A mirror multi-modal direct extraction method for measuring acoustic lining acoustic impedance

Abstract

The application discloses a mirror image multimodal direct extraction method for measuring acoustic liner acoustic impedance, and relates to the technical field of acoustic liner acoustic impedance measurement. The method is that a broken line array microphone is arranged on the opposite wall of an acoustic liner to simultaneously collect axial and lateral sound field information of a sound field, a multimodal Prony algorithm is used to realize full-modal decomposition of a three-dimensional multimodal sound field, a trust region method is introduced to solve an equation set, and finally, the acoustic liner acoustic impedance is analytically extracted. In this way, the lateral spacing of the array can be significantly improved, more sound field information can be obtained, the lateral modes can be better distinguished, the precision of the acoustic impedance extraction is significantly improved, the 3 kHz upper limit of the NASA method can be broken, the acoustic impedance extraction frequency under the three-dimensional multimodal aerodynamic sound field is greatly improved, and the extraction problem under nearly 10 kHz is solved.

Description

Technical Field

[0001] This invention belongs to the field of acoustic impedance measurement technology, specifically relating to a direct extraction method for mirror multimodal acoustic impedance measurement. Background Technology

[0002] Aircraft engine noise accounts for the largest proportion of aircraft noise, and acoustic liner accounts for more than half of its noise reduction, making it particularly crucial. The latest international civil aviation noise airworthiness standards have further reduced noise by as much as 7dB, but the space for noise reduction in aero-engines will be significantly compressed in the future. These factors greatly increase the difficulty of acoustic liner noise reduction, making the path to noise airworthiness certification for domestically produced large aircraft and aero-engines extremely challenging. Therefore, aero-engine acoustic liner technology, as an important part of "solving key technical problems of aero-engine nacelles," has been selected as one of the "Top Ten Major Industrial Technology Issues of 2021" by the China Association for Science and Technology.

[0003] The fan noise of modern aero-engine turbofans has a very wide frequency range, mainly distributed between 0.5 and 5.0 kHz, and features complex modal components and extremely high sound intensity. Its control poses a significant challenge to acoustic liner design, and there is an urgent need for experimental methods to extract acoustic impedance. Unlike traditional impedance tube methods that do not consider grazing flow and in-situ dual-microphone methods that require destructive installation, acoustic impedance extraction is a technique that measures the sound field distribution inside the tube under aeroacoustic conditions and extracts the actual acoustic impedance of the target acoustic liner accordingly. This allows verification that the acoustic liner has achieved the optimal acoustic impedance designed during the acoustic impedance optimization stage before it enters actual use. Wideband noise control presents an urgent need in this regard—to achieve acoustic impedance extraction technology covering the main frequency range of fan noise.

[0004] Currently, among the existing acoustic impedance extraction methods, two types of methods have the potential to meet the above requirements: the Objective Function Method (OFM) and the Straightforward Method (SFM).

[0005] The objective function method was developed by NASA's Langley Research Center in the 1980s. This method iteratively searches for the acoustic impedance of the acoustic liner while minimizing the objective function, where the objective function is defined as the residual between the measured and simulated sound field physical quantities. This process requires iterative simulation of the entire sound field using numerical methods. When only plane waves are incident within the rigid wall section of the flow tube, the computational cost of the required two-dimensional numerical simulation is already considerable. When higher transverse modes appear, the sound field along the width of the acoustic liner is also non-uniform, making three-dimensional numerical simulation unavoidable, and its computational burden impractical for engineering. Furthermore, the boundary conditions in the simulation need to be measured experimentally, which makes the method more difficult and may introduce larger errors. Watson et al. conducted such acoustic impedance extraction experiments using a controllable sound source array to generate master transverse higher-order modes. Buot del'Épine et al. proposed an OFM method based on the Bayesian method; Troian et al. developed a time-domain OFM method, both of which can be implemented in multiple transverse modes. These studies demonstrate the feasibility of the OFM method in three-dimensional sound fields. However, these studies either fail to raise the extraction frequency to the target level or cannot address the computational burden encountered in simulation iterations. In the latter case, practical extraction still requires the assumption of a plane incident wave, thus effectively setting an upper limit on the extraction frequency related to the pipe cross-section geometry; for example, the upper limit for a typical small-sized grazing incidence tube (GIT) at NASA Langley Research Center is approximately 3.0 kHz. Overall, the OFM method still does not adequately meet the extraction requirements covering the main frequency range of fan noise.

[0006] The direct extraction method, proposed by Jing Xiaodong et al. in 2008, is a method that extracts acoustic impedance in a single operation without iteration: an axially arranged microphone array is used to collect sound pressure levels in the pipe, and the Prony method is used for modal decomposition. The axial wavenumber of the minimum attenuation mode obtained from the decomposition is substituted into the characteristic equation to analytically calculate the acoustic impedance. This method avoids the computational burden, additional errors in boundary condition measurements, and convergence problems of the objective function faced by the full-field simulation in the OFM method. According to a comparative study by NASA Langley Research Center, in general, the SFM method is one to two orders of magnitude more efficient than the OFM method. However, SFM implicitly restricts the pipe sound field to only a single transverse mode; otherwise, the SFM method faces the challenge of full-mode decomposition, meaning it cannot determine which transverse mode the extracted axial wavenumber belongs to. However, creating a single-mode sound field in the pipe is not easy when higher-order modes are interrupted. In the experiments conducted by Watson et al. mentioned earlier, a sound source array using 32 speakers was required to create such a sound field within a large-size flow tube test rig (CDTR). Even so, the upper limit of the extraction frequency using the SFM method within this flow tube could only be extended to a level comparable to that of the GIT flow tube, which is still insufficient. To avoid the aforementioned full-modal decomposition, Medeiros et al. arranged a microphone array along the nodal line of one mode within the tube, thereby extracting acoustic impedance in two transverse modes. Essentially, this is still impedance extraction in a single transverse mode, and their results show that this method cannot be extended to include more transverse modes, which is a typical operating condition at high frequencies within a CDTR flow tube. Therefore, the SFM method also cannot meet the requirement of extending the upper limit of the extraction frequency.

[0007] The inventors previously proposed a multimodal direct extraction method (Multimodal-SFM) based on the SFM method. This method removes restrictions on the modal components of the sound field (plane waves or single higher-order modes), allowing the incident sound wave to be any combination of a plane wave and multiple higher-order modes. A microphone array is arranged along a diagonal on the opposite sidewall of the acoustic liner to collect wall sound pressure containing both axial and transverse modal information. By extending the Prony method, this method can automatically match the extracted axial wavenumber with the transverse mode, thus solving the problem of full-modal decomposition of a three-dimensional multimodal sound field. Acoustic impedance can be successfully extracted from the decomposed modes. In a 2018 paper, this method was validated by numerical experiments, effectively extending the upper frequency limit of extraction within a GIT flow tube to at least 6 kHz and successfully covering the main frequency range of fan noise. However, in this numerical experiment, a uniform background flow and infinitesimal microphone probes (measurement points) were used, while random background noise was artificially assigned. These factors differ to some extent from real-world testing conditions. Therefore, we conducted further experimental research to verify whether the method remains effective under actual shear flow and background noise conditions using a real microphone. Moreover, as a novel method, it still has the potential to further improve extraction accuracy and efficiency.

[0008] Through experimental research on the aforementioned multimodal direct extraction method, the inventors discovered that due to the small lateral spacing between measurement points, the method's ability to distinguish different lateral modes is still insufficient, resulting in unsatisfactory acoustic impedance extraction accuracy when multiple modes are present laterally. The fundamental problem lies in the limited lateral space of the flow tube experimental platform; the lateral spacing between measurement points is too small, making the experiment significantly affected by errors. For example, for the existing 51×51mm... 2 With a square cross-section tube and a commonly used 1 / 4-inch microphone, the lateral spacing between the measurement points is about 1.4 mm when the measurement points are arranged in a diagonal array. It is difficult to distinguish the lateral sound field characteristics from the sound pressure measured by the microphone. Summary of the Invention

[0009] The purpose of this invention is to provide a direct multimodal extraction method for measuring acoustic impedance of an acoustic liner, in order to solve the problem that the current direct multimodal extraction method still does not have a good enough ability to distinguish different modes in the lateral direction, resulting in unsatisfactory acoustic impedance extraction accuracy when multiple modes appear in the lateral direction.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] Firstly, a method for direct extraction of mirror-image multimodal acoustic impedance is provided, including:

[0012] A sound liner is installed flush with the first wall of a real flow tube with a square cross-section, and a Z-shaped zigzag array is installed on the second wall of the real flow tube. A microphone is used, and a sound source array is installed on the upstream and / or downstream rigid wall sections of the acoustic liner installation location within the actual flow tube. The actual flow tube contains a uniform flow, and the second wall surface is located on the opposite side of the first wall surface within the actual flow tube. The sound source array is used to generate a sound field containing multiple modes, the multiple modes including those decomposed according to the modal decomposition principle within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to Positive integers;

[0013] Start the sound source array, and through the The microphone measurements were obtained in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone;

[0014] According to the above Based on the sound pressure values ​​at several real measurement points, the following system of equations is established:

[0015]

[0016] In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row;

[0017] The system of equations is solved by least squares fitting based on the trust region algorithm, yielding... One intermediate coefficient;

[0018] According to the above Using intermediate coefficients, we obtain the roots of the following polynomial equation:

[0019]

[0020] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located in the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the modality of the column;

[0021] Based on the roots of the polynomial equation, and based on the second intermediate parameter The wavenumbers for each axis are calculated using the following defined formula:

[0022]

[0023] In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a set of real measuring points is indicated by the superscript "". “ in "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " “ in "This indicates the back-propagating sound wave in the actual flow tube;

[0024] Based on the wavenumbers of each axis, the wavenumbers of each longitudinal axis are calculated according to the following dispersion relation:

[0025]

[0026] In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The transverse width of the square cross-section is indicated by the fact that the transverse, longitudinal, and axial directions are all perpendicular to each other.

[0027] The acoustic impedance of the acoustic liner is calculated according to the following formula based on the respective longitudinal wavenumbers. :

[0028]

[0029] In the formula, This indicates the longitudinal height of the square cross-section.

[0030] Based on the above-mentioned invention, a novel scheme for direct multimodal extraction of acoustic impedance of an acoustic liner based on a piecewise linear array of measuring points is provided. This involves placing a piecewise linear array of microphones on the opposite sidewall of the acoustic liner to simultaneously acquire axial and lateral sound field information. The multimodal Prony algorithm is used to achieve full modal decomposition of the three-dimensional multimodal sound field. Furthermore, a trust region method is introduced to solve the equation system, ultimately analytically extracting the acoustic impedance of the acoustic liner. This not only significantly improves the lateral spacing of the array, obtaining more sound field information to better distinguish lateral modes and significantly improves the accuracy of acoustic impedance extraction, but also breaks the 3kHz frequency limit of the NASA method, greatly increasing the acoustic impedance extraction frequency in three-dimensional multimodal aerodynamic sound fields and solving the extraction problem at frequencies up to nearly 10kHz. In addition, its direct analytical calculation approach is three orders of magnitude more efficient than the NASA numerical iteration method, reaching international first-class levels and facilitating practical application and promotion.

[0031] In one possible design, after calculating the acoustic impedance of the acoustic liner, the method further includes:

[0032] Based on the wavenumbers along each axis, the amplitude of each mode is calculated using the following sound pressure expression:

[0033]

[0034] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the above In the modality located at the th Line and number The modal amplitude corresponding to the column's mode. Indicates the first The actual measurement points are in a rectangular coordinate system The horizontal coordinate in the middle, Indicates the first The actual measuring points are in the rectangular coordinate system The axial coordinates in the rectangular coordinate system The origin of the coordinate system is located at the intersection of the longitudinal sidewall of the actual flow tube and the reverse extension of the first segment of the broken line in the "Z"-shaped broken line array. In Indicates the axial direction. Indicates the longitudinal direction, Indicates the horizontal direction, the first The actual measuring points are in the rectangular coordinate system The coordinates in the diagram are represented as ;

[0035] Based on the amplitude of each modality, the following formula is used to calculate the amplitude of each modality. Reconstructed sound pressure values ​​at each of the actual measurement points:

[0036]

[0037] In the formula, Indicated in the first The restored sound pressure value at each actual measuring point;

[0038] Based on the sound pressure values ​​and restored sound pressure values ​​at each actual measurement point, the sound field residual is calculated using the following formula. :

[0039]

[0040] In the formula, Represents the L2 norm;

[0041] Determine whether the acoustic field residual is less than or equal to a preset residual threshold. If it is, the acoustic impedance calculation result of the acoustic liner is determined to be valid; otherwise, it is determined to be invalid.

[0042] In one possible design, after determining that the calculated acoustic impedance of the acoustic liner is valid, the method further includes:

[0043] Based on preset optimization conditions set according to repetitive modes, mode amplitudes and / or wavenumber values, the most suitable mode and the acoustic impedance corresponding to the mode are selected from the acoustic impedance calculation results of the acoustic liner as the final acoustic impedance extraction result of the acoustic liner.

[0044] In one possible design, after obtaining the results of multiple acoustic impedance calculations for the acoustic liner, the method further includes:

[0045] For each acoustic impedance calculation result in the multiple acoustic impedance calculation results of the acoustic liner, the corresponding acoustic field residual is calculated.

[0046] The acoustic impedance calculation result with the smallest sound field residual is selected from the multiple acoustic impedance calculation results of the acoustic liner. Based on the preset optimization conditions set according to the repetitive mode, mode amplitude and / or wavenumber values, the most suitable mode and the acoustic impedance corresponding to the mode are selected from the acoustic impedance calculation results as the final acoustic impedance extraction result of the acoustic liner.

[0047] In one possible design, the mirror multimodal direct extraction method is applicable to any aerodynamic acoustic field containing three-dimensional multimodalities, thus broadening the extraction frequency range.

[0048] In one possible design, the mirrored multimodal direct extraction method can improve the accuracy of lateral mode decomposition by increasing the lateral distance of the microphone.

[0049] The beneficial effects of the above scheme are:

[0050] (1) This invention creatively provides a novel scheme for direct multimodal extraction of acoustic impedance of a sound liner based on a polygonal array of measuring points. Specifically, a polygonal array of microphones is placed on the opposite sidewall of the sound liner to simultaneously collect axial and lateral sound field information. The multimodal Prony algorithm is used to achieve full modal decomposition of the three-dimensional multimodal sound field. Furthermore, a trust region method is introduced to solve the equation set, ultimately extracting the acoustic impedance of the sound liner analytically. This not only significantly increases the lateral spacing of the array, obtaining more sound field information to better distinguish lateral modes and significantly improve the accuracy of acoustic impedance extraction, but also breaks the NASA method's 3kHz frequency limit, greatly increasing the acoustic impedance extraction frequency under three-dimensional multimodal aerodynamic sound fields and solving the extraction problem at frequencies up to nearly 10kHz.

[0051] (2) Its direct analytical calculation method is three orders of magnitude more efficient than NASA’s numerical iteration method, and can reach the international first-class level.

[0052] (3) The validity of the acoustic impedance calculation result can also be determined based on the threshold comparison results of the acoustic field residual;

[0053] (4) The optimal mode can also be selected from the effective acoustic impedance calculation results / multiple acoustic impedance calculation results, and the acoustic impedance corresponding to the mode can be used as the final acoustic impedance extraction result, further ensuring the accuracy of the extraction result. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a schematic flowchart of the direct extraction method for measuring acoustic impedance of an acoustic liner provided in an embodiment of this application.

[0056] Figure 2 This is a schematic diagram showing the structural relationship between the sound source array, microphone, and acoustic liner provided in the embodiments of this application and the actual flow tube.

[0057] Figure 3 This is a schematic diagram illustrating the structural relationship between a mirror-symmetric hypothetical flow tube and a microphone array, provided for an embodiment of this application.

[0058] Figure 4 Example diagram of normalized acoustic admittance results in the frequency range of 100 to 9900 Hz, calculated based on this method, provided for embodiments of this application.

[0059] Figure 5An example diagram showing the normalized acoustic admittance results in the frequency range of 100 to 9900 Hz obtained by calculating the first reference acoustic liner 1 based on the method provided in this application embodiment.

[0060] Figure 6 An example diagram showing the normalized acoustic admittance results for the second reference acoustic liner liner 100 to 9900 Hz, calculated using this method, provided for embodiments of this application.

[0061] Figure 7 Example diagram showing the comparison of uncertainty results of acoustic impedance calculated by the present method for the first reference acoustic liner Liner1 under different axial spacings, provided for embodiments of this application.

[0062] Figure 8 An example diagram showing the comparison of the uncertainty of acoustic impedance calculated by the present method for the second reference acoustic liner liner LINE2 under different lateral spacings, provided for embodiments of this application.

[0063] Figure 9 Example diagram showing the comparison of uncertainties in acoustic impedance calculated for the first reference acoustic liner Liner1 under different M×N conditions, provided for embodiments of this application.

[0064] Figure 10 An example diagram showing the normalized acoustic impedance uncertainty results for the first reference acoustic liner Linear1 in the frequency range of 100 to 9900 Hz, calculated based on this method, for embodiments of this application.

[0065] Figure 11 An example diagram showing the normalized acoustic impedance uncertainty results for the first reference acoustic liner Linear1 in the frequency range of 100 to 9900 Hz, calculated based on this method, for embodiments of this application.

[0066] Figure 12 This is a schematic diagram of the structure of the mirror multimodal direct extraction device for measuring acoustic impedance of the acoustic liner provided in an embodiment of this application.

[0067] Figure 13 This is a schematic diagram of the structure of the mirror multimodal direct extraction system for measuring acoustic impedance of the acoustic liner provided in an embodiment of this application.

[0068] Figure 14 A schematic diagram of the structure of a computer device provided in an embodiment of this application.

[0069] In the above figures: 1-real flow tube; 2-sound source array; 3-microphone; 5-sound liner. Detailed Implementation

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be briefly introduced below in conjunction with the accompanying drawings and descriptions of the embodiments or the prior art. Obviously, the following description of the structure of the accompanying drawings is only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. It should be noted that the description of these embodiments is for the purpose of helping to understand the present invention, but does not constitute a limitation of the present invention.

[0071] It should be understood that although the terms "first" and "second", etc., may be used herein to describe various objects, these objects should not be limited by these terms. These terms are only used to distinguish one object from another. For example, the first object may be referred to as the second object, and similarly, the second object may be referred to as the first object, without departing from the scope of the exemplary embodiments of the invention.

[0072] It should be understood that the term "and / or" that may appear in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, or A and B exist simultaneously. Another example is A, B and / or C, which can mean that any one of A, B, and C or any combination thereof exists. The term " / and" that may appear in this document describes another relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone or A and B exist simultaneously. In addition, the character " / " that may appear in this document generally indicates that the related objects before and after it are in an "or" relationship.

[0073] Example:

[0074] like Figure 1 As shown, the mirror multimodal direct extraction method for measuring the acoustic impedance of a sounding sheet provided in the first aspect of this embodiment is used as an experimental method for measuring the acoustic impedance of a target sounding sheet, including but not limited to the following steps S1 to S8.

[0075] S1. An acoustic liner is installed flush with the first wall of a real flow tube having a square cross-section, and an acoustic liner arranged in a "Z"-shaped zigzag array is installed on the second wall of the real flow tube. A microphone is used, and a sound source array is installed on the upstream and / or downstream rigid wall sections of the acoustic liner installation location within the actual flow tube (i.e., the sound sources can be arranged upstream, downstream, or both upstream and downstream of the flow tube test section to emit sound signals and transmit them backward or forward to the acoustic liner test section). The actual flow tube contains a uniform flow, and the second wall surface is located on the opposite side of the first wall surface within the actual flow tube. The sound source array is used to generate a sound field containing multiple modes, the multiple modes including those decomposed according to the modal decomposition principle into modes within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to Positive integers.

[0076] S2. Activate the sound source array, and through the... The microphone measurements were obtained in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone.

[0077] S3. According to the above Based on the sound pressure values ​​at several real measurement points, the following system of equations is established:

[0078]

[0079] In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row.

[0080] S4. Solve the system of equations using the least squares method based on the trust region algorithm, and obtain... An intermediate coefficient.

[0081] S5. According to the above Using intermediate coefficients, we obtain the roots of the following polynomial equation:

[0082]

[0083] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located in the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the modality of the column.

[0084] S6. Based on the roots of the polynomial equation, and using the second intermediate parameter... The wavenumbers for each axis are calculated using the following defined formula:

[0085]

[0086] In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a set of real measuring points is indicated by the superscript "". “ in "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " “ in "" indicates the back-propagating sound wave in the actual flow tube.

[0087] S7. Based on the wavenumbers of each axis, the longitudinal wavenumbers are calculated according to the following dispersion relation:

[0088]

[0089] In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The width of the square cross-section is indicated by the horizontal width, and the horizontal, vertical and axial directions are perpendicular to each other.

[0090] S8. The acoustic impedance of the acoustic liner is calculated according to the following formula based on each longitudinal wavenumber. :

[0091]

[0092] In the formula, This indicates the longitudinal height of the square cross-section.

[0093] The mirror multimodal direct extraction technique for measuring acoustic impedance described in steps S1 to S8 is as follows: Based on the symmetry and periodicity of the rigid wall boundary conditions in a square pipe and the mathematical properties of the sound pressure expression, a new measurement point arrangement is used. A piecewise linear array is employed to measure the sound pressure, and a correspondence between the measurement point coordinates is established between the hypothetical sound field obtained from symmetry and the original sound field. Finally, the acoustic impedance is extracted using the principle of the multimodal direct extraction method. The detailed technical principles of the aforementioned approach are as follows (A) to (C).

[0094] (A) Design of acoustic impedance measurement platform for acoustic liner: such as Figure 2 As shown, the platform includes, but is not limited to, a real flow tube 1, a sound source array 2, and a microphone 3, wherein the real flow tube 1 has a vertical height of And the horizontal width is A square cross-section containing a Mach number of A uniform flow, wherein the lower longitudinal wall (i.e., the first wall) of the real flow tube 1 is flush with the longitudinal lower wall surface as the object of acoustic impedance measurement and the length is The acoustic liner 5; the sound source array 2 is installed in the upstream rigid wall section of the acoustic liner installation position inside the actual flow tube 1, and the number of microphones 3 is [missing information]. The components are arranged in a "Z"-shaped zigzag array on the longitudinal upper wall (i.e., the second wall) of the actual flow tube 1, thus allowing for the application of... The sound pressure data measured by the microphone 3 when the sound source array 2 is turned on is directly used to extract the acoustic impedance of the acoustic liner 5. For ease of subsequent description, the following rectangular coordinate system is established in the actual flow tube 1. The origin of the coordinate system is located at the intersection of the longitudinal sidewall of the actual flow tube 1 and the reverse extension of the first segment of the broken line in the "Z"-shaped broken line array. Indicates the axial direction. Indicates the longitudinal direction, The horizontal direction is indicated. Furthermore, the actual flow tube 1, the sound source array 2, and the microphone 3 can all be implemented using existing related experimental hardware; for example, the microphone 3 can be a 1 / 4-inch microphone.

[0095] (B) Sound propagation problem in a real flow tube: Consider the sound field with soft walls in the flow tube, and its complex sound pressure This is expressed by the following Helmholtz equation for convection:

[0096] (1)

[0097] In the formula, Let Hamiltonian operator be represented. Simultaneously, consider the continuity condition for the normal acoustic particle velocity at the rigid wall of the flow tube, and the Ingard-Myers impedance boundary condition at the impedance wall:

[0098] (2)

[0099] Solving equations (1) and (2) above using classical modal decomposition theory, the sound field can be written in the following series form:

[0100] (3)

[0101] In the formula, Indicates the position of the first Line and number The modal amplitude corresponding to the column's mode. Indicates the position of the first The transverse wavenumber corresponding to the mode of the line and has (The specific value can be determined through the eigenvalue problem of the transverse rigid wall condition). Representing a rectangular coordinate system The horizontal coordinate, Indicates the position of the first Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the position of the first Line and number The axial wavenumbers corresponding to the modes of the column, Represents the rectangular coordinate system axial coordinates, Represents the rectangular coordinate system The vertical coordinate. Additionally, the time component is omitted. .

[0102] Combine the above equation (3) with the dispersion relation. Substitute In this process, we can obtain the eigenvalue problem of the impedance wall:

[0103] (4)

[0104] As can be seen from equation (4) above, once the longitudinal wavenumber can be determined... Then the unknown acoustic impedance can be obtained. .

[0105] (C) Mirror Imaginary Sound Field, Microphone Array, and Impedance Extraction: Utilizing the mirror symmetry caused by rigid wall boundary conditions and the standing wave solution in the transverse direction, the impedance can be extracted... Figure 2 The actual sound field and microphone array are unfolded into an imaginary array based on mirror symmetry, such as... Figure 3 As shown, acoustic impedance is then extracted based on this.

[0106] Assuming the piecewise linear array has ( (representing positive integers greater than or equal to 3) segments, with the axial and lateral spacing between adjacent microphones being respectively... and Simultaneously, imagine: in a horizontal width of In the hypothetical flow tube, on the walls on the same side (i.e. Figure 2 and Figure 3 The lower wall of the hypothetical tube is also equipped with a sound liner with the same acoustic impedance as the sound liner to be solved; in the sound field of the hypothetical flow tube, there should exist a sound liner corresponding to the original sound field. Modalities, and in the original sound field The modal amplitudes of the modes correspond one-to-one, that is, we have In the hypothetical flow tube, there will be an array of microphones evenly spaced along a diagonal straight line, with axial and lateral spacing also being... and The microphone within one times the width of the original flow tube coincides with the first microphone measurement point of the polygonal array within the actual flow tube; the remaining parameters of the hypothetical flow tube (such as...) , , and The sound fields in the hypothetical flow tube are completely identical to those in the real flow tube. Therefore, the correspondence between the sound fields in the hypothetical flow tube and the real flow tube can be derived.

[0107] The first in the original real flow tube Real measurement points The sound pressure expression at that point can be derived from the aforementioned equation (3) to obtain the following form:

[0108] (5)

[0109] In the formula, According to equation (5) above, it can be found that the infinite series is truncated to... item.

[0110] Consider the sound field in a hypothetical flow tube. transverse wavenumber of modes In the original flow tube transverse wavenumber of modes Consistent. Substituting into the aforementioned equation (4), since the acoustic liner impedance is the same, then the longitudinal... The eigenvalue problem of the impedance condition in the direction remains unchanged, therefore we have Furthermore, according to the aforementioned dispersion relation, we have... Furthermore, since each mode of the two sound fields has a one-to-one correspondence with equal modal amplitudes, the sound field in the hypothetical flow tube is at the [missing value]. Each measuring point sound pressure at the location for:

[0111] (6)

[0112] The imaginary flow tube can flow along ( ) was split into Each width is Parts, such as Figure 3 As shown. Introducing variables. And there are To represent horizontal Given the coordinates of the direction, equation (6) can be rewritten as follows:

[0113] (7)

[0114] In the above formula (7) Based on parameters The parity is simplified, so the sound pressure It can be further written as:

[0115] Considering the facts, When it is even and When it is an odd number It is exactly the first one in a real flow tube. The distance of each actual measuring point from the side wall The distance, therefore there is This indicates that the sound pressure levels of the hypothetical sound field and the real sound field are at the corresponding... The values ​​at each measuring point are exactly equal. In fact, the entire hypothetical sound field is equivalent to the original sound field; the hypothetical sound field is at the boundary... and The parts in between include: when When the number is even, it represents a translation of the original sound field; when... When the number is odd, it is exactly a mirror image of the original sound field. Therefore, the equivalence of the real and imaginary microphone arrays can also be obtained through multiple mirror image operations of the sound field, which will not be explained in detail here.

[0116] Therefore, the problem of extracting acoustic impedance using a piecewise linear array in a real flow tube can be transformed into obtaining sound pressure using an equally spaced oblique linear array in an imaginary extended flow tube. The problem of extraction. Then introduce variables. (In a hypothetical flow tube, Indicates the first measuring point To simplify coordinate writing, the coordinates of the measuring point in the imaginary flow tube can be written as:

[0117] (9)

[0118] Meanwhile, the sound pressure expression can be written as:

[0119] (10)

[0120] Next, the impedance can be solved using the Prony method. Then, the first intermediate parameter is introduced. Second intermediate parameter The sound pressure expression (10) in the hypothetical sound field can be written as:

[0121] (11)

[0122] In the formula, the subscript Decomposed into and The sum. In the subsequent derivation, it can be found that the even-numbered terms... Sum of odd-numbered terms In the horizontal First mode (i.e., the aforementioned) In the modality located at the th In the mode of line, it can be used with two respectively. The polynomial equation of order is related. Finally, multiply both sides of the aforementioned equation (11) by... To construct the Prony polynomial, and then for all From 0 to Summation (using the symbol " ") (represented by ""), thus we can obtain the following system of equations:

[0123] (12)

[0124] In the formula, Indicates in relation to the first The sound pressure value at the hypothetical measurement point, the first The hypothetical measurement point and the first The actual measurement points coincide, making Can be Replace directly.

[0125] Taking the existence of two modes in the lateral direction as an example, that is Then, the system of equations can be written in the following form:

[0126] (13)

[0127] Based on the aforementioned technical principles, the polygonal microphone array can be unfolded into a diagonal array within an imaginary flow tube, and according to... The corresponding relationship is equivalent to the sound pressure. Further, by using the existing multimodal direct extraction method, the acoustic impedance of the acoustic liner can be obtained by solving equation (12): First, at least the following measurements are obtained. Sound pressure at each measuring point Then, the least squares method based on the trust region algorithm (a numerical method for solving nonlinear optimization problems, and also an iterative algorithm, which starts from a given initial solution and iterates step by step until a satisfactory approximate optimal solution is obtained) is used to fit and solve the system of equations (12) to obtain the solution. intermediate coefficients The axial wave number is then calculated using the polynomial equation and two intermediate parameters. The longitudinal wavenumber is then obtained from the dispersion relation. Finally, by solving equation (4), the acoustic impedance of the acoustic liner can be obtained. (That is, steps S2 to S8 mentioned above. The inventors have named this method the Mirror-based Multimodal Straightforward Method, MM-SFM). Furthermore, according to equation (4), since the longitudinal wavenumbers corresponding to each mode... Different values ​​result in different acoustic impedances of the acoustic liner obtained from the solution. Different results may occur, therefore, based on the aforementioned step S8, the result will be the same as described above. Each mode corresponds one-to-one The acoustic impedance of the acoustic liner can then be further optimized based on certain preferred conditions from the... The most suitable mode and the corresponding acoustic impedance are selected from the acoustic impedance of the acoustic liner to be the final acoustic impedance extraction result.

[0128] Compared to a width of The original diagonal array within a narrow conduit, as described above, can significantly improve the lateral spacing of the array by using a zigzag microphone array. For example, in an array with a cross-sectional size of 51×51mm... 2 In the pipeline, the lateral spacing of the polygonal microphone array can be increased from millimeters to several centimeters, thus obtaining more information to better distinguish lateral modes and significantly improve the accuracy of acoustic impedance extraction. That is, the mirror multimodal direct extraction method can improve the accuracy of lateral mode decomposition by increasing the lateral distance of the microphones when applied.

[0129] For the mirror multimodal direct extraction method described in steps S1 to S8 above, which measures the acoustic impedance of the acoustic liner, the following corresponding numerical experiments were conducted for verification: Commercial software COMSOL was used to perform finite element simulation of the sound field in the convection tube. With Ingard-Myers boundary conditions on the soft wall, the Helmholtz equation for convection was solved to calculate the sound pressure at the measuring point, simulating the experimental data. Theoretically, to verify the correctness and accuracy of the acoustic impedance extraction algorithm, any acoustic impedance reference value could be selected as the boundary condition for numerical experiments. However, to ensure that the simulation calculations match the experiments as closely as possible, two sets of acoustic impedance values ​​obtained from the acoustic impedance prediction model, with values ​​varying with frequency (representing two acoustic liners with different design parameters), and a special case involving a rigid wall, were selected as reference values ​​for comparison with the acoustic impedance calculated by this method.

[0130] In the simulation examples and experiments, the following methods were adopted: A square cross-section flow tube. Perfectly Matched Layers (PMLs) are set at both ends of the simulation model, i.e., the upstream and downstream openings of the flow tube, as non-reflective boundary conditions. 36 (i.e., ...) are arranged on the upper wall opposite the side where the acoustic liner is installed on the flow tube. The measuring points monitor the amplitude and phase of the sound pressure. Specifically, when the measuring points are positioned at the third division points of the flow tube's transverse direction (i.e., the transverse spacing...) At this point, the measuring point is exactly located in the transverse mode. At the nodes, the components of this mode do not contribute to the sound pressure value at the measuring point. When the axial spacing is selected in the example... And horizontal spacing At that time, the effective extraction frequency range can be extended to 9900Hz, which is less than Cutoff frequencies of the modes. Table 1 below lists the cutoff frequencies of each acoustic mode in the flow tube studied by this method. :

[0131] Table 1. Cutoff frequencies of various acoustic modes in the flow tube studied using this method.

[0132]

[0133] In the simulation experiments, the Monte Carlo method (MCM) was also introduced to parameterize the uncertainty of the algorithm affected by errors, in order to determine the optimal combination of parameters to be used in the experiment.

[0134] (a) Rigid Wall Verification: As a standard verification method for acoustic impedance extraction, the normalized acoustic admittance of a rigid wall is known to be 0. In a uniform flow velocity... axial spacing And horizontal spacing At that time, the normalized real part of acoustic admittance calculated by this method has a frequency range of 100–9900 Hz. and the virtual part The results are as follows Figure 4 As shown, the deviations of the real and imaginary parts from the reference values ​​are all within 0.05 across the entire frequency range, indicating that this method can effectively extract the acoustic admittance of a rigid wall in a sound field with the first three transverse modes.

[0135] (b) First reference acoustic liner Liner 1 and second reference acoustic liner Liner 2: Theoretically, the reference values ​​can be chosen arbitrarily to verify the effectiveness of the algorithm. To ensure the realism of the finite element simulation, the reference values ​​of the acoustic impedance are derived from the acoustic impedance prediction model of the ceramic tube acoustic liner based on the Zwikker and Kosten theory. The ceramic tube acoustic liner has good linearity, is insensitive to the grazing effect, and has the same impedance value under different basic flow velocities, thus making it an ideal reference for verifying the acoustic impedance extraction method. Table 2 below lists the parameters required to determine the acoustic impedance using the prediction model:

[0136] Table 2. Some parameters required to determine the reference values ​​for the acoustic lining of ceramic tubes

[0137]

[0138] At the velocity of a uniform flow axial spacing And horizontal spacing At that time, the normalized acoustic admittance results for the frequency range of 100–9900 Hz obtained by this method for the first reference acoustic liner 1 and the second reference acoustic liner 2 are as follows: Figure 5 and 6 As shown, the normalized acoustic impedance and acoustic impedance calculated by this method agree well with the reference values ​​at almost all frequencies except for a few frequencies. Even in complex sound fields with multiple modes of incidence and grazing flow at the high end of the spectrum, accurate acoustic impedance can be obtained.

[0139] (c) Uncertainty parameterization study: For indirect measurements, such as those focusing on the acoustic impedance of the acoustic liner in this method. It is necessary to consider the errors and uncertainties of individual measurement variables, as well as the uncertainties of these variables propagating these error factors to the calculation results through the Data Reduction Equation (DRE). Before conducting actual experiments, parameter analysis should be performed to select parameter combinations less affected by disturbances. MCM provides a method for complex or nonlinear models, its advantage being that it does not require calculating the first or higher-order partial derivatives of the sensitivity coefficients for uncertainty propagation. Therefore, it is suitable for highly nonlinear models or overly complex models (such as those involving numerical simulations).

[0140] Assume that all random errors in the experiment are ultimately propagated to the measured sound pressure levels. Add, to the finite element analysis results of the sound pressure amplitude and phase, random errors following a normal distribution (excluding the 5% rejection region). The maximum uncertainties for these normally distributed errors are respectively... and (normal distribution (Range). The following parameters are parametrically studied by adding the same random error to the sound pressure measurement values ​​obtained from numerical simulation: axial spacing of measurement points. Horizontal spacing Harmony field modal number .

[0141] Because the Prony method-based algorithm has strong nonlinearity, when using the MCM method for uncertainty analysis, the number of repeated calculations in the MCM can be appropriately reduced, for example, by taking... For 50 or 100 times, and use The mean of the repeated calculations is used as the expected value of the uncertainty, and twice the standard deviation is used as the coverage interval with a confidence level of 95% for the uncertainty.

[0142] (c1) Axial spacing of measuring points Effects on the velocity of a uniform flow Horizontal spacing And axial spacing Parametric studies were conducted for cases with diameters of 10mm, 14mm, 18mm, and 22mm, respectively. The results of the uncertainty comparison of the acoustic impedance calculated by this method for the first reference acoustic liner Liner1 are as follows: Figure 7 As shown: Overall, the extraction effect is related to the axial spacing of the measured points. The impact is relatively small; in the extremely low frequency range below 1000 Hz, due to the large absolute value of the acoustic impedance, the boundary becomes close to a rigid wall and is not easy to absorb sound, making the acoustic impedance essentially difficult to extract. The uncertainty of impedance extraction due to error is also significantly large in this frequency range; in the frequency range above 1000 Hz, it can be found that the axial spacing... When the impedance extraction effect is relatively small, it is significantly affected by sound pressure error in the high-frequency range (greater than 5000 Hz). This is because as the axial spacing of the microphones increases, the sound pressure attenuation between adjacent measurement points is greater, and the phase difference is also larger. This is beneficial for calculating a more accurate axial attenuation coefficient. However, when the axial spacing... After increasing the value to 18mm, the uncertainty in extracting the acoustic impedance is almost no longer affected, except in the range where the absolute value of the acoustic impedance is too large. The impact.

[0143] (c2) Lateral spacing of measuring points Effects on the velocity of uniform flow axial spacing And horizontal spacing Parametric studies were conducted for cases with diameters of 10.2 mm, 12.75 mm, 17 mm, and 25.5 mm, respectively. The results of the comparison of the uncertainty of the acoustic impedance calculated by this method for the second reference acoustic liner Liner2 are as follows: Figure 8 As shown: Horizontal spacing The uncertainty in the extracted acoustic impedance is significantly affected by errors; from a trend perspective, increasing the lateral spacing... This significantly improves the extraction accuracy due to errors, a trend that is even more pronounced in the high-frequency range (greater than 3251Hz), where multiple modes exist laterally. This is because increased lateral spacing allows for a larger standing wave phase difference between two measurement points, which is beneficial for identifying various lateral modes. This also proves that the approach of utilizing the symmetry and periodicity of the sound field to achieve a larger lateral spacing between measurement points in a hypothetical flow tube to improve M-SFM is correct. Furthermore, to achieve the goal of improving mode decomposition accuracy in the high-frequency range by increasing the lateral spacing, preferably, the... The lateral spacing between two adjacent microphones in a microphone array is positively correlated with the acoustic impedance extraction frequency.

[0144] (c3) Number of sound field modes Effects on the velocity of a uniform flow axial spacing Horizontal spacing And the number of sound field modes Parametric studies were conducted for cases 8, 10, and 12, respectively. The results of the comparison of the uncertainty of the acoustic impedance calculated by this method for the first reference acoustic liner Liner1 are as follows: Figure 9 As shown: Number of sound field modes The impact on the uncertainty of acoustic impedance extraction is mainly concentrated in the frequency range where the absolute value of acoustic impedance or acoustic impedance is large (making extraction more difficult). According to the modal decomposition theory, if the number of modes is too large or too small, it may be impossible to accurately reconstruct the sound field. In particular, when random errors are added, some non-existent modes may be affected by small errors and exhibit non-physical cut-off or interruption. This may ultimately cause a large disturbance in the acoustic impedance calculation results.

[0145] Based on the simulation results above, it can be seen that the direct extraction method of mirror multimodal modes is applicable to any aerodynamic acoustic field containing three-dimensional multimodal modes, thus broadening the extraction frequency range. For example, in the 51*51mm flow tube experiment, the frequency range can be covered up to 10kHz.

[0146] Therefore, based on the mirror multimodal direct extraction method for measuring acoustic impedance described in steps S1 to S8 above, a new scheme for direct multimodal extraction of acoustic impedance based on a piecewise linear measurement point arrangement is provided. This involves placing a piecewise linear array microphone on the opposite sidewall of the acoustic liner to simultaneously acquire axial and lateral sound field information. The multimodal Prony algorithm is used to achieve full modal decomposition of the three-dimensional multimodal sound field. Furthermore, a trust region method is introduced to solve the equation system, ultimately analytically extracting the acoustic impedance of the acoustic liner. This not only significantly improves the lateral spacing of the array, obtaining more sound field information to better distinguish lateral modes and significantly improves the accuracy of acoustic impedance extraction, but also breaks the 3kHz frequency limit of the NASA method, greatly increasing the acoustic impedance extraction frequency in three-dimensional multimodal aerodynamic sound fields and solving the extraction problem at frequencies up to nearly 10kHz. In addition, its direct analytical calculation approach is three orders of magnitude more efficient than the NASA numerical iteration method, reaching international first-class levels.

[0147] Based on the technical solution of the first aspect mentioned above, this embodiment also provides a possible design for determining whether the acoustic impedance calculation result is valid. That is, after calculating the acoustic impedance of the acoustic liner, the method further includes, but is not limited to, the following steps S9 to S12.

[0148] S9. Based on the wavenumbers of each axis, the amplitude of each mode is calculated using the following sound pressure expression:

[0149]

[0150] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the above In the modality located at the th Line and number The modal amplitude corresponding to the column's mode. Indicates the first The actual measurement points are in a rectangular coordinate system The horizontal coordinate in the middle, Indicates the first The actual measuring points are in the rectangular coordinate system The axial coordinates in the rectangular coordinate system The origin of the coordinate system is located at the intersection of the longitudinal sidewall of the actual flow tube and the reverse extension of the first segment of the broken line in the "Z"-shaped broken line array. In Indicates the axial direction. Indicates the longitudinal direction, Indicates the horizontal direction, the first The actual measuring points are in the rectangular coordinate system The coordinates in the diagram are represented as .

[0151] S10. Based on the amplitude of each modality, calculate the amplitude of the modal as follows: Reconstructed sound pressure values ​​at each of the actual measurement points:

[0152]

[0153] In the formula, Indicated in the first The restored sound pressure value at each actual measurement point.

[0154] In step S10, It is the actual sound pressure in the sound field measured in the experiment, by Starting from the above series of calculations, It is based on the modal decomposition method, which theoretically decomposes and reconstructs the sound pressure. The comparison between the two is used to examine whether the sound field has been correctly decomposed and reconstructed after calculation, thus defining the meaning of the residual.

[0155] S11. Based on the sound pressure values ​​and restored sound pressure values ​​at each actual measurement point, the sound field residual is calculated according to the following formula. :

[0156]

[0157] In the formula, This represents the L2 norm.

[0158] In step S11, although the direct extraction method only requires one calculation to obtain the acoustic impedance, in order to avoid the use of intermediate coefficients... Errors caused by improper initial value selection need to be addressed by using different random numbers as initial values ​​within a certain range for multiple calculations. For each calculation result, the corresponding sound field residual should be calculated to enable subsequent effective judgment.

[0159] S12. Determine whether the acoustic field residual is less than or equal to a preset residual threshold. If so, determine that the acoustic impedance calculation result of the acoustic liner is valid; otherwise, determine that it is invalid.

[0160] Therefore, based on the aforementioned possible design one, the validity of the acoustic impedance calculation result can also be determined based on the threshold comparison result of the acoustic field residual.

[0161] Based on the aforementioned possible design one, this embodiment also provides a possible design two for selecting the optimal mode from the effective acoustic impedance calculation results. That is, after determining that the acoustic impedance calculation results of the acoustic liner are valid, the method further includes, but is not limited to: selecting the most suitable mode and its corresponding acoustic impedance from the acoustic impedance calculation results of the acoustic liner according to preset preferred conditions set based on repetitive modes, mode amplitudes, and / or wavenumber values, as the final acoustic impedance extraction result for the acoustic liner. Theoretically, any solved mode should correspond to the same impedance; however, under random noise interference, not all modes can provide the correct impedance. Therefore, reliable selection criteria help determine which mode to use to calculate the acoustic impedance in practical applications.

[0162] This embodiment adopts the following criteria: (1) Repetitive modes, that is, in the effective extraction and calculation of decomposed modes, some modes may reappear during repeated extraction. These modes are more likely to actually exist and correspond to the correct impedance; (2) Mode amplitude, that is, modes with larger amplitudes are usually less affected by random noise, so they can be selected first (but it should be noted that when restoring the sound field, some modes with amplitudes much larger than the incident sound wave may appear. These modes may be cut off modes with extremely high axial attenuation rates, and these modes should not be selected); (3) Wavenumber value, that is, in all modes In the context of low-order forward propagation modes approaching rigid wall conditions, such as Modes with smaller axial attenuation coefficients are more likely to dominate in the sound field and are therefore more likely to exist physically (because their attenuation coefficients are smaller, the real part of the circumferential wavenumber of these modes will be numerically close to the axial wavenumber under rigid wall conditions, thus allowing for the identification of these modes). Based on the aforementioned criteria, the preset preferred conditions can be conventionally obtained. For example, in a uniform flow velocity... axial spacing Horizontal spacing And the number of sound field modes When the frequency range calculated using this method is extended to 9900Hz, a set of results for selecting the optimal parameters is as follows: Figure 10 and Figure 11 As shown.

[0163] Therefore, based on the aforementioned possible design two, the optimal mode can be selected from the effective acoustic impedance calculation results, and the acoustic impedance corresponding to the mode can be used as the final acoustic impedance extraction result, further ensuring the accuracy of the extraction result.

[0164] Based on the aforementioned possible design one, this embodiment also provides a possible design three for selecting the optimal mode from multiple acoustic impedance calculation results. That is, after obtaining the multiple acoustic impedance calculation results of the acoustic liner, the method further includes, but is not limited to: firstly, calculating the corresponding acoustic field residual for each acoustic impedance calculation result in the multiple acoustic impedance calculation results of the acoustic liner (see the aforementioned steps S9 to S11 for the specific calculation method); then, selecting the acoustic impedance calculation result with the smallest acoustic field residual from the multiple acoustic impedance calculation results of the acoustic liner, and selecting the most suitable mode and the acoustic impedance corresponding to the mode from the acoustic impedance calculation result based on the repetitive mode, mode amplitude and / or wavenumber values ​​(see the aforementioned possible design two for specific details) as the final acoustic impedance extraction result of the acoustic liner.

[0165] Therefore, based on the aforementioned possible design three, the optimal mode can be selected from the results of multiple acoustic impedance calculations, and the acoustic impedance corresponding to this mode can be used as the final acoustic impedance extraction result, further ensuring the accuracy of the extraction result.

[0166] The second aspect of this embodiment also provides a data processing method for measuring the acoustic impedance of an acoustic liner, based on the first aspect and any of the methods described in possible designs one to three. This method is executed by an experimental data processing device, such as an electronic device including a platform server, a personal computer (PC, which refers to a multi-purpose computer of a size, price, and performance suitable for personal use; desktop computers, laptops, mini-laptops, tablets, and ultrabooks are all personal computers), a smartphone, a personal digital assistant (PDA), or a wearable device. This method includes, but is not limited to, the following steps S101 to S107.

[0167] S101. Obtain from The measurements were obtained from the microphone and in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone. A microphone is arranged in a zigzag array on the second wall of a real flow tube with a square cross-section. An acoustic liner is mounted flush with the first wall of the real flow tube. An array of sound sources is also installed upstream and / or downstream of the acoustic liner's mounting location within the real flow tube. A uniform flow exists within the real flow tube. The first wall is located opposite the second wall within the real flow tube. The sound source array is used to generate a sound field containing multiple modes, which include modes decomposed according to the principle of modal decomposition within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to The sound pressure level is a positive integer, and the sound pressure value is measured by the corresponding microphone after the sound source array is activated.

[0168] S102. According to the above Based on the sound pressure values ​​at several real measurement points, the following system of equations is established:

[0169]

[0170] In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row.

[0171] S103. Solve the system of equations using the least squares method based on the trust region algorithm, and obtain... An intermediate coefficient.

[0172] S104. According to the above Using intermediate coefficients, we obtain the roots of the following polynomial equation:

[0173]

[0174] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located in the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the modality of the column.

[0175] S105. Based on the roots of the polynomial equation, and using the second intermediate parameter... The wavenumbers for each axis are calculated using the following defined formula:

[0176]

[0177] In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a set of real measuring points is indicated by the superscript "". “ in "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " “ in "" indicates the back-propagating sound wave in the actual flow tube.

[0178] S106. Based on the wavenumbers of each axis, the longitudinal wavenumbers are calculated according to the following dispersion relation:

[0179]

[0180] In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The width of the square cross-section is indicated by the horizontal width, and the horizontal, vertical and axial directions are perpendicular to each other.

[0181] S107. The acoustic impedance of the acoustic liner is calculated according to the following formula based on the respective longitudinal wavenumbers. :

[0182]

[0183] In the formula, This indicates the longitudinal height of the square cross-section.

[0184] The working process, working details and technical effects of the aforementioned method provided in the second aspect of this embodiment can be found in the method described in any of the first aspect and possible designs one to three, and will not be repeated here.

[0185] like Figure 12 As shown, the third aspect of this embodiment provides a virtual device for implementing the method described in the second aspect, which is arranged in an experimental data processing device and includes, but is not limited to, a sound pressure data acquisition module, an equation system establishment module, an equation system solving module, an equation root solving module, an axial wavenumber calculation module, a longitudinal wavenumber calculation module, and an acoustic impedance calculation module that are sequentially connected in communication.

[0186] The sound pressure data acquisition module is used to acquire data from... The measurements were obtained from the microphone and in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone. A microphone is arranged in a zigzag array on the second wall of a real flow tube with a square cross-section. An acoustic liner is mounted flush with the first wall of the real flow tube. An array of sound sources is also installed upstream and / or downstream of the acoustic liner's mounting location within the real flow tube. A uniform flow exists within the real flow tube. The first wall is located opposite the second wall within the real flow tube. The sound source array is used to generate a sound field containing multiple modes, which include modes decomposed according to the principle of modal decomposition within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to The sound pressure value is a positive integer, and the sound pressure value is measured by the corresponding microphone after the sound source array is activated;

[0187] The equation system establishment module is used to establish the equation system based on the equation system. Based on the sound pressure values ​​at several real measurement points, the following system of equations is established:

[0188]

[0189] In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row;

[0190] The equation-solving module is used to solve the equation system using the least squares fitting method based on the trust region algorithm, to obtain... One intermediate coefficient;

[0191] The equation root solving module is used to solve the equation root according to the... Using intermediate coefficients, we obtain the roots of the following polynomial equation:

[0192]

[0193] In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located in the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the modality of the column;

[0194] The axial wavenumber calculation module is used to calculate the wavenumber based on the roots of the polynomial equation and the second intermediate parameter. The wavenumbers for each axis are calculated using the following defined formula:

[0195]

[0196] In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a set of real measuring points is indicated by the superscript "". “ in "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " “ in "This indicates the back-propagating sound wave in the actual flow tube;

[0197] The longitudinal wavenumber calculation module is used to calculate each longitudinal wavenumber based on the wavenumbers along each axis, using the following dispersion relation:

[0198]

[0199] In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The transverse width of the square cross-section is indicated by the fact that the transverse, longitudinal, and axial directions are all perpendicular to each other.

[0200] The acoustic impedance calculation module is used to calculate the acoustic impedance of the acoustic liner according to the following formula based on each longitudinal wavenumber. :

[0201]

[0202] In the formula, This indicates the longitudinal height of the square cross-section.

[0203] The working process, working details and technical effects of the aforementioned device provided in the third aspect of this embodiment can be found in the method described in any of the first aspect and possible designs one to three, and will not be repeated here.

[0204] like Figure 2 and Figure 13 As shown, the fourth aspect of this embodiment provides a physical system employing the method described in the second aspect, including but not limited to a real flow tube 1, a sound source array 2, a microphone 3, and experimental data processing equipment. The real flow tube 1 has a square cross-section and contains a uniform flow within it. A first wall of the real flow tube 1 is used to flush-mount a sound liner 5, which serves as the object for acoustic impedance measurement. The first wall is parallel to the axial direction of the real flow tube 1. The sound source array 2 is installed upstream and / or downstream of the sound liner mounting position within the real flow tube 1, and is used to generate a sound field containing multiple modes, wherein the multiple modes include those decomposed according to the modal decomposition principle into modes within the sound field. One modality, Represents a positive integer greater than or equal to 1. Represents a positive integer greater than or equal to 2; the number of microphones 3 is... Several sound source arrays are arranged in a "Z"-shaped zigzag array on the second wall of the actual flow tube 1, used to measure the sound pressure value at each measuring point after the sound source array 2 is activated. Indicates greater than or equal to The positive integer, the second wall is located on the opposite side of the first wall within the real flow tube 2; the experimental data processing device is communicatively connected to each of the microphones 3, and is used to perform the method as described in the second aspect.

[0205] The working process, working details and technical effects of the aforementioned system provided in the fourth aspect of this embodiment can be found in the method described in any of the first aspect and possible designs one to three, and will not be repeated here.

[0206] like Figure 14As shown, the fifth aspect of this embodiment provides a computer device for performing the method as described in the second aspect, including a memory, a processor, and a transceiver sequentially and communicatively connected. The memory stores a computer program, the transceiver sends and receives messages, and the processor reads the computer program and executes the method as described in the second aspect. Specifically, the memory may include, but is not limited to, random-access memory (RAM), read-only memory (ROM), flash memory, first-in-first-out (FIFO) memory, and / or first-in-last-out (FILO) memory, etc.; the processor may include, but is not limited to, a microprocessor of the STM32F105 series. Furthermore, the computer device may also include, but is not limited to, a power supply module, a display screen, and other necessary components.

[0207] The working process, working details and technical effects of the aforementioned computer device provided in the fifth aspect of this embodiment can be found in the method described in any of the first aspect and possible designs one to three, and will not be repeated here.

[0208] The sixth aspect of this embodiment provides a computer-readable storage medium storing instructions comprising the method described in the second aspect, wherein the computer-readable storage medium stores instructions that, when executed on a computer, perform the method described in the second aspect. The computer-readable storage medium refers to a carrier for storing data, and may include, but is not limited to, computer-readable storage media such as floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or Memory Sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0209] The working process, working details and technical effects of the aforementioned computer-readable storage medium provided in the sixth aspect of this embodiment can be found in the methods described in any of the first aspect and possible designs one to three, and will not be repeated here.

[0210] The seventh aspect of this embodiment provides a computer program product containing instructions that, when executed on a computer, cause the computer to perform the method described in the second aspect. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0211] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A mirror image multimodal direct extraction method of measuring acoustic lining acoustic impedance, characterized in that, include: A sound liner is installed flush with the first wall of a real flow tube with a square cross-section, and a Z-shaped zigzag array is installed on the second wall of the real flow tube. A microphone is used, and a sound source array is installed on the upstream and / or downstream rigid wall sections of the acoustic liner installation location within the actual flow tube. The actual flow tube contains a uniform flow, and the second wall surface is located on the opposite side of the first wall surface within the actual flow tube. The sound source array is used to generate a sound field containing multiple modes, the multiple modes including those decomposed according to the modal decomposition principle within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to Positive integers; Start the sound source array, and through the The microphone measurements were obtained in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone; According to the sound pressure values of the real measurement points, the following equation group is established: ​ In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row; The least square method based on the trust region algorithm is used to solve the equation group to obtain an intermediate coefficient; According to the above Using intermediate coefficients, we obtain the roots of the following polynomial equation: In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located at the th , Line and number The intermediate coefficient of the column, Denotes the variable to be solved in the polynomial equation. Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the column's mode; Based on the roots of the polynomial equation, and based on the second intermediate parameter The wavenumbers for each axis are calculated using the following defined formula: In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a given set of real measuring points is indicated by the superscript "". "in" "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " "in" "This indicates the back-propagating sound wave in the actual flow tube; Based on the wavenumbers of each axis, the wavenumbers of each longitudinal axis are calculated according to the following dispersion relation: In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Describes the free space wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The transverse width of the square cross-section is indicated by the fact that the transverse, longitudinal, and axial directions are all perpendicular to each other. The acoustic impedance of the acoustic liner is calculated according to the following formula based on the respective longitudinal wavenumbers. : In the formula, This indicates the longitudinal height of the square cross-section.

2. The method for direct extraction of mirrored multimodal data according to claim 1, characterized in that, After calculating the acoustic impedance of the acoustic liner, the method further includes: Based on the wavenumbers along each axis, the amplitude of each mode is calculated using the following sound pressure expression: In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the above In the modality located at the th Line and number The modal amplitude corresponding to the column's mode. Indicates the first The actual measurement points are in a rectangular coordinate system The horizontal coordinate in the middle, Indicates the first The actual measuring points are in the rectangular coordinate system The axial coordinates in the rectangular coordinate system The origin of the coordinate system is located at the intersection of the longitudinal sidewall of the actual flow tube and the reverse extension of the first segment of the broken line in the "Z"-shaped broken line array. In Indicates the axial direction. Indicates the longitudinal direction, Indicates the horizontal direction, the first The actual measuring points are in the rectangular coordinate system The coordinates in the diagram are represented as ; Based on the amplitude of each modality, the following formula is used to calculate the amplitude of each modality. Reconstructed sound pressure values ​​at each of the actual measurement points: In the formula, Indicated in the first The restored sound pressure value at each actual measuring point; Based on the sound pressure values ​​and restored sound pressure values ​​at each actual measurement point, the sound field residual is calculated using the following formula. : In the formula, Represents the L2 norm; Determine whether the acoustic field residual is less than or equal to a preset residual threshold. If it is, the acoustic impedance calculation result of the acoustic liner is determined to be valid; otherwise, it is determined to be invalid.

3. The method for direct extraction of mirrored multimodal data according to claim 2, characterized in that, After determining that the acoustic impedance calculation result of the acoustic liner is valid, the method further includes: selecting the most suitable mode and the acoustic impedance corresponding to the mode from the acoustic impedance calculation result of the acoustic liner according to the preset preferred conditions set based on the repetitive mode, mode amplitude and / or wavenumber value, as the final acoustic impedance extraction result of the acoustic liner. Alternatively, after obtaining the multiple acoustic impedance calculation results of the acoustic liner, the method further includes: calculating the corresponding acoustic field residual for each acoustic impedance calculation result in the multiple acoustic impedance calculation results of the acoustic liner; selecting the first acoustic impedance calculation result with the smallest acoustic field residual from the multiple acoustic impedance calculation results of the acoustic liner, and selecting the most suitable mode and the acoustic impedance corresponding to the mode from the second acoustic impedance calculation result according to the preset preferred conditions set based on the repetitive mode, mode amplitude and / or wavenumber values, as the final acoustic impedance extraction result of the acoustic liner.

4. The method for direct extraction of mirrored multimodal data according to claim 1, characterized in that, The equations are derived based on the following principle of mirror acoustic array technology, which transforms a real flow tube into a hypothetical flow tube: Based on the actual flow tube and the "Z"-shaped zigzag array arrangement... For each microphone, according to classical mode decomposition theory, the sound field has the following series form: （3） In the formula, Represents complex sound pressure levels. Indicates the position of the first Line and number The modal amplitude corresponding to the column's mode. Indicates the position of the first The transverse wavenumber corresponding to the mode of the line and has , Representing a rectangular coordinate system The horizontal coordinate, Indicates the position of the first Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the position of the first Line and number The axial wavenumbers corresponding to the modes of the column, Represents the rectangular coordinate system axial coordinates, Represents the rectangular coordinate system The vertical coordinate of the rectangular coordinate system The origin of the coordinate system is located at the intersection of the longitudinal sidewall of the actual flow tube and the reverse extension of the first segment of the broken line in the "Z"-shaped broken line array; Utilizing the mirror symmetry caused by the rigid wall boundary conditions and the standing wave solution in the transverse direction, the actual sound field and microphone array are unfolded into a hypothetical array based on mirror symmetry: assuming the "Z"-shaped polygonal array has... The segments are divided into sections, and the axial and lateral spacing between adjacent microphones are respectively... and , Represents a positive integer greater than or equal to 3; and imagines a horizontal width of... In the hypothetical flow tube, acoustic liners with the same acoustic impedance as the acoustic liners to be solved are arranged on the walls on the same side; in the sound field of the hypothetical flow tube, there exists a sound field corresponding to the original sound field. Modalities, and in the original sound field The modal amplitudes of the modes correspond one-to-one, that is, we have In an imaginary flow tube, there is an array of microphones evenly spaced along a diagonal straight line, with axial and lateral spacing also being... and The microphone within one times the width of the original flow tube coincides with the first microphone measurement point of the polygonal array in the real flow tube; the remaining parameters of the hypothetical flow tube are completely consistent with those of the original real flow tube. The first in the original real flow tube Real measurement points The sound pressure expression at that point can be derived from the aforementioned equation (3) to obtain the following form: （5） In the formula, , Indicated in the first The sound pressure value at a real measurement point. Indicates the above In the modality located at the th Line and number The modal amplitude corresponding to the mode of the column; Based on the fact that the sound field of the hypothetical flow tube has the same transverse wavenumber, longitudinal wavenumber, axial wavenumber and modal amplitude as the original sound field in each mode, the sound field in the hypothetical flow tube in the first mode is obtained from the aforementioned equation (5). Each measuring point sound pressure at the location for: （6） Based on the hypothetical flow tube, it can flow along... ( ) was split into Each width is This part, and by introducing variables And there are To represent horizontal The coordinates of the direction can be rewritten from the previous equation (6) as follows: （7） based on Based on parameters The parity of is simplified, and the aforementioned equation (7) can be rewritten in the following form: Based on the fact that When it is even and When it is an odd number It is exactly the first one in a real flow tube. The distance of each actual measuring point from the side wall The distance, therefore there is Furthermore, in reality, the entire hypothetical sound field is equivalent to the original sound field, and the hypothetical sound field at the boundary... and The parts in between include: when When the number is even, it represents a translation of the original sound field; when... When the number is odd, it is exactly a mirror image of the original sound field. This allows the equivalence of the real and imaginary microphone arrays to be obtained through multiple mirror image symmetry operations on the sound field. Consequently, the problem of extracting acoustic impedance using a piecewise linear array in a real flow tube can be transformed into obtaining sound pressure using an equally spaced oblique linear array in an imaginary extended flow tube. The extraction problem; Introducing variables To simplify coordinate notation, the coordinates of the measuring point in the imaginary flow tube can be written as: （9） Meanwhile, the sound pressure expression can be written as: （10） Then introduce the first intermediate parameter Second intermediate parameter The sound pressure expression (10) in the hypothetical sound field can be written as: （11） In the formula, the subscript Decomposed into and sum; Multiply both sides of the aforementioned equation (11) by To construct the Prony polynomial, and then for all From 0 to Summing these equations, we can obtain the following system of equations: （12） In the formula, Indicates in relation to the first The sound pressure value at the hypothetical measuring point, the first The hypothetical measurement point and the first The actual measurement points coincide, making Can be Replace directly.

5. The method for direct extraction of mirrored multimodal data according to claim 1, characterized in that, The described mirror multimodal direct extraction method is applicable to any aerodynamic acoustic field containing three-dimensional multimodalities, thus broadening the extraction frequency range. And / or, the mirrored multimodal direct extraction method can improve the accuracy of lateral mode decomposition by increasing the lateral distance of the microphone when applied.

6. A method for direct extraction of mirror multimode acoustic impedance for measuring acoustic liner, characterized in that, Performed by experimental data processing equipment, including: Get by The measurements were obtained from the microphone and in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone. A microphone is arranged in a "Z"-shaped zigzag array on the second wall of a real flow tube with a square cross-section. An acoustic liner is mounted flush with the first wall of the real flow tube. An array of sound sources is also installed upstream and / or downstream of the acoustic liner's mounting location within the real flow tube. A uniform flow exists within the real flow tube. The first wall is located opposite the second wall within the real flow tube. The sound source array is used to generate a sound field containing multiple modes, which include modes decomposed according to the principle of modal decomposition within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to The sound pressure value is a positive integer, and the sound pressure value is measured by the corresponding microphone after the sound source array is activated; According to the above Based on the sound pressure values ​​at several real measurement points, the following system of equations is established: In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row; The system of equations is solved by least squares fitting based on the trust region algorithm, yielding... One intermediate coefficient; According to the above Using intermediate coefficients, we obtain the roots of the following polynomial equation: In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located at the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the column's mode; Based on the roots of the polynomial equation, and based on the second intermediate parameter The wavenumbers for each axis are calculated using the following defined formula: In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a given set of real measuring points is indicated by the superscript "". "in" "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " "in" "This indicates the back-propagating sound wave in the actual flow tube; Based on the wavenumbers of each axis, the wavenumbers of each longitudinal axis are calculated according to the following dispersion relation: In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The transverse width of the square cross-section is indicated by the fact that the transverse, longitudinal, and axial directions are all perpendicular to each other. The acoustic impedance of the acoustic liner is calculated according to the following formula based on the respective longitudinal wavenumbers. : In the formula, This indicates the longitudinal height of the square cross-section.

7. A mirror-image multimodal direct extraction device for measuring acoustic impedance of an acoustic liner, characterized in that, The experimental data processing equipment includes a sound pressure data acquisition module, an equation system establishment module, an equation system solution module, an equation root solution module, an axial wavenumber calculation module, a longitudinal wavenumber calculation module, and an acoustic impedance calculation module, which are connected in sequence via communication. The sound pressure data acquisition module is used to acquire data from... The measurements were obtained from the microphone and in The sound pressure values ​​at each actual measurement point, wherein the... The actual measurement points and the stated Each microphone corresponds to a specific microphone. A microphone is arranged in a "Z"-shaped zigzag array on the second wall of a real flow tube with a square cross-section. An acoustic liner is mounted flush with the first wall of the real flow tube. An array of sound sources is also installed upstream and / or downstream of the acoustic liner's mounting location within the real flow tube. A uniform flow exists within the real flow tube. The first wall is located opposite the second wall within the real flow tube. The sound source array is used to generate a sound field containing multiple modes, which include modes decomposed according to the principle of modal decomposition within the sound field. In each mode, the axis of the actual flow tube is parallel to the first wall surface and the second wall surface, respectively. Represents a positive integer greater than or equal to 1. Represents positive integers greater than or equal to 2. Indicates greater than or equal to The sound pressure value is a positive integer, and the sound pressure value is measured by the corresponding microphone after the sound source array is activated; The equation system establishment module is used to establish the equation system based on the equation system. Based on the sound pressure values ​​at several real measurement points, the following system of equations is established: In the formula, Indicated based on The set of numbers represented The continuous summation symbol and has , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. In the set of numbers The Middle One element, Indicated in the The first real measurement point The sound pressure value at a real measurement point. Indicates the interval Integer values ​​that take the value of 'm'. and Let represent the intermediate coefficients to be solved. Indicates the above In the modality located at the th The variables corresponding to the modality of the row; The equation-solving module is used to solve the equation system using the least squares fitting method based on the trust region algorithm, to obtain... One intermediate coefficient; The equation root solving module is used to solve the equation root according to the... Using intermediate coefficients, we obtain the roots of the following polynomial equation: In the formula, Indicates the interval Integer values ​​that take the value of 'm'. Indicates the interval Integer values ​​that take the value of 'm'. Indicated in the Among the intermediate coefficients and located at the th , Line and number The intermediate coefficient of the column, The variables representing the polynomial equation, Indicates the above In the modality located at the th The first intermediate parameter corresponding to the mode of the row, and the roots of the polynomial equation are respectively expressed as: and , Indicates the interval Integer values ​​that take the value of 'm'. Indicates the above In the modality located at the th Line and number The second intermediate parameter corresponding to the column's mode; The axial wavenumber calculation module is used to calculate the wavenumber based on the roots of the polynomial equation and the second intermediate parameter. The wavenumbers for each axis are calculated using the following defined formula: In the formula, The base of the natural logarithm. , Indicates the above In the modality located at the th , Line and number The axial wavenumber corresponding to the mode of the column, Indicated in the The axial distance between two adjacent real measuring points in a given set of real measuring points is indicated by the superscript "". "in" "" indicates the forward-propagating sound wave in the actual flow tube, indicated by the superscript " "in" "This indicates the back-propagating sound wave in the actual flow tube; The longitudinal wavenumber calculation module is used to calculate each longitudinal wavenumber based on the wavenumbers along each axis, using the following dispersion relation: In the formula, Describes the Mach number of the uniform flow and has , This represents the flow velocity of the uniform flow. Indicates the speed of sound. Represents the spatial free wavenumber and has , Indicates the frequency of the sound wave. Indicates the above In the modality located at the th Line and number The longitudinal wavenumber corresponding to the mode of the column, Indicates the above In the modality located at the th The transverse wavenumber corresponding to the mode of the line and has , The transverse width of the square cross-section is indicated by the fact that the transverse, longitudinal, and axial directions are all perpendicular to each other. The acoustic impedance calculation module is used to calculate the acoustic impedance of the acoustic liner according to the following formula based on each longitudinal wavenumber. : In the formula, This indicates the longitudinal height of the square cross-section.

8. A mirror-image multimodal direct extraction system for measuring acoustic impedance of an acoustic liner, characterized in that, It includes a real flow tube (1), a sound source array (2), a microphone (3) and experimental data processing equipment. The real flow tube (1) has a square cross-section and a uniform flow inside. The first wall of the real flow tube (1) is used to flush mount the acoustic liner (5) which is the object of acoustic impedance measurement. The first wall is parallel to the axis of the real flow tube (1). The sound source array (2) is installed in the upstream and / or downstream rigid wall sections of the acoustic liner installation position inside the real flow tube (1) to generate a sound field with multiple modes, wherein the multiple modes include modes that are decomposed according to the modal decomposition principle into modes within the sound field. One modality, Represents a positive integer greater than or equal to 1. Represents a positive integer greater than or equal to 2; The number of microphones (3) is The sound source array (2) is arranged in a "Z"-shaped zigzag array on the second wall of the real flow tube (1) to measure the sound pressure value at the measuring point after the sound source array (2) is activated. Indicates greater than or equal to A positive integer, wherein the second wall is located on the opposite side of the first wall within the real flow tube (1); The experimental data processing device is communicatively connected to each of the microphones (3) to execute the mirror multimodal direct extraction method as described in claim 6.

9. A computer device, characterized in that, The device includes a memory, a processor, and a transceiver that are sequentially and communicatively connected. The memory is used to store a computer program, the transceiver is used to send and receive messages, and the processor is used to read the computer program and execute the mirror multimodal direct extraction method as described in claim 6.

10. A computer-readable storage medium, characterized in that... The computer-readable storage medium stores instructions that, when executed on a computer, perform the image multimodal direct extraction method as described in claim 6.

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