Method and system for detecting liquid density in a filled pipe based on frequency-modulated ultrasonic guided waves

Abstract

The application discloses a method and system for detecting liquid density in a liquid-filled pipeline based on frequency-modulated ultrasonic guided waves, and the method adopts ultrasonic guided waves to detect the liquid density in the liquid-filled pipeline. In the embodiment, the liquid density in the liquid-filled pipeline is detected by using ultrasonic guided waves with good conductivity, without needing to consider that two transducers must be placed directly opposite each other, and the liquid inside the pipeline with different setting positions can be detected, and a very high voltage is not needed to excite the ultrasonic transducer. That is, the method can accurately and practically detect the liquid in the liquid-filled pipeline, and can better realize nondestructive detection of the liquid density parameter inside a sealed pipeline or container, has high reliability, and is favorable for actual promotion and use.

Description

Technical Field

[0001] This invention relates to the field of liquid-filled pipeline inspection technology, and in particular to a method and system for detecting the density of liquid inside a liquid-filled pipeline based on frequency-modulated ultrasonic guided waves. Background Technology

[0002] Currently, when inspecting liquid-filled sealed pipelines, the common practice to monitor the working conditions inside the pipeline is to measure the liquid density. Monitoring the liquid density helps determine if the pipeline is functioning properly. Existing technologies generally employ three methods for detecting liquid density in liquid-filled sealed pipelines: embedded sensors, radiation detection, and ultrasonic penetration. Embedded sensors typically cause irreversible damage to the pipeline's inner wall; radiation detection utilizes the strong penetrating power and linearity of gamma rays, X-rays, and neutrons, and its attenuation characteristics during propagation to understand the heterogeneity of the tested object, but it is expensive, inefficient, and carries certain risks; ultrasonic penetration utilizes the difference in acoustic impedance between different liquids, detecting a weak transmitted signal at the other end.

[0003] In practical applications, the ultrasonic penetration method is generally used to detect the density of liquid in a closed, liquid-filled pipe. However, this method has limitations. The two transducers must be placed facing each other. If the pipe is placed in a corner or other special circumstances, it is impossible to install or measure. Furthermore, the ultrasonic penetration method requires extremely high voltage to excite the ultrasonic transducer. Therefore, it places high demands on the materials of the signal generation circuit and the transducer. This makes the use of the ultrasonic penetration method highly limited by various factors and difficult to achieve large-scale application. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the low practical feasibility of using ultrasonic penetration methods in existing technologies, and to propose a method and system for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] The first aspect of this invention provides a method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves. The method employs ultrasonic guided waves to detect the density of the liquid in the pipe, specifically including:

[0007] Obtain all information about the pipeline being inspected, including: the material, inner diameter, and outer diameter of the pipeline being inspected;

[0008] Two points are randomly selected on the outer wall of the pipe to be tested, as the first test point and the second test point. One of the first test point and the second test point is an ultrasonic transmitter and the other is an ultrasonic receiver.

[0009] The ultrasonic transmitter emits ultrasonic signals, which are excited to form ultrasonic longitudinal waves and ultrasonic transverse waves inside the pipe being tested. The ultrasonic longitudinal waves and ultrasonic transverse waves are reflected by the inner wall of the pipe being tested to form ultrasonic guided wave signals.

[0010] The ultrasonic receiver receives and samples the ultrasonic guided wave, and quantifies and stores the acquired ultrasonic guided wave waveform.

[0011] The ultrasonic longitudinal and transverse waves generated by the excitation are pulse-compressed with the ultrasonic guided wave waveform received by the ultrasonic receiver to obtain the wave number in a certain time sequence. At the same time, based on all the information of the tested pipe, the phase velocity and group velocity of the ultrasonic guided wave inside the tested pipe when it is not filled with liquid are obtained.

[0012] Repeat the above steps to obtain the phase velocity and group velocity of the ultrasonic guided wave when it is filled with liquid in the pipe under test. At the same time, based on the phase velocity and group velocity of the ultrasonic guided wave when it is not filled with liquid in the pipe under test, and the order of receiving the ultrasonic guided wave, determine the liquid density parameters inside the pipe.

[0013] In some alternative embodiments, the method for obtaining the phase velocity and group velocity of the ultrasonic guided wave inside the unfilled pipe includes:

[0014] Select a point as a mass point and obtain the spatial coordinate system displacement parameters of that mass point;

[0015] Based on the particle parameters, the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves in the tested pipe are obtained, and the displacement component information of ultrasonic longitudinal waves in the liquid is obtained based on the particle parameters.

[0016] Based on the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves in the tested pipe, and the displacement component information of ultrasonic longitudinal waves in the liquid, the boundary condition parameters inside the tested pipe are obtained.

[0017] In some optional embodiments, it also includes:

[0018] Based on the obtained boundary condition parameters inside the pipe under test, and combined with the solution of the basic equation, the dispersion equation relating the dispersion curve inside the pipe under test to the ultrasonic guided wave is obtained.

[0019] Based on the obtained dispersion equation, when the physical parameters of the tested pipe remain unchanged, the phase velocity and group velocity of a certain mode of the ultrasonic guided wave at the corresponding frequency will change as the liquid density inside the tested pipe changes. The signal received after the ultrasonic guided wave signal propagates in the tested pipe is processed and analyzed to obtain the liquid density parameters inside the tested pipe.

[0020] In some optional embodiments, the method for obtaining the boundary condition parameters inside the detected pipe includes:

[0021] Define the displacement parameters of the spatial coordinate system as follows:

[0022] u r =u r (r, θ) u θ =u θ (r, θ) u z =0

[0023] Among them, u r u is the radial displacement of the particle. θ Let u be the circumferential displacement of the particle. z This represents the displacement along the z-axis in the cylindrical coordinate system (r, θ, z);

[0024] Ultrasonic longitudinal waves and ultrasonic transverse waves can propagate within the pipe being inspected. The displacement component parameters of the ultrasonic longitudinal waves and ultrasonic transverse waves within the pipe being inspected are:

[0025]

[0026] Where φ and ψ are the longitudinal wave potential function and the transverse wave potential function in the pipe being tested, respectively;

[0027] Only ultrasonic longitudinal waves can propagate in liquids. The displacement component information of ultrasonic longitudinal waves in liquids is as follows:

[0028]

[0029] in, L φ is the longitudinal wave potential function in the liquid. L u r Radial displacement of particles in a liquid L u θ This represents the circumferential displacement of a particle in a liquid.

[0030] Combining Equations 1 and 2, we can derive:

[0031]

[0032] Where k is the wave number, ω is the angular frequency, and e is ignored in the following derivation. -iωt It satisfies the wave equation;

[0033] When the pipe being inspected is filled with liquid, its outer surface is under stress-free boundary conditions, with zero radial and normal stresses. Assuming the liquid inside the pipe has no viscous stress, and because the inner wall of the pipe and the liquid are in close contact, they have the same displacement. Furthermore, the forces acting on each other are mutual; the force exerted by the liquid on the inner wall of the pipe and the force exerted by the inner wall of the pipe on the liquid are equal in magnitude and opposite in direction, forming a pair of reaction forces. Based on these conditions, the boundary condition parameters inside the pipe can be derived as follows:

[0034] σ rθ | r＝a =0, σ rr | r＝a =0, σ rθ | r＝b =0

[0035] σ rr | r＝a = L σ rr | r＝n u r | r＝a = L u r | r＝a Formula 4

[0036] Where, σ rθ σ is the circumferential stress on the inner wall of the pipe being tested. rr The radial stress on the inner wall of the pipe being inspected. L σ rr Let be the radial stress of the liquid, where a is the inner diameter of the pipe being tested and b is the outer diameter of the pipe being tested.

[0037] In some alternative embodiments, the method for obtaining the liquid density parameter inside the pipe being tested includes:

[0038] Based on the fundamental equation, we obtain:

[0039]

[0040] Where, ρ l ρ and ρ' are the liquid density and the pipe density, respectively.

[0041] From equations 4 and 5, we obtain:

[0042]

[0043] Where M = kb,k t k is the transverse wave number. l Let k be the P-wave number, and k t =ω / c t kl=ω / cl c t c l These represent the transverse and longitudinal wave velocities of the pipe material, J. M (x) and Y M (x) are the first and second type Bessel functions, respectively; that is, in this embodiment, by pre-observing the transverse wave velocity and longitudinal wave velocity of the pipe to be detected, and based on the ω obtained by the detection as the angular frequency, the transverse wave number and longitudinal wave number of the ultrasonic guided wave are derived.

[0044] According to Equation 6, the dispersion equation can be derived:

[0045]

[0046] In Equation 7, when D1 = 0, it is the dispersion curve when the inside of the tested pipe is not filled with liquid;

[0047] Therefore, when the physical parameters of the pipe under test remain unchanged, as the liquid density inside the pipe changes, the phase velocity and group velocity of a certain mode of the ultrasonic guided wave at the corresponding frequency will change. By processing and analyzing the signal received after the ultrasonic guided wave signal propagates in the pipe under test, the liquid density parameters inside the pipe under test can be obtained.

[0048] In some alternative embodiments, the ultrasonic signal is a high-voltage pulse signal, a low-voltage continuous signal, or a frequency-modulated signal.

[0049] A second aspect of the present invention provides a system for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves, employing the method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves as described in any one of the first aspects, the system comprising:

[0050] An ultrasonic transducer is placed at both the first and second detection points.

[0051] Among the two ultrasonic transducers at the first and second detection points, one is a transmitting transducer used to convert electrical signals into ultrasonic signals; the other is a receiving transducer used to convert the mechanical vibration on the inner wall of the pipe being tested into electrical signals.

[0052] The beneficial effects of this invention are as follows:

[0053] In this invention, the liquid density inside a filled pipe is detected using ultrasonic guided waves with good conductivity. This eliminates the need for two transducers to be placed directly opposite each other, allowing for detection of liquids inside pipes at different locations. Furthermore, it eliminates the need for extremely high voltages to excite the ultrasonic transducers. Therefore, this method achieves accurate and practical detection of liquids inside filled pipes, and also enables better non-destructive testing of liquid density parameters inside sealed tubes or containers. It offers high reliability and is beneficial for practical promotion and application. Attached Figure Description

[0054] Figure 1 This is an overall schematic diagram of a method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves provided in an embodiment of the present invention;

[0055] Figure 2 This is a dispersion curve diagram for two different liquid densities in a method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves provided in an embodiment of the present invention.

[0056] The markings in the diagram are as follows:

[0057] 1. Ultrasonic transducer; 2. Pipeline under test; 3. Outer wall of pipe under test; 4. Inner wall of pipe under test; 5. Liquid; α. Inner diameter of pipe under test; b. Outer diameter of pipe under test. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0059] If the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Furthermore, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0060] Example 1

[0061] Reference Figure 1 and Figure 2 To address the shortcomings of existing technologies that use ultrasonic penetration methods for detecting the density of liquids inside pipes due to their limited practical application, this invention provides a method for detecting the density of liquids inside filled pipes based on frequency-modulated ultrasonic guided waves. This method utilizes ultrasonic guided waves with excellent conductivity to detect the liquid density within the filled pipe, eliminating the need for two transducers to be placed directly opposite each other. It can detect liquids inside pipes at different locations and does not require extremely high voltages to excite the ultrasonic transducers. Therefore, this method achieves accurate and practical detection of liquids inside filled pipes, and also enables better non-destructive testing of the internal liquid density parameters of sealed pipes or containers. It boasts high reliability and is conducive to practical promotion and application.

[0062] The method specifically includes:

[0063] Obtain all information about the pipeline being inspected, including: the material, inner diameter, and outer diameter of the pipeline being inspected;

[0064] Two points are randomly selected on the outer wall of the pipe to be tested, as the first test point and the second test point. One of the first test point and the second test point is an ultrasonic transmitter and the other is an ultrasonic receiver.

[0065] The ultrasonic transmitter emits ultrasonic signals, which are excited to form ultrasonic longitudinal waves and ultrasonic transverse waves inside the pipe being tested. The ultrasonic longitudinal waves and ultrasonic transverse waves are reflected by the inner wall of the pipe being tested to form ultrasonic guided wave signals.

[0066] The ultrasonic receiver receives and samples the ultrasonic guided wave, and quantifies and stores the acquired ultrasonic guided wave waveform.

[0067] The ultrasonic longitudinal and transverse waves generated by the excitation are pulse-compressed with the ultrasonic guided wave waveform received by the ultrasonic receiver to obtain the wave number in a certain time sequence. At the same time, based on all the information of the tested pipe, the phase velocity and group velocity of the ultrasonic guided wave inside the tested pipe when it is not filled with liquid are obtained.

[0068] Repeat the above steps to obtain the phase velocity and group velocity of the ultrasonic guided wave when the pipe is filled with liquid. Simultaneously, based on the phase velocity and group velocity of the ultrasonic guided wave when the pipe is not filled with liquid, and the order in which the ultrasonic guided waves are received, the liquid density parameters inside the pipe are determined. In this embodiment, the ultrasonic guided wave is used to detect two states inside the pipe (one without liquid and the other with liquid), and then the liquid density is derived based on the detection results. Specifically: first, a dispersion equation is constructed based on the phase velocity and group velocity of the ultrasonic guided wave when the pipe is not filled with liquid, and all information about the pipe. Then, the pipe is filled with liquid, and the ultrasonic guided wave behavior during liquid filling is substituted into the dispersion equation to derive the liquid density. This method enables the detection of liquid density within filled pipes using highly conductive ultrasonic guided waves, eliminating the need for two transducers to be placed directly opposite each other. It allows for detection of liquids inside pipes at different locations and eliminates the need for extremely high voltages to excite the ultrasonic transducers. In short, this method provides accurate and practical detection of liquids within filled pipes, and also enables better non-destructive testing of liquid density parameters in closed tubes or containers. Its high reliability facilitates its widespread adoption and application.

[0069] In some alternative embodiments, the method for obtaining the phase velocity and group velocity of the ultrasonic guided wave inside the unfilled pipe includes:

[0070] Select a point as a mass point and obtain the spatial coordinate system displacement parameters of that mass point;

[0071] Based on the particle parameters, the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves in the tested pipe are obtained, and the displacement component information of ultrasonic longitudinal waves in the liquid is obtained based on the particle parameters.

[0072] Based on the displacement component parameters of the ultrasonic longitudinal wave and ultrasonic transverse wave within the tested pipe, and the displacement component information of the ultrasonic longitudinal wave in the liquid, the boundary condition parameters inside the tested pipe are obtained. In this embodiment, when only considering the circumferential guiding wave, the Z-axis related terms can be simply ignored, and the displacement parameter of the spatial coordinate system represented by the particle is defined as:

[0073] u r =u r (r, θ) u θ =u θ (r, θ) u z =0

[0074] Among them, u r u is the radial displacement of the particle. θ Let u be the circumferential displacement of the particle.z This represents the displacement along the z-axis in the cylindrical coordinate system (r, θ, z);

[0075] Ultrasonic longitudinal waves and ultrasonic transverse waves can propagate within the pipe being inspected. The displacement component parameters of the ultrasonic longitudinal waves and ultrasonic transverse waves within the pipe being inspected are:

[0076]

[0077] Where φ and ψ are the longitudinal wave potential function and the transverse wave potential function in the pipe being tested, respectively;

[0078] Only ultrasonic longitudinal waves can propagate in liquids. The displacement component information of ultrasonic longitudinal waves in liquids is as follows:

[0079]

[0080] in, L φ is the longitudinal wave potential function in the liquid. L u r Radial displacement of particles in a liquid L u θ This represents the circumferential displacement of a particle in a liquid.

[0081] Combining Equations 1 and 2, we can derive:

[0082]

[0083] Where k is the wave number, ω is the angular frequency, and e is ignored in the following derivation. -iωt It satisfies the wave equation;

[0084] When the pipe being inspected is filled with liquid, its outer surface is under stress-free boundary conditions, with zero radial and normal stresses. Assuming the liquid inside the pipe has no viscous stress, and because the inner wall of the pipe and the liquid are in close contact, they have the same displacement. Furthermore, the forces acting on each other are mutual; the force exerted by the liquid on the inner wall of the pipe and the force exerted by the inner wall of the pipe on the liquid are equal in magnitude and opposite in direction, forming a pair of reaction forces. Based on these conditions, the boundary condition parameters inside the pipe can be derived as follows:

[0085] σ rθ | r＝a =0, σ rr | r＝a =0, σ rθ | r＝b =0

[0086] σ rr | r＝a = L σ rr | r＝a ur | r＝a = L u r | r＝a Formula 4

[0087] Where, σ rθ σ is the circumferential stress on the inner wall of the pipe being tested. rr The radial stress on the inner wall of the pipe being inspected. L σ rr Let be the radial stress of the liquid, where a is the inner diameter of the pipe being tested and b is the outer diameter of the pipe being tested.

[0088] In some alternative embodiments, the method for obtaining the liquid density parameter inside the pipe being tested includes:

[0089] Based on the fundamental equation, we obtain:

[0090]

[0091] Where, ρ l ρ and ρ' are the liquid density and the pipe density, respectively.

[0092] From equations 4 and 5, we obtain:

[0093]

[0094] Where M = kb,k t k is the transverse wave number. l Let k be the P-wave number, and k t =ω / c t k l =ω / c l c t c l These represent the transverse and longitudinal wave velocities of the pipe material, J. M (x) and Y M (x) are the first and second type Bessel functions, respectively;

[0095] According to Equation 6, the dispersion equation can be derived:

[0096]

[0097] In Equation 7, when D1 = 0, it is the dispersion curve when the inside of the tested pipe is not filled with liquid;

[0098] Therefore, when the physical parameters of the pipe under test remain unchanged, as the liquid density inside the pipe changes, the phase velocity and group velocity of a certain mode of the ultrasonic guided wave at the corresponding frequency will change. By processing and analyzing the signal received after the ultrasonic guided wave signal propagates in the pipe under test, the liquid density parameters inside the pipe under test can be obtained.

[0099] In this embodiment, the ultrasonic signal is a high-voltage pulse signal, a low-voltage continuous signal, or a frequency-modulated signal. Specifically, in this embodiment, the ultrasonic transducer at the first detection point / second detection point excites the ultrasonic signal, which can be a high-voltage pulse (series) signal, a low-voltage continuous signal, a frequency-modulated signal, etc. While high-voltage pulse signals have high time resolution, their energy is low due to their narrow pulse width; low-voltage continuous signals carry higher energy but have lower time resolution; and frequency-modulated signals combine the advantages of both. Therefore, in this embodiment, preferably, the excitation signal of the ultrasonic transducer is a frequency-modulated signal.

[0100] Reference Figure 2 In this embodiment, to demonstrate the feasibility of the method for detecting the liquid density in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves, an example is given. The pipe being tested is made of SU304, with an inner diameter of 0.04 m and an outer diameter of 0.0449 m. Two liquids with densities of 0.79 and 1 are filled into the pipe. Figure 2 It can be seen that when liquids of different densities are filled into the pipe under test, the modes at different frequencies are different and the corresponding phase velocities are also different. Therefore, the density of the liquid in the pipe under test can be determined based on the measured ultrasonic echoes, phase velocities, group velocities, etc.

[0101] Example 2

[0102] A second aspect of the present invention provides a system for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves, employing the method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves as described in any one of the first aspects, the system comprising:

[0103] An ultrasonic transducer is placed at both the first and second detection points.

[0104] Among the two ultrasonic transducers at the first and second detection points, one is a transmitting transducer used to convert electrical signals into ultrasonic signals; the other is a receiving transducer used to convert the mechanical vibration on the inner wall of the pipe being tested into electrical signals.

[0105] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for detecting the density of liquid in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves, characterized by... The characteristic is that the method uses ultrasonic guided waves to detect the density of the liquid inside the filling pipe, specifically including: Obtain all information about the pipeline being inspected, including: the material, inner diameter, and outer diameter of the pipeline being inspected; Two points are randomly selected on the outer wall of the pipe to be tested, as the first test point and the second test point. One of the first test point and the second test point is an ultrasonic transmitter and the other is an ultrasonic receiver. The ultrasonic transmitter emits ultrasonic signals, which are excited to form ultrasonic longitudinal waves and ultrasonic transverse waves inside the pipe being tested. The ultrasonic longitudinal waves and ultrasonic transverse waves are reflected by the inner wall of the pipe being tested to form ultrasonic guided wave signals. The ultrasonic receiver receives and samples the ultrasonic guided wave, and quantifies and stores the acquired ultrasonic guided wave waveform. The ultrasonic longitudinal and transverse waves generated by the excitation are pulse-compressed with the ultrasonic guided wave waveform received by the ultrasonic receiver to obtain the wave number in a certain time sequence. At the same time, based on all the information of the tested pipe, the phase velocity and group velocity of the ultrasonic guided wave inside the tested pipe when it is not filled with liquid are obtained. Repeat the above steps to obtain the phase velocity and group velocity of the ultrasonic guided wave during liquid filling in the tested pipe; When the physical parameters of the tested pipe remain unchanged, as the density of the liquid filling the tested pipe changes, the phase velocity and group velocity of a certain mode of the ultrasonic guided wave at the corresponding frequency will change; based on the ultrasonic guided wave received in the tested pipe when it is not filled with liquid and when it is filled with liquid, the liquid density parameters inside the pipe can be derived. The method further includes: Based on the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves in the tested pipe, and the displacement component information of ultrasonic longitudinal waves in the liquid, the boundary condition parameters inside the tested pipe are obtained. The boundary condition parameters inside the inspected pipe are: Formula 4 in, The circumferential stress is the inner wall of the pipe being tested. The radial stress on the inner wall of the pipe being inspected. Let be the radial stress of the liquid, where b is the inner diameter of the pipe being inspected, and b is the outer diameter of the pipe being inspected. For the radial displacement of the particle, This represents the radial displacement of a particle in a liquid. Methods for obtaining the liquid density parameters inside the pipe being tested include: Based on the fundamental equation, we obtain: Formula 5 in, and These are the liquid density and the pipe density, respectively. From equations 4 and 5, we obtain: Formula 6 in, , The transverse wave number, Let be the P-wave number, and , , Angular frequency, These refer to the transverse wave velocity and longitudinal wave velocity of the pipe material, respectively. and These are the first and second type Bessel functions, respectively. According to Equation 6, the dispersion equation can be derived: Formula 7 In Equation 7, when The value is the dispersion curve when the inside of the tested pipe is not filled with liquid.

2. The method for detecting the liquid density in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves according to claim 1, characterized in that, Methods for obtaining the phase velocity and group velocity of ultrasonic guided waves inside an unfilled pipe include: Select a point as a mass point and obtain the spatial coordinate system displacement parameters of that mass point; Based on the particle parameters, the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves in the tested pipe are obtained, and the displacement component information of ultrasonic longitudinal waves in the liquid is obtained based on the particle parameters. Based on the displacement component parameters of ultrasonic longitudinal waves and ultrasonic transverse waves within the tested pipe, and the displacement component information of ultrasonic longitudinal waves in the liquid, the boundary condition parameters inside the tested pipe are obtained.

3. The method for detecting the liquid density in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves according to claim 2, characterized in that, Also includes: Based on the obtained boundary condition parameters inside the pipe under test, and combined with the solution of the basic equation, the dispersion equation relating the dispersion curve inside the pipe under test to the ultrasonic guided wave is obtained. Based on the obtained dispersion equation, when the physical parameters of the tested pipe remain unchanged, the phase velocity and group velocity of a certain mode of the ultrasonic guided wave at the corresponding frequency will change as the liquid density inside the tested pipe changes. The signal received after the ultrasonic guided wave signal propagates in the tested pipe is processed and analyzed to obtain the liquid density parameters inside the tested pipe.

4. The method for detecting the liquid density in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves according to claim 3, characterized in that, Methods for obtaining the boundary condition parameters inside the inspected pipe include: Define the displacement parameters of the spatial coordinate system as follows: ， in, For the radial displacement of the particle, For the circumferential displacement of the particle, cylindrical coordinate system middle Displacement in the axial direction; Ultrasonic longitudinal waves and ultrasonic transverse waves can propagate within the pipe being inspected. The displacement component parameters of the ultrasonic longitudinal waves and ultrasonic transverse waves within the pipe being inspected are: Formula 1 in, , These are the longitudinal wave potential function and the transverse wave potential function in the pipeline being tested, respectively. Only ultrasonic longitudinal waves can propagate in liquids. The displacement component information of ultrasonic longitudinal waves in liquids is as follows: Formula 2 in, The longitudinal wave potential function in a liquid Radial displacement of particles in a liquid This represents the circumferential displacement of a particle in a liquid. Combining Equations 1 and 2, we can derive: Formula 3 in, For wave number, Let be the angular frequency, which will be ignored in the following derivation. It satisfies the wave equation; When the inside of the pipe being tested is filled with liquid, its outer surface is a stress-free boundary condition with zero radial and normal stress. Assuming that the liquid inside the pipe has no viscous stress, and that the inner wall of the pipe and the liquid are in close contact, they have the same displacement, and that the forces are mutual, the force exerted by the liquid on the inner wall of the pipe and the force exerted by the inner wall of the pipe on the liquid are a pair of reaction forces that are equal in magnitude and opposite in direction. Based on the above conditions, the boundary condition parameters inside the pipe being tested are derived.

5. A method for detecting the liquid density in a liquid-filled pipe based on frequency-modulated ultrasonic guided waves according to any one of claims 1 to 4, characterized in that, The ultrasonic signal is a high-voltage pulse signal, a low-voltage continuous signal, or a frequency-modulated signal.

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