CN105651215B - A kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition - Google Patents
A kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition Download PDFInfo
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- CN105651215B CN105651215B CN201610165884.5A CN201610165884A CN105651215B CN 105651215 B CN105651215 B CN 105651215B CN 201610165884 A CN201610165884 A CN 201610165884A CN 105651215 B CN105651215 B CN 105651215B
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- 238000000034 method Methods 0.000 title claims abstract description 35
- 238000009675 coating thickness measurement Methods 0.000 title claims abstract description 8
- 239000000523 sample Substances 0.000 claims abstract description 61
- 238000000576 coating method Methods 0.000 claims abstract description 57
- 239000011248 coating agent Substances 0.000 claims abstract description 53
- 239000000463 material Substances 0.000 claims abstract description 30
- 239000011247 coating layer Substances 0.000 claims abstract description 20
- 238000001228 spectrum Methods 0.000 claims description 35
- 238000001514 detection method Methods 0.000 claims description 22
- 238000005259 measurement Methods 0.000 claims description 12
- CSCPPACGZOOCGX-UHFFFAOYSA-N Acetone Chemical compound CC(C)=O CSCPPACGZOOCGX-UHFFFAOYSA-N 0.000 claims description 6
- 238000004458 analytical method Methods 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000008878 coupling Effects 0.000 claims description 4
- 238000010168 coupling process Methods 0.000 claims description 4
- 238000005859 coupling reaction Methods 0.000 claims description 4
- 239000010410 layer Substances 0.000 claims description 4
- 239000011159 matrix material Substances 0.000 claims description 4
- 238000002604 ultrasonography Methods 0.000 claims description 4
- 238000013016 damping Methods 0.000 claims description 3
- 239000003960 organic solvent Substances 0.000 claims description 3
- 230000003746 surface roughness Effects 0.000 claims description 3
- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 claims description 2
- 239000012459 cleaning agent Substances 0.000 claims description 2
- 238000005070 sampling Methods 0.000 claims description 2
- 238000005516 engineering process Methods 0.000 abstract description 11
- 238000010183 spectrum analysis Methods 0.000 abstract description 6
- 238000007689 inspection Methods 0.000 abstract description 3
- 239000000203 mixture Substances 0.000 abstract description 3
- 238000009683 ultrasonic thickness measurement Methods 0.000 abstract description 3
- 230000001066 destructive effect Effects 0.000 abstract description 2
- 239000003822 epoxy resin Substances 0.000 description 3
- 229920000647 polyepoxide Polymers 0.000 description 3
- 229910000838 Al alloy Inorganic materials 0.000 description 2
- PEDCQBHIVMGVHV-UHFFFAOYSA-N Glycerine Chemical compound OCC(O)CO PEDCQBHIVMGVHV-UHFFFAOYSA-N 0.000 description 2
- 238000009434 installation Methods 0.000 description 2
- 239000000758 substrate Substances 0.000 description 2
- 241000208340 Araliaceae Species 0.000 description 1
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical group [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 230000002745 absorbent Effects 0.000 description 1
- 239000002250 absorbent Substances 0.000 description 1
- 238000010521 absorption reaction Methods 0.000 description 1
- 239000011230 binding agent Substances 0.000 description 1
- 230000032798 delamination Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 239000000428 dust Substances 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 239000003344 environmental pollutant Substances 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 235000011187 glycerol Nutrition 0.000 description 1
- -1 greasy dirt Substances 0.000 description 1
- 230000008676 import Effects 0.000 description 1
- 239000006101 laboratory sample Substances 0.000 description 1
- 210000003739 neck Anatomy 0.000 description 1
- 238000010422 painting Methods 0.000 description 1
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- 238000003672 processing method Methods 0.000 description 1
- 241000894007 species Species 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B17/00—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations
- G01B17/02—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations for measuring thickness
- G01B17/025—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations for measuring thickness for measuring thickness of coating
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- Investigating Or Analyzing Materials By The Use Of Ultrasonic Waves (AREA)
- Length Measuring Devices Characterised By Use Of Acoustic Means (AREA)
Abstract
A kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition, belongs to material ultrasonic non-destructive inspection techniques field.The measuring method includes the ultrasonic pulse-echo detecting system of reflectoscope, delay block probe, digital oscilloscope and the computer composition for installing MATLAB softwares using a set of.It is unknown and there is fluctuation under different technical parameters or heterogeneous conditions and cause the problem of coating layer thickness can not be measured for echo-signal aliasing, the velocity of sound during coating ultrasonic thickness measurement, using ultrasonic pulse-echo technology, inverting is carried out simultaneously to sample coatings thickness and velocity of ultrasonic sound with reference to ultrasonic sound pressure reflection coefficient amplitude spectral analysis method and Relative coefficient.The measuring method have the advantages that definite principle, be easily achieved, matching precision it is high, overcome that existing Gauss-Newton inversion method computing is complicated, initial value is chosen require limitation that is higher, being difficult to use in engineer applied, with good prospect for promotion and application.
Description
Technical field
The present invention relates to a kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition, belong to the inspection of material ultrasonic non-destructive
Survey technology field.
Background technology
Coating material is widely used to many necks such as Aero-Space, oil-gas transportation, automobile making and biomedical engineering
Domain, occupies more and more consequence in field of engineering technology.In a series of indexs for characterizing coating performance, thickness is not only
It is a parameter for characterizing coating itself physical dimension, and performance to coating and life-span have a significant impact, coating layer thickness
Do not reach or be all unable to reach desired effects more than design load, and thickness is excessive or uneven is also possible to reduce its bond strength
And service life, cause coating plasticity to be deteriorated and even result in coating localized delamination.Therefore, accurate measurement is carried out to thickness has turned into
Ensure the important means of coating performance.
In existing coating thickness measurement technology, ultrasonic pulse-echo technology is due to definite principle, realizing simple, non-demolition
Property and it is applied widely the advantages of, among the thickness measure for being widely used in layered medium material.When coating layer thickness compared with
Greatly, its thickness can be surveyed by traditional ultrasonic transit time method when aliasing does not occur for coating surface ripple and interface echo
Amount；When coating layer thickness is relatively thin, and the propagation time of ultrasonic wave in the coating is less than its pulse width, coating surface ripple and boundary wave
Will occur aliasing, ultrasonic transit time method is no longer applicable.Will by sound pressure reflection coefficient amplitude spectral analysis method (URCAS)
Time-domain signal, which transforms to frequency domain progress processing, can effectively solve this problem.However, found during ultrasonic thickness measurement, no matter
It is that ultrasonic transit time method or URCAS signal processing methods are required to the velocity of sound of coating for known quantity, but due to by technique
The influence of the factors such as parameter, Coating Non-Uniformity, the velocity of sound of coating is often to be unknown and there is certain fluctuation in diverse location.
Zhao Yang, Lin Li etc. propose to use the Gaussian-Newton method progress inverting based on binary nonlinear equation, can be in the coating velocity of sound
Its thickness and velocity of ultrasonic sound are determined in the case of unknown simultaneously, and it is excellent that this method has that local convergence speed is fast, matching precision is high etc.
Point, but higher is required to the selection of initial value, if initial value selection is improper to this may result in only converging to locally optimal solution very
Do not restrained to equation, it is impossible to obtain inversion result.It is real to coating sample present invention introduces the Relative coefficient in statistics
Survey sound pressure reflection coefficient amplitude spectrum and apply shelf theory sound pressure reflection coefficient amplitude spectrum matrix in the range of ultrasound detection effective band
The matching analysis is carried out one by one, and the thickness of thin layer and the velocity of sound of correspondence maximum correlation coefficient are optimal inversion result.
The content of the invention
It is an object of the invention to provide a kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition.This method is used
It is a set of to include the ultrasound of reflectoscope, delay block probe, digital oscilloscope and the computer composition for installing MATLAB softwares
Pulse echo detecting system.For echo-signal aliasing, the velocity of sound during coating ultrasonic thickness measurement it is unknown and different process ginseng
There is fluctuation under number or heterogeneous conditions and cause the problem of coating layer thickness can not be measured, using ultrasonic pulse-echo technology, with reference to
Ultrasonic sound pressure reflection coefficient amplitude spectral analysis method and Relative coefficient enter simultaneously to sample coatings thickness and velocity of ultrasonic sound
Row inverting.This method have the advantages that definite principle, be easily achieved, matching precision it is high, overcome existing Gauss-Newton inverting side
Method computing is complicated, requirement limitation that is higher, being difficult to use in engineer applied is chosen to initial value, with good popularization and application
Prospect.
The technical solution adopted for the present invention to solve the technical problems is：A kind of painting thickness under velocity of ultrasonic sound unknown condition
Measuring method is spent, using a set of including super supersonic detector, delay block probe, digital oscilloscope and installation MATLAB softwares
Computer constitute ultrasonic pulse-echo detecting system；The measuring method uses the following steps：
(a) specimen surface is handled
Tested coating sample surface is handled using absolute ethyl alcohol or acetone cleaning agent, removes what specimen surface was present
Greasy dirt, organic solvent pollution thing, are suitably polished, it is ensured that sample using the fine sandpaper position larger to specimen surface roughness
Surfacing, and suitable couplant guarantee delay block probe and the good coupling being tested between coating sample are chosen according to coating characteristic
Close；
(b) material properties are determined
Understand density, the velocity of sound of acoustic attenuation coefficient and probe delay block and base material, the density of tested sample coating
Material properties, respective acoustic impedance is calculated according to the velocity of sound and density of probe delay block and base material；
(c) ultrasonic probe is chosen
Suitable delay block ultrasound is chosen according to tested sample coating layer thickness, acoustical damping properties and the requirement to accuracy of detection
Probe, acoustic attenuation thin to coating layer thickness is small, accuracy of detection requires high, and thickness measuring precision is improved from high frequency probe；To coating layer thickness
Greatly, acoustic attenuation is serious, accuracy of detection requires low, and echo-signal can not be known caused by avoiding high frequency attenuation serious from low-frequency probe
Not；
(d) parameter setting is detected
Pulse recurrence frequency PRF, ENERGY E nergy, gain G ain, wave filter are arranged as required on reflectoscope
Bandwidth detection parameter；
(e) data acquisition
According to step (a)-(d) completion specimen surfaces are handled, material properties are determined, probe is chosen and detection parameter is set
Postpone, then delay block probe is placed in tested sample surface by one delay block time domain echo-signal of collection as reference signal,
Digital oscilloscope gain, detecting way, average time, sampling frequency parameters are adjusted, complete, stable coating tim e- domain detection is obtained
Signal；
(f) coating sound pressure reflection coefficient amplitude spectrum is calculated
The time-domain signal that digital oscilloscope is collected is imported in computer, and FFT is carried out to it using data processing software
Conversion obtains the amplitude spectrum of reference signal | A (f) | and the amplitude spectrum of detection signal | A (f) |*, effective frequency is obtained according to formula (1)
Bandwidth undercoating surveys sound pressure reflection coefficient amplitude spectrum | r (f；d,c2)|*：
The material properties parameter obtained in step (b) is updated in formula (2) and obtains the internally coated theory of effective bandwidth
Sound pressure reflection coefficient amplitude spectrum | r (f；d,c2)|：
In formula, subscript 1,2,3 represents probe delay block, coating and base material, r respectively12、r23To represent heterogeneous material
It is thickness of thin layer, c to expect the sound pressure reflection coefficient at interface, d2It is respectively the rate of sound and attenuation of sound coefficient of coating with α (f)；
(g) correlation coefficient matching method is analyzed
By assigning formula (2) coating thickness d and velocity of sound c2A series of consecutive variations values, obtain theoretical sound pressure reflection system
Number amplitude spectrum matrix is as parent, and the reflectance magnitude obtained using formula (3) to theoretical calculation is composed | r (f) | and actual inspection
The reflectance magnitude spectrum measured | r (f) |*Carry out the matching analysis, correlation coefficient r one by one in -6dB effective bandsp(d,c2) most
Big position corresponding d and c2The as optimal inversion result of tested sample coating layer thickness and the velocity of sound：
Wherein, N represents data points of the time-domain signal after FFT in the range of effective band, and subscript i represents i-th
Individual frequency values；|r(f；d,c2) | with | r (f；d,c2)|*The theoretical sound pressure reflection coefficient amplitude with actual measurement respectively in effective band
Spectrum,WithThe theoretical arithmetic with the sound pressure reflection coefficient amplitude spectrum of actual measurement respectively in effective band
Average value.
The invention has the advantages that：Coating thickness measurement method under this velocity of ultrasonic sound unknown condition is using a set of
The ultrasonic pulse that computer including reflectoscope, delay block probe, digital oscilloscope and installation MATLAB softwares is constituted
Echo detecting system, coating layer thickness is conjointly employed in by sound pressure reflection coefficient amplitude spectral analysis technology and Relative coefficient
Among Ultrasonic NDT.The ultrasonic time domain echo-signal of coating is obtained using ultrasonic pulse-echo technology, sound pressure reflection is utilized
Coefficient amplitude spectral analysis technology is extracted to ultrasonic feature parameter, by between actual measurement and theoretical sound pressure reflection coefficient amplitude spectrum
Relevant matches are analyzed, and the binary nonlinear equation without solving complexity is anti-while coating layer thickness can be achieved with velocity of ultrasonic sound
Drill, overcome complicated existing Gauss-Newton inversion method computing, initial value selection difficulty, the limitation for being difficult to use in engineer applied
Property.This method have the advantages that definite principle, be easily achieved, matching precision it is high, with good prospect for promotion and application.
Brief description of the drawings
Patent of the present invention is described further with reference to the accompanying drawings and examples.
The hardware connection diagram of Fig. 1 ultrasonic pulse-echo detecting systems.
Fig. 2 reference signal y (t) and its corresponding amplitude spectrum | A (f) |.
Fig. 3 coatings detection signal y (t)*And its corresponding amplitude spectrum | A (f) |*。
Fig. 4-6dB effective frequency belt widths undercoating surveys sound pressure reflection coefficient amplitude spectrum | r (f；d,c2)|*。
Fig. 5 different-thickness combines corresponding correlation coefficient r with the velocity of soundp(d,c2)。
Fig. 6 is surveyed to be contrasted with the sound pressure reflection coefficient amplitude spectrum under optimal coupling condition.
In figure：1st, supersonic detector, 2, delay block probe, 3, coating, 4, base material, 5, digital oscilloscope, 6, meter
Calculation machine.
Embodiment
USIP40 supersonic detectors, the delay block of the ultrasonic pulse-echo detecting system that this method is used as shown in Figure 1
Probe and the computer composition for being provided with MATLAB softwares.Laboratory sample in the present embodiment is magnetic loss type radar-wave absorbing
Coating sample (absorbent is carbonyl iron dust, and binding agent main component is epoxy resin, and base material is flat aluminium alloy plate), coating
Thickness and velocity of ultrasonic sound are unknown quantity, coating time domain echo-signal are obtained using ultrasonic pulse-echo technology, with reference to ultrasonic sound
Pressure reflectance magnitude spectral analysis method and Relative coefficient carry out inverting simultaneously to sample coatings thickness and velocity of ultrasonic sound.
Methods described uses the following steps：
(a) specimen surface is handled.Tested coating sample surface is handled using acetone, removing specimen surface may deposit
The pollutant such as greasy dirt, organic solvent, suitably polished using the fine sandpaper position larger to specimen surface roughness, really
Protect specimen surface smooth, and glycerine is chosen as couplant guarantee delay block probe according to coating characteristic and is tested between coating sample
Good coupling.
(b) material properties are determined.Understand density, acoustic attenuation coefficient and probe delay block and the substrate of tested sample coating
The material properties such as the velocity of sound, the density of material.Known coating species is magnetic loss type absorption coating, thickness is about 0.2mm, close
Spend for 3290kg/m3, acoustic attenuation coefficient α (f)=1.47f+8.51E (- 4) f4；Delay block of material is epoxy resin, and the velocity of sound is
2316.6m/s, density is 1045.5kg/m3；Aluminum alloy substrate acoustic velocity of material is that 6480m/s, density are 2700kg/m3。
(c) ultrasonic probe is chosen.Chosen according to tested sample coating layer thickness, acoustical damping properties and the requirement to accuracy of detection
Suitable delay block ultrasonic probe.If coating layer thickness is relatively thin, acoustic attenuation is smaller, accuracy of detection requires high, high frequency should be selected
Pop one's head in improve thickness measuring precision；If coating layer thickness is larger, acoustic attenuation is serious, accuracy of detection requires relatively low, low frequency should be selected
Probe is with echo-signal None- identified caused by avoiding high frequency attenuation serious.Because acoustic attenuation is more serious in microwave absorbing coating, this
Embodiment is from Olympus 5MHz monocrystalline ultrasonic probes and is equipped with a diameter of 6mm epoxy resin delay block and is detected.
(d) parameter setting is detected.Pulse recurrence frequency PRF is set on USIP40 reflectoscopes：500Hz, energy
Energy：10 μ J, gain G ain：20dB, filter bandwidht：0-10MHz.
(e) data acquisition.According to step (a)-(d) completion specimen surfaces are handled, material properties are determined, probe is chosen
A delay block time domain echo-signal y (t) is gathered first as reference signal with after detection parameter setting, then visits delay block
Head is placed in tested sample surface, adjusts the gain of parameter such as digital oscilloscope gain, detecting way, average time, sample frequency complete
Whole, stable coating tim e- domain detection signal y (t)*。
(f) coating sound pressure reflection coefficient amplitude spectrum is calculated.The time-domain signal that digital oscilloscope is collected imports computer
In, the amplitude spectrum that FFT obtains reference signal is carried out to it using data processing software | A (f) | and the amplitude of detection signal
Spectrum | A (f) |*, -6dB effective frequency belt widths undercoating actual measurement sound pressure reflection coefficient amplitude spectrum is obtained according to formula (1) | r (f；d,
c2)|*：
The material properties obtained in step (b) are updated in formula (2) and obtain the internally coated theory of -6dB effective bandwidths
Sound pressure reflection coefficient amplitude spectrum | r (f；d,c2)|：
In formula, subscript 1,2,3 represents probe delay block, coating and base material, r respectively12、r23To represent heterogeneous material
It is thickness of thin layer, c to expect the sound pressure reflection coefficient at interface, d2It is respectively the rate of sound and attenuation of sound coefficient of coating with α (f).
(g) correlation coefficient matching method is analyzed.By assigning formula (2) coating thickness d and velocity of sound c2A series of consecutive variations
Value, obtains theoretical sound pressure reflection coefficient amplitude spectrum matrix as parent, the reflectance factor obtained using formula (3) to theoretical calculation
Amplitude spectrum | r (f) | and the actually detected reflectance magnitude spectrum arrived | r (f) |*Carry out matching point one by one in -6dB effective bands
Analysis, correlation coefficient rpThe corresponding d of (d, c2) maximum position and c2 is tested sample coating layer thickness and the optimal inverting knot of the velocity of sound
Really.
Wherein, N represents data points of the time-domain signal after FFT in the range of effective band, and subscript i represents i-th
Individual frequency values；|r(f；d,c2) | with | r (f；d,c2)|*The theoretical sound pressure reflection coefficient amplitude with actual measurement respectively in effective band
Spectrum,WithThe theoretical arithmetic with the sound pressure reflection coefficient amplitude spectrum of actual measurement respectively in effective band
Average value.
As shown in table 1, absolute error is 5 μ between coating layer thickness inversion result and actual measurement parameter for inversion result and measurement error
M-8 μm, relative error be 2.53%-3.72%, between the velocity of sound and actual value absolute error be 4.3m/s-6.4m/s, relative error
For 2.51%-3.75%, engineering detecting requirement is met.
The microwave absorbing coating sample parametric inversion result of table 1 and error
Claims (1)
1. a kind of coating thickness measurement method under velocity of ultrasonic sound unknown condition, it is characterized in that：Visited using a set of including ultrasonic wave
Hinder instrument, delay block probe, digital oscilloscope and the ultrasonic pulse-echo detection system that the computer of MATLAB softwares is constituted is installed
System；The measuring method uses the following steps：
(a) specimen surface is handled
Tested coating sample surface is handled using absolute ethyl alcohol or acetone cleaning agent, the oil that specimen surface is present is removed
Dirty, organic solvent pollution thing, is suitably polished, it is ensured that sample table using the fine sandpaper position larger to specimen surface roughness
Face is smooth, and chooses suitable couplant guarantee delay block probe and the good coupling being tested between coating sample according to coating characteristic
Close；
(b) material properties are determined
Understand the density, the velocity of sound of acoustic attenuation coefficient and probe delay block and base material, density material of tested sample coating
Attribute, respective acoustic impedance is calculated according to the velocity of sound and density of probe delay block and base material；
(c) ultrasonic probe is chosen
Suitable delay block ultrasound is chosen according to tested sample coating layer thickness, acoustical damping properties and the requirement to accuracy of detection to visit
Head, acoustic attenuation thin to coating layer thickness is small, accuracy of detection requires high, and thickness measuring precision is improved from high frequency probe；To coating layer thickness
Greatly, acoustic attenuation is serious, accuracy of detection requires low, and echo-signal can not be known caused by avoiding high frequency attenuation serious from low-frequency probe
Not；
(d) parameter setting is detected
Pulse recurrence frequency PRF, ENERGY E nergy, gain G ain, filter bandwidht are arranged as required on reflectoscope
Detect parameter；
(e) data acquisition
According to step (a)-(d) completion specimen surfaces are handled, material properties are determined, probe is chosen and detection parameter setting
Afterwards, a delay block time domain echo-signal is gathered as reference signal, and delay block probe is then placed in tested sample surface, adjusted
Whole digital oscilloscope gain, detecting way, average time, sampling frequency parameters, obtain complete, stable coating tim e- domain detection letter
Number；
(f) coating sound pressure reflection coefficient amplitude spectrum is calculated
The time-domain signal that digital oscilloscope is collected is imported in computer, and FFT is carried out to it using data processing software
Obtain the amplitude spectrum of reference signal | A (f) | and the amplitude spectrum of detection signal | A (f) |*, effective band is obtained according to formula (1) wide
Spend undercoating actual measurement sound pressure reflection coefficient amplitude spectrum | r (f；d,c2)|*：
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Reflectance magnitude is composed | r (f；d,c2)|：
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In formula, subscript 1,2,3 represents probe delay block, coating and base material, r respectively12、r23To represent Bimaterial in terface
Sound pressure reflection coefficient, d be thickness of thin layer, c2It is respectively the rate of sound and attenuation of sound coefficient of coating with α (f)；
(g) correlation coefficient matching method is analyzed
By assigning formula (2) coating thickness d and velocity of sound c2A series of consecutive variations values, obtain theoretical sound pressure reflection coefficient width
Spectrum matrix is spent as parent, the reflectance magnitude spectrum obtained using formula (3) to theoretical calculation | r (f) | arrived with actually detected
Reflectance magnitude spectrum | r (f) |*Carry out the matching analysis, correlation coefficient r one by one in -6dB effective bandsp(d,c2) dominant bit
Put corresponding d and c2The as optimal inversion result of tested sample coating layer thickness and the velocity of sound：
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Wherein, N represents data points of the time-domain signal after FFT in the range of effective band, and subscript i represents i-th of frequency
Rate value；|r(f；d,c2) | with | r (f；d,c2)|*The theoretical sound pressure reflection coefficient amplitude spectrum with actual measurement respectively in effective band,WithThe theoretical arithmetic average with the sound pressure reflection coefficient amplitude spectrum of actual measurement respectively in effective band
Value.
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