Low-frequency hydrophone sensitivity calculation method and system based on equivalent parameters

Abstract

The application belongs to the technical field of hydrophones, and discloses a low-frequency hydrophone sensitivity calculation method and system based on equivalent parameters. The application is aimed at the problem that the existing low-frequency hydrophone sensitivity calibration method mainly depends on the output voltage of the hydrophone under specific excitation to deduce the sensitivity, and cannot directly quantitatively characterize the sensitivity from the piezoelectric material parameters. Starting from the equivalent parameters, the quantitative relationship between the piezoelectric constant and the equivalent parameters is obtained based on the axisymmetric mode and the spherical symmetric mode, and the sensitivity of the low-frequency hydrophone is quantitatively characterized in the forward direction through the average radius and the piezoelectric constant. The application realizes the accurate correlation between the acoustic quantity and the electrical quantity through the equivalent parameters, can provide a simple and effective analysis method for the characterization of the working characteristics of the hydrophone, and the measurement process of the equivalent parameters is relatively simple, without relying on complex external acoustic equipment, and can be completed through conventional electronic measurement equipment such as an impedance analyzer.

Description

Technical Field

[0001] This invention belongs to the field of hydrophone technology, and specifically relates to a method and system for calculating the sensitivity of low-frequency hydrophones based on equivalent parameters. It is applicable to forward quantitative characterization of the sensitivity of low-frequency hydrophones using piezoelectric material parameters. Background Technology

[0002] As the core transducer in underwater acoustic systems, the accurate evaluation of hydrophone performance is crucial for the reliability of marine acoustic measurements, underwater target detection, and underwater acoustic communication systems. With the rapid development of modern underwater acoustic technology, the precise measurement of hydrophone parameters has become a key technical aspect for improving the overall performance of underwater acoustic systems.

[0003] While existing hydrophone calibration methods each possess their own theoretical advantages, they face numerous challenges in practical applications. Common hydrophone calibration methods currently include, for example, the coupled-cavity reciprocity method, the vibrating liquid column method, the standing wave tube / traveling wave tube method, the hydrostatic excitation method, the free-field comparison method, and the laser vibration measurement / interferometry method.

[0004] The coupled-cavity reciprocity method requires three transducers in a small-volume rigid water cavity to determine the absolute sound pressure sensitivity using the electroacoustic reciprocity theorem. Although the transferred coupled-cavity reciprocity method can solve the problem of repeatedly measuring the coupled-cavity volume parameters when calibrating different hydrophones, it requires more transducers and has higher equipment complexity.

[0005] The vibrating liquid column method requires sealing the hydrophone to be calibrated at the bottom of a vertical circular tube filled with water. The entire tube vibrates sinusoidally along the axis, and the liquid column forms a controllable sound pressure field under the action of gravity and elasticity. The sound pressure can be calculated by measuring the acceleration and depth of the liquid column. It requires complex devices such as a signal source, power amplifier, bottom excitation source and high-precision accelerometer.

[0006] The standing wave tube / traveling wave tube method forms a controllable planar standing wave or traveling wave in a sound tube composed of rigid or sound-absorbing ends. The sensitivity of the hydrophone is calculated by measuring the sound pressure distribution. The accuracy depends on the performance stability of the standard hydrophone.

[0007] The hydrostatic excitation method requires generating quasi-static to low-frequency changing pressure in a closed water chamber using a piston or bellows. The sensitivity is obtained by comparison with a standard pressure sensor. It requires a precise alternating hydrostatic pressure system, and the device is relatively large.

[0008] The free-field comparison method involves placing the hydrophone to be calibrated and the standard hydrophone in the same sound field position in an anechoic pool or large water tank, and comparing their output voltages. This method requires a large anechoic space and is a type of relative calibration.

[0009] Laser vibrometrics / interferometry uses a laser vibrometer to measure the particle velocity of a thin film or small buoy located close to the acoustic center of a hydrophone, combined with... The correction yields a standard sound pressure level, enabling non-contact absolute calibration, but this requires high standards for the optical path, water quality, and film uniformity.

[0010] The existing methods described above all require the construction of specific excitation conditions for the hydrophone under test, and then the sensitivity is derived by measuring the hydrophone output. They cannot directly use the piezoelectric material parameters to quantitatively characterize the sensitivity in the forward direction.

[0011] In summary, traditional hydrophone calibration methods generally suffer from problems such as high equipment dependence, cumbersome operation procedures, and limited measurement accuracy, making it difficult to meet the urgent needs of modern underwater acoustic measurement for high efficiency, accuracy, and convenience. Summary of the Invention

[0012] The purpose of this invention is to propose a method for calculating the sensitivity of low-frequency hydrophones based on equivalent parameters. This method starts from equivalent parameters and obtains the piezoelectric constant based on axisymmetric and spherical symmetric modes. The quantitative relationship with equivalent parameters, and further through the relationship between average radius and piezoelectric constant. Forward quantitative characterization of the sensitivity of low-frequency hydrophones can significantly reduce the dependence on professional equipment for hydrophone sensitivity characterization, while also significantly shortening the measurement cycle and improving measurement efficiency.

[0013] To achieve the above objectives, the present invention adopts the following technical solution: The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters includes the following steps: Step 1. Give the formula for the open-circuit receiving voltage sensitivity when using a piezoelectric ring as the piezoelectric element in a low-frequency hydrophone, and simplify it to the formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; Step 2. Based on the relevant theory of axisymmetric modes, the piezoelectric constant is adjusted using the equivalent parameters of the piezoelectric ring. The piezoelectric ring was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively. The final calculated sensitivity formula for the piezoelectric ring is as follows: ; in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

[0014] The above provides a method for calculating the sensitivity of a low-frequency hydrophone using a piezoelectric ring as the piezoelectric element. This invention also provides a method for calculating the sensitivity of a low-frequency hydrophone using a piezoelectric sphere as the piezoelectric element, as follows: The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters includes the following steps: Step 1. Give the formula for the open-circuit receiving voltage sensitivity when using a piezoelectric spherical shell as the piezoelectric element in a low-frequency hydrophone, and simplify it to the formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; Step 2. Based on the relevant theory of spherical symmetry modes, the equivalent parameters of the piezoelectric spherical shell are used to adjust the piezoelectric constant. The piezoelectric sphere shell was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively. The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ; in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

[0015] Furthermore, based on the aforementioned method for calculating the sensitivity of low-frequency hydrophones based on equivalent parameters, this invention also proposes a corresponding system for calculating the sensitivity of low-frequency hydrophones based on equivalent parameters, which adopts the following technical solution: A low-frequency hydrophone sensitivity calculation system based on equivalent parameters includes the following modules: The sensitivity characterization simplification module is used to provide the open-circuit receiving voltage sensitivity formula when a piezoelectric ring is used as the piezoelectric element of a low-frequency hydrophone, and to simplify it to a formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization ; ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of axisymmetric modes and the equivalent parameters of the piezoelectric ring. The piezoelectric ring was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively. The final calculated sensitivity formula for the piezoelectric ring is as follows: ; in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

[0016] The above describes a sensitivity calculation system for a low-frequency hydrophone using a piezoelectric ring as the piezoelectric element. This invention also provides a sensitivity calculation system for a low-frequency hydrophone using a piezoelectric spherical shell as the piezoelectric element, as follows: A low-frequency hydrophone sensitivity calculation system based on equivalent parameters includes the following modules: The sensitivity characterization simplification module provides a formula for the open-circuit receiving voltage sensitivity when a piezoelectric sphere is used as the piezoelectric element in a low-frequency hydrophone, and simplifies it to a value based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of spherical symmetry modes and the equivalent parameters of the piezoelectric sphere. The piezoelectric sphere shell was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively. The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ; in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

[0017] Furthermore, based on the aforementioned method for calculating the sensitivity of low-frequency hydrophones based on equivalent parameters, this invention also proposes a computer device comprising a memory and one or more processors.

[0018] Executable code is stored in memory. When the processor executes the executable code, it implements the steps of the above-described method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters.

[0019] Furthermore, based on the aforementioned method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters, this invention also proposes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of the aforementioned method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters.

[0020] The present invention has the following advantages: As mentioned above, existing low-frequency hydrophone sensitivity calibration methods mainly rely on the output voltage of the hydrophone under specific excitation to infer the sensitivity, and cannot directly use piezoelectric material parameters for forward quantitative characterization of sensitivity. This invention proposes a low-frequency hydrophone sensitivity calculation method based on equivalent parameters. Since the resonant characteristics of a hydrophone are closely related to the piezoelectric material parameters, equivalent parameters can better correlate these parameters. When the hydrophone is at its resonant frequency, the dynamic characteristics of its internal piezoelectric elements can be accurately described by an equivalent model composed of electronic components such as resistors, capacitors, and inductors. The core advantage of this method is that it achieves a precise correlation between acoustic and electrical quantities through equivalent parameters, thereby providing a simple and effective analytical means for characterizing the hydrophone's operating characteristics. The measurement process of equivalent parameters is relatively simple and does not require complex external acoustic equipment. It can be completed using conventional electronic measurement equipment such as impedance analyzers. This simplified measurement process not only significantly reduces the dependence on professional equipment but also significantly shortens the measurement cycle, which is beneficial for improving measurement efficiency. Attached Figure Description

[0021] Figure 1 This is a flowchart of a low-frequency hydrophone sensitivity calculation method based on equivalent parameters in an embodiment of the present invention; the figure shows the sensitivity calculation process when a piezoelectric ring is used as the piezoelectric element of the low-frequency hydrophone. Figure 2 This is a flowchart of a low-frequency hydrophone sensitivity calculation method based on equivalent parameters in an embodiment of the present invention; the figure shows the sensitivity calculation process when a piezoelectric sphere shell is used as the piezoelectric element of the low-frequency hydrophone. Figure 3 This is an equivalent circuit diagram of the piezoelectric element in an embodiment of the present invention; wherein... Figure 3 In the diagram, (a) is the electromechanical equivalent circuit, (b) is the non-series resonant equivalent circuit, (c) is the series resonant equivalent circuit, and (d) is the 1 kHz equivalent circuit. Figure 4 The figures show the impedance and phase angle curves of the PZT-51 piezoelectric ceramic spherical shell near the resonant frequency in a specific embodiment of the present invention; wherein... Figure 4 In the text, (a), (b), and (c) represent PZT-51 piezoelectric ceramic spherical shells #1, #2, and #3, respectively. Figure 5The figures show the impedance and phase angle curves of the PZT-41 piezoelectric ceramic ring near the resonant frequency in a specific embodiment of the present invention; wherein... Figure 5 In the text, (a), (b), and (c) represent PZT-41 piezoelectric ceramic rings #4, #5, and #6, respectively. Figure 6 The figures show the impedance and phase angle curves of the PZT-51 piezoelectric ceramic ring near the resonant frequency in a specific embodiment of the present invention; wherein... Figure 6 In the diagram, (a), (b), and (c) represent PZT-51 piezoelectric ceramic rings #7, #8, and #9, respectively. Figure 7 The figures show the impedance and phase angle curves of the PZT-51 piezoelectric ceramic spherical shell near 1 kHz in a specific embodiment of the present invention; wherein... Figure 7 In the text, (a), (b), and (c) represent PZT-51 piezoelectric ceramic spherical shells #1, #2, and #3, respectively. Figure 8 The figures show the impedance and phase angle curves of the PZT-41 piezoelectric ceramic ring near 1 kHz in a specific embodiment of the present invention; wherein... Figure 8 In the text, (a), (b), and (c) represent PZT-41 piezoelectric ceramic rings #4, #5, and #6, respectively. Figure 9 The figures show the impedance and phase angle curves of the PZT-51 piezoelectric ceramic ring near 1 kHz in a specific embodiment of the present invention; wherein... Figure 9 In the diagram, (a), (b), and (c) represent PZT-51 piezoelectric ceramic rings #7, #8, and #9, respectively. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: Example 1 This embodiment 1 describes a method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters. Starting from the equivalent parameters, this method derives the quantitative relationship between the piezoelectric constant and the equivalent parameters based on axisymmetric and spherical modes. Then, it uses the average radius and piezoelectric constant to perform forward quantitative characterization of the sensitivity of the low-frequency hydrophone, which helps to significantly reduce the dependence of hydrophone sensitivity characterization on professional equipment, while also significantly shortening the measurement cycle and improving measurement efficiency.

[0023] The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters in this embodiment includes the following steps: Step 1. Give the formula for the open-circuit receiving voltage sensitivity when using a piezoelectric ring or piezoelectric sphere as the piezoelectric element in a low-frequency hydrophone, and simplify it to the formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is .

[0024] Specifically, the commonly used geometric structures for piezoelectric elements in low-frequency hydrophones include thin spherical shells and thin circular rings.

[0025] According to the static theory of spherical hydrophones and circular tube hydrophones, in the low-frequency state, the operating frequency of piezoelectric elements is significantly lower than the resonant frequency, exhibiting elastic control characteristics, for radially polarized piezoelectric spherical shells and piezoelectric rings.

[0026] Under the boundary condition of an air-backed inner surface, based on the elastic statics model and the piezoelectric equation, the open-circuit receiving voltage sensitivities of the piezoelectric ring and piezoelectric spherical hydrophones can be obtained, as shown below: ; .

[0027] in Indicates the sensitivity of the piezoelectric ring. This indicates the sensitivity of the piezoelectric sphere shell. and It is the piezoelectric voltage constant. This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is , .

[0028] Because the wavelength of the sound wave is much longer than the thickness of the piezoelectric element when receiving at low frequencies, there is only vibration and no stretching wave in the radial direction. When the thickness is very small, the piezoelectric ring is mainly subjected to transverse stress, while the piezoelectric spherical shell is mainly subjected to planar stress.

[0029] When both the inner radius and the outer radius are taken as the average radius At that time, the above can be used as well as The formula simplifies to the following formula, where This formula represents the simplified piezoelectric sensitivity of a piezoelectric ring or spherical shell. Only the symbol is considered.

[0030] .

[0031] Step 2. Based on the relevant theories of axisymmetric and spherical symmetric modes, the piezoelectric constant is determined using the equivalent parameters of the piezoelectric element. The piezoelectric element was characterized and substituted into a simplified sensitivity expression to calculate its sensitivity.

[0032] like Figure 1 As shown, for a piezoelectric toroidal hydrophone, its piezoelectric constant is... The sensitivity formula for the piezoelectric ring is as follows: piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively.

[0033] The final calculated sensitivity formula for the piezoelectric ring is as follows: ; in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

[0034] like Figure 2 As shown, for a piezoelectric spherical hydrophone, its piezoelectric constant is... The sensitivity formula for the piezoelectric sphere shell is as follows: piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively.

[0035] The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ; in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

[0036] The following discusses the piezoelectric constant. The quantitative relationship with the equivalent parameters and the sensitivity calculation of the piezoelectric element are explained in detail.

[0037] Near the series resonant frequency, the impedance and resonant characteristics of the piezoelectric element are similar to those of the piezoelectric element. The impedance and resonance characteristics of the circuit are very similar; therefore, the electromechanical equivalent diagram of the piezoelectric element can be obtained using electromechanical analogy, as shown below. Figure 3 As shown in (a).

[0038] Where m is the mass of the piezoelectric element, For the mechanical compliance of piezoelectric elements, Let n be the mechanical damping of the piezoelectric element, and n be the electromechanical conversion coefficient. Using the electromechanical conversion coefficient n... Figure 3 The right-hand side parameter in (a) is equivalent to Figure 3 After the left side of (a), the equivalent circuit of the piezoelectric element can be obtained, such as Figure 3 The non-series resonant equivalent circuit is shown in (b).

[0039] in For dynamic inductance, It is a dynamic capacitor. It is a dynamic resistor, forming a series branch of the piezoelectric element. The static capacitance, which is the capacitance of the piezoelectric element when it stops vibrating, forms the parallel branch of the piezoelectric element. At the series resonant frequency, the equivalent circuit can be simplified as follows: Figure 3 As shown in (c) in the figure.

[0040] At a frequency of 1 kHz, the equivalent circuit can be simplified to: Figure 3 As shown in (d) in the figure, the free capacitance .

[0041] Taking a piezoelectric element using a piezoelectric ring as an example, the piezoelectric constant... Equivalent parameter characterization and The calculation process is as follows:

[0042] Define the dynamic inductance of a piezoelectric element With quality Dynamic capacitor With mechanical compliance The electromechanical conversion is shown in equations (1) and (2). Combining these equations, we can obtain equation (3), which is expressed as follows: (1) (2) (3) Next, based on the relevant theories in the axisymmetric mode of thin rings, the piezoelectric constants of the piezoelectric rings are derived. .

[0043] The masses of the piezoelectric rings are given respectively. Mechanical compliance Free capacitance and electromechanical coupling coefficient The formulas are shown in formulas (4), (5), (6), and (7), respectively.

[0044] (4) (5) (6) (7) in The piezoelectric strain constant is It is the elastic compliance constant. Where is the dielectric constant. The resonant frequency, The resonant frequency is the anti-resonant frequency; substituting equations (4) and (5) into equation (3), we obtain the piezoelectric ring's... and , The quantitative relationship is shown in equation (8): (8) From equation (6), we obtain the piezoelectric ring. and The quantitative relationship is shown in equation (9): (9) From equation (7), we obtain the piezoelectric ring. As shown in equation (10): (10) Substituting equation (10) into equation (11), we obtain the piezoelectric ring. and , , Quantitative relationship: (11) Substituting equations (7), (8), and (9) into (11), we obtain: , , The piezoelectric constant characterized As shown in equation (12): (12) Substituting formula (12) into the simplified sensitivity The expression, calculated using the following formula, gives the sensitivity of the piezoelectric ring: (13)

[0045] When a piezoelectric element uses a piezoelectric spherical shell, its piezoelectric constant is... Equivalent parameter characterization and The calculation process is as follows:

[0046] Similarly, the dynamic inductance of a piezoelectric element is defined. With quality Dynamic capacitor With mechanical compliance The electromechanical conversion is shown in equations (14) and (15). Combining these equations, we can obtain equation (16), which is expressed as follows: (14) (15) (16) Next, based on the relevant theories in the spherical symmetry mode of thin spherical shells, the piezoelectric constant of the piezoelectric ring is derived. .

[0047] First, the mass m and mechanical compliance of the piezoelectric sphere shell are given. Free capacitance and planar electromechanical coupling coefficient As shown in formulas (17), (18), (19), and (20).

[0048] (17) (18) (19) (20) in The piezoelectric strain constant is This represents the elastic compliance constant in the direction of plane stress. Where is the dielectric constant. The resonant frequency, The resonant frequency is given; substituting equations (17) and (18) into equation (16), we obtain the piezoelectric sphere shell. As in equation (21): (twenty one) in , They represent The elastic compliance constant in the directions of the orthogonal components of the two plane stresses.

[0049] From equation (19), the piezoelectric sphere shell is obtained. As shown in equation (22): (twenty two) From equation (20), the piezoelectric sphere shell is obtained. As in equation (23): (twenty three) Formula (23) Substituting into equation (24), we obtain the piezoelectric sphere shell. and , , Quantitative relationship: (twenty four) Substituting equations (20), (21), and (22) into equation (24), we obtain the equivalent parameters of the piezoelectric sphere shell. , , The piezoelectric constant characterized As shown in equation (25): (25) Substituting formula (25) into the simplified sensitivity The expression, calculated using the following formula, gives the sensitivity of the piezoelectric ring: (26)

[0050] Furthermore, this invention uses the impedance frequency method and the phase angle frequency method to process the impedance and phase angle data near the resonant frequency and 1 kHz, thereby obtaining the equivalent parameters of the piezoelectric element. , , The solution process is as follows: according to Figure 3 (b) and Figure 3 The non-series resonant equivalent circuit and series resonant equivalent circuit of the piezoelectric element corresponding to (c) in the diagram, and the impedance Z and phase angle near the resonant frequency. The formula is obtained from equations (27) and (28) as follows: (27) (28) in For dynamic resistance, Indicates angular velocity, It represents the imaginary unit.

[0051] At the resonant frequency Take from both sides and ,Will and corresponding , and , Enter equation (27), and solve simultaneously to obtain... and As shown in equations (29) and (30) respectively: (29) (30) in Indicates the frequency offset. and These represent offsets to the left and right at the resonant frequency, respectively. The subsequent frequency value, , and , They represent and The corresponding angular velocity and impedance value.

[0052] Will and corresponding , and , Substituting into equation (28), we obtain and As shown in equations (31) and (32): (31) (32) in , They represent and The corresponding phase angle value.

[0053] Free capacitance The impedance value corresponding to a frequency of 1 kHz is obtained according to equation (33): (33) in 1 kHz, The impedance value is at 1 kHz.

[0054] In addition, three piezoelectric elements, namely PZT-41 ring, PZT-51 ring and PZT-51 spherical shell, were prepared in this embodiment. The resonant frequency and impedance and phase angle of each element were measured at 1 kHz using an impedance analyzer under three measurement parameter settings. The equivalent parameters of the hydrophone were obtained by using the impedance frequency method and the phase angle frequency method.

[0055] First, piezoelectric elements were prepared. Lead zirconate titanate (Pb(Zr,Ti)O3, abbreviated as PZT) is one of the most widely used piezoelectric ceramic materials. In order to compare the sensitivity characteristics of piezoelectric elements with different shapes and materials, three piezoelectric elements were prepared.

[0056] Three of each type of piezoelectric element are included, specifically PZT-51 piezoelectric ceramic spherical shells (1#, 2#, 3#), PZT-41 piezoelectric ceramic rings (4#, 5#, 6#), and PZT-51 piezoelectric ceramic rings (7#, 8#, 9#).

[0057] The inner and outer radii a and b, and the piezoelectric constant of each piezoelectric element are given. , Substituting the corresponding sensitivities of the piezoelectric ring or piezoelectric sphere, the results are shown in Table 1. The piezoelectric material parameters related to the sensitivity for both materials are shown in Table 2.

[0058] Table 1. Dimensions and Theoretical Sensitivity of Piezoelectric Elements

[0059] As can be seen from Table 1, for piezoelectric rings of the same radius, the sensitivity of the PZT-41 piezoelectric ring is slightly greater than that of the PZT-51 piezoelectric sphere shell, and the geometry and size have a more significant impact on the sensitivity.

[0060] Table 2 Piezoelectric material parameters of PZT-51 and PZT-41

[0061] Next, impedance and phase angle data were measured. The measuring equipment used was an Agilent 4292A precision impedance analyzer, with a measurement frequency range of 40 Hz to 110 MHz, a basic impedance accuracy of ±0.08%, a sampling point count of 2 to 801, and a frequency resolution of 1 mHz. These specifications meet the accuracy requirements of the experimental measurements in this study.

[0062] Test items selected: impedance Z and phase angle Connect the positive and negative terminals of the piezoelectric element to the impedance analyzer, adjust the appropriate frequency range, save the impedance measurement results of each piezoelectric element in sequence, and then export the data to the host computer for data processing.

[0063] Considering that different measurement parameters of the instrument may affect the measurement results, three modes were used to measure each test sample. The measurement parameter settings for the three modes are shown in Table 3.

[0064] The frequency range for Mode 1 is selected with the resonant frequency of each sample as the center, 200 Hz to the left and right, for a total of 400 Hz. The sampling point is set to 801, with a frequency interval of 0.5 Hz. At 1 kHz, 20 Hz to the left and right, for a total of 40 Hz, with a frequency interval of 0.05 Hz.

[0065] Based on the sampling points of Mode 1, Mode 2 extends the target frequency range to 60 kHz~100 kHz and 500 Hz~1 kHz respectively. In the 60 kHz~100 kHz range, the frequency interval of 50 Hz is increased to 1 Hz by interpolation.

[0066] Mode 3 reduces the sampling points to 201 based on the frequency range of Mode 2. In the 60 kHz to 100 kHz range, interpolation is used to increase the frequency interval from 200 Hz to 1 Hz. The specific interpolation method will not be described here.

[0067] Table 3 Impedance Analyzer Measurement Parameter Settings

[0068] The impedance and phase angle measurements of each piezoelectric element in Mode 1 are as follows: Figures 4 to 9 As shown in the figure, the minimum impedance, minimum impedance frequency, series resonant impedance, series resonant frequency, and 1 kHz impedance extracted from it are shown in Table 4.

[0069] Table 4 Impedance and frequency of each piezoelectric element under minimum impedance and series resonance.

[0070] As can be seen from Table 4, the deviations between the minimum impedance and series resonant impedance, and between the minimum impedance frequency and series resonant frequency of each piezoelectric element are small, which conforms to the first-order approximation relationship under low-frequency conditions.

[0071] The differences in measurement results among the three samples of the same piezoelectric element were small, while the differences in measurement results among different types of samples were more obvious. For PZT-51 spherical shells and rings made of the same material, the resonant frequency of the spherical shell was significantly higher than that of the ring.

[0072] At the same size, the resonant frequency of the PZT-41 ring is slightly higher than that of the PZT-51 ring, indicating that the resonant characteristics can significantly reflect the differences in piezoelectric material parameters and shape dimensions of different piezoelectric elements.

[0073] In this embodiment, for three different materials and shapes of piezoelectric elements, the impedance and phase angle at the resonant frequency and around 1 kHz are measured using an impedance analyzer under normal conditions. Then, the piezoelectric elements are vulcanized to make hydrophones. The sensitivity is calibrated in a standing wave tube using the standard hydrophone comparison method, thereby obtaining a benchmark result for comparing deviations.

[0074] The standing wave tube comparison method, a commonly used secondary calibration method, offers advantages such as high repeatability and reliable results. Therefore, this method was chosen to calibrate the sensitivity of each test sample individually. After vulcanization, the test samples were fixed at the center of the rotating device, and their depth was adjusted to be the same as that of the standard hydrophone.

[0075] Using control software on a computer, a sinusoidal signal is emitted, amplified by an amplifier, and then emitted upward through a planar piston sound source at the bottom of the tube, forming a planar standing wave field in the tube. The output voltages of the two are compared to determine the sensitivity of the hydrophone being calibrated. The sensitivity calculation method is as shown in Equation (34), and the sensitivity calibration results of each sample are shown in Table 5.

[0076] (34) in (dB) represents the free-field sensitivity of a standard hydrophone. (V) is the open-circuit voltage of the hydrophone being calibrated. (V) represents the open-circuit voltage of a standard hydrophone. (m) represents the immersion depth of a standard hydrophone. (m) represents the immersion depth of the vector hydrophone being calibrated. For wave number, (Hz) is the frequency, and c(m / s) is the speed of sound in the medium.

[0077] Table 5. Sensitivity calibration results and statistical indicators for 9 samples using the standing wave tube comparison method.

[0078] Table 5 shows that all three piezoelectric elements exhibit good frequency response consistency within the 50 Hz to 1 kHz range. Among the PZT-51 spherical shell elements, #1 exhibits the largest fluctuation, with a standard deviation of 0.393 dB and a maximum standard error of 0.105 dB. Among the PZT-41 circular ring elements, #4 exhibits the largest fluctuation, with a standard deviation of 0.471 dB and a standard error of 0.126 dB. Among the PZT-51 circular ring elements, #8 exhibits the largest fluctuation, with a standard deviation of 0.413 dB and a standard error of 0.110 dB. Overall, the data dispersion is low. Compared with the theoretical calculation results, the absolute value of the deviation between the average value and the theoretical value of the standing wave tube calibration sensitivity does not exceed 0.69 dB. This indicates a high degree of agreement between the standing wave tube calibration results and the theoretical calculation results, and the measured average value can be used as the benchmark result in the 50 Hz to 1 kHz frequency range.

[0079] Finally, the impedance frequency method and the phase frequency method were used to process the fitting data of each sample after cubic spline interpolation with a frequency interpolation interval of 1 Hz in each mode. The sensitivity results for each case are shown in Table 6.

[0080] Table 6 shows the processing results of data collected from 9 samples under three different modes using two different methods.

[0081] As can be seen from Table 6, for the impedance frequency method or the phase angle frequency method, different measurement parameter settings have little impact on the sensitivity results. Using interpolation can reduce the number of sampling points while ensuring a certain level of accuracy.

[0082] Comparing the sensitivity results of PZT-41 and PZT-51 rings under the three modes, it can be seen that the sensitivity of PZT-41 ring is greater than that of PZT-51 ring. This indicates that the equivalent parameter method can sense subtle changes in piezoelectric material parameters and has certain application potential in real-time tracking of piezoelectric material parameters as environmental conditions change.

[0083] Based on the calibration results of the standing wave tube comparison method, the sensitivity deviations for each case are shown in Table 7.

[0084] Table 7. Sensitivity deviation of each sample relative to the standing wave tube calibration value under each treatment condition.

[0085] As can be seen from Table 7, the sensitivity results obtained by the method of the present invention have small deviations, with the maximum deviation being 1.04 dB.

[0086] Example 2 This embodiment 2 describes a low-frequency hydrophone sensitivity calculation system based on equivalent parameters. This system is based on the same inventive concept as the low-frequency hydrophone sensitivity calculation method based on equivalent parameters in embodiment 1 above.

[0087] The system for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters in this embodiment includes the following modules: The sensitivity characterization simplification module is used to provide the open-circuit receiving voltage sensitivity formula when a piezoelectric ring is used as the piezoelectric element of a low-frequency hydrophone, and to simplify it to a formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization .

[0088] ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is .

[0089] And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of axisymmetric modes and the equivalent parameters of the piezoelectric ring. The piezoelectric ring was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity.

[0090] piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively.

[0091] The final calculated sensitivity formula for the piezoelectric ring is as follows: ; in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

[0092] The above describes a sensitivity calculation system for a low-frequency hydrophone using a piezoelectric ring as the piezoelectric element. This invention also provides a sensitivity calculation system for a low-frequency hydrophone using a piezoelectric spherical shell as the piezoelectric element, as follows: A low-frequency hydrophone sensitivity calculation system based on equivalent parameters includes the following modules: The sensitivity characterization simplification module provides a formula for the open-circuit receiving voltage sensitivity when a piezoelectric sphere is used as the piezoelectric element in a low-frequency hydrophone, and simplifies it to a value based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ; in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is .

[0093] And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of spherical symmetry modes and the equivalent parameters of the piezoelectric sphere. The piezoelectric sphere shell was characterized and substituted into a simplified sensitivity expression to calculate its sensitivity.

[0094] piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ; in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively.

[0095] The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ; in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

[0096] It should be noted that any content not mentioned in the above-described functional modules of the system described in Embodiment 2 can be referred to the step description of the corresponding method in Embodiment 1 above, and will not be repeated in detail here.

[0097] Example 3 This embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it implements the steps of the low-frequency hydrophone sensitivity calculation method based on equivalent parameters described in embodiment 1 above.

[0098] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0099] Example 4 This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, is used to implement the steps of the low-frequency hydrophone sensitivity calculation method based on equivalent parameters in embodiment 1 above.

[0100] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0101] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters, characterized in that, Includes the following steps: Step 1. Give the formula for the open-circuit receiving voltage sensitivity when using a piezoelectric ring as the piezoelectric element in a low-frequency hydrophone, and simplify it to the formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ； in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; Step 2. Based on the relevant theory of axisymmetric modes, the piezoelectric constant is adjusted using the equivalent parameters of the piezoelectric ring. The piezoelectric ring was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. in piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ； in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively. The final calculated sensitivity formula for the piezoelectric ring is as follows: ； in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

2. The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters according to claim 1, characterized in that, In step 2, the piezoelectric constant Equivalent parameter characterization and The calculation process is as follows: Define the dynamic inductance of a piezoelectric element With quality Dynamic capacitor With mechanical compliance The electromechanical conversion is shown in equations (1) and (2). Combining these equations, we can obtain equation (3), which is expressed as follows: (1) (2) (3) Where n is the electromechanical conversion coefficient; and the masses of the piezoelectric rings are given respectively. Mechanical compliance Free capacitance and electromechanical coupling coefficient The formulas are shown in formulas (4), (5), (6), and (7), respectively; (4) (5) (6) (7) in The piezoelectric strain constant is It is the elastic compliance constant. Where is the dielectric constant. The resonant frequency, The resonant frequency is the anti-resonant frequency; substituting equations (4) and (5) into equation (3), we obtain the piezoelectric ring's... and , The quantitative relationship is shown in equation (8): (8) From equation (6), we obtain the piezoelectric ring. and The quantitative relationship is shown in equation (9): (9) From equation (7), we obtain the piezoelectric ring. As shown in equation (10): (10) Substituting equation (10) into equation (11), we obtain the piezoelectric ring. and , , Quantitative relationship: (11) Substituting equations (7), (8), and (9) into (11), we obtain: , , The piezoelectric constant characterized As shown in equation (12): (12) Substituting formula (12) into the simplified sensitivity The expression, calculated using the following formula, gives the sensitivity of the piezoelectric ring: (13) 。 3. A method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters, characterized in that, Includes the following steps: Step 1. Give the formula for the open-circuit receiving voltage sensitivity when using a piezoelectric spherical shell as the piezoelectric element in a low-frequency hydrophone, and simplify it to the formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ； in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; Step 2. Based on the relevant theory of spherical symmetry modes, the equivalent parameters of the piezoelectric spherical shell are used to adjust the piezoelectric constant. The piezoelectric sphere shell was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. in piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ； in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively. The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ； in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

4. The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters according to claim 3, characterized in that, In step 2, the piezoelectric constant Equivalent parameter characterization and The calculation process is as follows: Define the dynamic inductance of a piezoelectric element With quality Dynamic capacitor With mechanical compliance The electromechanical conversion is shown in equations (14) and (15). Combining these equations, we can obtain equation (16), which is expressed as follows: (14) (15) (16) Where n is the electromechanical conversion coefficient; and the mass m and mechanical compliance of the piezoelectric sphere shell are given respectively. Free capacitance and planar electromechanical coupling coefficient As shown in formulas (17), (18), (19), and (20); (17) (18) (19) (20) in The piezoelectric strain constant is This represents the elastic compliance constant in the direction of plane stress. Where is the dielectric constant. The resonant frequency, It is the anti-resonant frequency; Substituting equations (17) and (18) into equation (16), we obtain the piezoelectric sphere shell. As in equation (21): (21) in , They represent The elastic compliance constant in the directions of the orthogonal components of the two plane stresses; From equation (19), the piezoelectric sphere shell is obtained. As shown in equation (22): (22) From equation (20), the piezoelectric sphere shell is obtained. As in equation (23): (23) Formula (23) Substituting into equation (24), we obtain the piezoelectric sphere shell. and , , Quantitative relationship: (24) Substituting equations (20), (21), and (22) into equation (24), we obtain the equivalent parameters of the piezoelectric sphere shell. , , The piezoelectric constant characterized As shown in equation (25): (25) Substituting formula (25) into the simplified sensitivity The expression, calculated using the following formula, gives the sensitivity of the piezoelectric ring: (26) 。 5. The method for calculating the sensitivity of a low-frequency hydrophone based on equivalent parameters according to claim 2 or 4, characterized in that, In step 2, the impedance frequency method and phase angle frequency method are used to process the impedance and phase angle data near the resonant frequency and 1 kHz, thereby obtaining the equivalent parameters of the piezoelectric element. , , The solution process is as follows: Based on the non-series resonant equivalent circuit and the series resonant equivalent circuit of a piezoelectric element, the impedance Z and phase angle near the resonant frequency are... The formula is obtained from equations (27) and (28) as follows: (27) (28) in For dynamic resistance, Indicates angular velocity, Represents the imaginary unit; At the resonant frequency Take from both sides and ,Will and corresponding , and , Enter equation (27), and solve simultaneously to obtain... and As shown in equations (29) and (30) respectively: (29) (30) in Indicates the frequency offset. and These represent offsets to the left and right at the resonant frequency, respectively. The subsequent frequency value, , and , respectively and The corresponding angular velocity and impedance values; Will and corresponding , and , Substituting into equation (28), we obtain and As shown in equations (31) and (32): (31) (32) in , They represent and The corresponding phase angle value; Free capacitance The impedance value corresponding to a frequency of 1 kHz is obtained according to equation (33): (33) in 1 kHz, The impedance value is at 1 kHz.

6. A low-frequency hydrophone sensitivity calculation system based on equivalent parameters, characterized in that, Includes the following modules: The sensitivity characterization simplification module is used to provide the open-circuit receiving voltage sensitivity formula when a piezoelectric ring is used as the piezoelectric element of a low-frequency hydrophone, and to simplify it to a formula based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization ; ； in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of axisymmetric modes and the equivalent parameters of the piezoelectric ring. The piezoelectric ring was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. in piezoelectric constant Equivalent parameters of piezoelectric rings , , The following formula is used to characterize it: ； in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric ring, respectively. The final calculated sensitivity formula for the piezoelectric ring is as follows: ； in The thickness is along the radial direction of the piezoelectric ring. The height along the axial direction of the piezoelectric ring. The density is the piezoelectric material density.

7. A low-frequency hydrophone sensitivity calculation system based on equivalent parameters, characterized in that, Includes the following modules: The sensitivity characterization simplification module provides a formula for the open-circuit receiving voltage sensitivity when a piezoelectric sphere is used as the piezoelectric element in a low-frequency hydrophone, and simplifies it to a value based on the average radius. and piezoelectric constant Simplified sensitivity of the characterization The expression is: ； in This is the open-circuit voltage of the piezoelectric element. Low-frequency sound pressure level, Let the inner radius be , The outer radius is ; And a sensitivity calculation module, used to calculate the piezoelectric constant based on the relevant theory of spherical symmetry modes and the equivalent parameters of the piezoelectric sphere. The piezoelectric sphere shell was characterized and substituted into the simplified sensitivity expression to calculate its sensitivity. in piezoelectric constant Equivalent parameters of the piezoelectric sphere shell , , The following formula is used to characterize it: ； in , , These represent the dynamic capacitance, dynamic inductance, and free capacitance of the piezoelectric sphere shell, respectively. The final calculated sensitivity formula for the piezoelectric sphere shell is as follows: ； in The thickness is along the radial direction of the piezoelectric sphere shell. This indicates the density of the piezoelectric material.

8. A computer device, comprising a memory and one or more processors; characterized in that, The memory stores executable code, which, when executed by the processor, is used to implement the low-frequency hydrophone sensitivity calculation method based on equivalent parameters as described in any one of claims 1 to 5.

9. A computer-readable storage medium having a program stored thereon; characterized in that, When executed by the processor, the program is used to implement the low-frequency hydrophone sensitivity calculation method based on equivalent parameters as described in any one of claims 1 to 5.

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