--the comprehensive scanning of 180 °.When scanning with when damaging identical relative to the angle of linear piezoelectric transducer array, damage signal can pass through this spatial filter, the amplitude maximum of synthesis response, and when scanning other angle, because damage is not in this orientation, so signal cannot pass through spatial filter, synthesis response amplitude is less, the response signal intensity obtained after carrying out filtering to each orientation carries out characterization image, can obtain the angle of structural damage relative to linear piezoelectric transducer array.Whole azimuth filtering scanning process does not need to rely on Lamb wave signal velocity of propagation structurally, effectively can eliminate the impact of complicated Aviation Composite Structure velocity of wave difference, apply more and more wider at present in complicated Aviation Composite Structure health monitoring.But, for impact injury, due to the start time of impact signal cannot be determined, the propagation course of impact signal also namely cannot be obtained.So, utilize spatial filter algorithm can only obtain the angle of position relative to linear piezoelectric transducer array of structural impact, can not determine the position coordinates of impact.This seriously constrains the application of spatial filter algorithm in monitoring structural health conditions.
Summary of the invention
For solving the problem, the present invention proposes a kind of calm fast positioning method of structural impact based on two-dimentional linear array and spatial filter, implementation space wave filter to the location of structural impact, and eliminates complicated Aviation Composite Structure velocity of wave difference to the impact of im-pact location.
The present invention adopts following technical scheme for solving its technical matters:
Based on the calm fast positioning method of structural impact of two-dimentional linear array and spatial filter, comprise the steps:
Step one: arrange two-dimensional linear piezoelectric sensor array
According to monitoring structural health conditions demand, the piezoelectric sensor array element of N number of same model is used to form a linear piezoelectric transducer array, structurally arrange two linear piezoelectric transducer arrays, horizontal ordinate, the ordinate of Liang Tiao linear piezoelectric transducer array center's point all can not be identical, that is:
x 1≠
x 2and
y 1≠
y 2, (
x 1,
y 1) be the central point of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the central point of No. 2 linear piezoelectric transducer arrays, thus form a two-dimensional structure Impact monitoring region, wherein N be greater than 2 integer;
Step 2: gather structural impact response signal
Setting structure impact sampling parameter, utilizes two-dimensional linear piezoelectric sensor array to gather structural impact response signal
f(
t);
Step 3: extract and build and impact arrowband Lamb wave complex signal
The continuous Complex Wavelet Transform of Shannon is adopted to extract and build broadband impulse response signal
f(
t) in arrowband Lamb wave complex signal composition
z(
t), as shown in Equation (1)
（1）
Wherein:
In formula:
z(
t) for impacting arrowband Lamb wave complex signal,
f(
w) be broadband impulse response signal
f(
t) Fourier transform, Ψ
shan-
a,b (
w) be the continuous plural mother wavelet function Ψ of Shannon
shan-
a,b (
t) Fourier transform, Ψ
shan-
a,b (
t) be the continuous plural mother wavelet function of Shannon,
afor the scale factor of the continuous plural morther wavelet of Shannon,
bfor the time factor of the continuous plural morther wavelet of Shannon,
f b for the band width of the continuous plural morther wavelet of Shannon,
f c for the centre frequency of the continuous plural morther wavelet of Shannon;
w c =2
π f c ;
w b =2
π f b ;
Step 4: to the impact arrowband Lamb wave complex signal of two linear piezoelectric transducer arrays
z(
t) carry out spatial filtering respectively
First the maximum filtering wave number value of spatial filter is asked for according to the array element distance of linear piezoelectric transducer array, as shown in Equation (2)
（2）
In formula:
k x, max
for the maximum filtering wave number value of this linear piezoelectric transducer array manifold wave filter, △
xfor the array element distance of this linear piezoelectric transducer array,
πfor circular constant;
Then according to monitoring structural health conditions mission requirements, filtering angular range and the angular resolution △ of spatial filter is determined
θ; One of them spatial filtering angle selected
θ, the wave number of spatial filter under this angle is calculated according to formula (3)
k x
（3）
According to formula (4), its spatial filtering weighting function is calculated to each array element in linear piezoelectric transducer array again
（4）
In formula:
φ(
x) for horizontal ordinate be
xthe spatial filtering weighting function of piezoelectric sensor,
xfor array element in linear piezoelectric transducer array is to the distance of linear array central point;
For the impact arrowband Lamb wave complex signal of each array element, use the spatial filtering weighting function of formula (4), calculate this array element and impact the response signal of arrowband Lamb wave complex signal after spatial filtering, then the filter response signal of each array element is synthesized, as the spatial filtering synthesis response signal of this angle lower linear piezoelectric sensor array, as shown in Equation (5)
（5）
In formula:
for spatial filtering angle
θthe spatial filtering synthesis response signal of lower linear piezoelectric sensor array,
nfor the element number of array of linear piezoelectric transducer array,
φ(
x n ) for horizontal ordinate be
x n the spatial filtering weighting function of piezoelectric sensor,
z(
x n ,
t) for horizontal ordinate be
x n the impact arrowband Lamb wave complex signal of piezoelectric sensor,
x n for the horizontal ordinate of array element;
This spatial filtering angle is calculated again according to formula (6)
θthe intensity of lower spatial filtering synthesis response signal
（6）
In formula:
e(
θ) be spatial filtering angle
θthe intensity of lower spatial filtering synthesis response signal,
for
θthe spatial filtering synthesis response signal of angle lower linear piezoelectric sensor array,
tfor spatial filtering synthesis response signal
signal length;
Choose next spatial filtering angle
θ+ △
θaccording to the intensity of the spatial filtering synthesis response signal of this angle lower linear piezoelectric sensor array of workflow management above, after treating that whole monitored areas angle calculation is complete, be normalized the spatial filtering synthesis response signal intensity of all angles is unified, angle---the damage probability curve that generating structure impacts, wherein damage probability, " spatial filtering synthesis response signal intensity " the maximum angle after being namely normalization is the angle of impact position relative to this linear piezoelectric transducer array;
According to above flow process, computation structure impacts angle---the damage probability curve relative to another linear piezoelectric transducer array, and the angle that wherein damage probability is maximum is the angle of impact position relative to this linear piezoelectric transducer array;
Step 5: structural impact is located without velocity of wave
Because two linear piezoelectric transducer arranged in arrays are perpendicular or parallel two kinds of modes, so divide both of these case to carry out locating without velocity of wave to structural impact respectively here:
(1) when Line 1 piezoelectric sensor array is vertical with No. 2 linear piezoelectric transducer arrays
（7）
In formula:
θ 1for structural impact is relative to the angle of Line 1 piezoelectric sensor array,
θ 2for structural impact is relative to the angle of No. 2 linear piezoelectric transducer arrays, (
x 1,
y 1) be the center point coordinate of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the center point coordinate of No. 2 linear piezoelectric transducer arrays, (
x,
y) be the position coordinates of structural impact;
Solving the position coordinates that linear equation in two unknowns group (7) obtains structural impact is:
（8a）
When
θ 1=90 °,
θ 2when ≠ 90 °
（8b）
When
θ 1≠ 90 °,
θ 2when=90 °
（8c）
When
θ 1=90 °,
θ 2when=90 °
（8d）
(2) when Line 1 piezoelectric sensor array and No. 2 linear piezoelectric transducer array parallel
（9）
In formula:
θ 1for structural impact is relative to the angle of Line 1 piezoelectric sensor array,
θ 2for structural impact is relative to the angle of No. 2 linear piezoelectric transducer arrays, (
x 1,
y 1) be the center point coordinate of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the center point coordinate of No. 2 linear piezoelectric transducer arrays, (
x,
y) be the position coordinates of structural impact;
Solving the position coordinates that linear equation in two unknowns group (9) obtains structural impact is:
（10a）
When
θ 1=90 °,
θ 2when ≠ 90 °
（10b）
When
θ 1≠ 90 °,
θ 2when=90 °
（10c）。
Beneficial effect of the present invention is as follows:
1, the location of spatial filter algorithm to structural impact is achieved.
2, signal processing does not need to rely on Lamb wave signal velocity of propagation structurally, realizes locating without velocity of wave of structural impact, thus eliminates complicated Aviation Composite Structure velocity of wave difference to the impact of im-pact location.
3, the present invention helps lend some impetus to the application of spatial filter algorithm in engineering structure health monitoring field.
Accompanying drawing explanation
Fig. 1 (a) is based on the linear piezoelectric transducer array of second vertical arrangement and the calm fast positioning method schematic diagram of the structural impact of spatial filter algorithm, and Fig. 1 (b) is based on the linear piezoelectric transducer array of two-dimensional parallel arrangement and the calm fast positioning method schematic diagram of the structural impact of spatial filter algorithm.
Fig. 2 is the signal processing flow figure of the calm fast positioning method of structural impact based on two-dimensional linear piezoelectric sensor array and spatial filter algorithm.
Fig. 3 is in embodiment, and piezoelectric sensor is arranged, the schematic diagram of structural impact position and two-dimensional direct angle coordinate system.
Fig. 4 (a) is the structural impact response signal of Line 1 piezoelectric sensor array, and Fig. 4 (b) is the structural impact response signal of No. 2 linear piezoelectric transducer arrays.
Fig. 5 (a) is the impulse response signal that in No. 2 linear piezoelectric transducer arrays, No. 1 piezoelectric sensor gathers, Fig. 5 (b) is the Fourier transform result of No. 1 piezoelectric sensor impulse response signal in No. 2 linear piezoelectric transducer arrays, Fig. 5 (c) is that in No. 2 linear piezoelectric transducer arrays, No. 1 piezoelectric sensor impulse response signal extracts and the 20kHz built impact arrowband Lamb wave complex signal through the continuous Complex Wavelet Transform of Shannon, Fig. 5 (d) is the Fourier transform result that in No. 2 linear piezoelectric transducer arrays, No. 1 piezoelectric sensor impulse response signal impacts the solid part signal of arrowband Lamb wave complex signal through the 20kHz that the continuous Complex Wavelet Transform of Shannon extracts.
Fig. 6 (a) is the real part oscillogram of structural impact response signal through the 20kHz impact arrowband Lamb wave complex signal that the continuous Complex Wavelet Transform of Shannon extracts of Line 1 piezoelectric sensor array, and Fig. 6 (b) is the real part oscillogram of structural impact response signal through the 20kHz impact arrowband Lamb wave complex signal that the continuous Complex Wavelet Transform of Shannon extracts of No. 2 linear piezoelectric transducer arrays.
Fig. 7 (a) is structural impact angle-damage probability curve that the 20kHz impact arrowband Lamb wave complex signal of Line 1 piezoelectric sensor array obtains after spatial filtering, and Fig. 7 (b) is structural impact angle---the damage probability curve that the 20kHz impact arrowband Lamb wave complex signal of No. 2 linear piezoelectric transducer arrays obtains after spatial filtering.
Embodiment
Below in conjunction with accompanying drawing, the invention is described in further details.
This method uses two-dimensional linear piezoelectric sensor array to gather the impulse response signal of monitored structure, the continuous Complex Wavelet Transform of Shannon is adopted to extract and build the arrowband Lamb wave complex signal composition in the impulse response signal of broadband, then the spatial filter algorithm utilizing velocity of wave to have nothing to do asks for the angle of structural impact relative to each linear piezoelectric transducer array, finally use the position coordinates impacting and calculate structural impact without velocity of wave ranging formula, thus achieve spatial filter algorithm locating without velocity of wave structural impact.
First according to monitoring structural health conditions mission requirements, structurally arrange two linear piezoelectric transducer arrays, require that the horizontal ordinate of Liang Tiao linear piezoelectric transducer array center's point, ordinate all can not be identical, that is:
x 1≠
x 2and
y 1≠
y 2, (
x 1,
y 1) be the central point of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the central point of No. 2 linear piezoelectric transducer arrays, thus form a two-dimentional monitored area, as shown in Figure 1 (a) and Fig 1 (b) shows.
Fig. 2 is the signal processing flow figure of the calm fast positioning method of structural impact that the present invention is based on two-dimensional linear piezoelectric sensor array and spatial filter algorithm: when structure is impacted, and two-dimensional linear piezoelectric sensor array gathers impulse response signal; The continuous Complex Wavelet Transform of Shannon is adopted to extract and build the arrowband Lamb wave complex signal composition in the impulse response signal of broadband; The filtering basic parameter of setting space wave filter; Article two, linear piezoelectric transducer array carries out spatial filtering to the impact arrowband Lamb wave complex signal extracted respectively, obtains the angle of structural impact position relative to each bar linear piezoelectric transducer array; Use the position coordinates impacting and calculate structural impact without velocity of wave ranging formula.
Embodiment test specimen is glass fibre epoxy composite panel, is of a size of 600mm × 600mm × 2mm, and ply stacking-sequence is [0
2/ 90
4/ 0
2]
2S, each layer thickness is 0.125mm.Sensing element is PZT-5 type piezoelectric sensor, and the diameter of piezoelectric sensor is 8mm, thickness is 0.4mm.Percussion tool uses mechanical type spring ram hammer, and impact head top is semisphere, and diameter is 10mm.Data acquisition equipment uses the aeronautic structure health monitoring systems of Nanjing Aero-Space University's independent research.
The present embodiment comprises the steps:
Step one: arrange two-dimensional linear piezoelectric sensor array
Adopt 7 piezoelectric sensors to form a homogenous linear piezoelectric sensor array, the distance of adjacent two piezoelectric sensor central points is 10mm.Use two-dimensional parallel arrangement, wherein the piezoelectric sensor label of Line 1 piezoelectric sensor array is from left to right followed successively by 1 ~ 7, and the piezoelectric sensor label of No. 2 linear piezoelectric transducer arrays is from left to right followed successively by 7 ~ 1.With the central point of Line 1 piezoelectric sensor array be true origin, axis is
xaxle, the direction perpendicular to array is
yaxle, builds two-dimensional direct angle coordinate system in composite panel, then the center point coordinate of No. 2 linear piezoelectric transducer arrays is (20mm, 500mm), and the monitored area of two-dimensional linear piezoelectric sensor array is 600mm × 500mm.The schematic diagram of Specimen Shape, piezoelectric sensor position and two-dimensional direct angle coordinate system as shown in Figure 3.
Step 2: gather structural impact response signal
Arrange aeronautic structure health monitoring systems and work in Passive Mode, test parameters is set to: trigger voltage is 3V, and pre-acquired length is 1000 sampled points, and sample frequency is 1MHz, and sampling length is 5000 sampled points.Mechanical type spring ram hammer is used to apply in (-110mm, 250mm) position to impact, as shown in Figure 3.Article two, the impulse response signal that arrives of linear piezoelectric transducer array acquisition is as shown in Fig. 4 (a) He Fig. 4 (b).
Step 3: extract and build and impact arrowband Lamb wave complex signal
The centre frequency of the continuous plural morther wavelet of Shannon is set
f c for the band width of the continuous plural morther wavelet of 20kHz, Shannon
f b for 8kHz, use formula (1):
extract and build the 20kHz arrowband Lamb wave complex signal in the impulse response signal of broadband.For the impulse response signal of No. 1 piezoelectric sensor in No. 2 linear piezoelectric transducer arrays, the continuous Complex Wavelet Transform of its Shannon is as Fig. 5 (a)---shown in Fig. 5 (d).Article two, the solid part signal of the impulse response signal of each piezoelectric sensor of linear piezoelectric transducer array after the continuous Complex Wavelet Transform of Shannon is as shown in Fig. 6 (a) He Fig. 6 (b).
Step 4: respectively spatial filtering is carried out to the impact arrowband Lamb wave complex signal of two linear piezoelectric transducer arrays
In the present embodiment, the maximum wave number value of the spatial filter of two linear piezoelectric transducer arrays is:
（11）
In formula:
k x, max
for the maximum filtering wave number value of Line 1 piezoelectric sensor array in the present embodiment and No. 2 linear piezoelectric transducer array manifold wave filters, △
xfor the array element distance of Line 1 piezoelectric sensor array and No. 2 linear piezoelectric transducer arrays in the present embodiment,
πfor circular constant constant.
The filtering angular range of setting space wave filter is 0 °--180 °, angular resolution is 1 °, carry out spatial filtering to impact arrowband Lamb wave complex signal, structural impact angle-damage probability curve that Line 1 piezoelectric sensor array and the filtering of No. 2 linear piezoelectric transducer arrays go out as shown in Figure 7.Can obtain structural impact position relative to the angle of Line 1 piezoelectric sensor array from Fig. 7 (a) and Fig. 7 (b) is 113.4 °, and structural impact position is 62.1 ° relative to the angle of No. 2 linear piezoelectric transducer arrays.
Step 4: structural impact is located without velocity of wave
Use and impact without velocity of wave ranging formula (10a):
the position coordinates calculating structural impact is:
（12）
Positioning result (-109mm, 254mm) is 4mm with the distance error of real impact position (-110mm, 250mm).
Claims (1)
1., based on the calm fast positioning method of structural impact of two-dimentional linear array and spatial filter, it is characterized in that, comprise the steps:
Step one: arrange two-dimensional linear piezoelectric sensor array
According to monitoring structural health conditions demand, the piezoelectric sensor array element of N number of same model is used to form a linear piezoelectric transducer array, structurally arrange two linear piezoelectric transducer arrays, horizontal ordinate, the ordinate of Liang Tiao linear piezoelectric transducer array center's point all can not be identical, that is:
x 1≠
x 2and
y 1≠
y 2, (
x 1,
y 1) be the central point of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the central point of No. 2 linear piezoelectric transducer arrays, thus form a two-dimensional structure Impact monitoring region, wherein N be greater than 2 integer;
Step 2: gather structural impact response signal
Setting structure impact sampling parameter, utilizes two-dimensional linear piezoelectric sensor array to gather structural impact response signal
f(
t);
Step 3: extract and build and impact arrowband Lamb wave complex signal
The continuous Complex Wavelet Transform of Shannon is adopted to extract and build structural impact response signal
f(
t) in impact arrowband Lamb wave complex signal composition
z(
t), as shown in Equation (1)
（1）
Wherein:
In formula:
z(
t) for impacting arrowband Lamb wave complex signal,
f(
w) be structural impact response signal
f(
t) Fourier transform, Ψ
shan-
a,b (
w) be the continuous plural mother wavelet function of Shannon
ψ shan-
a,b (
t) Fourier transform,
ψ shan-
a,b (
t) be the continuous plural mother wavelet function of Shannon,
afor the scale factor of the continuous plural morther wavelet of Shannon,
bfor the time factor of the continuous plural morther wavelet of Shannon,
f b for the band width of the continuous plural morther wavelet of Shannon,
f c for the centre frequency of the continuous plural morther wavelet of Shannon;
w c =2
π f c ;
w b =2
π f b ;
Step 4: to the impact arrowband Lamb wave complex signal of two linear piezoelectric transducer arrays
z(
t) carry out spatial filtering respectively
First the maximum filtering wave number value of spatial filter is asked for according to the array element distance of linear piezoelectric transducer array, as shown in Equation (2)
（2）
In formula:
k x, max
for the maximum filtering wave number value of this linear piezoelectric transducer array manifold wave filter, △
xfor the array element distance of this linear piezoelectric transducer array,
πfor circular constant;
Then according to monitoring structural health conditions mission requirements, filtering angular range and the angular resolution △ of spatial filter is determined
θ; One of them spatial filtering angle selected
θ, the wave number of spatial filter under this angle is calculated according to formula (3)
k x
（3）
According to formula (4), its spatial filtering weighting function is calculated to each array element in linear piezoelectric transducer array again
（4）
In formula:
φ(
x) for horizontal ordinate be
xthe spatial filtering weighting function of piezoelectric sensor,
xfor array element in linear piezoelectric transducer array is to the distance of linear array central point;
For the impact arrowband Lamb wave complex signal of each array element, use the spatial filtering weighting function of formula (4), calculate this array element and impact the response signal of arrowband Lamb wave complex signal after spatial filtering, then the filter response signal of each array element is synthesized, as the spatial filtering synthesis response signal of this angle lower linear piezoelectric sensor array, as shown in Equation (5)
（5）
In formula:
for spatial filtering angle
θthe spatial filtering synthesis response signal of lower linear piezoelectric sensor array,
nfor the element number of array of linear piezoelectric transducer array,
φ(
x n ) for horizontal ordinate be
x n the spatial filtering weighting function of piezoelectric sensor,
z(
x n ,
t) for horizontal ordinate be
x n the impact arrowband Lamb wave complex signal of piezoelectric sensor,
x n for the horizontal ordinate of array element;
This spatial filtering angle is calculated again according to formula (6)
θthe intensity of lower spatial filtering synthesis response signal
（6）
In formula:
e(
θ) be spatial filtering angle
θthe intensity of lower spatial filtering synthesis response signal,
for
θthe spatial filtering synthesis response signal of angle lower linear piezoelectric sensor array,
tfor spatial filtering synthesis response signal
signal length;
Choose next spatial filtering angle
θ+ △
θaccording to the intensity of the spatial filtering synthesis response signal of this angle lower linear piezoelectric sensor array of workflow management above, after treating that whole monitored areas angle calculation is complete, be normalized the spatial filtering synthesis response signal intensity of all angles is unified, angle-damage probability curve that generating structure impacts, wherein damage probability, " spatial filtering synthesis response signal intensity " the maximum angle after being namely normalization is the angle of impact position relative to this linear piezoelectric transducer array;
According to above flow process, computation structure impacts the angle-damage probability curve relative to another linear piezoelectric transducer array, and the angle that wherein damage probability is maximum is the angle of impact position relative to this linear piezoelectric transducer array;
Step 5: structural impact is located without velocity of wave
Because two linear piezoelectric transducer arranged in arrays are perpendicular or parallel two kinds of modes, so divide both of these case to carry out locating without velocity of wave to structural impact respectively here:
(1) when Line 1 piezoelectric sensor array is vertical with No. 2 linear piezoelectric transducer arrays
（7）
In formula:
θ 1for structural impact is relative to the angle of Line 1 piezoelectric sensor array,
θ 2for structural impact is relative to the angle of No. 2 linear piezoelectric transducer arrays, (
x 1,
y 1) be the center point coordinate of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the center point coordinate of No. 2 linear piezoelectric transducer arrays, (
x,
y) be the position coordinates of structural impact;
Solving the position coordinates that linear equation in two unknowns group (7) obtains structural impact is:
（8a）
When
θ 1=90 °,
θ 2when ≠ 90 °
（8b）
When
θ 1≠ 90 °,
θ 2when=90 °
（8c）
When
θ 1=90 °,
θ 2when=90 °
（8d）
(2) when Line 1 piezoelectric sensor array and No. 2 linear piezoelectric transducer array parallel
（9）
In formula:
θ 1for structural impact is relative to the angle of Line 1 piezoelectric sensor array,
θ 2for structural impact is relative to the angle of No. 2 linear piezoelectric transducer arrays, (
x 1,
y 1) be the center point coordinate of Line 1 piezoelectric sensor array, (
x 2,
y 2) be the center point coordinate of No. 2 linear piezoelectric transducer arrays, (
x,
y) be the position coordinates of structural impact;
Solving the position coordinates that linear equation in two unknowns group (9) obtains structural impact is:
（10a）
When
θ 1=90 °,
θ 2when ≠ 90 °
（10b）
When
θ 1≠ 90 °,
θ 2when=90 °
（10c）。
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