CN103197283A - Auditory localization device based on electrical analogue coupling structure - Google Patents

Abstract

The invention relates to a sound source localization device based on an electrical analog coupling structure, comprising an input module, a coupling processing module, an output module and a post-processing module connected in sequence, the input module receives an acoustic signal and converts it into a current signal, and the coupling The processing module amplifies the phase of the current signal of the input module, and transmits the amplified voltage signal to the output module, and the output module converts the voltage into a digital signal and transmits it to the post-processing module, and the post-processing module calculates the orientation information of the sound source . Compared with the prior art, the invention has the advantages of compact structure, high precision, good signal immediacy, wide application range and the like.

Description

A sound source localization device based on an electrical analog coupling structure

technical field

The invention relates to the field of acoustic positioning, in particular to a sound source localization device based on an electrical analog coupling structure.

Background technique

American scholars R.N.Miles, Robert and others studied the auditory orientation mechanism of Ormia ochracea in the 1990s, and found that the sound localization ability of the parasitic fly benefited from its auditory organ with a coupling structure, and in recent years In 2010, a second-level silicon microcrystalline microphone diaphragm was developed. The diaphragm was shaped by silicon micro-processing manufacturing technology, and the vibration signal was obtained by laser diffraction technology, thereby realizing the directivity characteristics of a pressure-difference microphone close to ideal.

In foreign countries, literature search found that the United States Patent No. US6963653B1, the publication date is 2005.11.8, and the patent name is multi-level directional microphone diaphragm. The patent states that "this invention has the characteristics of miniaturization, which is a two-stage silicon microcrystalline microphone diaphragm, which is shaped by silicon micromachining manufacturing technology." The patent describes a differential pressure microphone and its orientation characteristics, but the positioning method proposed by it only has the function of two-dimensional sound positioning.

In China, a novelty search found that the Chinese patent number CN101226235A, the publication date is 2008.7.23, and the patent name is a three-dimensional positioning method of sound source based on mechanical coupling diaphragm. Based on the in-depth exploration of the structural characteristics, positioning principle and nonlinear dynamic mechanism of the micro-biological acoustic sensing positioning system, this patent proposes a mechanical model that accurately describes the auditory sensing system of parasitic flies, and masters the auditory sensing system of parasitic flies. The biomechanical parameters of the system and their influence on the dynamic characteristics of the system, the vibration characteristic quantity of the system is obtained from the mechanically coupled diaphragm structure, and the relationship between the characteristic quantity and the direction information of the sound source is established, and the precise solution is calculated by a certain algorithm. Acoustic incident angle, thus a three-dimensional sound source positioning method is obtained, which solves the theoretical problem of coupling structure sound source localization in three-dimensional space. However, the laboratory model of the above method is difficult to process, and requires high processing and assembly accuracy. In addition, it is also restricted by factors such as material properties, shape, and processing technology, so the accuracy of sound source identification is difficult to meet the requirements.

Contents of the invention

The object of the present invention is to provide a sound source localization device based on an electrical analog coupling structure in order to overcome the above-mentioned defects in the prior art.

The purpose of the present invention can be achieved through the following technical solutions:

A sound source localization device based on an electrical analog coupling structure, characterized in that it includes an input module, a coupling processing module, an output module and a post-processing module connected in sequence, the input module receives an acoustic signal and converts it into a current signal, and the The coupling processing module amplifies the phase of the current signal of the input module, and transmits the amplified voltage signal to the output module, and the output module converts the voltage into a digital signal and sends it to the post-processing module, and the post-processing module calculates the orientation of the sound source information.

The input module includes a preprocessing module and three piezoelectric sensors, the piezoelectric sensors are excited by the sound source signal to generate a voltage signal and transmit it to the preprocessing module, and the preprocessing module converts the voltage signal into a current signal.

The preprocessing module is provided with a voltage amplifier for amplifying weak voltage signals.

The coupling processing module includes three parallel input and output branches and a coupling circuit, the input modules are respectively connected to the input ends of the three input and output branches, and the output ends of the three input and output branches are respectively connected to the output module, so The three input and output branches mentioned above are also respectively connected with the coupling loop.

Each input and output branch has a group of resistors and capacitors connected in parallel, the coupling loop is composed of three inductors connected in series, the resistors are connected in series with the input module, and the capacitors are connected in parallel with the output module, so One end of the above-mentioned capacitor is grounded, and the other end is connected between two adjacent inductors.

An ammeter is set between the resistor and the input module, and a voltmeter is set between the capacitor and the inductance.

The output module includes an A/D converter, a conditioner, and a collector connected in sequence, and the A/D converter converts the voltage signal into a digital signal, and the digital signal is conditioned by the conditioner to sample the signal through the collector , oscilloscope display and save.

The post-processing module calculates the azimuth information of the sound source by using a coupling processing method according to the obtained three amplified phase differences.

The sound source orientation information refers to the geometric relationship between the incident direction of the sound source and the piezoelectric sensor, that is, the longitude θ and latitude α in the spherical coordinate system determined by the piezoelectric sensor.

The coupling processing method refers to a processing process of simulating mechanical coupling in an acoustic-electric analogy manner.

The analogy relationship between mechanical coupling and circuit coupling is shown in the following table:

mechanical coupling circuit coupling

m C c 1/R k 1/L _c f I x u

The mechanical coupling structure is shown in Figure 2. D ₁ , D ₂ , D ₃ are three acoustic receiving diaphragms, the diaphragm area is S, B ₁ , B ₂ , B ₃ are three connecting rods, the fulcrum of the connecting rods is O, and the passing stiffness between the connecting rods is Spring connection for k ₃ .

Using the acoustic-electrical analogy, the above structural diagram can be compared to a circuit diagram, as shown in FIG. 3 . They both have the same differential equation:

$\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="m"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">m</figure-callout></span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="m"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">m</figure-callout></span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\end{array}\right]\left[\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]\left[\begin{array}{ccc}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="c"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">c</figure-callout></span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="c"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">c</figure-callout></span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; c</span>}\end{array}\right]\left[\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

为：In the mechanical coupling method, the transfer function between the system input sound pressure p and the displacement of each diaphragm

for:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}& {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; B</span>}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; s\&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; s\&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ {\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; s\&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}\end{array}\right]<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

为时延相关参数，矩阵参数为：

is the delay-related parameter, and the matrix parameter is:

$\frac{A_1}{B}=\frac{1}{3({\mathrm{<figure-callout\; id="2"\; label="ms"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">ms</figure-callout>}}^2+\mathrm{cs}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout>}}_1+{4k}_3)}+\frac{2}{3({\mathrm{<figure-callout\; id="2"\; label="ms"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">ms</figure-callout>}}^2+\mathrm{cs}+{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout>}}_1+k_3)}$ , (3)

$\frac{{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="ms"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">ms</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cs</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="ms"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">ms</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cs</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="k"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}$

为位移x的一次导数，为位移x的二次导数；Among them, f is the main frequency of the sound source, ω=2πf, i is the imaginary unit, s=iω/f; m is the quality of the mechanical coupling diaphragm, which corresponds to the size C of the capacitance in the circuit; c is the diaphragm and the sound transmission The damping of the medium corresponds to the reciprocal 1/R of the resistance in the circuit; k ₁ is the equivalent stiffness of the diaphragm, and k ₃ the stiffness of the spring between the connecting rods corresponds to the reciprocal 1/Lc of the inductance in the circuit. x is the displacement of the diaphragm, corresponding to the voltage U in the circuit,

is the first derivative of displacement x, is the second derivative of displacement x;

s ₁ , s ₂ , and s ₃ are three piezoelectric sensors, H ₁₃ is the transfer function between piezoelectric sensors s ₁ and s ₃ , H ₂₃ is the transfer function between piezoelectric sensors s ₂ and s ₃ , According to the above formula can be obtained:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="13"\; label="h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">h</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}}$

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}}{{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; p</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In this way, the relationship between H ₁₃ , H ₂₃ and time delay (τ ₁ , τ ₂ , τ ₃ ) is established.

The positioning method is used to calculate and obtain real-time sound source direction information, and the formula of its geometric relationship is:

$\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="c"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">c</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$

$\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="d\; c"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="0"\; label="d\; c"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">\; </figure-callout>}}{\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">c</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Combining (4) and (5), the relationship between the azimuth and H ₁₃ , H ₂₃ can be obtained, the specific formula is:

$\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\sqrt{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

in:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="i"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">i</figure-callout></span>}\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; \&omega;d</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{}_{}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C\&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; i\&omega;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{}_{}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C\&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; i\&omega;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{D.}}_2=\frac{c_0}{\mathrm{<figure-callout\; id="3"\; label="i"\; filenames="HDA00003091293700023.png"\; state="\{\{state\}\}">i</figure-callout>}3\mathrm{\&omega;d}}\ln [\frac{\frac{1}{{\mathrm{<figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">L</figure-callout>}}_c}{h}_{}{}_{13}+(-{\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})h_{\mathrm{twenty\; three}}+\frac{1}{L_c}}{({-\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c}){\mathrm{<figure-callout\; id="13"\; label="h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">h</figure-callout>}}_{13}+\frac{1}{L_c}{h}_{\mathrm{twenty\; three}}+\frac{1}{L_c}}$ , (8)

$<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">L</figure-callout></span><figure-callout\; id="13"\; label="L\; c\; h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{}_{}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C\&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; i\&omega;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; C\&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; i\&omega;</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="13"\; label="h"\; filenames="HDA00003091293700013.png"\; state="\{\{state\}\}">h</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}}<span\; class="notranslate">\; ]</span>$

In the above formula, c ₀ is the sound propagation speed in the medium, which is a known constant, and d is the radius from the piezoelectric sensor to the center point.

Compared with the prior art, the present invention has the following advantages:

1. The mechanical coupling is replaced by circuit coupling, which overcomes the processing difficulties and processing errors in mechanical coupling, realizes the function of phase amplification, and thus realizes the positioning capability.

2. Coupling parameters are implemented with simple components such as resistors, inductors, and capacitors, and each component is easy to match and realize.

3. Coupling parameters can be optimized to suit different measurement requirements.

4. The coupling branch is three input and output branches, so as to obtain two sets of effective transfer functions, which can be used for positioning in three-dimensional space, and the accuracy is improved compared with the mechanical system.

Description of drawings

Fig. 1 is a structural block diagram of the present invention.

Fig. 2 is a mechanical structure diagram referred to in the present invention.

Fig. 3 is a schematic circuit diagram of the coupling module of the present invention.

Fig. 4 is an excitation diagram of the current signal of the coupling module in the embodiment of the present invention.

Fig. 5 is a graph of the voltage signal response of the coupling module in the embodiment of the present invention.

Fig. 6 is a layout orientation diagram of the piezoelectric sensor of the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

As shown in Figure 1, a sound source localization device based on an electrical analog coupling structure includes an input module 1, a coupling processing module 2, an output module 3 and a post-processing module 4 connected in sequence, the input module 1 receives an acoustic signal and Converted to a current signal, the coupling processing module 2 amplifies the phase of the current signal input to the module 1, and transmits the amplified voltage signal to the output module 3, and the output module 3 converts the voltage into a digital signal and transmits it to the post-processing module 4. The post-processing module 4 calculates the orientation information of the sound source.

The input module 1 includes a preprocessing module and three piezoelectric sensors, the piezoelectric sensors are excited by the sound source signal to generate a voltage response, and the preprocessing module converts the voltage response into a current signal. The preprocessing module can choose to add a voltage amplifier to adjust the appropriate voltage amplitude without distorting the voltage waveform, so that the weak voltage signal is amplified, and the voltage amplifier can also filter within a certain range to reduce signal interference.

The output module 3 includes an A/D converter, a conditioner, and a collector, the A/D converter converts the voltage signal into a digital signal, and the collector samples, displays and saves the signal.

The post-processing module calculates the orientation information of the sound source by using a coupling processing method according to the three amplified phase differences.

As shown in Figure 3, the coupling processing module 2 includes three parallel input and output branches 201 and a coupling circuit 202, the three outputs of the input module 1 are respectively connected to the three input and output branches, and one end of the input and output branches is grounded , and the other end is connected to the coupling loop 202 and the output module 3 . Each of the input and output branches has a set of parallel resistors and capacitors (R1 and C1, R2 and C2, R3 and C3), and the coupling loop 202 has three connected inductances L _c 1, L _c 2, L _c3 . The current sources Is _i , i=1, 2, 3 are not actual current sources, but simulate current input signals from the input module 1 . The three input and output branches are respectively connected with ammeter and voltmeter, and I _i , V _i , i=1, 2, 3 respectively test the input current and output voltage.

The core of the present invention is to realize the amplification of the signal phase difference through the coupling circuit, and the coupling circuit parameter of the present embodiment is:

part symbol parameter size unit R1, R2, R3 resistance 156 Kiloohm (kΩ) C1, C2, C3 Capacitance 1.53 millifarad (mF) L _c 1, L _c 2, L _c 3 Inductance value 0.4 Millihenry (mH) Is1, Is2, Is3 current value 1 Ampere (A) (θ,α) angle of incidence see table below degree(°) d Sensor Radius 0.05 meter (m) c0 speed of sound 340 meter per second (m/s)

Note that the parameters used here do not represent optimal parameters, but are only used as conditions for explaining and verifying the phase difference of coupling amplification.

As shown in Figures 4 and 5, the input current (Figure 4) has no amplitude difference and a small phase difference. After passing through the coupling circuit, the output voltage (Figure 5) has a small amplitude and a more obvious phase difference. Obviously, the phase difference is amplified.

As shown in Figure 6, the piezoelectric sensors s1, s2, and s3 are arranged at points 1, 2, and 3 on the xy plane, the sound source is S, and the incident angle of the sound source is (θ, α). Substituting the parameters in the above table into the formulas (1), (2) and (3) respectively, through the calculation of the transfer function between the output currents, the incident angle can be solved from the formulas (4), (5) and (6) , select the calculated average value as the positioning result, as shown in the following table:

(theta, alpha) [input] Simulation results maximum error (30°, 87°) (31.197°, 85.864°) 1.136° (30°, 84°) (31.578°, 83.007°) 1.578° (30°, 81°) (31.377°, 80.140°) 1.377° (30°, 78°) (31.093°, 77.268°) 1.093°

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements within the spirit and principles of the present invention should be included in the protection scope of the present invention Inside.

Claims (10)

1. auditory localization device based on the electric analogy coupled structure, it is characterized in that, comprise the load module, coupling processing module, output module and the post-processing module that connect successively, described load module receives acoustical signal and is converted to current signal, described coupling processing module is amplified the phase place of the current signal of load module, and the voltage signal that amplifies passed to output module, described output module is that digital signal is imported post-processing module into voltage transitions, and described post-processing module is calculated the azimuth information of sound source.

2. a kind of auditory localization device based on the electric analogy coupled structure according to claim 1, it is characterized in that, described load module comprises pretreatment module and three piezoelectric sensors, described piezoelectric sensor is subjected to the sound-source signal excitation to produce voltage signal and it is transferred to pretreatment module, and described pretreatment module is converted to current signal with voltage signal.

3. a kind of auditory localization device based on the electric analogy coupled structure according to claim 2 is characterized in that, described pretreatment module is provided with the voltage amplifier that the weak voltage signal is amplified.

4. a kind of auditory localization device based on the electric analogy coupled structure according to claim 2, it is characterized in that, described coupling processing module comprises input and output branch road and coupling circuit of three parallel connections, load module is connected with the input end of three input and output branch roads respectively, the output terminal of described three input and output branch roads is connected with output module respectively, and described three input and output branch roads also are connected with coupling circuit respectively.

5. a kind of auditory localization device based on the electric analogy coupled structure according to claim 4, it is characterized in that, every the input and output branch road all has one group of parallel resistor and electric capacity, described coupling circuit is made of three inductance of connecting successively, described resistance and load module are connected in series, described electric capacity and output module are connected in parallel, described electric capacity one end ground connection, and the other end is connected between the two adjacent inductance.

6. a kind of auditory localization device based on the electric analogy coupled structure according to claim 5 is characterized in that, is provided with reometer between described resistance and the load module, is provided with voltage table between described electric capacity and the inductance.

7. a kind of auditory localization device based on the electric analogy coupled structure according to claim 1, it is characterized in that, described output module comprises A/D converter, conditioner, the collector that connects successively, described A/D converter is converted to digital signal with voltage signal, this digital signal through conditioner conditioning back by collector to signal sample, oscillography shows and preserve.

8. a kind of auditory localization device based on the electric analogy coupled structure according to claim 5 is characterized in that, described post-processing module according to three amplifications that obtain after phase differential, adopt coupled processing method to calculate the azimuth information of sound source.

9. a kind of auditory localization device based on the electric analogy coupled structure according to claim 8, it is characterized in that, described sound bearing information refers to the geometric relationship between sound source incident direction and the piezoelectric sensor, i.e. longitude θ and latitude a in the spherical coordinate system of being determined by piezoelectric sensor.

10. a kind of auditory localization device based on the electric analogy coupled structure according to claim 9, it is characterized in that, described coupled processing method refers to that the mode of employing sound-electrical analogy simulates the processing procedure of mechanical couplings, in the mechanical couplings method, the transport function between system's input acoustic pressure and each vibrating diaphragm displacement

For:

$\left[\begin{array}{c}{H}_{x_{1}p}\\ H_{x_{2}p}\\ H_{x_{3}p}\end{array}\right]=\left[\begin{array}{ccc}{A}_1/B& A_2/B& A_2/B\\ A_2/B& A_1/B& A_2/B\\ A_2/B& A_2/B& A_1/B\end{array}\right]\left[\begin{array}{c}{e}^{{\mathrm{s\&tau;}}_1}\\ e^{{\mathrm{s\&tau;}}_2}\\ e^{{\mathrm{s\&tau;}}_3}\end{array}\right],---\left(1\right)$

Be the time delay correlation parameter, matrix parameter is:

$\frac{A_1}{B}=\frac{1}{3({\mathrm{ms}}^2+\mathrm{cs}+k_1+{4k}_3)}+\frac{2}{3({\mathrm{ms}}^2+\mathrm{cs}+k_1+k_3)},$ (2)

$\frac{A_2}{B}=\frac{1}{3({\mathrm{ms}}^2+\mathrm{cs}+k_1+{4k}_3)}-\frac{1}{3({\mathrm{ms}}^2+\mathrm{cs}+k_1+k_3)}$

Wherein, f is the predominant frequency of sound source, ω=2 π f, and i is imaginary unit, s=i ω/f; M is the quality of mechanical coupling diaphragm, corresponding to the big or small C of electric capacity in the circuit; C is the damping of vibrating diaphragm and sound bearing medium, the 1/R reciprocal of the size of resistance in the corresponding circuits; k ₁Be the equivalent stiffness of vibrating diaphragm, k ₃The rigidity of spring between the connecting rod is all corresponding to the 1/Lc reciprocal of the size of inductance in the circuit;

s ₁, s ₂, s ₃Be respectively three piezoelectric sensors, H ₁₃Be piezoelectric sensor s ₁With s ₃Between transport function, H ₂₃Be piezoelectric sensor s ₂With s ₃Between transport function, can get according to above-mentioned formula:

$H_{13}=\frac{H_{x_{1}p}}{H_{x_{3}p}}$

$H_{23}=\frac{H_{x_{2}p}}{H_{x_{2}p}},---\left(3\right)$

Set up H ₁₃, H ₂₃With time delay (τ ₁, τ ₂, τ ₃) between relation;

Adopt localization method to calculate and obtain real-time Sounnd source direction information, the formula of its geometric relationship is:

$\frac{({\mathrm{\&tau;}}_3-{\mathrm{\&tau;}}_2)c_0}{\sqrt{3}d}=\sin \mathrm{\&theta;}\sin \mathrm{\&alpha;}=D_1$ (4)

$\frac{({\mathrm{\&tau;}}_2-{\mathrm{\&tau;}}_1)+({\mathrm{\&tau;}}_3-{\mathrm{\&tau;}}_1)}{3d}{c}_0=\sin \mathrm{\&theta;}\cos \mathrm{\&alpha;}=D_2$

In conjunction with (3) and (4), can obtain position angle and H ₁₃, H ₂₃Between relation, concrete formula is:

$\sin \mathrm{\&theta;}=\sqrt{D_1^2+D_2^2}$

$\sin \mathrm{\&alpha;}=\frac{D_1}{\sqrt{D_1^2+D_2^2}},---\left(5\right)$

Wherein:

$D_1=\frac{c_0}{i\sqrt{3}\mathrm{\&omega;d}}\ln \frac{\frac{1}{L_c}{H}_{13}+\frac{1}{L_c}{H}_{23}+(-{\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})}{\frac{1}{L_c}{H}_{13}+(-{\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})H_{23}+\frac{1}{L_c}},---\left(6\right)$

$D_2=\frac{c_0}{i3\mathrm{\&omega;d}}\ln [\frac{\frac{1}{L_c}{H}_{13}+(-{\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})H_{23}+\frac{1}{L_c}}{({-\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})H_{13}+\frac{1}{L_c}{H}_{23}+\frac{1}{L_c}}$ (7)

$+\ln \frac{\frac{1}{L_c}{H}_{13}+\frac{1}{L_c}{H}_{23}+({-\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})}{({-\mathrm{C\&omega;}}^2+\frac{\mathrm{i\&omega;}}{R}+\frac{2}{L_c})H_{13}+\frac{1}{L_c}{H}_{23}+\frac{1}{L_c}}],$

In the above-mentioned formula, c ₀Being the sound propagation velocity in the medium, is a known constant, and d is that piezoelectric sensor is to the radius of central point.

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