A copper tube grain size detection method based on ultrasonic attenuation

Abstract

A kind of copper tube grain size detection method based on ultrasonic attenuation, establish detection model, model detection and data acquisition, ultrasonic probe excites the original wave of frequency f m , and the time series signal of original wave is collected;Determine detection scheme: determine the parameter in model, obtain experimental data, extract experimental data, calculate amplitude attenuation coefficient, establish the functional relationship between grain size and amplitude attenuation coefficient, solve the function of grain size and amplitude attenuation coefficient by fitting;Obtain the functional relationship z=f (α) between grain size z and amplitude attenuation coefficient α, the advantages of the present application are: accurately deduced the functional relationship between the sound pressure attenuation coefficient of ultrasonic detection copper tube and the grain size of copper tube. The difference multi-learning step method is used to solve the functional relationship between the sound pressure attenuation coefficient and the grain size of copper tube, which greatly improves the solving efficiency. Real-time control strategy of learning step is adopted, which avoids the divergence of solving process caused by random selection of learning step.

Description

Technical Field

[0001] This invention relates to the field of material grain size detection, and in particular to a method for detecting the grain size of copper tubes based on ultrasonic attenuation. Background Technology

[0002] Currently, copper tube grain size testing is mainly conducted offline. This involves cutting a section of copper tube, polishing the end face, etching the tube, and finally observing and photographing the grain size under a microscope. This method suffers from problems such as long testing cycles, low efficiency, and the inability to perform online testing. Summary of the Invention

[0003] This invention employs a method for detecting the grain size of copper tubes based on ultrasonic attenuation. It establishes a functional relationship between the sound pressure attenuation coefficient of the ultrasonic probe and the grain size of the copper tube. Without damaging the copper tube, it can achieve both offline and online detection, improving detection efficiency and ensuring the quality of the copper tube.

[0004] The aforementioned method for detecting the grain size of copper tubes based on ultrasonic attenuation specifically includes establishing a detection model and determining a detection scheme:

[0005] I. Establishing a detection model

[0006] A detection model for copper tube grain size based on ultrasonic attenuation is used. In the model, the ultrasonic probe is a water immersion probe; the wave source of the ultrasonic probe is a disk wave source, which excites pulsed ultrasonic waves belonging to longitudinal waves; the diameter of the disk wave source is Ds, the axis of the disk wave source passes through the axis O of the copper tube, and the distance between the disk wave source and the copper tube is l; the medium between the disk wave source and the copper tube is water; the outer diameter of the copper tube is D, the inner diameter is d, and the inner hole is filled with air; the copper tube has a linear velocity v relative to the disk wave source.

[0007] The process of model testing and data acquisition is as follows:

[0008] (I). The ultrasonic probe emitting the disk-shaped wave source in A The frequency of excitation at 0 point is f m The original wave, which belongs to the longitudinal wave pulse ultrasound, and in A The time series signal of the original wave was acquired at 0 point. x 0, x 1, ..., x I-1 );

[0009] (ii). Frequency is f m The original wave from A Starting at 0:00, it travels through the water medium to the water / copper interface, and after reflection at the water / copper interface, it travels through the water medium to... AAt 0:00, this is the first echo; no data is collected from the first echo.

[0010] (III) Frequency is f m The original wave from A Starting at 0:00, it travels through the water medium to the water / copper interface, refracts through the water / copper interface into the copper medium, undergoes total internal reflection at the copper / air interface back into the copper medium, then refracts through the copper / water interface into the water medium, and finally reaches... A At 0:00, this is the second echo; regarding the second echo, at A The echo signal is received at 0:00, and the time series signal of the echo signal is acquired. y 0, y 1, ..., y I-1 );

[0011] II. Determine the testing plan:

[0012] (a) Determine the parameters in the model

[0013] Determine the parameter fm in the model; fm is the frequency of the original wave excited by the ultrasonic probe at point A0.

[0014] Determine the parameters in the model l ; l This represents the distance between the disk wave source and the copper tube.

[0015] Determine the parameters in the model D s ; D s The diameter of the crystal in the ultrasonic probe;

[0016] Determine the parameter D in the model; D is the outer diameter of the copper tube being tested;

[0017] Determine the parameter d in the model; d is the inner diameter of the copper tube being tested.

[0018] Determine the parameter v in the model; v is the linear velocity of the copper tube relative to the ultrasonic probe;

[0019] (II) Obtaining Experimental Data

[0020] J copper tubes with known grain size zj (j = 1, 2, 3, ..., J) are selected. Considering the accuracy of grain size prediction in practical applications after fitting the functional relationship between grain size and attenuation coefficient, the following selection is made for each grain size. z j ( j = 1,2,3,..., J )of JWhen sampling a single copper tube, the following conditions must be met:

[0021]

[0022]

[0023] In the formula, ; ; This represents the maximum possible grain size of copper tubes in actual engineering applications. This represents the minimum grain size that may occur in copper tubes during actual engineering applications; additionally, it must meet the following requirements. J A copper tube sample z j ( j = 1,2,3,..., J In the interval Evenly distributed in the middle;

[0024] Following the model detection and data acquisition process of the detection model, the grain size was respectively... z j ( j = 1,2,3,..., J )of J A copper tube sample was tested and data was collected. ( j = 1,2,3,..., J )and ( j = 1,2,3,..., J );in, ( j = 1,2,3,..., J (This is for grain size) z j The j Time-series signals of the original waves collected from one copper tube sample (Note: total) J Group data, needs to be collected J If it can be guaranteed that the ultrasonic probe is used every time; A The frequency emitted at 0 is f m If the original waves are all the same, then only one sampling is needed. ( j = 1,2,3,..., J (This is for grain size) z j The j The time-series signal of the second echo collected from a copper tube sample;

[0025] (III) Extraction of experimental data

[0026] right ( j = 1,2,3,..., J Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . ;

[0027] right ( j = 1,2,3,..., J Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . ;

[0028] (iv) Calculate the amplitude attenuation coefficient

[0029] Depend on and Calculate J The known grain size is z j The amplitude attenuation coefficient of the copper tube ,in j = 1,2,3,… J ;

[0030] (v). Establish the functional relationship between grain size and amplitude attenuation coefficient.

[0031] Establish grain size z With amplitude attenuation coefficient α Functional relationship ;

[0032] (vi). Fitting and solving the function of grain size and amplitude attenuation coefficient

[0033] Grain size obtained from experiments z j ( j = 1,2,3,..., J ) and amplitude attenuation coefficient ( j = 1,2,3,… J )right Perform a fitting solution;

[0034] III. Obtaining Experimental Data

[0035] Following the model detection and data acquisition process of the detection model, the grain size was respectively... z j ( j = 1,2,3,..., J )of JA copper tube sample was tested and data was collected. ( j = 1,2,3,..., J )and ( j = 1,2,3,..., J );in, ( j = 1,2,3,..., J (This is for grain size) z j The j Time-series signals of the original waves collected from one copper tube sample (Note: total) J Group data, needs to be collected J If it can be guaranteed that the ultrasonic probe is used every time; A The frequency emitted at 0 is f m If the original waves are all the same, then only one sampling is needed. ( j = 1,2,3,..., J (This is for grain size) z j The j The time-series signal of the second echo collected from a copper tube sample;

[0036] Here, the number of copper tube samples is taken. J for J = 15; According to the sampling theorem, take the sampling frequency. f s for f s = 50MHz, then the number of sampling points I for ;

[0037] IV. Extraction of Experimental Data

[0038] right ( j = 1,2,3,..., J ; J = 15; I = 20) According to

[0039]

[0040] j = 1,2,3,..., J , J = 15; I = 20;

[0041] Perform a Fourier transform to extract the frequency components.f The amplitude of the harmonic is denoted as . ( j = 1,2,…, J ); take here f = 2.5MHz;

[0042] right ( j = 1,2,3,..., J ; J = 15; I = 20) According to

[0043]

[0044] j = 1,2,3,..., J , J = 15; I = 20;

[0045] Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . ( j = 1,2,…, J ); take here f = 2.5MHz;

[0046] V. Calculate the amplitude attenuation coefficient

[0047] definition

[0048]

[0049] Here, is the amplitude attenuation coefficient, where, H 0 represents the frequency of the original wave. f The amplitude of the harmonics, H 1 represents the echo of the original wave with frequency . f The amplitude of the harmonics;

[0050] Depend on and ( j = 1,2,3,..., J ; J = 15) Calculate the amplitude attenuation coefficient ( j = 1, 2, 3, ..., J ; J = 15), the calculation formula is as follows:

[0051] , j = 1,2,3,..., J ;J = 15;

[0052] VI. Establish the functional relationship between grain size and amplitude attenuation coefficient.

[0053] like Figure 1 As shown, let the frequency of the wave source at point A0 be... f The sound pressure of the harmonics is P If the value is 0, then after considering the dielectric attenuation, A 1 point sound pressure P 1 (i.e., the incident sound pressure at the water / copper interface) is

[0054]

[0055] In the formula, α w The medium attenuation coefficient is the coefficient for water medium. B 1 is a coefficient. Then the sound wave is from A 1 point refracted into the copper medium and reached A 2 points, and consider the sound pressure after medium attenuation. P 2 is

[0056]

[0057] In the formula, α Cu The dielectric attenuation coefficient of copper dielectric is denoted as . B 2 is a coefficient. ; sound waves A Two points are reflected back into the copper medium via total internal reflection at the copper / air interface and reach... A 1. Considering the sound pressure level after medium attenuation. P 3 is

[0058]

[0059] In the formula, α Cu The dielectric attenuation coefficient of copper dielectric is denoted as . B 3 is the coefficient. ; sound waves A 1 point of refraction into the water medium and reach A 0 point and considering the sound pressure after medium attenuation P 4

[0060]

[0061] In the formula, α w The medium attenuation coefficient is the coefficient for water medium. B 4 is the coefficient. ;

[0062] achievable

[0063]

[0064] Then there is

[0065]

[0066] because

[0067]

[0068] In the formula, C 1. C 2 is an undetermined constant; F Here are the anisotropy coefficients; z The diameter of the copper dielectric grains; f The frequency of the ultrasonic wave; q , p For index;

[0069] achievable

[0070]

[0071] make

[0072]

[0073]

[0074] And because

[0075]

[0076] Then there is

[0077]

[0078] In the formula, ; ; ;because In order to make Therefore, it is necessary ;

[0079] make

[0080]

[0081] Then there is

[0082]

[0083] Grain size z With amplitude attenuation coefficient α Functional relationship for

[0084]

[0085] in, r 1. r 2 and r 3 is a coefficient to be determined, and ; ; ; ; ;

[0086] If let

[0087]

[0088] but

[0089]

[0090] in, r 1. r 2 and r 3 is a coefficient to be determined;

[0091] VII. Fitting and solving the function of grain size and amplitude attenuation coefficient

[0092] (I) Establishing the residual function

[0093] Undetermined coefficients in the formula r 1. r 2 and r 3 can be achieved through... Obtained by fitting the formula;

[0094] according to ,Depend on J Grain size of a copper tube sample z j ( j = 1,2,3,..., J ) can be obtained

[0095] , j = 1,2,3,..., J ;

[0096] Let the residual function for

[0097]

[0098] And then there are

[0099]

[0100]

[0101]

[0102] Find the residual function When it is the minimum value r 1. r 2 and r The value of 3 will be the value at this time. r 1. r 2 and r Substitute the value of 3 The grain size can then be determined. z With amplitude attenuation coefficient α Functional relationship ;

[0103] (II) On the residual function Perform fitting and solution

[0104] (III) Obtaining the function of grain size and amplitude attenuation coefficient

[0105] The fitting results , , Substitution Grain size can then be obtained. z With amplitude attenuation coefficient α Functional relationship ,for

[0106] .

[0107] The aforementioned residual function Perform fitting and solution The specific method is as follows:

[0108] Depend on and ( Fitting residual function Solve The process (i.e., the specific steps of computer programming) is as follows:

[0109] Step 1: Parameter Initialization

[0110] right learning rate Initialization, generally It is generally recommended to take ;

[0111] right and Learning rate to the left of the minimum value Initialization, recommended It is recommended to take ;

[0112] right and Learning rate to the right of the minimum value Initialization, recommended It is recommended to take ;

[0113] For the maximum number of iterations initialization, Generally, the number is taken as a multiple of 10 (or 100, 1000, 10000, etc.); generally, it is taken as... ;

[0114] For the iteration counter initialization, ;

[0115] Expected accuracy of iteration initialization, It is a very small positive number, usually taken as... ;

[0116] right initial value ( Initialize and retrieve for Random numbers within;

[0117] right initial value ( Initialize and retrieve for Random numbers within;

[0118] right initial value ( Initialize and retrieve for Random numbers within;

[0119] Step 2: Calculate the value of the residual function for the initial values.

[0120] Will , , Substitute into the following formula to calculate the first... ( The value of the residual function in the )th iteration;

[0121]

[0122] in, and It is known that ;

[0123] Step 3: Determine whether the value of the residual function of the initial value meets the accuracy requirements.

[0124] like ( If the required accuracy is achieved, then there is no need to enter the iteration process. At this point (i.e.) (time) , , That's the result I wanted;

[0125] like ( If the accuracy requirement is not met, then... value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Right now

[0126] , , ,

[0127] The "=" sign in the formula indicates "assignment"; then the iteration process begins, proceeding to the fourth step;

[0128] Step 4: Iteration counter counting

[0129] Increment the iteration counter by 1, that is

[0130]

[0131] The "=" sign in the formula indicates "assignment";

[0132] Step 5: Calculate the... During step iteration value

[0133] Calculate the first one according to the following formula During step iteration Value:

[0134]

[0135]

[0136] Step 6: Calculate the... During step iteration value

[0137] Calculate the following method: During step iteration Value:

[0138] when hour, for

[0139]

[0140]

[0141] Then proceed directly to step eight;

[0142] when hour, for

[0143]

[0144]

[0145] Then proceed to step seven;

[0146] Step 7: Judge and ensure

[0147] when If so, proceed directly to step eight;

[0148] when At that time, Assigned Then return to step six;

[0149] Step 8: Calculate the... During step iteration value

[0150] Calculate the following method: During step iteration Value:

[0151] when hour, for

[0152]

[0153]

[0154] Then proceed directly to step ten;

[0155] when hour, for

[0156]

[0157]

[0158] Then proceed to the ninth step;

[0159] Step 9: Judge and ensure

[0160] when If so, proceed directly to step ten;

[0161] when At that time, Assigned Then return to step eight;

[0162] Step 10: Calculate the... The value of the residual function in the next iteration

[0163] Will , , Substitute into the following formula to calculate the first... The value of the residual function in the next iteration;

[0164]

[0165] in, and It is known that ;

[0166] Step 11: Determine the first... Does the value of the residual function in the next iteration meet the accuracy requirements?

[0167] like If the required accuracy is achieved, the iteration process ends. , , That's the result I wanted;

[0168] like If the accuracy requirement is not met, then... value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Right now

[0169] , , ,

[0170] The "=" sign in the formula indicates "assignment"; then proceed to step twelfth.

[0171] like If so, proceed to step twelfth after handling one of the following four situations;

[0172] Scenario 1:

[0173] when ,and, At that time, Assigned ,Bundle Assigned ,Right now

[0174] ,

[0175] The "=" sign in the formula indicates "assignment";

[0176] Scenario 2:

[0177] when ,and, At that time, Assigned ,Bundle Assigned ,Bundle Assigned ,Right now

[0178] , ,

[0179] The "=" sign in the formula indicates "assignment";

[0180] Scenario 3:

[0181] when ,and, At that time, Assigned ,Bundle Assigned ,Bundle Assigned ,Right now

[0182] , ,

[0183] The "=" sign in the formula indicates "assignment";

[0184] Scenario 4:

[0185] when ,and, At that time, Assigned ,Bundle Assigned ,Right now

[0186] ,

[0187] The "=" sign in the formula indicates "assignment";

[0188] Step 12: Determine if the required number of iterations has been reached.

[0189] like The iteration process continues, returning to step four;

[0190] like The iteration process reaches the maximum number of iterations; if it is necessary to increase the maximum number of iterations, then increase it here. The value of is determined, and then the process proceeds to the fourth step; if no further iterations are needed, the iteration process ends at this point. , , It is the final result of the iteration.

[0191] Advantages of this invention:

[0192] I. Based on the theory of ultrasonic detection, the functional relationship between the sound pressure attenuation coefficient of the ultrasonic detection copper tube and the grain size of the copper tube was accurately derived.

[0193]

[0194] Where z is the grain size of the copper tube, α is the attenuation coefficient, and r1, r2 and r3 are coefficients to be determined.

[0195] Second, the differential multi-learning step method is adopted to solve the functional relationship between the sound pressure attenuation coefficient and the grain size of the copper tube, which greatly improves the solution efficiency.

[0196] Third, when solving the functional relationship between the sound pressure attenuation coefficient and the copper tube grain size, a real-time control strategy for the learning step size was adopted to avoid the divergence in the solution process caused by randomly selecting the learning step size. Attached Figure Description

[0197] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0198] Figure 1 This is a schematic diagram of a copper tube grain size detection model based on ultrasonic attenuation. Detailed Implementation

[0199] Example 1

[0200] A method for detecting the grain size of copper tubes based on ultrasonic attenuation, characterized in that: the method specifically includes establishing a detection model and determining a detection scheme.

[0201] I. Establishing a detection model

[0202] A model for detecting copper tube grain size based on ultrasonic attenuation is as follows: Figure 1 As shown in the model, the ultrasonic probe is a water immersion probe. The wave source of the ultrasonic probe is a disc-shaped wave source, which excites pulsed ultrasonic waves belonging to the longitudinal wave category. The diameter of the disc-shaped wave source is Ds, and the axis of the disc-shaped wave source passes through the axis O of the copper tube, with a distance of l between the disc-shaped wave source and the copper tube. The medium between the disc-shaped wave source and the copper tube is water. The outer diameter of the copper tube is D, and the inner diameter is d, with air as the medium inside the inner hole. The copper tube has a linear velocity v relative to the disc-shaped wave source.

[0203] The process of model testing and data acquisition is as follows:

[0204] (I). The ultrasonic probe emitting the disk-shaped wave source in A The frequency of excitation at 0 point is f m The original wave, which belongs to the longitudinal wave pulse ultrasound, and in A The time series signal of the original wave was acquired at 0 point. x 0, x 1, ..., x I-1 ).

[0205] (ii). Frequency is f m The original wave from A Starting at 0:00, it travels through the water medium to the water / copper interface, and after reflection at the water / copper interface, it travels through the water medium to... A At 0:00, this is the first echo. No data is collected from the first echo.

[0206] (III) Frequency is f m The original wave from A Starting at 0:00, it travels through the water medium to the water / copper interface, refracts through the water / copper interface into the copper medium (copper pipe wall), then undergoes total internal reflection at the copper / air interface back to the copper medium (copper pipe wall), refracts again through the copper / water interface into the water medium, and finally reaches... A At 0:00, this is the second echo. Regarding the second echo, at... A The echo signal is received at 0:00, and the time series signal of the echo signal is acquired. y 0, y 1, ..., y I-1 ).

[0207] II. Determine the testing plan:

[0208] (a) Determine the parameters in the model

[0209] Determine the parameters in the model fm . f m For the ultrasonic probe in A The frequency of the original wave generated at 0.

[0210] Determine the parameters in the model l . l This represents the distance between the disk wave source and the copper tube.

[0211] Determine the parameters in the model D s . D s This is the diameter of the crystal in the ultrasonic probe.

[0212] Determine the parameters in the model D . D The outer diameter of the copper tube being inspected.

[0213] Determine the parameters in the model d . d The inner diameter of the copper tube being tested.

[0214] Determine the parameters in the model v . v The linear velocity of the copper tube relative to the ultrasonic probe.

[0215] (II) Obtaining Experimental Data

[0216] Select J The known grain size is z j ( j = 1,2,3,..., J The copper tube is used. Considering the accuracy of grain size prediction in practical applications after fitting the functional relationship between grain size and attenuation coefficient, a grain size of 1000 g / cm³ is selected. z j ( j = 1,2,3,..., J )of J When sampling a single copper tube, the following conditions must be met:

[0217]

[0218]

[0219] In the formula, ; ; This represents the maximum possible grain size of copper tubes in actual engineering applications. This represents the minimum grain size that may occur in copper tubes during actual engineering applications. Additionally, it must meet the following requirements: JA copper tube sample z j ( j = 1,2,3,..., J In the interval It is evenly distributed in the middle.

[0220] According to the detection model (such as) Figure 1 The model testing and data acquisition process, respectively, is performed on grain sizes of... z j ( j =1,2,3,... J )of J A copper tube sample was tested and data was collected. ( j = 1,2,3,..., J )and ( j = 1,2,3,..., J ).in, ( j = 1,2,3,..., J (This is for grain size) z j The j Time-series signals of the original waves collected from one copper tube sample (Note: total) J Group data, needs to be collected J Next. If it can be guaranteed that the ultrasound probe is in [a certain position] each time... A The frequency emitted at 0 is f m If the original waves are all the same, then only one sampling is needed. ( j = 1,2,3,..., J (This is for grain size) z j The j The time-series signal of the second echo collected from a copper tube sample.

[0221] (III) Extraction of experimental data

[0222] right ( j = 1,2,3,..., J Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . .

[0223] right ( j = 1,2,3,..., J Perform a Fourier transform to extract the frequency components.f The amplitude of the harmonic is denoted as . .

[0224] (iv) Calculate the amplitude attenuation coefficient

[0225] Depend on and Calculate J The known grain size is z j The amplitude attenuation coefficient of the copper tube ,in j = 1,2,3,… J .

[0226] (v). Establish the functional relationship between grain size and amplitude attenuation coefficient.

[0227] Establish grain size z With amplitude attenuation coefficient α Functional relationship .

[0228] (vi). Fitting and solving the function of grain size and amplitude attenuation coefficient

[0229] Grain size obtained from experiments z j ( j = 1,2,3,..., J ) and amplitude attenuation coefficient ( j = 1,2,3,… J )right Perform a fitting solution.

[0230] Determine the parameters in the model

[0231] (a) Determine the parameters in the model D and d

[0232] Pick D = 92mm, d = 42mm, then the wall thickness is .

[0233] 2. Determine the parameters in the model. f m

[0234] f m For the ultrasonic probe in A The frequency of the original wave generated at point 0. For example... Figure 1 As shown, in order to reach AThe first and second echoes at 0 o'clock must not interfere with each other in time, which requires that...

[0235]

[0236] In the formula, c 2 represents the velocity of the longitudinal ultrasonic wave in the copper medium. c 2 = 4700m / s. Therefore, the acoustic probe is at A The frequency of the longitudinal wave pulse ultrasound excited at 0 point f m Must meet

[0237]

[0238] In practical engineering projects, ultrasonic testing frequencies are typically in the range of 0.5MHz to 10MHz. Therefore, this project recommends... f m = 2.5MHz, at this time, the wall thickness of the copper tube being tested Must meet This project The requirements are met.

[0239] 3. Determine the parameters in the model. D s

[0240] D s This represents the diameter of the disk-based wave source, specifically the diameter of the disk wafer. Here, we take... D s =16mm.

[0241] 4. Determine the parameters in the model. l

[0242] l This represents the distance between the disk wave source and the copper tube.

[0243] The near-field length of this model N for

[0244]

[0245] Make the ultrasound probe at A The frequency emitted at 0 is f m The highest frequency of the longitudinal wave pulse ultrasound spectrum is f c ,but f c The wavelength of the corresponding harmonic λ for

[0246]

[0247] achievable

[0248]

[0249] In this project, D s = 16mm, f c = 3.5MHz (i.e.) f m The highest frequency of the spectrum of a 2.5MHz pulsed ultrasound is f c = 3.5MHz), c 1 = 1480m / s .

[0250] Since the water distance in actual engineering projects is generally 10mm to 50mm, in this project... l The value is selected within the range of 10mm to 50mm.

[0251] 5. Determine the parameters in the model. v

[0252] v This represents the linear velocity of the copper tube relative to the disk wave source (i.e., the disk wafer). In this project, v = 400mm / min≈6.667 mm / s.

[0253] like Figure 1 As shown, let the ultrasound from A 1 o'clock A Return at 2 o'clock A Within 1 hour, the distance the copper tube moves is l v ,but l v for

[0254]

[0255] but Therefore, in the model v Take as v = 0mm / s, that is, at the point where J When conducting experiments on individual copper tubes, the effect of the copper tube's speed is not considered.

[0256] III. Obtaining Experimental Data

[0257] According to the detection model (such as) Figure 1 The model testing and data acquisition process, respectively, is performed on grain sizes of... z j (j =1,2,3,... J )of J A copper tube sample was tested and data was collected. ( j = 1,2,3,..., J )and ( j = 1,2,3,..., J ).in, ( j = 1,2,3,..., J (This is for grain size) z j The j Time-series signals of the original waves collected from one copper tube sample (Note: total) J Group data, needs to be collected J Next. If it can be guaranteed that the ultrasound probe is in [a certain position] each time... A The frequency emitted at 0 is f m If the original waves are all the same, then only one sampling is needed. ( j = 1,2,3,..., J (This is for grain size) z j The j The time-series signal of the second echo collected from a copper tube sample.

[0258] Here, the number of copper tube samples is taken. J for J = 15. According to the sampling theorem, the sampling frequency is taken as 15. f s for f s = 50MHz, then the number of sampling points I for .

[0259] IV. Extraction of Experimental Data

[0260] right ( j = 1,2,3,..., J ; J = 15; I = 20) According to

[0261]

[0262] j = 1,2,3,..., J , J = 15; I= 20.

[0263] Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . ( j = 1,2,…, J Take it here. f = 2.5MHz.

[0264] right ( j = 1,2,3,..., J ; J = 15; I = 20) According to

[0265]

[0266] j = 1,2,3,..., J , J = 15; I = 20.

[0267] Perform a Fourier transform to extract the frequency components. f The amplitude of the harmonic is denoted as . ( j = 1,2,…, J Take it here. f = 2.5MHz.

[0268] V. Calculate the amplitude attenuation coefficient

[0269] definition

[0270]

[0271] Here, is the amplitude attenuation coefficient, where, H 0 represents the frequency of the original wave. f The amplitude of the harmonics, H 1 represents the echo of the original wave with frequency . f The amplitude of the harmonics.

[0272] Depend on and ( j = 1,2,3,..., J ; J = 15) Calculate the amplitude attenuation coefficient ( j = 1, 2, 3, ..., J ; J = 15), the calculation formula is as follows:

[0273] , j = 1,2,3,..., J ; J = 15.

[0274] VI. Establish the functional relationship between grain size and amplitude attenuation coefficient.

[0275] like Figure 1 As shown, let the frequency of the wave source at point A0 be... f The sound pressure of the harmonics is P If the value is 0, then after considering the dielectric attenuation, A 1 point sound pressure P 1 (i.e., the incident sound pressure at the water / copper interface) is

[0276]

[0277] In the formula, α w The medium attenuation coefficient is the coefficient for water medium. B 1 is a coefficient. Then the sound wave is from A 1 point refracted into the copper medium and reached A 2 points, and consider the sound pressure after medium attenuation. P 2 is

[0278]

[0279] In the formula, α Cu The dielectric attenuation coefficient of copper dielectric is denoted as . B 2 is a coefficient. Sound waves are generated by A Two points are reflected back into the copper medium via total internal reflection at the copper / air interface and reach... A 1. Considering the sound pressure level after medium attenuation. P 3 is

[0280]

[0281] In the formula, α Cu The dielectric attenuation coefficient of copper dielectric is denoted as . B 3 is the coefficient. Sound waves are generated by A 1 point of refraction into the water medium and reach A 0 point and considering the sound pressure after medium attenuation P 4

[0282]

[0283] In the formula, α w The medium attenuation coefficient is the coefficient for water medium.B 4 is the coefficient. .

[0284] achievable

[0285]

[0286] Then there is

[0287]

[0288] because

[0289]

[0290] In the formula, C 1. C 2 is an undetermined constant; F Here are the anisotropy coefficients; z The diameter of the copper dielectric grains; f The frequency of the ultrasonic wave; q , p For exponents.

[0291] achievable

[0292]

[0293] make

[0294]

[0295]

[0296] And because

[0297]

[0298] Then there is

[0299]

[0300] In the formula, ; ; ;because In order to make Therefore, it is necessary .

[0301] make

[0302]

[0303] Then there is

[0304]

[0305] Grain size zWith amplitude attenuation coefficient α Functional relationship for

[0306]

[0307] in, r 1. r 2 and r 3 is a coefficient to be determined, and ; ; ; ; .

[0308] If let

[0309]

[0310] but

[0311]

[0312] in, r 1. r 2 and r 3 is a coefficient to be determined.

[0313] VII. Fitting and solving the function of grain size and amplitude attenuation coefficient

[0314] (I) Establishing the residual function

[0315] Undetermined coefficients in the formula r 1. r 2 and r 3 can be achieved through... It is obtained by fitting the formula.

[0316] according to ,Depend on J Grain size of a copper tube sample z j ( j = 1,2,3,..., J ) can be obtained

[0317] , j = 1,2,3,..., J .

[0318] Let the residual function for

[0319]

[0320] And then there are

[0321]

[0322]

[0323]

[0324] Find the residual function When it is the minimum value r 1. r 2 and r The value of 3 will be the value at this time. r 1. r 2 and r Substitute the value of 3 The grain size can then be determined. z With amplitude attenuation coefficient α Functional relationship .

[0325] (II) On the residual function Perform fitting and solution

[0326] Depend on and ( Fitting residual function Solve The process (i.e., the specific steps of computer programming) is as follows:

[0327] Step 1: Parameter Initialization

[0328] right learning rate Initialization, generally It is generally recommended to take .

[0329] right and Learning rate to the left of the minimum value Initialization, recommended It is recommended to take .

[0330] right and Learning rate to the right of the minimum value Initialization, recommended It is recommended to take .

[0331] For the maximum number of iterations initialization, Generally, it is taken as an integer multiple of 10 (or 100, 1000, 10000, etc.). .

[0332] For the iteration counter initialization, .

[0333] Expected accuracy of iteration initialization, It is a very small positive number, usually taken as... .

[0334] right initial value ( Initialize and retrieve for Random numbers within.

[0335] right initial value ( Initialize and retrieve for Random numbers within.

[0336] right initial value ( Initialize and retrieve for Random numbers within.

[0337] Step 2: Calculate the value of the residual function for the initial values.

[0338] Will , , Substitute into the following formula to calculate the first... ( The value of the residual function after ) iterations.

[0339]

[0340] in, and It is known that .

[0341] Step 3: Determine whether the value of the residual function of the initial value meets the accuracy requirements.

[0342] like ( If the required accuracy is achieved, then there is no need to enter the iteration process. At this point (i.e.) (time) , , That's the result I wanted.

[0343] like ( If the accuracy requirement is not met, then... value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Right now

[0344] , , ,

[0345] The "=" sign in the formula indicates "assignment". Then the iteration process begins, proceeding to the fourth step.

[0346] Step 4: Iteration counter counting

[0347] Increment the iteration counter by 1, that is

[0348]

[0349] The "=" in the formula means "assignment".

[0350] Step 5: Calculate the... During step iteration value

[0351] Calculate the first one according to the following formula During step iteration Value:

[0352]

[0353]

[0354] Step 6: Calculate the... During step iteration value

[0355] Calculate the following method: During step iteration Value:

[0356] when hour, for

[0357]

[0358]

[0359] Then proceed directly to step eight;

[0360] when hour, for

[0361]

[0362]

[0363] Then proceed to the seventh step.

[0364] Step 7: Judge and ensure

[0365] when If so, proceed directly to step eight;

[0366] when At that time, Assigned Then return to step six.

[0367] Step 8: Calculate the... During step iteration value

[0368] Calculate the following method: During step iteration Value:

[0369] when hour, for

[0370]

[0371]

[0372] Then proceed directly to step ten;

[0373] when hour, for

[0374]

[0375]

[0376] Then proceed to the ninth step.

[0377] Step 9: Judge and ensure

[0378] when If so, proceed directly to step ten;

[0379] when At that time, Assigned Then return to step eight.

[0380] Step 10: Calculate the... The value of the residual function in the next iteration

[0381] Will , , Substitute into the following formula to calculate the first... The value of the residual function in the next iteration.

[0382]

[0383] in, and It is known that .

[0384] Step 11: Determine the first... Does the value of the residual function in the next iteration meet the accuracy requirements?

[0385] like If the required accuracy is achieved, the iteration process ends. , , That's the result I wanted.

[0386] like If the accuracy requirement is not met, then... value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Bundle value assigned to ,Right now

[0387] , , ,

[0388] The "=" sign in the formula indicates "assignment". Then proceed to step twelf.

[0389] like If so, proceed to step twelfth after handling one of the following four situations.

[0390] Scenario 1:

[0391] when ,and, At that time, Assigned ,Bundle Assigned ,Right now

[0392] ,

[0393] The "=" in the formula means "assignment".

[0394] Scenario 2:

[0395] when ,and, At that time, Assigned ,Bundle Assigned ,Bundle Assigned ,Right now

[0396] , ,

[0397] The "=" in the formula means "assignment".

[0398] Scenario 3:

[0399] when ,and, At that time, Assigned ,Bundle Assigned ,Bundle Assigned ,Right now

[0400] , ,

[0401] The "=" in the formula means "assignment".

[0402] Scenario 4:

[0403] when ,and, At that time, Assigned ,Bundle Assigned ,Right now

[0404] ,

[0405] The "=" in the formula means "assignment".

[0406] Step 12: Determine if the required number of iterations has been reached.

[0407] like The iteration process continues, returning to step four.

[0408] like The iteration process reaches the maximum number of iterations. If it's necessary to increase the maximum number of iterations at this point, then increase it here. The value of is determined, and then the process proceeds to the fourth step; if no further iterations are needed, the iteration process ends at this point. , , It is the final result of the iteration.

[0409] (III) Obtaining the function of grain size and amplitude attenuation coefficient

[0410] The fitting results , , Substitution Grain size can then be obtained. z With amplitude attenuation coefficient α Functional relationship ,for

[0411] .

[0412] Matters not covered in this invention are common knowledge.

[0413] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for detecting the grain size of copper tubes based on ultrasonic attenuation, characterized in that: I. Establishing a detection model A detection model for copper tube grain size based on ultrasonic attenuation is used. In the model, the ultrasonic probe is a water immersion probe; the wave source of the ultrasonic probe is a disk wave source, which excites pulsed ultrasonic waves belonging to longitudinal waves; the diameter of the disk wave source is Ds, the axis of the disk wave source passes through the axis O of the copper tube, and the distance between the disk wave source and the copper tube is l; the medium between the disk wave source and the copper tube is water; the outer diameter of the copper tube is D, the inner diameter is d, and the inner hole is filled with air; the copper tube has a linear velocity v relative to the disk wave source. The process of model testing and data acquisition is as follows: (I) An ultrasonic probe emitting a disk-shaped wave source excites a wave at point A0 with a frequency of f. m The original wave, which is a pulsed ultrasonic wave belonging to the longitudinal wave category, was collected at point A0, and the time sequence signal (x0, x1, ..., x...) of the original wave was acquired. I-1 ); (II) Frequency f m The original wave starts from point A0, passes through the water medium and reaches the water / copper interface. The reflected wave at the water / copper interface is the first echo, which is not collected. It is refracted through the water / copper interface into the copper medium, then undergoes total internal reflection at the copper / air interface and returns to the copper medium. It is then refracted through the copper / water interface into the water medium and reaches point A0. This is the second echo. For the second echo, the echo signal is received at point A0, and the time series signal (y0, y1, ..., y2) of the echo signal is acquired. I-1 ); II. Determine the testing plan: (I) Determine the values ​​of the parameters fm, l, Ds, D, and d in the model. (II) Obtaining Experimental Data Select J copper tubes with known grain size zj, j = 1, 2, 3, ..., J, which must satisfy the following conditions: With max >z max_sj With min <z min_sj In the formula, z max = max(z1, z2, ..., z J );z min =min(z1, z2, ..., z) J );z max_sj、 z min_sj This refers to the maximum and minimum grain sizes that copper tubes may exhibit in practical engineering applications; additionally, it is necessary to satisfy z... j In the interval [z min , z max Evenly distributed within; J copper tube samples were tested and data were collected. The original wave is a time-series signal; This is the time-series signal of the second echo; (III) Extraction of Experimental Data right , Perform a Fourier transform to extract the amplitude of the harmonic with frequency component f = 2.5MHz, denoted as . and (iv) Calculate the amplitude attenuation coefficient Depend on and Calculate the amplitude attenuation coefficient α of the copper tube. j ; (V) Establishing the functional relationship between grain size and amplitude attenuation coefficient Establish a functional relationship between grain size z and amplitude attenuation coefficient α: z = f(α); (vi) Fitting and solving the function of grain size and amplitude attenuation coefficient Grain size z obtained from experiments j and amplitude attenuation coefficient α j We fit and solve for z = f(α); III. Obtaining Experimental Data The sample size J of copper tubes is J = 15; according to the sampling theorem, the sampling frequency f is taken as... s f s =50MHz, then the number of sampling points I is IV. Extraction of Experimental Data V. Calculate the amplitude attenuation coefficient Depend on and Calculate the amplitude attenuation coefficient α j j = 1, 2, 3, ..., J; J = 15, the calculation formula is as follows: VI. Establish the functional relationship between grain size and amplitude attenuation coefficient. Let the sound pressure of the harmonic wave with frequency f from the wave source at point A0 be P0, α w、 α Cu For water and copper media, B1, B2, B3, and B4 are coefficients, where B1 > 0, B2 > 0, B3 > 0, and B4 > 0. achievable but because a Cu =C1f+C2Fz q f p In the formula, C1 and C2 are undetermined constants; F is the anisotropy coefficient; q and p are exponents; achievable make again but With q =E1-E2α In the formula, Z > 0; q ∈ (-∞, +∞); α ∈ (-∞, 0); because E2 > 0, in order to make (E1 - E2α) > 0, E1 must be > 0; make but Where r1, r2, and r3 are coefficients to be determined, and z∈(0,+∞); r1∈(-∞,+∞); r2∈(0,+∞); r3∈(0,+∞); VII. Fitting and solving the function of grain size and amplitude attenuation coefficient (I) Establishing the residual function The undetermined coefficients r1, r2, and r3 in the formula can be obtained by fitting the formula u = r1ln(r2 - r3α); Let the residual function E be but Find the values ​​of r1, r2, and r3 when the residual function is at its minimum, and substitute them into the equation. Then z = f(α) can be obtained; (II) Fitting the residual function to solve for r1, r2, and r3 (III) Obtaining the function of grain size and amplitude attenuation coefficient The fitting results Substitution for .

2. The method for detecting the grain size of copper tubes based on ultrasonic attenuation according to claim 1, characterized in that: The specific method for fitting and solving the residual function E = f(r1, r2, r3) to obtain r1, r2, and r3 is as follows: From α j and u j For the numbers j = 1, 2, 3, ..., J; J = 15, the process of fitting the residual function E = f(r1, r2, r3) and solving for r1, r2, r3, i.e., the specific steps of computer programming, is as follows: Step 1: Parameter Initialization The learning rate η1 of r1 is initialized, generally η1∈(0,1), and it is recommended to take η1=0.1; The learning rate η for r2 and r3 when they are to the left of the minimum value z Initialization, η is recommended z ∈(0, 0.1), it is recommended to take η. z ∈0.0001; The learning rate η for r2 and r3 when they are to the right of the minimum. y Initialization, η is recommended y = (0, 100), it is recommended to take η. y =50; Initialize the maximum number of iterations G. G is generally a multiple of 10, 100, 1000, or 10000; take G = 5000. Initialize the iteration counter g, g = 0; Expected accuracy E for iteration * Initialization, E * It is a very small positive number, usually taken as E. * =10 -5 ; Initial value of r1 Initialize g=0 and take A random number within the range (0, 1); Initial value of r2 Initialize g=0 and take A random number within the range (0, 0.01); Initial value of r3 Initialize g=0 and take A random number within the range (0, 0.1); Step 2: Calculate the value of the residual function for the initial values. Will Substitute into the following formula to calculate the value of the residual function for the g-th and g=0th iterations; Among them, u j and α j Given that J = 15; Step 3: Determine whether the value of the residual function of the initial value meets the accuracy requirements. If E g ≤E * If g = 0, then the accuracy requirement has been met, and there is no need to enter the iteration process. This is the case when g = 0. That's the result I wanted; If E g >E * If g = 0, then the required precision has not been met. value assigned to Bundle value assigned to Bundle value assigned to Put E g The value assigned to E m ,Right now AND m =And g The "=" in the formula means "assignment"; then the iteration process begins, proceeding to the fourth step; Step 4: Iteration counter counting Increment the iteration counter by 1, that is g = g + 1 The "=" in the formula means "assignment"; Step 5: Calculate the value at step g. value Calculate the result of the g-th iteration using the following formula. Value: Step 6: Calculate the value at step g. value Calculate the result of the g-th iteration using the method below. Value: when hour, for Then proceed directly to step eight; when hour, for Then proceed to step seven; Step 7: Judge and ensure when If so, proceed directly to step eight; when At that time, Assign to η y Then return to step six; Step 8: Calculate the value at step g. value Calculate the result of the g-th iteration using the method below. Value: when hour, for Then proceed directly to step ten; when hour, for Then proceed to the ninth step; Step 9: Judge and ensure when If so, proceed directly to step ten; when At that time, Assign to η y Then return to step eight; Step 10: Calculate the value of the residual function in the g-th iteration. Will Substitute into the following formula to calculate the value of the residual function in the g-th iteration; Among them, u j and α j Given that J = 15; Step 11: Determine whether the value of the residual function in the g-th iteration meets the accuracy requirements. If E g ≤E * If the required accuracy is achieved, the iteration process ends. That's the result I wanted; If E m >E g >E * If the accuracy requirement is not met, then... value assigned to Bundle value assigned to Bundle value assigned to Put E g The value assigned to E m ,Right now AND m =And g The "=" in the formula indicates "assignment"; then proceed to step twelf; If E g ≥E m If so, proceed to step twelfth after handling one of the following four situations; Scenario 1: when and, hour, Bundle Assign to η1, and Assign to η z ,Right now The "=" in the formula means "assignment"; Scenario 2: when and, hour, Bundle Assign to η1, and Assign to η z ,Bundle Assign to η y ,Right now The "=" in the formula means "assignment"; Scenario 3: when and, hour, Bundle Assign to η1, and Assign to η z ,Bundle Assign to η y ,Right now The "=" in the formula means "assignment"; Scenario 4: when and, hour, Bundle Assign to η1, and Assign to η y ,Right now The "=" in the formula means "assignment"; Step 12: Determine if the required number of iterations has been reached. If g < G, the iteration process continues and returns to step four; If g ≥ G, the iteration process reaches the maximum number of iterations. If it's necessary to increase the maximum number of iterations, then increase the value of G and proceed to step four. If it's not necessary to increase the number of iterations, the iteration process ends at this point. It is the final result of the iteration.

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