Method for optimizing geometric parameters of ultrasonic transducer for online thickness measurement of cable insulation layer

Abstract

The invention provides an optimization method for geometric parameters of an ultrasonic transducer for online thickness measurement of a cable insulation layer, and belongs to the field of ultrasonic transducer optimization design. According to the method, a cable is dispersed into a plurality of spatial positions according to cable vibration characteristics, and the optimization problem of the ultrasonic transducer is formed; decision optimization indexes of the average amplitude, the minimum amplitude, the amplitude variance and the cost of secondary reflection signals at multiple spatial positions are established, then the amplitudes are converted into surface receiving sound pressure, quantitative calculation of the sound pressure is achieved through a distributed point source method, a decision matrix is established, and the surface receiving sound pressure is calculated. And then selecting a relatively optimal transducer geometric parameter scheme by adopting a multi-weight comprehensive approximation ideal solution sorting method. According to the method, the problem of low signal amplitude in the traditional thickness measurement process can be effectively solved, and the construction of a better online measurement system can be supported, so that the development cost and time are reduced, and a new thought is provided for the optimization design of an ultrasonic measurement system in a complex environment.

Description

Technical Field

[0001] The present invention relates to the field of optimized design of ultrasonic transducers, and particularly to an optimization method for geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulating layer. Background Art

[0002] During the cable manufacturing process, problems such as non-compliance or non-uniformity of the wall thickness of the insulating layer caused by equipment performance fluctuations, process parameter precision control, etc. are relatively common, affecting the quality of cable products and the production costs of enterprises. For example, although an over-thick insulating layer meets the standards and safety requirements, it causes material waste, increases the weight of the cable, and further increases the manufacturing, transportation, and installation costs, not meeting the requirements of green manufacturing; an under-thin insulating layer may lead to electrical performance failure, seriously affecting the safety of the cable, resulting in cable scrapping and losses to production enterprises. Therefore, accurately measuring the thickness and its uniformity of the insulating layer during the production process is the key to ensuring cable quality, enterprise competitiveness, and environmentally optimized production. Ultrasonic technology, with its characteristics of high precision, non-destructiveness, and economy, has been widely used in the field of industrial non-destructive testing, especially performing excellently in material defect detection, thickness measurement, and detection of complex geometric surfaces. Both ultrasonic defect detection and thickness measurement rely on the characteristics of ultrasonic reflection signals. The ultrasonic reflection field is highly correlated with the transducer parameters, the surface spatial parameters of the object to be measured, and the alignment of the probe with the object to be measured. Currently, ultrasonic thickness measurement is mainly used for flat surfaces, surfaces with small curvature, or static objects, where the reflection field is relatively stable. When the surface of the object to be measured (such as a thin cable) has a large local curvature, ultrasonic energy will be scattered by the curved surface, resulting in the ultrasonic transducer being unable to fully receive all acoustic energy, causing redundant peaks in the echo signal, a decrease in signal-to-noise ratio, and phase shift. The multiple transmissions of sound waves further attenuate the amplitude of the second reflection signal, making it difficult to accurately estimate the transit time, causing a larger measurement error and not meeting the requirements of high-precision measurement. Secondly, high-frequency vibrations will occur during the cable production process (which cannot be completely eliminated by methods such as installing damping devices), causing the cable, especially a thin cable with a large curvature, to deviate from the acoustic axis range of the transducer, making it impossible to align with each other, causing acoustic wave scattering, further reducing and fluctuating the amplitude of the echo signal, and increasing the difficulty of accurately determining the transit time. Therefore, to achieve accurate detection of the on-line thickness of the cable insulating layer based on ultrasound, it is necessary to combine the curvature parameters of the cable, consider the influence of its vibration on the ultrasonic sound field, etc., and the measurement distance to match and optimize its measurement system.

[0003] Currently, the discussion on transducer parameters mostly focuses on the optimization of design parameters. The optimization goal rarely considers the response and matching of the actual measured object to the transducer, and there is a lack of discussion on the transducer parameters in response to the actual physical model. At the same time, the research using acoustic theory is only limited to analyzing the change of transducer output trend due to parameter changes, without involving the method of establishing a combined optimization scheme for ultrasonic transducers directly facing the measurement system. Moreover, the current research on optimizing detection parameters through acoustic modeling still only targets static objects, and there is no relevant research on moving objects.

[0004] Therefore, in view of the requirements of optimizing the establishment of an on-line ultrasonic measurement system for cable insulation layers and economic adaptability, it is necessary to design a quantitative optimization combination method for ultrasonic transducers. Summary of the Invention

[0005] The purpose of the present invention is to provide an optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer, so as to solve the technical problems that the amplitude and signal-to-noise ratio of the reflected echo signal are low during the on-line ultrasonic detection of a large-curvature vibrating cable insulation layer, which affect the measurement. And it effectively solves the problem of low signal amplitude in the traditional thickness measurement process.

[0006] A quantitative optimization method for the geometric parameters of an ultrasonic transducer is proposed to optimize the matching of the ultrasonic transducer and the signal. Decision optimization indexes such as the average amplitude, minimum amplitude, amplitude variance, and cost of the secondary reflection signal at multiple spatial positions are established. The distributed point source method is used to quantitatively calculate the sound pressure, and the multi-weight comprehensive technique for order preference by similarity to ideal solution (TOPSIS) is used to select the relatively optimal transducer geometric parameter scheme.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] An optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer, the method comprising the following steps:

[0009] Step 1: Discretize the vibration space of the production cable, measure the maximum amplitude of the cable vibration, and discretize the vibration space range into several spatial positions of stationary cables according to the vibration characteristics;

[0010] Step 2: Establish an evaluation system for transducer parameters;

[0011] Step 3: Use the distributed point source method to calculate the surface sound pressure for each transducer geometric parameter selection scheme;

[0012] Step 4: Sort all the scheme data by the multi-weight comprehensive TOPSIS method, and select the scheme closest to the ideal solution.

[0013] Further, the specific process of Step 2 is as follows:

[0014] Step 2.1 According to the cable specifications that need to be ultrasonically detected online, measure the vibration amplitude during online production, and select a preselected transducer geometry scheme group according to the amplitude.

[0015] Step 2.2 Ensure the average value of the peak values of the secondary reflection signals, the minimum amplitude of the secondary reflection signals, and the stability, and convert the indicators into the average sound pressure, the minimum sound pressure, and the sound pressure variance respectively.

[0016] Furthermore, in the average sound pressure, corresponding to the average value of the peak values of the second reflection signals, it reflects the overall amplitude voltage magnitude of the reflection signals received by the transducer, denoted by a i1 represents the average received sound pressure of the i-th preselected transducer scheme, and is defined as:

[0017]

[0018] where P in represents the average surface sound pressure received by the transducer when the cable is at the n-th spatial position under the i-th transducer scheme.

[0019] Furthermore, in the minimum sound pressure, corresponding to the minimum amplitude of the secondary reflection signals, during dynamic detection, the vibration of the cable will deviate from the acoustic axis of the transducer, resulting in a decrease in the amplitude of the reflection signals. The minimum amplitude of the secondary reflection signals reflects the performance under extreme conditions. By ensuring this value, the integrity of the measurement can be guaranteed. The minimum sound pressure a i2 under the i-th transducer scheme for the N discrete spatial positions of the cable vibration is defined as:

[0020] a i2 = min{|P i1 |, |P i2 |, …, |P iN |}.

[0021] P iN is the sound pressure at the N discrete spatial positions of the cable vibration under the i-th transducer scheme.

[0022] 5. According to the optimization method of the geometric parameters of the ultrasonic transducer for on-line thickness measurement of the cable insulation layer described in claim 2, it is characterized in that: in the sound pressure variance, reflecting the stability of the signal amplitude, to ensure accurate measurement, it is also necessary to ensure that the amplitude difference of the reflection signals within the vibration range is less than the set value, that is, the set stability. The stability of the signal amplitude is defined as the variance a i3 of the sound pressure received by the transducer surface at all discrete positions of the cable under the i-th transducer scheme. The smaller the variance, the better the stability of the reflection signal. Therefore, there is:

[0023]

[0024] Among them, the average sound pressure and the minimum sound pressure are extremely large type indicators, and the sound pressure variance is an extremely small type indicator. In addition to the performance indicators, since the prices of ultrasonic transducers of different specifications are different, which affects the economy of the measurement system and the optimization selection, the manufacturing cost a of the transducer i4 is used as a decision-making indicator, and the specific value depends on the geometric parameters and material costs of the transducer.

[0025] Furthermore, the specific process of step 3 is as follows:

[0026] In step 3.1, the sound field distribution inside the medium is regarded as the superposition of the actions of an infinite number of point sources at the edge of the medium interface in this domain. When considering the transmission and reflection of sound waves, the interface is replaced by two layers of point sources distributed on both sides of the interface, that is, the in-interface point sources generate an outward reflection field, and the out-of-interface point sources generate an inward transmission field. By establishing a system of equations for the continuity conditions of boundary stress and displacement, that is, the normal stress is continuous, the tangential stress is 0, and the normal displacement is continuous, the source intensity vector calculation is realized by establishing the boundary stress and displacement continuity equations:

[0027]

[0028] To ensure the convergence of the results, the distance between the transducer point source and the transducer interface is r s1 = λ / 2π, where λ is the wavelength, and the distance between the transducer point sources The distance from the other interface point source to the corresponding surface is r sn = λ ns / 2π, where λ ns is the shear wave wavelength of the corresponding material, and the distance between the centers of the point sources is The number of point sources on both sides of the insulation layer interface is related to the transducer diameter. To ensure accurate calculation, the modeling length in the cable axis direction is set to be the same as the transducer diameter;

[0029] In step 3.2, according to the sound pressure obtained from the system of equations, the sound pressure is integrated on the transducer surface, and the average sound pressure received by the transducer can be expressed as:

[0030]

[0031] In the formula, ρ and c w represent the density and sound velocity in water, S represents the surface area of the transducer, and v(x, ω) represents the particle velocity at the microelement on the transducer surface. Since the transducer surface has been discretized into several point sources in the distributed point source method, it is transformed into finding the average value:

[0032]

[0033] In the formula, v represents the v-th point source, and P in(x1, x2, x3) represents the sound pressure value at the coordinate (x1, x2, x3). Thus, the received sound pressure of the cable at the nth discrete spatial position under a certain transducer scheme i can be calculated based on the vibration amplitude of the cable.

[0034] Furthermore, the specific process of step 4 is as follows:

[0035] Step 4.1: To avoid subjectivity, this paper uses the decision matrix of the normalized combined scheme as the basic data, and calculates the weights respectively using three objective analysis methods: the entropy weight method, the coefficient of variation method, and the standard correlation idea method, and then comprehensively obtains the final weight;

[0036] The values calculated by the distributed point source method form the decision matrix A, and it is transformed into the matrix R through the index positive transformation.

[0037]

[0038] Step 4.2: Based on the data and weights, the technique for order preference by similarity to an ideal solution (TOPSIS) is used to perform multi-objective decision-making ranking on all schemes to achieve optimization.

[0039] Furthermore, the specific process of calculating the weights using the entropy weight method, the coefficient of variation method, and the standard correlation idea method is as follows:

[0040] (1) For the weight calculation based on the entropy weight method, first calculate the proportion p of the jth index of the ith scheme ij ;

[0041]

[0042] where r ij is the element of the positive transformation matrix of the data in A, i is the scheme to be evaluated, and then calculate the entropy value E of the jth index j :

[0043]

[0044] Finally, calculate the weight ω of the jth index j determined by the redundancy reflected by its information entropy, that is:

[0045]

[0046] (2) For the index weight calculation based on the coefficient of variation method, the coefficient of variation method reflects the discrete degree of each index. The greater the discrete degree, the greater the contribution of the index to the overall difference, and the higher the weight should be. For the jth index, first calculate its mean value and standard deviation σ j :

[0047]

[0048] Secondly, calculate the relative dispersion degree of the j-th index, i.e., the coefficient of variation CV j

[0049]

[0050] Finally, calculate the weight ω according to the coefficient of variation of the index j

[0051]

[0052] (3) Calculation of index weights based on the standard - correlation method. The standard - correlation method determines the weights by considering the comparison intensity of the indices and the conflict degree between indices, and calculates the Pearson correlation coefficient ρ of the j - th index with respect to the k - th index jk :

[0053]

[0054] The information content C of the j - th index j is determined by the standard deviation and the correlation coefficient with other indices. Finally, calculate the weights ω of each index according to the information content j :

[0055]

[0056] The comprehensive weight of the decision - making index is obtained by calculating the mean of the three objective weight calculation results obtained:

[0057]

[0058] where ω1, ω2, ω3, ω4 represent the weights of the average sound pressure, minimum sound pressure, sound - pressure variance, and cost index respectively. Finally, the multi - weight comprehensive technique for order preference by similarity to ideal solution (TOPSIS) evaluation system is used to optimize different transducer geometric - parameter schemes

[0059] Furthermore, the specific process of using the technique for order preference by similarity to ideal solution (TOPSIS) to conduct multi - objective decision - making ranking for all schemes is as follows:

[0060] (1) Convert all indices into indices greater than the set value. The average sound pressure and minimum sound pressure are already large - type indices, and the cost and variance are small - type indices. Thus, obtain the positive matrix R:

[0061]

[0062] (2) Perform weighted normalization on the R data to obtain the normalized decision - making matrix Z:

[0063]

[0064] (3) Determine the ideal solution E+ and the negative ideal solution E - , select the maximum and minimum values of each column index in the normalized matrix Z to form E + and E - ;

[0065] (4) Calculate the distance between each solution and the ideal solution and the distance to the negative ideal solution

[0066]

[0067]

[0068] (5) Calculate the closeness of each solution to the optimal solution:

[0069]

[0070] where 0 ≤ C i ≤ 1, the closer C i is to 1, the better the solution, and thus the optimal solution is selected.

[0071] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0072] The present invention can support the construction of a better online measurement system, thereby reducing the development cost and time. It provides new ideas for the detection of ultrasonic transducers in cables with large curvature and dynamic cables, and provides a reference for the selection and optimization of transducer parameters based on acoustic field modeling in the future. This method is also applicable to cables or small tubular workpieces with different materials, sizes and vibration characteristics. It only needs to re-enter the transducer size parameters, the spatial position parameters of the transducer surface, the spatial position parameters of the cable, the internal and external cable sizes, and the material parameters and perform calculations in the distributed point source model in Chongqing, and then use the technique for order preference by similarity to ideal solution to compare the preselected transducer parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is the overall flowchart of the method of the present invention.

[0074] Figure 2 is the discretized cable spatial position diagram of the present invention.

[0075] Figure 3 is the cable modeling schematic diagram of the present invention.

[0076] Figure 4 is the normalized sound pressure data diagram of the present invention.

[0077] Figure 5 is the experimental ultrasonic signal comparison diagram of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0078] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and preferred embodiments. However, it should be noted that many details listed in the specification are only for the purpose of enabling the reader to have a thorough understanding of one or more aspects of the present invention, and these aspects of the present invention can be implemented even without these specific details.

[0079] like Figures 1-5 As shown, a method for selecting geometric parameters of ultrasonic transducers for ultrasonic online detection of cable insulation layer based on distributed point source method and approximate ideal solution sorting method comprises the following steps:

[0080] Step 1: Determine the measurement cable specifications and discretize the cable vibration space. Measure the maximum amplitude of the cable vibration, and discretize its vibration space range into multiple spatial positions of static cables according to its vibration characteristics. Take the 4 square copper core cable as the test object to demonstrate and verify the process and effectiveness of selecting the most suitable ultrasonic transducer to build an insulation thickness detection system using the method in this paper. The cylindrical cross-sectional area of the cable copper core is 4mm 2 (outer diameter is 1.92mm), the thickness t of the PVC insulation layer is required to be at least 0.8mm, so the curvature is relatively large. The cable is in unbounded water. The relevant material parameters are shown in Table 1. Assuming that the maximum vibration amplitude of the cable during production is D = 5mm, the spatial position of the cable under vibration is discretized into 17 different positions according to the vibration characteristics, such as Figure 2 shown.

[0081] Table 1 Material parameters

[0082]

[0083] Step 2.1: According to the specifications of the cable to be ultrasonically tested online, measure its vibration amplitude during online production, and select a preselected transducer geometry solution group based on the amplitude.

[0084] To ensure accurate thickness measurement, the center frequency of the transducer is selected as 10MHz, and the radius R of the transducer chip is initially selected according to the vibration amplitude. c There are five types: 5, 6, 7, 8, and 9 mm. As the chip radius increases, the minimum focal length increases accordingly. There are 11 types of f at each radius, forming a total of 55 combination schemes, as shown in Table 2.

[0085] Table 2 Combinations of ultrasonic transducer chip radius (mm) and focal length (mm) at 10MHz frequency

[0086]

[0087] Step 2.2 Ensure the average value of the peak of the secondary reflection signal, the minimum amplitude of the secondary reflection signal, and the stability. Convert the above indicators into average sound pressure, minimum sound pressure, and sound pressure variance respectively.

[0088] Average sound pressure:

[0089] Corresponding to the average value of the peak of the second reflection signal, it reflects the overall amplitude voltage size of the reflection signal received by the transducer, denoted by a i1 The average received sound pressure of the i-th transducer preselection scheme is defined as:

[0090]

[0091] where P in represents the average surface sound pressure received by the transducer when the cable is at the n-th spatial position under the i-th transducer scheme.

[0092] Minimum sound pressure:

[0093] Corresponding to the minimum amplitude of the secondary reflection signal. In dynamic detection, the vibration of the cable will deviate from the acoustic axis of the transducer, resulting in a decrease in the amplitude of the reflection signal. The minimum amplitude of the secondary reflection signal reflects the performance in extreme cases, and ensuring this value can guarantee the integrity of the measurement. The minimum sound pressure a among the N discrete spatial positions of the cable vibration under the i-th transducer scheme i2 is defined as:

[0094] a i2 = min{|P i1 |, |P i2 |, …, |P iN |}

[0095] Sound pressure variance:

[0096] Reflects the stability of the signal amplitude. To ensure accurate measurement, it is also necessary to ensure that the amplitude difference of the reflection signal within the vibration range is small, that is, it has good stability. The stability of the signal amplitude is defined as the variance a of the sound pressure received by the transducer surface at all discrete positions of the cable under the i-th transducer scheme i3 , the smaller the variance, the better the stability of the reflection signal. Therefore, there is:

[0097]

[0098] where the average sound pressure and the minimum sound pressure are extremely large indicators, and the sound pressure variance is an extremely small indicator. In addition to the performance indicators, since the prices of ultrasonic transducers of different specifications are different, which affects the economy of the measurement system and affects the optimization. Therefore, the manufacturing cost a of the transducer i4 is used as a decision-making indicator, and the specific value depends on the geometric parameters and material costs of the transducer.

[0099] Step 3.1 The sound field distribution inside the medium can be regarded as the superposition of the actions of an infinite number of point sources at the edge of the medium interface in this domain. When considering the transmission and reflection of sound waves, two layers of point sources distributed on both sides of the interface are used at the interface, that is, the in-interface point sources generate an outward reflection field, and the out-of-interface point sources generate an inward transmission field. By establishing a system of equations for the continuity conditions of boundary stress and displacement, that is, the normal stress is continuous, the tangential stress is 0, and the normal displacement is continuous, the source intensity vector calculation is realized. The cable modeling is as Figure 3 shown

[0100]

[0101] To ensure the convergence of the results, the distance between the transducer point source and the transducer interface is r s1 =λ / 2π (λ is the wavelength), and the transducer point sources are separated by The distance of other interface point sources from the corresponding surface is r sn =λ ns / 2π (λ ns is the shear wave wavelength of the corresponding material), and the distance between the centers of the point sources is The number of point sources on both sides of the insulation layer interface is related to the diameter of the transducer. To ensure accurate calculation, the modeling length in the cable axis direction is set to be the same as the transducer diameter.

[0102] Step 3.2 According to the sound pressure obtained from the system of equations, the sound pressure is integrated on the transducer surface, and the average sound pressure received by the transducer can be expressed as:

[0103]

[0104] In the formula, ρ and c w represent the density and sound velocity in water, S represents the surface area of the transducer, and v(x,ω) represents the particle velocity at the microelement on the transducer surface. Since the transducer surface has been discretized into multiple point sources in the distributed point source method, therefore, it is transformed into finding the average value:

[0105]

[0106] In the formula, v represents the v-th point source, and P in (x1,x2,x3) represents the sound pressure value at the coordinates (x1,x2,x3). Thus, the received sound pressure of the cable at the n-th discrete spatial position under a certain transducer scheme i can be calculated according to the vibration amplitude of the cable.

[0107] In the index calculation of the preselected transducer scheme, the output loss caused by the change in the wafer radius is ignored, and the output sound pressure on the transducer surface is inversely proportional to the wafer area. Figure 4The average sound pressure, minimum sound pressure, and sound pressure variance received on the transducer surface obtained by the D modeling method for parameter combinations of different transducers. As can be seen from the figure, when the radius of the transducer wafer remains unchanged, as the focal length increases, the average sound pressure and minimum sound pressure received by the transducer gradually decrease, indicating that as the propagation distance increases, the influence of the defocusing effect becomes more obvious. At the same focal length, the smaller the radius, the higher the sound pressure received on the transducer surface (ignoring extreme cases). On the other hand, increasing the focal length brings better variance performance. This is because increasing the focal length results in a longer focal region, and the incident sound pressure of the cable at the edge of vertical vibration is relatively larger than that in the short focal region. For the 5 and 6 mm wafer radius specifications, when the cable vibrates horizontally to the maximum amplitude, the radiation sound field of the transducer cannot cover the entire cable, resulting in the received minimum sound pressure being significantly lower than that of transducers with other wafer radius specifications. And compared with transducers of other radius specifications, the 5 mm wafer radius transducer has a smaller selected focal length range, larger fluctuations in the received sound pressure caused by vibration, larger variance, and poorer stability performance. At the same focal length, as the wafer radius of the transducer increases, the area of the transducer wafer becomes larger, the output sound pressure decreases, and the average received sound pressure decreases accordingly, but the stability performance is better.

[0108] Step 4.1 To avoid subjectivity, this paper uses the decision matrix of the normalized combination scheme as the basic data, and uses three objective analysis methods, namely the entropy weight method, the coefficient of variation method, and the standard correlation idea, to calculate the weights respectively, and then comprehensively obtain the final weight. The weight calculation methods for each method are as follows. The values calculated by the distributed point source method form the decision matrix A, and it is transformed into the matrix R through index positive normalization.

[0109]

[0110] (1) Weight calculation based on the entropy weight method. First, calculate the proportion p of the j-th index of the i-th scheme ij .

[0111]

[0112] Among them, r ij is the element of the positive normalization matrix of the data in A, and i is the scheme to be evaluated. Then calculate the entropy value E of the j-th index j .

[0113]

[0114] Finally, calculate the weight ω of the j-th index j Determined by the redundancy reflected by its information entropy, that is:

[0115]

[0116] (2) Calculation of index weights based on the coefficient of variation method. The coefficient of variation method reflects the degree of dispersion of each index. The greater the degree of dispersion, the greater the contribution of the index to the overall difference, and the higher the weight should be. For the j-th index, first calculate its mean and standard deviation σ j :

[0117]

[0118] Secondly, calculate the relative degree of dispersion of the j-th index, that is, the coefficient of variation CV j

[0119]

[0120] Finally, calculate the weight ω according to the coefficient of variation of each index j

[0121]

[0122] (3) Calculation of index weights based on the standard correlation method. The standard correlation method determines the weight by considering the comparison intensity of the indexes and the degree of conflict between the indexes. Calculate the Pearson correlation coefficient ρ of the j-th index with respect to the k-th index jk :

[0123]

[0124] The information content C of the j-th index j is determined by its standard deviation and the correlation coefficient with other indexes. Finally, calculate the weight ω of each index according to the information content j .

[0125]

[0126] Based on the calculation results of the three objective weights obtained by the above methods, the comprehensive weight of the decision-making index is obtained by calculating their mean values.

[0127]

[0128] Among them, ω1, ω2, ω3, ω4 represent the weights of the average sound pressure, minimum sound pressure, sound pressure variance, and cost index respectively. As shown in Table 3.

[0129] Table 3 Calculation Results of Objective Analysis Method Weights

[0130]

[0131] Step 4.2 Based on the above data and weights, use the technique for order preference by similarity to an ideal solution (TOPSIS) to perform multi-objective decision-making ranking on all schemes to achieve optimization. The algorithm process is as follows:

[0132] (1) Convert all indicators into maximization indicators. In the method proposed in this paper, the average sound pressure and the minimum sound pressure are already maximization indicators, while the cost and variance are minimization indicators. Thus, the positive matrix R is obtained.

[0133]

[0134] (2) Perform weighted normalization on the R data to obtain the normalized decision matrix Z.

[0135]

[0136] (3) Determine the ideal solution E + and the negative ideal solution E - . Select the maximum and minimum values of each column index in the normalized matrix Z to form E + and E - .

[0137] (4) Calculate the distance between each scheme and the ideal solution and the distance between each scheme and the negative ideal solution

[0138]

[0139] (5) Calculate the closeness of each scheme to the optimal solution.

[0140]

[0141] Among them, 0 ≤ C i ≤ 1, and the closer C i is to 1, the better the scheme. Thus, the optimal scheme is selected. The final results are shown in Table 4.

[0142] Table A.1 Ranking results of multi-weight aggregated TOPSIS and objective weight calculation methods

[0143]

[0144]

[0145]

[0146] To verify the correctness of the foregoing simulation data and optimization results, a physical experiment was carried out using a single-transmitter and single-receiver line-focusing ultrasonic transducer (center frequency 10 MHz, radius 7 mm, focal length 21 mm) according to the above calculation results. At the same time, ultrasonic transducers of the same type with wafer radii of 7 mm, focal lengths of 30 mm, and wafer radii of 9 mm and focal lengths of 30 mm were used for comparative experiments, which were respectively called transducers 1, 2, and 3. The experimental comparison between transducers 1 and 2 was used to prove that under the same wafer radius as described above, the larger the focal length, the lower the amplitude of the received signal. The experimental comparison between transducers 2 and 3 was used to prove that under the same focal length as described above, the larger the radius, the lower the amplitude of the received signal. The excitation / reception of ultrasonic signals was realized through a separate ultrasonic acquisition card, and a personal PC was used to communicate with the ultrasonic acquisition card for the setting of the excitation signal and the acquisition and recording of ultrasonic signals. The transducer was clamped at the end of a three-axis robotic arm, and the precise control of the three-axis movement of the robotic arm was realized through an industrial control PC. The cable was specified as a 4-square wire and was suspended in water through a cylindrical clamping tool. The ultrasonic board card was excited by a square wave signal with an excitation voltage of 200 V, a pulse width of 50 ns, an impedance of 50 Ω, a receiving gain of +50 dB, and a signal sampling frequency of 100 MHz. First, the horizontal position of the transducer was adjusted through the industrial control PC to make the cable axis in the center of the transducer. Secondly, the vertical gap of the robotic arm was adjusted, and the transducer was moved to make the cable at the center of the focus. The vibration of the cable was replaced by moving the robotic arm to offset the cable from the acoustic axis and focus of the transducer. The discrete points of vibration were the same as those in the foregoing example method, with a total of 17 recording points. The maximum offset amplitude was set to 5 mm, and the personal PC was used to record the peak value of the second echo of the Ascan.

[0147] Figure 5 The intercepted cables were respectively at Figure 2Waveform diagrams received by three different specifications of line-focusing ultrasonic transducers at position 1 (no vibration of the cable), position 3 (maximum vibration amplitude in the vertical direction), and position 7 (maximum vibration amplitude in the horizontal direction) defined in . The left vertical axis represents the signal amplitude in percentage, the right logarithmic vertical axis represents the signal variance, and the horizontal axis represents the sampling points. It can be seen that under the same input conditions, the signal amplitude received by the transducer with a 9-mm wafer radius is significantly smaller than that of the transducer with a 7-mm wafer radius. When the wafer radius is 7 mm, the amplitudes of the first wave and the secondary reflection signal are both the best, and the transducer with a 21-mm focal length performs better than the transducer with a 30-mm focal length. When the cable is at the maximum horizontal offset position (position 7), the signal of the 7-mm radius transducer weakens significantly, while the signal amplitude of the 9-mm radius transducer remains almost unchanged. However, since the overall signal amplitude of the 9-mm wafer radius transducer is significantly lower than that of the 7-mm radius signal, the signal feedback under the same conditions is worse. From the above results, it can be seen that the overall signal amplitude of the 7-mm wafer radius and 21-mm focal length ultrasonic transducer is slightly better than that of the 7-mm wafer radius and 30-mm focal length ultrasonic transducer, and significantly better than that of the 9-mm wafer radius and 30-mm focal length ultrasonic transducer, reflecting that the trend of the model calculation results is consistent with the experimental measurement results in terms of amplitude, and the selected scheme is effective. This provides a quantitative numerical optimization method for building an actual ultrasonic measurement system, which can reduce the test cost and improve the performance of the ultrasonic measurement system. The average amplitude of the secondary signal of the relatively optimal transducer for the test cable selected according to the method in this paper is increased by 4.85% and 112.02% respectively compared with other transducers.

[0148] Matters not covered by this invention are well-known technologies.

[0149] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. An optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer, characterized in that: The method includes the following steps: Step 1: Discretize the vibration space of the production cable, measure the maximum amplitude of the cable vibration, and discretize the vibration space range into several spatial positions of the stationary cable according to the vibration characteristics; Step 2: Establish an evaluation system for the transducer parameters; Step 3: Calculate the surface sound pressure for each transducer geometric parameter selection scheme using the distributed point source method; Step 4: Sort all the scheme data using the multi-weight comprehensive technique for order preference by similarity to ideal solution (TOPSIS) method, and select the scheme closest to the ideal solution.

2. The optimization method of the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 1, characterized in that: The specific process of Step 2 is as follows: Step 2.1 According to the cable specifications that need to be ultrasonically detected online, measure the vibration amplitude during online production, and select a preselected group of transducer geometric schemes according to the amplitude; Step 2.2 Ensure the average value of the peak value of the secondary reflection signal, the minimum amplitude of the secondary reflection signal, and the stability, and convert the indicators into the average sound pressure, the minimum sound pressure, and the sound pressure variance respectively.

3. The optimization method of the geometric parameters of the ultrasonic transducer for on-line thickness measurement of the cable insulation layer according to claim 2, characterized in that: In the average sound pressure, the average value corresponding to the peak value of the second reflection signal reflects the overall amplitude voltage magnitude of the reflection signal received by the transducer, denoted as a i1 The average received sound pressure of the i-th transducer preselection scheme is defined as: Among them, P in represents the average surface sound pressure received by the transducer when the cable is at the nth spatial position under the ith transducer scheme.

4. An optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 2, characterized in that: At the minimum sound pressure, the amplitude of the minimum secondary reflection signal corresponds. During dynamic detection, cable vibration will deviate from the acoustic axis of the transducer, resulting in a decrease in the amplitude of the reflection signal. The minimum amplitude of the secondary reflection signal reflects the performance in extreme cases. By ensuring this value, the integrity of the measurement can be guaranteed. The minimum sound pressure a among the N discrete spatial positions of cable vibration under the i-th transducer scheme i2 is defined as: a i2 = min{|P i1 |, |P i2 |, …, |P iN |}。 P iN is the sound pressure at N discrete spatial positions of the cable vibration under the i-th transducer scheme.

5. An optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 2, characterized in that: In the sound pressure variance, which reflects the stability of the signal amplitude, to ensure accurate measurement, it is also necessary to ensure that the amplitude difference of the reflected signal within the vibration range is less than the set value, that is, the set stability. The stability of the signal amplitude is defined as the variance a of the sound pressure received on the transducer surface at all discrete positions of the cable under the i-th transducer scheme. i3 , the smaller the variance, the better the stability of the reflected signal. Therefore, we have: Among them, the average sound pressure and the minimum sound pressure are extremely large type indicators, and the sound pressure variance is an extremely small type indicator. In addition to the performance indicators, since the prices of ultrasonic transducers of different specifications are different, it affects the economy of the measurement system and the optimization selection. Therefore, the manufacturing cost a of the transducer i4 is used as a decision-making indicator, and the specific value depends on the geometric parameters and material costs of the transducer.

6. The optimization method of the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 1, characterized in that: The specific process of Step 3 is as follows: Step 3.1 Consider the sound field distribution inside the medium as the superposition of the actions of an infinite number of point sources at the edge of the medium interface in this domain. When considering the transmission and reflection of sound waves, the interface is replaced by two layers of point sources distributed on both sides of the interface, that is, the in-interface point sources generate an outward reflection field, and the out-of-interface point sources generate an inward transmission field. By establishing a system of equations for the continuity conditions of boundary stress and displacement, that is, the normal stress is continuous, the tangential stress is 0, and the normal displacement is continuous, and by establishing the boundary stress and displacement continuity equations, the calculation of the source strength vector is realized: To ensure the convergence of the results, the distance between the transducer point source and the transducer interface is r s1 = λ / 2π, where λ is the wavelength, and the transducer point sources are separated by The other interface point source is at a distance r from the corresponding surface sn = λ ns / 2π, λ ns is the shear wave wavelength of the corresponding material, and the distance between the centers of the point sources is The number of point sources on both sides of the insulation layer interface is related to the transducer diameter. To ensure accurate calculations, the modeling length in the cable axis direction is set to be the same as the transducer diameter; Step 3.2 Integrate the sound pressure obtained from the system of equations on the surface of the transducer, and the average sound pressure received by the transducer can be expressed as: where ρ and c w represent the density and the sound speed in water, S represents the surface area of the transducer, and v(x, ω) represents the particle velocity at the infinitesimal element on the transducer surface. Since the transducer surface has been discretized into a number of point sources in the distributed point source method, it is thus transformed into finding the average value: where \(v\) represents the \(v\)-th point source, \(P\) in (x1, x2, x3) represents the sound pressure value at the coordinate (x1, x2, x3). Thus, based on the vibration amplitude of the cable, the received sound pressure of the cable at the \(n\)-th discrete spatial position under a certain transducer scheme \(i\) can be calculated.

7. The optimization method of the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 1, characterized in that: The specific process of Step 4 is as follows: Step 4.1: To avoid subjectivity, this paper uses the decision matrix of the normalized combined scheme as the basic data, and uses three objective analysis methods, namely the entropy weight method, the coefficient of variation method, and the standard correlation idea method, to calculate the weights respectively, and then comprehensively obtain the final weights; The values calculated by the distributed point source method form the decision matrix A, and it is transformed into the matrix R through the positive processing of the indicators; Step 4.2: Based on the data and weights, use the technique for order preference by similarity to ideal solution (TOPSIS) method to perform several objective decision-making rankings on all the schemes to achieve optimization.

8. An optimization method for the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 7, characterized in that: The specific process of calculating the weights using the entropy weight method, the coefficient of variation method, and the standard correlation idea method is as follows: (1) Weight calculation based on the entropy weight method. First, calculate the proportion p of the j-th index of the i-th solution ij ; where r ij is an element of the positive matrix of the data in A, i is the scheme to be evaluated, and then calculate the entropy value E j of the j-th index: Finally, calculate the weight ω of the j-th index j which is determined by the redundancy reflected by its information entropy, i.e.: (2) Index weight calculation based on the coefficient of variation method. The coefficient of variation method reflects the degree of dispersion of each index. The greater the degree of dispersion, the greater the contribution of the index to the overall difference, and the higher the weight should be. For the j-th index, first calculate its mean and standard deviation σ j : Secondly, calculate the relative dispersion degree of the j-th index, i.e., the coefficient of variation CV j Finally, calculate the weight ω according to the coefficient of variation of the indicators j (3) Calculation of index weights based on the standard - room correlation method. The standard - room correlation method determines weights by considering the comparison strength of indicators and the conflict degree between indicators, and calculates the Pearson correlation coefficient ρ of the j - th indicator with respect to the k - th indicator jk : The information content C of the j-th index j It is determined by the standard deviation and the correlation coefficient with other indices. Finally, the weight ω of each index is calculated based on the information content j : The three objective weight calculation results obtained are used to obtain the comprehensive weight of the decision-making indicators by calculating their mean values: Among them, ω1, ω2, ω3, ω4 represent the weights of the average sound pressure, the minimum sound pressure, the sound pressure variance, and the cost index respectively. Finally, through the multi-weight comprehensive technique for order preference by similarity to ideal solution (TOPSIS) evaluation system, the different transducer geometric parameter schemes are optimized.

9. The optimization method of the geometric parameters of an ultrasonic transducer for on-line thickness measurement of a cable insulation layer according to claim 8, characterized in that: The specific process of using the technique for order preference by similarity to ideal solution (TOPSIS) method to perform several objective decision-making rankings on all the schemes is as follows: (1) Convert all the indicators into indicators greater than the set value. The average sound pressure and the minimum sound pressure are already positive-type indicators, and the cost and variance are negative-type indicators. Thus, the positive matrix R is obtained: (2) Perform weighted normalization on the R data to obtain the normalized decision matrix Z: (3) Determine the ideal solution E + and the negative ideal solution E - , select the maximum and minimum values of each column index in the normalized matrix Z to form E + and E - ; (4) Calculate the distance between each solution and the ideal solution and the distance to the negative ideal solution (5) Calculate the proximity of each scheme to the optimal solution: where 0 ≤ C i ≤ 1, and the closer C i is to 1, the better the solution, so as to select the optimal solution.

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