CN110308206A - Based on EMD generalized phase arrangement entropy to the discrimination method of close metal material - Google Patents

Based on EMD generalized phase arrangement entropy to the discrimination method of close metal material Download PDF

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CN110308206A
CN110308206A CN201910731126.9A CN201910731126A CN110308206A CN 110308206 A CN110308206 A CN 110308206A CN 201910731126 A CN201910731126 A CN 201910731126A CN 110308206 A CN110308206 A CN 110308206A
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贺西平
马明明
张小凤
贺升平
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Shaanxi Normal University
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    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04Analysing solids
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention belongs to metal material Ultrasonic Nondestructive technical fields, more particularly to a kind of discrimination method based on based on EMD generalized phase arrangement entropy to close metal material, mainly pre-processed by metal material, acquire ultrasonic original signal, empirical mode decomposition extracts high-frequency signal, determine that identification can be completed in the arrangement entropy comparison of high-frequency signal generalized phase, the present invention is that the Ultrasonic Nondestructive technology based on EMD generalized phase arrangement plan method is applied to close metal material identification field for the first time, or damage pollution-free to detection metal material, it is quick time saving, identification effect is stablized, tool has significant practical applications.

Description

Based on EMD generalized phase arrangement entropy to the discrimination method of close metal material
Technical field
The invention belongs to metal Undamaged determination technical fields, in particular to a kind of to arrange entropy to phase based on EMD generalized phase The discrimination method of nearly metal material.
Background technique
The development of industrial technology is inseparable with metal material, and existing mineral resources can no longer meet the need of economic development It asks, properties similar metals material can be used as the substitute of production and living, but the fields pair such as some aspects are for example military, space flight The specific demand of metal material, needs whether strict inspection metal material meets the requirements, therefore metal material clustering recognition is increasingly It is important.
Traditional metal material discrimination method has physics identification and chemistry identification.Wherein, physics identification is by metal What Macroscopic physical feature or its microscopic feature shown in physical process carried out.Common method has sense organ identification, breaks Mouth identification and spark identification etc..Due to physics discrimination method is simple, conveniently, easy to operate, live property it is good and analyze precision can From qualitative to sxemiquantitative, for general common metal material, these methods have been able to satisfy requirement, but there are also-fixed limitation, Such as some discrimination methods damage, and these method errors are all bigger, it is sometimes not bery accurate.Chemistry identification is to pass through Chemical reaction analyzes the constituent of metal to recognize the method for being which kind of metal.Common chemical composition analysis method has titration Analysis method, gravimetry and volumetric analysis etc..Chemical discrimination method is unable to on-line analysis, more complex and damage.For The anti-counterfeiting identification of precious metal material or precious metal collection in practice, these methods are obviously very improper.
The abundant information that material internal and surface texture are not only carried in the echo-signal that ultrasonic testing system obtains, can also Characterize the heterogeneous microstructure of metal material.Therefore Ultrasonic NDT is used, gold is extracted based on EMD generalized phase arrangement plan method Belong to the feature of material as label, is used for Fast Identification.
Summary of the invention
In order to overcome the shortcomings of the prior art, the present invention provides one kind to arrange entropy pair based on EMD generalized phase The discrimination method of close metal material can rapidly identify different metal materials, realize the lossless of metal material Identify.
The technical scheme adopted by the invention is that:
Of the invention arranges entropy to the discrimination method of close metal material based on EMD generalized phase, comprises the steps of:
(1) time-domain signal is acquired
Transmitting-receiving probe is connect with pulse reception/transmitter, couplant is added and is placed in the surface with reference to metal material, ultrasound Probe transmitting pulse signal, by received with pulse/oscillograph that connect of transmitter is to the received echo-signal of transmitting-receiving probe It is sampled, through multiple repairing weld and is averaged, obtain the time domain waveform with reference to metal material;
(2) characteristic component is extracted
Successively divided using Empirical mode decomposition time domain waveform X (t) with reference to metal material collected to step (1) It solves, then the characteristic component entropy g of the echo-signal with reference to metal material is calculated with generalized phase arrangement plan methodq,δ;It is described Generalized phase arrangement plan method formula are as follows:
Wherein, v represents the position of data sequence in the characteristic signal extracted with reference to metal material, PVIt represents and refers to metal material Expect the probability of same position sequence occur in the characteristic signal data sequence extracted;Q is represented in amplification metal material characteristic signal There is the value of same position probability, δ, which is represented in the amplification metal material characteristic signal of index again, there is the value of same position probability, R, which is represented, amplifies the real number value that the same position probability for the characteristic signal data sequence extracted can be chosen, R ∈ (0,1];
(3) characteristic component of material to be detected is extracted
The characteristic component entropy of the echo-signal of material to be detected is extracted with step (1) and the identical method of step (2);
(4) characteristic component compares
By the reference gold of the characteristic component entropy of the echo-signal of the obtained material to be detected of step (3) and step (2) The characteristic component entropy for belonging to the echo-signal of material is compared, if the two is consistent, detected materials and reference metal material are same Matter completes identification;Otherwise, step (5) is carried out;
(5) it repeats to compare
Another metal material for being different from step (1) is chosen as metal material is referred to, repeats step (1)~(4), directly To the material for determining detected materials.
It further limits, the step (2) specifically:
2.1) identification step (1) acquires the local extremum of the time domain waveform signal X (t) with reference to metal material, connects pole Big value obtains coenvelope line, and connection minimum obtains lower envelope line, obtains equal value sequence m according to upper and lower envelope1
2.2) empirical mode decomposition is carried out to original signal using following formula, determines IMF component;
X(t)-mi(t)=hi(t), i ∈ n
mi(t) the equal value sequence of i-th of signal to be decomposed or more envelope line computation is represented;hi(t) i-th decomposed is represented Characteristic component;
Work as hi(t) meet following two condition: being Local Symmetric and zero point and extreme point number phase about zero-mean line Deng;When the mean value of envelope up and down that signal local maximum and minimum define is 0, then hiIt (t) is IMF component;
2.3) the characteristic component entropy of the IMF component of step (2.2) decomposition is determined using generalized phase arrangement plan method, Middle generalized phase arrangement plan method formula are as follows:
It further limits, the step (2.3) is specially
(2.3.1) seeks the instantaneous phase sequence θ of each IMF signal with reference to metal material using Hilbert transform method (i), sequence length N;
(2.3.2) carries out phase space reconfiguration to the instantaneous phase sequence θ (i) that step (2.3.1) acquires, and obtains reproducing sequence Zj, reproducing sequence number is N- (m-1) * t;
Zj=[θ (j), θ (j+t) ..., θ (j+ (m-1) t)], 1≤j≤N- (m-1) t
Wherein m is phase space reconfiguration dimension, and t is the time delay of reconstruct;
(2.3.3) is by reproducing sequence ZjK is arranged as by numerical value ascending order1,k2,…km, obtain position sequence Sj, and determine position The identical sequence number of sequence, is denoted as Numv
Sj=(k1,k2,…km), 1≤j≤N- (m-1) τ
(2.3.4) using step (2.3.3) various arrangements occur frequency as its probability, then obtain various arrangements Probability is
(2.3.5) utilizes two parameter entropy Sq,δDefine it is appropriate go out with reference to metal material echo-signal characteristic component entropy Value gq,δ,
It further limits, the pulse voltage of the pulse reception/transmitter is 100~300V, pulse recurrence frequency 100 ~300Hz;Oscillograph sampling rate is 100MHz~5GHz, and sampling number is 1000~5000 times;Receive and dispatch the center frequency of probe Rate is 1~10MHz.
It further limits, the couplant is water or glycerol.
Further limit, it is described with reference to metal material be pure metal or alloy, intermetallic compound and special metal material, The pure metal material be beryllium, magnesium, aluminium, indium, germanium, tin, lead, antimony, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, zinc, yttrium, zirconium, niobium, molybdenum, Ruthenium, rhodium, palladium, silver, cadmium, hafnium, tantalum, tungsten, iridium, platinum or gold.
Of the invention arranges entropy to the discrimination method of close metal material based on EMD generalized phase, mainly utilizes metal Material internal microstructural differences extract the characteristic component of significant difference, using EMD generalized phase arrangement plan method to otherness Characteristic component handled, realize the ultrasonic wave Undamaged determination of close metal material, compared with prior art, have it is following excellent Point:
(1) method of the invention only needs to make ultrasonic wave transmitting probe that inspection can be completed from a certain face contact object to be detected It surveys, damage or pollution will not be generated to material itself, easy to operate, safety, equipment is light, quick time saving.
(2) identification identification effect of the invention is stablized, using EMD generalized phase arrangement plan method to the significant difference of extraction The signal characteristic component of property is handled, and algorithm is simple, and speed is fast, and error is small, can be realized accurate identification.
(3) two parameter entropy Sq, δ, adjustment parameter q and δ have been firstly introduced in discrimination method of the invention, it being capable of amplification time Nuance in sequence also introduces the phase information of time series, however it is functional independence that Phase synchronization is associated with amplitude Phenomenon, and phase information includes more key messages, keeps extraction metal material characteristic quantity identification effect significant.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of time-domain signal acquisition system.
Fig. 2 is the time domain waveform with reference to metal material.
Fig. 3 is the exploded view of the time domain waveform with reference to metal material.
Specific embodiment
Technical solution of the present invention is further described now in conjunction with embodiment.
Of the invention comprises the steps of the discrimination method of close metal material based on EMD generalized phase arrangement entropy:
(1) time-domain signal is acquired
Referring to Fig. 1, signal acquisition is carried out using the time-domain signal acquisition system of Fig. 1, is 1~10MHz by centre frequency Transmitting-receiving probe connect with pulse reception/transmitter that pulse voltage is 100~300V, repetition rate is 100~300Hz, general Couplant water or glycerol are applied to the surface with reference to metal material, and ultrasonic probe emits pulse signal, transmitted/received by connecing with pulse The oscillograph for penetrating instrument connection samples the received echo-signal of transmitting-receiving probe, and sampling rate is 100MHz~5GHz, is adopted It is averaged for sample 1000~5000 times, obtains the time domain waveform with reference to metal material, referring to fig. 2;
(2) characteristic component is extracted
Successively divided using Empirical mode decomposition time domain waveform X (t) with reference to metal material collected to step (1) Referring to Fig. 3, then the characteristic component entropy of the echo-signal with reference to metal material is calculated with generalized phase arrangement plan method in solution gq,δ;Specifically:
2.1) local extremum of identification step (1) time domain waveform signal X (t) collected, connection maximum obtain packet Winding thread, connection minimum obtain lower envelope line, obtain equal value sequence m according to upper and lower envelope1
2.2) empirical mode decomposition is carried out using following formula clock synchronization domain plethysmographic signals, determines IMF component;
X(t)-mi(t)=hi(t), i ∈ n
Mi (t) represents the equal value sequence of signal to be decomposed or more envelope line computation;Hi (t) represents the characteristic component decomposed;
Conversion are as follows:
h1(t)=X (t)-m1(t)
h2(t)=h1(t)-m2(t)
hi(t)=hi-1(t)-mi(t)
I operation is repeated, by IMF1It is come out from time domain waveform Signal separator, surplus r1(t) the original letter new as one Number, circulation executes decomposition step;After nth iteration calculates, the r that is shown below is obtainedn(t), work as rn(t) when tending to monotonic function, It decomposes and terminates.
r2(t)=r1(t)-IMF2(t)
r3(t)=r2(t)-IMF3(t)
…………
rn(t)=rn-1(t)-IMFn(t)
Wherein rn (t) indicates to decompose the average tendency of remainder and signal;
The decomposition of instant domain plethysmographic signal is shown below, and obtains n IMF component and a surplus rn,
When hi (t) meets following two condition: being Local Symmetric and zero point and extreme point number phase about zero-mean line Deng;The mean value of envelope up and down that signal local maximum and minimum define is 0, then hi (t) is IMF component;
2.3) the characteristic component entropy for the IMF component that step (2.2) are decomposed is calculated using generalized phase arrangement plan method, i.e.,
(2.3.1) seeks the instantaneous phase sequence θ (i) with reference to metal material IMF signal, sequence using Hilbert transform method Column length is N;
(2.3.2) carries out phase space reconfiguration to the instantaneous phase sequence θ (i) that step (2.3.1) acquires, and obtains reproducing sequence Zj, reproducing sequence number is N- (m-1) * t;
Zj=[θ (j), θ (j+t) ..., θ (j+ (m-1) t)], 1≤j≤N- (m-1) t
Wherein m is phase space reconfiguration dimension, and t is the time delay of reconstruct;
(2.3.3) is by reproducing sequence ZjK is arranged as by numerical value ascending order1,k2,…km, obtain position sequence Sj, and determine position The identical sequence number of sequence, is denoted as Numv
Sj=(k1,k2,…km), 1≤j≤N- (m-1) τ
(2.3.4) using step (2.3.3) various arrangements occur frequency as its probability, then obtain various arrangements Probability is
(2.3.5) utilizes two parameter entropy Sq,δDefinition calculate the characteristic component entropy of the echo-signal with reference to metal material Value gq,δ
Wherein, v represents the position of data sequence in the characteristic signal extracted with reference to metal material, PVIt represents and refers to metal material Expect the probability of same position sequence occur in the characteristic signal data sequence extracted;Q is represented in amplification metal material characteristic signal There is the value of same position probability, δ, which is represented in the amplification metal material characteristic signal of index again, there is the value of same position probability, R, which is represented, amplifies the real number value that the same position probability for the characteristic signal data sequence extracted can be chosen, R ∈ (0,1];
(3) characteristic component of material to be detected is extracted
The characteristic component entropy of the echo-signal of material to be detected is extracted with step (1) and the identical method of step (2);
(4) characteristic component compares
By the reference gold of the characteristic component entropy of the echo-signal of the obtained material to be detected of step (3) and step (2) The characteristic component entropy for belonging to the echo-signal of material is compared, if the two is consistent, detected materials and reference metal material are same Matter completes identification;Otherwise, step (5) is carried out;
(5) it repeats to compare
Another metal material for being different from step (1) is chosen as metal material is referred to, repeats step (1)~(4), directly To the material for determining detected materials.
Metal material to be detected of the invention can be beryllium, magnesium, aluminium, indium, germanium, tin, lead, antimony, titanium, vanadium, chromium, manganese, iron, The pure metal such as cobalt, nickel, zinc, yttrium, zirconium, niobium, molybdenum, ruthenium, rhodium, palladium, silver, cadmium, hafnium, tantalum, tungsten, iridium, platinum or gold or its alloy or gold Compound and special metal material between category.
Embodiment 1
Using 304 stainless steels of known mark as metal material is referred to, three kinds of material profiles are cylindrical body, thickness 15mm, diameter 47.1mm, detected materials as shown in table 1 distinguish reference numerals 1#, 2#, 3#, and identification process is specifically by following step It is rapid to realize:
1 three kinds of detected materials of table
Each component generalized phase arranges entropy entropy after calculating the empirical mode decomposition of 1# detected materials.
Each component generalized phase of 1# detected materials known to table 2 arranges entropy
Three kinds of detected materials are respectively acquired into 10 signals, 10 IMF1 components of three kinds of detected materials is respectively obtained, makes even Mean value.
3 three kinds of stainless steel material IMF1 characteristic components of table
Stainless steel 1#, which is used as, refers to metal material, and the maximum value in reference metal material IMF1 entropy is denoted as gmax= 17.39, minimum value is denoted as gmin=16.63, and by mean valueAs the entropy of reference metal material, threshold definitions For Δ=gmax-gmin=0.76;
Same method determines detected materials characteristic component g and refers to metal material characteristic componentIt is compared, ifThen metal material to be measured is recognized with metal material homogeneity, completion is referred to.IfThen metal material to be measured Material repeats operation above with reference to metal material with reference to metal material not homogeneity, then changing another metal material and be used as, up toThen metal material to be measured is recognized with metal material homogeneity, completion is referred to.
The identification result of 4 three kinds of stainless steel materials of table
Embodiment 2
Using 304 stainless steel 2# of known mark as reference material, three kind of 304 stainless steel metal material distinguishes reference numerals 1#, 2#, 3# import three kinds of material characteristics as material to be identified, and specific identification is realized by following steps:
304 stainless steel metal material 2# and other two kinds of stainless steel materials 1#, 3# phase are mixed, their shapes are cylinder In shape, with example 1, with a thickness of 15mm, diameter 47.1mm.
The present embodiment will select reference material surface to be polished, cleaned up.Select Panametrics-DNT 5077PR pulse reception/transmitter, the transmitting-receiving probe of connection centre frequency 5MHZ and the oscillography of Tektronix-DPO5034B number Device, other operations are identical as example 1.
Reference material and detected materials characteristic value are extracted respectively.
Each component of stainless steel material 2# known to table 5 arranges entropy
Other steps are same as Example 1, and the identification result of metal material to be measured is as follows:
6 stainless steel material 2# clustering recognition rate of table
Embodiment 3
Using 304 stainless steel 3# of known mark as reference material, three kind of 304 stainless steel metal material distinguishes reference numerals 1#, 2#, 3# import three kinds of material characteristics as material to be identified, and specific method is realized by following steps:
304 stainless steel metal material 3# and other two kinds of stainless steel materials 1#, 2# phase are mixed, their shapes are cylinder Shape, as in Example 1, with a thickness of 15mm, diameter 47.1mm.
The present embodiment is based on EMD generalized phase arrangement plan method and recognizes metal material method, and step 1 will be selected and refer to material It polished, cleaned up in material surface.Panametrics-DNT5077PR pulse reception/transmitter is selected, centre frequency is connected The transmitting-receiving probe of 5MHZ and Tektronix-DPO5034B digital oscilloscope, other operations are same as Example 1.
Each component of stainless steel material 3# known to table 7 arranges entropy
Other steps are same as Example 1, and the identification result of metal material to be measured is as follows:
8 stainless steel material 3# discrimination power of table
Test result: show to arrange entropy to close METAL EXTRACTION feature based on EMD generalized phase by test comparison, adopt Analyzing close metal material with KNN algorithm has the effect of that identification is stable, guarantees that classification results are accurate.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention Protection scope.

Claims (7)

1. based on EMD generalized phase arrangement entropy to the discrimination method of close metal material, it is characterised in that comprise the steps of:
(1) time-domain signal is acquired
Transmitting-receiving probe is connect with pulse reception/transmitter, couplant is added and is placed in the surface with reference to metal material, ultrasonic probe Emit pulse signal, by received with pulse/oscillograph that connect of transmitter pops one's head in received echo-signal progress to the transmitting-receiving Sampling, through multiple repairing weld and is averaged, and obtains the time domain waveform with reference to metal material;
(2) characteristic component is extracted
It is successively decomposed using Empirical mode decomposition time domain waveform X (t) with reference to metal material collected to step (1), then The characteristic component entropy g of the echo-signal with reference to metal material is calculated with generalized phase arrangement plan methodq,δ;The broad sense Phase arrangement entropy algorithmic formula are as follows:
Wherein, v represents the position of data sequence in the characteristic signal extracted with reference to metal material, PVRepresentative is mentioned with reference to metal material Occurs the probability of same position sequence in the characteristic signal data sequence taken;Q is represented to be occurred in amplification metal material characteristic signal The value of same position probability, δ, which is represented in the amplification metal material characteristic signal of index again, there is the value of same position probability, R generation The real number value that the same position probability for the characteristic signal data sequence that table amplification is extracted can be chosen, R ∈ (0,1];
(3) characteristic component of material to be detected is extracted
The characteristic component entropy of the echo-signal of material to be detected is extracted with step (1) and the identical method of step (2);
(4) characteristic component compares
By the reference metal material of the characteristic component entropy of the echo-signal of the obtained material to be detected of step (3) and step (2) The characteristic component entropy of the echo-signal of material is compared, if the two is consistent, detected materials and reference metal material homogeneity are complete At identification;Otherwise, step (5) is carried out;
(5) it repeats to compare
Another metal material for being different from step (1) is chosen as metal material is referred to, step (1)~(4) are repeated, until really Make the material of detected materials.
2. the discrimination method according to claim 1 based on EMD generalized phase arrangement entropy to close metal material, feature It is: the step (2) specifically:
2.1) identification step (1) acquires the local extremum of the time domain waveform signal X (t) with reference to metal material, connects maximum Coenvelope line is obtained, connection minimum obtains lower envelope line, obtains equal value sequence m according to upper and lower envelope1
2.2) empirical mode decomposition is carried out to original signal using following formula, determines IMF component;
X(t)-mi(t)=hi(t), i ∈ n
mi(t) the equal value sequence of i-th of signal to be decomposed or more envelope line computation is represented;hi(t) ith feature decomposed is represented Component;
Work as hi(t) meet following two condition: being that Local Symmetric and zero point and extreme point number are equal about zero-mean line;Letter When the mean value of envelope up and down that number local maximum and minimum define is 0, then hiIt (t) is IMF component;
2.3) the characteristic component entropy that the IMF component of step (2.2) decomposition is determined using generalized phase arrangement plan method, wherein extensively Adopted phase arrangement entropy algorithmic formula are as follows:
3. the discrimination method according to claim 2 based on EMD generalized phase arrangement entropy to close metal material, feature Be: the step (2.3) is specially
(2.3.1) seeks the instantaneous phase sequence θ (i) of each IMF signal with reference to metal material using Hilbert transform method, Sequence length is N;
(2.3.2) carries out phase space reconfiguration to the instantaneous phase sequence θ (i) that step (2.3.1) acquires, and obtains reproducing sequence Zj, weight Structure sequence number is N- (m-1) * t;
Zj=[θ (j), θ (j+t) ..., θ (j+ (m-1) t)], 1≤j≤N- (m-1) t
Wherein m is phase space reconfiguration dimension, and t is the time delay of reconstruct;
(2.3.3) is by reproducing sequence ZjK is arranged as by numerical value ascending order1,k2,…km, obtain position sequence Sj, and determine position sequence Identical sequence number, is denoted as Numv
Sj=(k1,k2,…km), 1≤j≤N- (m-1) τ
(2.3.4) using step (2.3.3) various arrangements occur frequency as its probability, then obtain the probability of various arrangements For
(2.3.5) utilizes two parameter entropy Sq,δDefine it is appropriate go out with reference to metal material echo-signal characteristic component entropy gq,δ,
4. the discrimination method according to claim 1 based on EMD generalized phase arrangement entropy to close metal material, feature Be: the pulse voltage of the pulse reception/transmitter is 100~300V, pulse recurrence frequency is 100~300Hz;Oscillograph Sampling rate is 100MHz~5GHz, and sampling number is 1000~5000 times;The centre frequency of transmitting-receiving probe is 1~10MHz.
5. the discrimination method according to claim 1 based on EMD generalized phase arrangement entropy to close metal material, feature Be: the couplant is water or glycerol.
6. described in any item according to claim 1~5 arrange entropy to the identification side of close metal material based on EMD generalized phase Method, it is characterised in that: the reference metal material is pure metal or alloy, intermetallic compound and special metal material.
7. the discrimination method according to claim 6 based on EMD generalized phase arrangement entropy to close metal material, feature Be: the pure metal material be beryllium, magnesium, aluminium, indium, germanium, tin, lead, antimony, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, zinc, yttrium, zirconium, Niobium, molybdenum, ruthenium, rhodium, palladium, silver, cadmium, hafnium, tantalum, tungsten, iridium, platinum or gold.
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杜必强等: "基于EMD 和小波熵阈值算法的超声回波信号降噪", 《中国测试》 *

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