Piezoelectric transducer design method based on wavenumber domain optimization and resonance compensation

Abstract

The invention provides a piezoelectric transducer design method based on wavenumber domain optimization and resonance compensation, belongs to the technical field of piezoelectric transducers, and solves the problems that a piezoelectric patch resonant frequency compensation algorithm is complex and high in application difficulty, and the resonant frequency of a piezoelectric patch is not compensated from the piezoelectric patch. Smoothing the impedance data to obtain a smoothed frequency-impedance curve; s2, performing normalization processing on the smoothed frequency-impedance curve to obtain amplitude-frequency characteristics of the electrode; s3, mapping the measured amplitude-frequency characteristic function to a wavenumber domain to construct a wavenumber domain function; s4, converting the wavenumber domain function into a physical space by using inverse Fourier transform to obtain a spatial domain structure of the excitation electrode; and S5, carrying out thresholding processing on the spatial domain structure of the excitation electrode to obtain an electrode spatial structure for processing.

Description

Technical Field

[0001] The present invention relates to a design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation, belonging to the technical field of piezoelectric transducers. Background Art

[0002] Piezoelectric wafers, as the core hardware for ultrasonic detection, play an important role in the field of non-destructive testing. For the detection results, the signal amplitude is one of the key parameters in non-destructive testing because it directly affects the identification and evaluation of material defects. However, when the piezoelectric wafer operates near the resonance frequency, a small frequency change will cause a drastic fluctuation in the output signal amplitude. At the resonance peak, the signal amplitude will be greatly enhanced, and once deviating from this frequency, the amplitude will rapidly decay, with a difference of even hundreds of times between the two, which will lead to an overly large dynamic range of the signal during the detection process, making the interpretation of defect signals more complex. Therefore, developing a fast and effective resonance frequency compensation method for piezoelectric wafers is of great significance for improving the system stability and accuracy.

[0003] Currently, most existing studies attempt to solve this problem from the perspective of signal processing, without compensating the resonance frequency from the piezoelectric wafer itself, and often have a high application difficulty. Dong Wuwen proposed a receiving transducer based on piezoelectric ceramics in the patent CN218848051U. This transducer can obtain a flat signal frequency response below the frequency of the resonance point, but it does not solve the problem of signal distortion near the resonance point, and the operating frequency is still restricted by the resonance frequency. Xu Jiawen et al. proposed a least squares method for extracting the resonance frequency in the patent CN114564985A. Although this method extracts the resonance frequency through a complex algorithm to guide the compensation of the resonance frequency, this method relies on subsequent processing circuits and a large number of preliminary experiments, with a high practical application difficulty and cost. Summary of the Invention

[0004] The present invention aims to solve the problems of complex resonance frequency compensation algorithms for piezoelectric wafers, high application difficulty, and not compensating the resonance frequency from the piezoelectric wafer itself, and further proposes a design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0006] Step 1: Calculate the impedance of the piezoelectric wafer and plot the frequency-impedance curve, and smooth the impedance data to obtain the smoothed frequency-impedance curve;

[0007] Step 2: Obtain the amplitude-frequency characteristics of the electrode based on the smoothed frequency-impedance curve, and construct the wavenumber domain function of the electrode according to the amplitude-frequency characteristics of the electrode;

[0008] Step 3: Perform inverse Fourier transform and threshold processing on the wavenumber domain function of the constructed electrode to obtain the spatial structure of the piezoelectric transducer, thus completing the design of the piezoelectric transducer.

[0009] Preferably, Step 1 specifically includes:

[0010] Step 1.1: Calculate the impedance Z(f) of the piezoelectric sheet based on the equivalent circuit model;

[0011] Step 1.2: Calculate the amplitude characteristic T p (f) of the piezoelectric sheet based on the impedance Z(f) of the piezoelectric sheet, and plot the frequency-impedance curve according to the amplitude characteristic T p (f) of the piezoelectric sheet and the amplitude-frequency characteristic T e (f) of the electrode;

[0012] Step 1.3: Eliminate the resonance peak in the frequency-impedance curve in the total amplitude-frequency characteristic by matching the amplitude-frequency characteristic of the electrode with the impedance characteristic of the piezoelectric sheet;

[0013] Step 1.4: Measure the original impedance Z(f j ) of the piezoelectric sheet through an impedance analyzer and replace the impedance data in the frequency-impedance curve, and perform smoothing processing on the original impedance Z(f j ) using the average moving smoothing method to remove the high-frequency noise of the data points and obtain the smoothed frequency-impedance curve;

[0014] The calculation formula for the impedance Z(f) of the piezoelectric sheet is:

[0015]

[0016] In formula (1), R is the loss resistance, L is the equivalent inductance, C is the equivalent capacitance, ω = 2πf is the angular frequency, and the resonance peak is located near the resonance frequency ;

[0017] The calculation formula for the total amplitude-frequency characteristic is:

[0018] T total (f) = T p (f) · T e (f) (2);

[0019] In formula (2), T total (f) is the total amplitude-frequency characteristic;

[0020] The calculation formula for the amplitude characteristic T p (f) of the piezoelectric sheet is:

[0021]

[0022] In formula (3), Y(f) is the admittance characteristic of the piezoelectric sheet. To make T total (f) flat, the amplitude-frequency characteristic T e (f) of the electrode should satisfy:

[0023]

[0024] The expression for the smoothing process of the original impedance Z(f i ) is:

[0025]

[0026] In formula (5), is the data point after smoothing, N is the size of the smoothing window, and Z(f j ) is the original impedance.

[0027] Preferably, step 2 specifically includes:

[0028] Step 2.1: Normalize and fit the impedance data in the smoothed frequency-impedance curve to obtain the amplitude-frequency characteristic;

[0029] Step 2.2: Map the amplitude-frequency characteristic of the electrode to a wavenumber domain function to construct the wavenumber domain function of the electrode.

[0030] Preferably, step 2.1 specifically includes:

[0031] Step 2.1.1: Normalize the impedance data in the smoothed frequency-impedance curve and scale the amplitude of the impedance data to the interval [0,1];

[0032] Step 2.1.2: Use a high-order polynomial to fit the impedance data, and convert the polynomial coefficients of the high-order polynomial to c = [c0, c1,..., c n T to obtain the converted fitting function;

[0033] Step 2.1.3: Organize all the observed data and polynomial terms in the converted fitting function into a matrix form to obtain matrix A, vector c, and output vector B;

[0034] Step 2.1.4: Convert the fitting problem into a matrix equation through matrix A, vector c, and output vector B, and minimize the sum of squared errors through the matrix equation to obtain the most fitting polynomial function P″(f);

[0035] Step 2.1.5: Uniformly take N independent variable equally spaced points f min , f max on the obtained polynomial function P″(f), and for each f i , for each f i ​, the corresponding amplitude-frequency characteristic function P″(f) is calculated through the most fitting polynomial function P″(f i ), where the independent variable equidistant points f i have an interval of Δf;

[0036] The expression for normalization processing is:

[0037]

[0038] In formula (6), is the peak value of the smoothed impedance data, is the impedance data after normalization;

[0039] The expression for high-order polynomial fitting processing is:

[0040] P(f) = c0 + c1f + c2f 2 +…+ c 30 f n (7);

[0041]

[0042] In formulas (7) and (8), P(f) is the fitted polynomial, and its amplitude P(f i ) is the impedance value, and c0, c1, …, c n are the polynomial coefficients obtained through the fitting method;

[0043] The expression for the converted fitting function is:

[0044]

[0045] The expression for matrix A is:

[0046]

[0047] The expression for output vector B is:

[0048]

[0049] The expression for the matrix equation is:

[0050] A·c = B(12);

[0051] In formula (12), c is the optimal polynomial coefficient;

[0052] The expression for the optimal polynomial coefficient c is:

[0053] c = (A T A) -1 A T B(13);

[0054] In formula (13), A T is the transpose of matrix A, and (A T A) -1 is the inverse matrix of matrix A;

[0055] The expression of the equidistant points f of the independent variable i is:

[0056] f i = f min + i·Δf, where i = 0, 1, 2,..., N - 1 (14);

[0057] The expression of the interval Δf of the equidistant points f of the independent variable i is:

[0058]

[0059] The expression of the amplitude-frequency characteristic function P″(f i ) is:

[0060] P″(f i ) = c0 + c1f i + c2f i 2 + … + c 30 f i n (16).

[0061] Preferably, step 2.2 specifically includes:

[0062] Step 2.2.1: Set that the spiral shape of the Archimedean spiral is determined by the polar coordinate system, and the radius r i and the angle θ i vary with i;

[0063] Step 2.2..2: Through the polar coordinate and Cartesian coordinate conversion formula, convert the polar coordinates (r i , θ i ) of the i-th point on the spiral into Cartesian coordinates (x i , y i );

[0064] Step 2.2.3: Take the function value z i , y i ) at the coordinate (x i ) as P″(f i ), and obtain the wavenumber domain space point (x i , y i , z i ) representation;

[0065] Step 2.2.4: Based on the wavenumber domain space point (xi , y i , z i ) represents the calculated wavenumber vector of the target electrode

[0066] Step 2.2.5: Based on the wavenumber vector of the target electrode Construct the wavenumber domain function T e (k);

[0067] The radius r of the helix i The expression is:

[0068] r i = r min + i·Δr (17);

[0069] In formula (17), r min is the initial radius, and Δr is the radius increment for each point;

[0070] The angle θ of the helix i The expression is:

[0071] θ i = θ min + i·Δθ(18);

[0072] In formula (18), θ min is the initial angle, and Δθ is the angle increment for each point;

[0073] The Cartesian coordinates (x i , y i ) The expression is:

[0074]

[0075] (x i , y i ) The function value z i The expression is:

[0076] z i = P″(f i )(20);

[0077] The wavenumber domain space point (x i , y i , z i ) is expressed as:

[0078]

[0079] The wavenumber vector of the target electrode The expression is:

[0080]

[0081] In formula (22), r min is the initial radius, indicating the starting point of the wave number domain. Δr is the radius step, which is used to control the wave number domain point to gradually expand outward along the spiral line. min is the initial angle, indicating the starting direction of the spiral line, Δθ is the angle step, which is used to control the discrete density of wave number domain points on the spiral line, P″(f i ) is the frequency domain characteristic sampling value, representing the wave number domain amplitude intensity of the corresponding point, are the two-dimensional coordinates of the points in the wavenumber domain and the corresponding amplitudes;

[0082] Wavenumber domain function T e The expression of (k) is:

[0083]

[0084] In formula (23), T e (k j ) is the corresponding weight of the frequency domain characteristics.

[0085] Preferably, step 3 specifically includes:

[0086] Step 3.1: Use the inverse Fourier transform to transform the wavenumber domain function T e (k) converting to physical space to obtain the spatial domain structure of the excitation electrode;

[0087] Step 3.2: Thresholding the spatial domain structure of the excitation electrode for processing the electrode spatial structure;

[0088] The expression of the spatial domain structure of the excitation electrode is:

[0089]

[0090] In formula (24), T e (x,y) is the spatial domain structure of the excitation electrode.

[0091] The beneficial effects of the present invention are:

[0092] 1. The present invention adjusts the structure of the excitation electrode so that the electrode amplitude-frequency characteristic and the piezoelectric sheet amplitude-frequency characteristic are multiplied to be constant, thereby significantly reducing the amplitude-frequency fluctuation, accurately locating the resonance peak of the piezoelectric sheet and optimizing it in a targeted manner, and expanding the working range of the piezoelectric sheet while ensuring the working stability of the piezoelectric sheet. This method greatly reduces the problem of signal amplitude distortion, improves the linearity and stability of the signal, and enables the transducer output to have a higher signal-to-noise ratio, meeting the needs of high-precision scenarios.

[0093] 2. In terms of practical applications, the present invention does not rely on complex external circuit regulation. Instead, it directly achieves intrinsic physical compensation by optimizing the electrode shape and distribution, simplifying the system design. The wavenumber domain intensity function can be used to flexibly adjust the electrode distribution to achieve precise control of the dynamic compensation of the piezoelectric sheet characteristics, providing a simple and reliable mathematical model for the resonance compensation method.

[0094] 3. The overall complexity of the algorithm applied in the present invention shows a characteristic of logarithmic linear growth, which is particularly suitable for large-scale data processing. On the premise of effectively realizing the resonance frequency compensation of the piezoelectric sheet, the present invention also has significant advantages in memory usage and operation speed, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 is a schematic flow chart of a piezoelectric transducer design method based on wavenumber domain optimization and resonance compensation provided by the present invention;

[0096] Figure 2 is a curve graph of impedance analysis results provided by the present invention;

[0097] Figure 3 is a schematic diagram of the wavenumber domain function created by the present invention;

[0098] Figure 4 is a schematic diagram of the space and distribution of the electrodes provided by the present invention;

[0099] Figure 5 is a schematic diagram showing the consistent resonance peak effect of the overall admittance curve of the transducer before and after the electrode structure design compensation provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0100] Combined with Figures 1-5 to illustrate this embodiment. As Figure 1 shown, the steps of a piezoelectric transducer design method based on wavenumber domain optimization and resonance compensation described in this embodiment include:

[0101] S1: Plot the frequency-impedance curve of the piezoelectric sheet, smooth the impedance data, and obtain the smoothed frequency-impedance curve;

[0102] S101: As the core component of the transducer, the impedance characteristics of the piezoelectric sheet determine the existence of the resonance peak. The impedance Z(f) of the piezoelectric sheet can be expressed by the equivalent circuit model as:

[0103]

[0104] In formula (1), R is the loss resistance, L is the equivalent inductance, C is the equivalent capacitance, ω = 2πf is the angular frequency, and at the resonance frequency Nearby, the mechanical and electrical characteristics reach resonance, and the impedance amplitude changes sharply, showing a resonance peak.

[0105] S102: To suppress the resonance peak, in this embodiment, starting from the overall amplitude-frequency characteristic of the transducer, which is determined by the product of the amplitude-frequency characteristic T p (f) of the piezoelectric element and the amplitude-frequency characteristic T e (f) of the electrode:

[0106] T total (f) = T p (f) · T e (f)(2);

[0107] In formula (2), T total (f) is the overall amplitude-frequency characteristic;

[0108] The amplitude characteristic T p (f) of the piezoelectric element is calculated by the formula:

[0109]

[0110] In formula (3), Y(f) is the admittance characteristic of the piezoelectric element. The key to suppressing the resonance peak lies in designing the amplitude-frequency characteristic T e (f) of the electrode to make T total (f) as flat as possible. For this purpose, the electrode characteristics need to satisfy:

[0111]

[0112] S103: By matching the amplitude-frequency characteristic of the electrode with the impedance characteristic of the piezoelectric element, the cancellation of the resonance peak can be achieved in the overall amplitude-frequency characteristic.

[0113] To ensure the accuracy of compensation, in actual operation, the original impedance Z(f i ) of the piezoelectric element should be measured by an impedance analyzer. Subsequently, the data should be smoothed using the moving average smoothing method:

[0114]

[0115] In formula (5), is the data point after smoothing, N is the size of the smoothing window, Z(f j ) is the original impedance, and the moving average smoothing method reduces the high-frequency noise by calculating the average value of N points around each data point.

[0116] Combining the above steps, in this embodiment, impedance analysis is performed on a 1.5-mm-thick piezoelectric element, and the impedance analysis results are as shown in Figure 2As shown, for the impedance curve of the piezoelectric sheet (before(Z)), it can be found that there is an obvious resonance peak near 240 kHz. Smooth and denoise this curve, and perform least squares fitting on it using a 30th-order curve. The curve after fitting (after(Z)) is smooth and its trend is consistent with the circular curve.

[0117] S2: Normalize the smoothed frequency-impedance curve to obtain the amplitude-frequency characteristics of the electrode;

[0118] S201: Normalize the impedance data in the smoothed frequency-impedance curve and scale the amplitude of the impedance data to the interval [0, 1];

[0119] The expression for the normalization process is:

[0120]

[0121] In formula (6), is the peak value of the smoothed impedance data, is the impedance data after normalization;

[0122] This step scales the amplitude of the data to the interval [0, 1], thereby eliminating the differences in amplitude under different experimental conditions and facilitating subsequent processing.

[0123] S202: In order to further smooth the experimental data and reduce the complexity of the transducer, in this embodiment, a high-order polynomial is used to fit the data:

[0124] P(f) = c0 + c1f + c2f 2 +…+ c 30 f n (7);

[0125]

[0126] In formulas (7) and (8), P(f) is the fitted polynomial, and its amplitude P(f i ) is the impedance value, c0, c1, …, c n are the polynomial coefficients obtained by the fitting method;

[0127] S203: Convert the polynomial coefficients of the high-order polynomial to c = [c0, c1,..., c n T , and obtain the converted fitting function;

[0128] The expression of the converted fitting function is:

[0129]

[0130] ​S204: To minimize the sum of squared errors, in this embodiment, a matrix equation is first constructed. All the observed data and polynomial terms are arranged in matrix form to obtain matrix A, vector c, and output vector B. Specifically, each row of matrix A corresponds to a data point, and the columns are composed of the various powers of the impedance values at each frequency:

[0131] The expression of matrix A is:

[0132]

[0133] The expression of output vector B is:

[0134]

[0135] The expression of the matrix equation is:

[0136] S205: Through the above steps, the fitting problem can be transformed into a matrix equation:

[0137] A·c = B (12);

[0138] In formula (12), c is the optimal polynomial coefficient;

[0139] According to the least squares principle, the optimal coefficient c satisfies the following equation:

[0140] c = (A T A) -1 A T B (13);

[0141] In formula (13), A T is the transpose of matrix A, and (A T A) -1 is the inverse matrix of matrix A;

[0142] Through this solution method, the optimal polynomial coefficient c can be obtained, thereby obtaining the most fitting polynomial function P″(f). Then, N equidistant points f min , f max of the independent variable are uniformly taken on the interval [f i . The interval between these points is Δf. The equidistant point f i is defined as:

[0143] The expression of the equidistant point f i of the independent variable is:

[0144] f i = f min + i·Δf, where i = 0, 1, 2,..., N - 1 (14);

[0145] The equidistant point f iThe expression for the interval Δf is as follows:

[0146]

[0147] S206: For each f i , calculate the corresponding function value P″(f i ) through the polynomial P(f):

[0148] P″(f i ) = c0 + c1f i + c2f i 2 + … + c 30 f i n (16).

[0149] S3: Map the measured amplitude-frequency characteristic function to the wavenumber domain to construct a wavenumber-domain function;

[0150] It is found by consulting the literature that the Archimedean spiral is a mathematically simple spiral curve with linear growth characteristics. The wavenumber-domain function derived from this curve has the characteristics of unique correspondence between wavenumber and directivity, which is convenient for the design of the wavenumber-domain function.

[0151] S301: Set the shape of the spiral to be determined by the polar coordinate system, where the radius r i and the angle θ i vary with i and satisfy the following form:

[0152] r i = r min + i·Δr (17);

[0153] θ i = θ min + i·Δθ (18);

[0154] In formulas (17) and (18), r min is the initial radius, Δr is the radius increment for each point, θ min is the initial angle, and Δθ is the angle increment for each point;

[0155] S302: The polar coordinates of the i-th point on the spiral are (r i , θ i ). According to the conversion formula between polar coordinates and Cartesian coordinates, the Cartesian coordinates (x i , y i ) of the i-th point on the spiral can be expressed as:

[0156]

[0157] The function at (x i , yi ) The function value z pointed out i is P″(f i ), that is:

[0158] z i = P″(f i ) (20);

[0159] Therefore, the wavenumber domain space point (x i , y i , z i ) is expressed as:

[0160]

[0161] S303: Based on the wavenumber domain space point (x i , y i , z i ), calculate the wavenumber vector of the target electrode

[0162]

[0163] In formula (22), r min is the initial radius, representing the starting point position of the wavenumber domain. Δr is the radius step, used to control the gradual outward expansion of the wavenumber domain points along the spiral. θ min is the initial angle, representing the starting direction of the spiral. Δθ is the angle step, used to control the discrete density of the wavenumber domain points on the spiral. P″(f i ) is the sampling value of the frequency domain characteristic, representing the wavenumber domain amplitude intensity of the corresponding point, is the two-dimensional coordinate and the corresponding amplitude value of the wavenumber domain point;

[0164] S304: Through the wavenumber domain vector , the wavenumber domain function T e (k) can be constructed:

[0165]

[0166] In formula (23), T e (k j ) is the corresponding weight of the frequency domain characteristic.

[0167] The wavenumber domain function T e (k) describes the characteristics of the electrode in the wavenumber domain. The intensity T e (k j ) of each discrete point reflects the corresponding weight of the frequency domain characteristic. As Figure 3 shown, the point set generated by the spiral distribution determines the shape of the wavenumber domain function.

[0168] S4: Use the inverse Fourier transform to convert the wavenumber-domain function to the physical space to obtain the spatial-domain structure of the excitation electrode;

[0169] The expression of the spatial-domain structure of the excitation electrode is:

[0170]

[0171] In formula (24), T e (x, y) is the spatial-domain structure of the excitation electrode.

[0172] S5: Threshold the spatial-domain structure of the excitation electrode to obtain the electrode spatial structure for machining;

[0173] The spatial distribution of the electrode calculated in this embodiment is as Figure 4 shown, and the electrode shape is a finger-like structure with spiral characteristics.

[0174] Through the above derivation, it can be found that the total time complexity of the present invention mainly consists of three parts: the fitting of the piezoelectric impedance-frequency curve, the mapping of the amplitude-frequency characteristic to the wavenumber domain, and the two-dimensional inverse Fourier transform from the wavenumber domain to the spatial domain. Among them, the complexity of the fitting process is O(N f ·d), the complexity of the point-by-point mapping of the amplitude-frequency characteristic is O(N f ), and the complexity of the inverse Fourier transform is O(N k ·logN k ). The total complexity of the algorithm is O(N f ·d)+O(N f )+O(N k ·logN k ), where N f ≈N k , and the fitting order d is small. Therefore, the total complexity of the algorithm can be approximately simplified to O(N k ·logN k ), showing a logarithmic-linear growth characteristic, which is particularly suitable for large-scale data processing.

[0175] In contrast, traditional iterative optimization algorithms such as genetic algorithms have a complexity of O(N·G), where N is the number of optimization variables and G is the number of iterations. Since N and G are usually large (e.g., N = 10 3 , G = 10 2 ), the complexity of this algorithm is high, which will lead to a significant increase in calculation time. In addition, the direct optimization algorithm needs to search the high-dimensional space point by point, with high memory requirements and difficult to expand, and it is difficult to realize the design of complex electrode structures.

[0176] Therefore, on the premise of effectively realizing the resonance frequency compensation of the piezoelectric sheet, the present invention also has significant advantages in memory usage and operation speed, and has good application prospects.

[0177] In addition, this embodiment was tested, and the test results are as Figure 5 shown. The curve (before) in the upper part is the admittance curve of the piezoelectric sheet, and the curve (after) in the lower part depicts the overall admittance curve of the transducer after compensation by the electrode structure design. It can be seen that the resonance peak decays to 3.3% of the original, and the compensation effect is good.

[0178] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to form equivalent embodiments with equivalent changes within the scope of the technical solution of the present invention. However, as long as it does not depart from the technical solution content of the present invention, any simple modification, equivalent replacement, and improvement made to the above embodiments according to the technical essence of the present invention within the spirit and principle of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation, characterized in that The steps of the design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation include: Step 1: Calculate the impedance of the piezoelectric wafer and draw the frequency-impedance curve, and smooth the impedance data to obtain the smoothed frequency-impedance curve; Step 2: Obtain the amplitude-frequency characteristic of the electrode based on the smoothed frequency-impedance curve, and construct the wavenumber domain function of the electrode according to the amplitude-frequency characteristic of the electrode; Step 3: Perform inverse Fourier transform and thresholding on the constructed wavenumber domain function of the electrode to obtain the spatial structure of the piezoelectric transducer, and complete the design of the piezoelectric transducer.

2. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation according to claim 1, characterized in that Step 1 specifically includes: Step 1.1: Calculate the impedance Z(f) of the piezoelectric wafer based on the equivalent circuit model; Step 1.2: Calculate the amplitude characteristic T of the piezoelectric wafer based on the impedance Z(f) of the piezoelectric wafer, and plot the frequency-impedance curve according to the amplitude characteristic T p (f) of the piezoelectric wafer in the total amplitude-frequency amplitude of the transducer and the amplitude-frequency characteristic T p (f) of the electrode and the amplitude-frequency characteristic T e (f) of the electrode; p (f), and based on the amplitude characteristic T p (f) of the piezoelectric wafer in the total amplitude-frequency amplitude of the transducer and the amplitude-frequency characteristic T e (f) of the electrode, plot the frequency-impedance curve; Step 1.3: By matching the amplitude-frequency characteristic of the electrode with the impedance characteristic of the piezoelectric wafer, eliminate the resonance peak in the frequency-impedance curve in the total amplitude-frequency characteristic; Step 1.4: Measure the original impedance Z(f j ) of the piezoelectric sheet by an impedance analyzer and replace the impedance data in the frequency-impedance curve. Use the moving average smoothing method to smooth the original impedance Z(f j ), remove the high-frequency noise of the data points, and obtain the smoothed frequency-impedance curve; The calculation formula for the impedance Z(f) of the piezoelectric wafer is: In formula (1), R is the loss resistance, L is the equivalent inductance, C is the equivalent capacitance, ω = 2πf is the angular frequency, and the resonance peak is located at the resonance frequency nearby; The calculation formula for the total amplitude-frequency characteristic is: T total f() = T p f() · T e f(2); In formula (2), T total (f) is the total amplitude-frequency characteristic; Amplitude characteristic T of piezoelectric sheet p (f) is calculated by the formula: In Equation (3), Y(f) is the admittance characteristic of the piezoelectric element. To make T total (f) flat, the amplitude-frequency characteristic T e (f) of the electrode should satisfy: Original impedance Z(f j ) The expression after smoothing is: In formula (5), is the smoothed data point, N is the size of the smoothing window, and Z(f j ) is the original impedance.

3. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Normalize and fit the impedance data in the smoothed frequency-impedance curve to obtain the amplitude-frequency characteristic; Step 2.2: Map the amplitude-frequency characteristic of the electrode to the wavenumber domain function and construct the wavenumber domain function of the electrode.

4. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation according to claim 3, characterized in that Step 2.1 specifically includes: Step 2.1.1: Normalize the impedance data in the smoothed frequency-impedance curve, and scale the amplitude of the impedance data to the interval [0,1]; Step 2.1.2: Use a high-order polynomial to fit the impedance data, and convert the polynomial coefficients of the high-order polynomial into \(c = [c_0, c_1,\cdots, c n T , and obtain the converted fitting function;​ Step 2.1.3: Organize all the observed data and polynomial terms in the converted fitting function into matrix form to obtain matrix A, vector c, and output vector B; Step 2.1.4: Convert the fitting problem into a matrix equation through matrix A, vector c, and output vector B, and minimize the sum of squared errors through the matrix equation to obtain the most fitting polynomial function P″(f); Step 2.1.5: The obtained polynomial function P″(f) is in the interval [f min ,f max ] uniformly select N independent variable equidistant points f i , for each f i , the corresponding amplitude-frequency characteristic function P″(f) is calculated by the best fitting polynomial function P″(f i ), where the independent variable is equidistant from point f i The interval is Δf; The expression for normalization processing is: In formula (6), is the peak value of the smoothed impedance data, is the impedance data after normalization; The expression for high-order polynomial fitting processing is: P(f) = c0 + c1f + c2f 2 +…+ c 30 f n (7); In Formulas (7) and (8), P(f) is the fitted polynomial, and its amplitude P(f i ) is the impedance value, and c0, c1, …, c n are the polynomial coefficients obtained by the fitting method; The expression for the converted fitting function is: The expression for matrix A is: The expression for output vector B is: The expression for the matrix equation is: A·c = B(12); In formula (12), c is the optimal polynomial coefficient; The expression for the optimal polynomial coefficient c is: c = (A T A) -1 A T B(13); In formula (13), A T is the transpose of matrix A, and (A T A) -1 is the inverse matrix of matrix A; Independent variable equally spaced point f i The expression is: f i = f min + i·Δf, where i = 0, 1, 2, ..., N - 1 (14); Equidistant points of the independent variable f i The expression for the interval Δf is as follows: Amplitude-frequency characteristic function P″(f i ) is expressed as:

5. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation according to claim 3, characterized in that, Step 2.2 specifically includes: Step 2.2.1: Set that the spiral shape of the Archimedean spiral is determined by a polar coordinate system, and the radius r i and the angle θ i vary with i; Step 2.2..2: Convert the polar coordinates (r i , θ i ) of the i-th point on the helix to Cartesian coordinates (x i , y i ) through the polar and Cartesian coordinate conversion formulas; Step 2.2.3: Take the function value z at the coordinate (x i , y i ) as P″(f i ), and obtain the representation of the wavenumber domain spatial point (x i , y i , z i , z i ); Step 2.2.4: Based on the spatial point (x i , y i , z i ) in the wavenumber domain, calculate the wavenumber vector of the target electrode Step 2.2.5: Based on the wavenumber vector of the target electrode Construct the wavenumber domain function T e (k); The radius r of the spiral i has the expression: r i = r min + i·Δr (17); In formula (17), r min is the initial radius, and Δr is the radius increment for each point; The angle θ of the spiral i has the following expression: θ i = θ min + i·Δθ(18); In formula (18), θ min is the initial angle, and Δθ is the angle increment for each point; The expression of Cartesian coordinates (x i , y i ) is as follows: (x i , y i ) The function value z of the point i has the following expression: z i = P″(f i )(20); The spatial point (x i , y i , z i ) in the wavenumber domain is expressed as: Wave number vector of the target electrode The expression is as follows: In formula (22), r min is the initial radius, representing the starting point position in the wavenumber domain. Δr is the radius step, used to control the gradual outward expansion of the wavenumber domain points along the helix. θ min is the initial angle, representing the starting direction of the helix. Δθ is the angle step, used to control the discrete density of the wavenumber domain points on the helix. P″(f i ) is the sampling value of the frequency domain characteristic, representing the wavenumber domain amplitude intensity of the corresponding point, which is the two-dimensional coordinate and the corresponding amplitude value of the wavenumber domain point; Wavenumber domain function T e (k) is expressed as: In formula (23), T e (k j ) is the corresponding weight of the frequency domain characteristic.

6. A design method of a piezoelectric transducer based on wavenumber domain optimization and resonance compensation according to claim 1, characterized in that Step 3 specifically includes: Step 3.1: Use the inverse Fourier transform to transform the wavenumber domain function T e (k) to the physical space to obtain the spatial domain structure of the excitation electrode; Step 3.2: Perform thresholding on the spatial domain structure of the excitation electrode to obtain the electrode spatial structure for processing; The expression for the spatial domain structure of the excitation electrode is: In formula (24), T e (x, y) is the spatial domain structure of the excitation electrode.

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