Engine pipeline acoustic mode identification method based on cross-spectrum matrix

Abstract

The invention relates to an engine pipeline acoustic modal identification method based on a cross-spectrum matrix, and the method comprises the steps: arranging M microphones on the circumferential pipe wall of a to-be-detected pipeline, enabling the M microphones to be arranged at intervals in the axial direction of the to-be-detected pipeline to form a circumferential sound transmission array, and carrying out the recognition measurement of the acoustic modal of the pipeline through employing the M microphones, the obtained noise sound pressure signals serve as time domain signals, a measurement cross-spectrum matrix of noise signals measured by the M microphones is obtained through conversion from the time domain signals to frequency domain signals, self-spectrum elements in the measurement cross-spectrum matrix are removed, and a simulation model cross-spectrum matrix with the self-spectrum elements removed is correspondingly established; enabling the mean square error between the measurement cross spectrum matrix and the simulation model cross spectrum matrix to be minimum, and obtaining an engine pipeline acoustic mode identification result capable of suppressing the background noise. According to the invention, when the microphone is damaged or the signal is interfered, the damaged or received microphone signal is eliminated, and the acoustic mode of the engine pipeline can still be identified.

Description

Technical Field

[0001] This invention relates to the field of acoustic modal recognition technology for aero-engine pipes. Background Technology

[0002] The unique intake and exhaust pipe layout of aero gas turbine engines ensures that their noise always propagates outward through the airflow pipes in a distinctive acoustic mode. It is well known that, apart from the jet noise source exposed to free space and propagating as spherical waves, the noise generated by other components of an aero engine always first propagates through the circular or annular intake / exhaust pipes to the engine inlet and nozzle outlet, and then radiates outward through the engine inlet and outlet.

[0003] According to the basic theory of duct acoustics, within a circular (annular) airflow duct, due to the influence of the duct wall boundary conditions, only a specific type of sound wave can propagate along the duct. This specific type of sound wave structure is usually called an acoustic mode. In a circular (annular) duct, the duct acoustic mode is characterized by rotational motion around the duct axis (circumferential mode) and radial amplitude profile described by Bessel functions (radial mode). The propagation characteristics of the duct acoustic mode are determined by the specific geometry and size of the duct, as well as the flow field characteristics within the duct.

[0004] Since broadband turbulent noise propagates in the engine duct as a statistically averaged modal wave, its acoustic energy is distributed across various "cut-off" modes. Therefore, the study of broadband noise requires the use of statistical methods to describe the acoustic modes of broadband noise ducts.

[0005] As early as 1972, Harel & Perulli et al. proposed using the Cross Spectral Approach to identify and measure the acoustic modes of broadband noise pipes. They were the first to replace hot-wire anemometers with microphones in sound pressure measurement. Bolleter et al. (1973) used the Cross Spectral Density Approach to study the acoustic modes of broadband noise pipes. This method decomposes the broadband noise power into various modes by measuring the cross-correlation function between different microphones. However, in their study, they assumed that there was no reflection at the pipe end walls and ignored the influence of airflow in the pipe.

[0006] Kerschen et al. (1981) developed the first decoupling method that can be used for both single-tone noise and broadband noise pipe acoustic modes—the instantaneous approach—and analyzed the modal decomposition principle of the method and its suppression characteristics for flow noise.

[0007] In the field of broadband noise acoustic power measurement in pipelines, based on the research of Chung et al. (1977), Michalke et al. (1996), and Chun et al. (2003), Enghardt (2004) proposed a method for measuring broadband noise acoustic power of fans based on pipeline acoustic mode recognition—the reference microphone method.

[0008] In recent years, research on the turbulent broadband noise duct acoustic modes of aero-engines has gradually become a research hotspot and focus in the field of aeroacoustics. Internationally, various duct acoustic mode identification methods have been successfully developed, including the instantaneous approach, the cross-correlation-based approach (MDCC), and the reference sensor approach.

[0009] In summary, although many methods for identifying the acoustic modes of pipelines with turbulent broadband noise have been developed, the following shortcomings still exist: (1) In actual experimental measurements, microphone damage or interference with some microphone signals is frequently encountered, rendering traditional pipeline acoustic mode identification methods unusable; (2) Traditional pipeline acoustic mode identification methods require the use of a uniformly distributed circumferential microphone array. In actual measurements, issues such as hardware obstruction may prevent the uniform arrangement of the circumferential microphones, thus affecting the use of pipeline acoustic mode identification methods; (3) Traditional pipeline acoustic mode identification methods cannot overcome the influence of background noise. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of the prior art and provide an engine pipe acoustic mode identification method that can still identify the acoustic modes even when the microphone is damaged or the signal is interfered with, and the damaged or interfered microphone signal is removed. The method allows for arbitrary changes in the microphone distribution according to the actual measurement object and environment. At the same time, during use, the method reduces the impact of background noise on mode identification by removing the self-spectral elements in the cross-spectral matrix.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for identifying engine duct acoustic modes based on cross-spectral matrix, comprising the following steps: Step 1: Arrange and install [equipment] on the circumferential wall of the pipe to be tested. M One microphone, and M A microphone is arranged at intervals along the axial direction of the pipe under test to form a circumferential sound transmission array; in, MIf the value is greater than or equal to 2, and the axial spacing is either equal or non-equal, then... M Maximum circumferential mode decomposition order of each microphone K =( M -1) / 2 rounds down; use M Using one microphone to perform pipe acoustic modal recognition measurement, we obtain... M The noise sound pressure level signals from each microphone are used as time-domain signals, and combined with... M The time difference between the sound signals received by each microphone is obtained. M The cross-correlation function of the noise sound pressure signal measured by each microphone at each noise frequency and the cross-power spectrum function of the Fourier transform of the measured signals from any two microphones are used to obtain... M The cross-spectral matrix of the noise signal measured by each microphone; The Fourier transform is the process of converting a time-domain signal into a frequency-domain signal. Step 2: Establish the frequency settings. M The simulation model of a microphone, since the sound field inside a circular or annular rigid-walled pipe is composed of the linear superposition of waves of different modes, is based on the maximum circumferential modal identification order. K , construct in sequence M The analog model signals of each microphone and the cross-spectral matrices of the analog models of different modes; Step 3: Determine the cross-spectral matrix of the simulation models for different modes. M The circumferential modal amplitudes of each microphone are used to minimize the root mean square error between the measured cross-spectral matrix and the simulated model cross-spectral matrix, thus obtaining the engine pipe acoustic modal identification result. By removing the autospectral elements of the measured cross-spectral matrix and the simulated model cross-spectral matrix during the calculation process, the engine pipe acoustic modal identification result with background noise can be obtained.

[0012] Furthermore, in step one, the stated M A microphone is fixed on the circumferential outer wall of the inlet and outlet pipes of the test pipe on the annular blade cascade or aero-engine test bench to realize the pipe acoustic mode recognition measurement in the inlet and outlet directions of the test pipe.

[0013] Furthermore, in step one, the stated M The noise sound pressure signals measured by any two of the microphones are: and and the noise sound pressure signal Recorded as the number m The time-domain signal of the noise sound pressure level of each microphone. Recorded as the number n The time-domain signal of the noise sound pressure level of each microphone is then: M Cross-correlation function of noise signals measured by each microphone Represented as: , In the formula, yes M The time difference between the sound signals received by each microphone t yes M The time it takes for each microphone to receive a sound signal. m and n They represent the first m The and the first n One microphone, M Indicates the total number of microphones; Therefore, the first m The and the first n Noise sound pressure signal measured by one microphone and Cross-power spectrum function after Fourier transform for: , In the formula, , Indicates the frequency of the noise; get, M The cross-spectral matrix of the noise signal measured by each microphone for: , In the formula, M This indicates the total number of microphones.

[0014] Furthermore, in step two, the constructed M Analog model signal of one microphone for: , In the formula, k Indicates the modal order; Representing modes k The amplitude; For the first m The model signal of one microphone; Indicates the steering vector; m Indicates the first m One microphone; θ m Indicates the first m The circumferential angle of each microphone; Furthermore, the cross-spectral matrix of the simulation models for different modalities was constructed. for: , in, Indicates conjugate transpose; ,expressk The power spectrum of the first mode; m and n They represent the first m The and the first n One microphone, that is M Any two microphones from the microphones. K This represents the order of the maximum circumferential mode identification.

[0015] Furthermore, step three specifically involves: Determine the M One microphone k Circumferential mode B k The value of makes the cross-spectral matrix measured Cross-spectral matrix of simulation model The mean square deviation between F ( B Minimum: , In the formula, k Indicates the modal order; ,express k The power spectrum of the first mode; Indicates conjugate transpose; and Indicates the steering vector; m and n They represent the first m No. and n Microphone; M Indicates the total number of microphones; K The order of the maximum circumferential modal identification; Next, it expands into the following form: , in, , , , In the formula, m and n They represent the first m The and the first n One microphone; , , , Both represent steering vectors; Indicates conjugate transpose; k and u Indicates the modal order; M Indicates the total number of microphones; In order to F( B Let the smallest be: , That is, solving a minimization problem: , In the formula, k and u Indicates the modal order. B k express k Power spectrum of first mode amplitude; Then, written as a matrix equation: , In the formula: , , , Solve the matrix equations to obtain the circumferential modes of each order. B k The value of .

[0016] Furthermore, to reduce the impact of background noise, the autospectral elements in the measured cross-spectral matrix and the simulated model cross-spectral matrix are first removed. and That is, removing the minimization problem U u middle m = n The elements are then used to perform matrix calculations to suppress background noise, resulting in more accurate modal identification and clearer imaging.

[0017] Furthermore, modal identification calculations are performed at each of the noise frequencies from 0 to 10000 Hz.

[0018] The beneficial effects of this invention are as follows: Compared with traditional engine pipe acoustic mode identification methods, the innovation of the engine pipe acoustic mode identification method (SOMOX) based on cross-spectral matrix provided by this invention lies in: (1) The SOMOX method can be applied to both uniformly distributed circumferential microphone arrays and non-uniformly distributed circumferential microphone arrays. (2) If the microphone is damaged or the signal is interfered with during actual measurement, the damaged or interfered microphone signal can be removed, and the engine pipe acoustic mode can still be identified.

[0019] (3) The modal identification method based on cross-spectral matrix can remove the self-spectral elements in the cross-spectral matrix during the calculation process, reduce the influence of background noise, and obtain more accurate modal identification results. Attached Figure Description

[0020] Figure 1. Schematic diagram of acoustic modal test measurement for pipeline; Figure 2. Schematic diagram of a uniformly distributed circumferential microphone array; Figure 3. Schematic diagram of a circumferential microphone array for removing anomalous signals; Figure 4. Pipe acoustic mode recognition results of a uniformly distributed circumferential microphone array; Figure 5. Pipe acoustic mode recognition results of the circumferential microphone array after removing abnormal signals; Figure 6. Comparison of pipe acoustic modal recognition results between a typical circumferential microphone array with uniform frequency distribution and a microphone array with abnormal signals removed. Figure 7. Pipeline acoustic mode recognition results of a circumferential microphone array with self-spectral elements removed from the cross-spectral matrix. Detailed Implementation

[0021] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0022] To achieve the above objectives, the present invention provides the following specific embodiments: Example 1: A method for identifying engine duct acoustic modes based on cross-spectral matrix, comprising the following steps: S01, Arranged on the circumferential wall of the pipe to be tested. M One microphone, and M A microphone is arranged at intervals along the axial direction of the pipe under test to form a circumferential sound transmission array; in, M If the value is greater than or equal to 2, and the axial spacing is either equal or non-equal, then... M Maximum circumferential mode decomposition order of each microphone K =( M -1) / 2 rounds down; M A microphone is fixed on the circumferential outer wall of the inlet and outlet pipes of the test pipe on the annular blade cascade or aero-engine test bench to realize the pipe acoustic mode recognition measurement in the inlet and outlet directions of the test pipe.

[0023] S02, M The noise sound pressure signals measured by any two of the microphones are: and and the noise sound pressure signal Recorded as the number m The time-domain signal of the noise sound pressure level of each microphone. Recorded as the number n The time-domain signal of the noise sound pressure level of each microphone is then: M Cross-correlation function of noise signals measured by each microphone Represented as: , In the formula, yes M The time difference between the sound signals received by each microphone t yes M The time it takes for each microphone to receive a sound signal. m and n They represent the first m The and the first n One microphone, M This indicates the total number of microphones.

[0024] S03, regarding the first m The and the first n Noise sound pressure signal measured by one microphone and Fourier transform, cross-power spectrum function after Fourier transform for: , In the formula, , Indicates the frequency of the noise; get, M The cross-spectral matrix of the noise signal measured by each microphone for: , In the formula, M This indicates the total number of microphones.

[0025] The Fourier transform is the process of converting a time-domain signal into a frequency-domain signal.

[0026] S04. Constructing at each of the noise frequencies from 0 to 10000 Hz. M Analog model signal of one microphone for: , In the formula, k Indicates the modal order; Representing modes k The amplitude; For the first m The model signal of one microphone; Indicates the steering vector; m Indicates the first m One microphone; θ m Indicates the first m The circumferential angle of each microphone.

[0027] S05. Since the sound field inside a circular or annular rigid-walled pipe is composed of the linear superposition of waves of different modes, the identification order is based on the maximum circumferential mode. K Cross-spectral matrices of simulation models with different modalities for: , in, Indicates conjugate transpose; ,express k The power spectrum of the first mode; m and n They represent the first m The and the first n One microphone, that is M Any two microphones from the microphones. K This represents the order of the maximum circumferential mode identification.

[0028] S06. Based on the cross-spectral matrix of the simulation models for different modes, determine the... M One microphone k Circumferential mode B k The value of makes the cross-spectral matrix measured Cross-spectral matrix of simulation model The mean square deviation between F ( B Minimum: , In the formula, k Indicates the modal order; ,express k The power spectrum of the first mode; Indicates conjugate transpose; and Indicates the steering vector; m and n They represent the first m No. and n Microphone; M Indicates the total number of microphones; K The order of the maximum circumferential modal identification; Next, it expands into the following form: , in, , , , In the formula, m and n They represent the first m The and the first nOne microphone; , , , Both represent steering vectors; Indicates conjugate transpose; k and u Indicates the modal order; M Indicates the total number of microphones; In order to F ( B Let the smallest be: , That is, solving a minimization problem: , In the formula, k and u Indicates the modal order. B k express k Power spectrum of first mode amplitude; Then, written as a matrix equation: , In the formula: , , , Solve the matrix equations to obtain the circumferential modes of each order. B k The value of .

[0029] Example 2: Same as Example 1, except that in S06, in order to reduce the influence of background noise, the autospectral elements in the measured cross-spectral matrix and the simulated model cross-spectral matrix are first removed. and That is, removing the minimization problem U u middle m = n The elements are then used to perform matrix calculations to suppress background noise, resulting in more accurate modal identification and clearer imaging.

[0030] For example Figure 1-7 As shown, to further illustrate the technical solution and effects of the present invention, the present invention provides the following specific example: A method for engine pipeline acoustic mode recognition, the specific steps of which are as follows: Step 1: As Figure 1 As shown, modal identification of the annular blade cascade test bench was carried out using 32 circumferential microphones, with the 32 microphones arranged around the circumference of the pipe in the annular blade cascade test bench. like Figure 2As shown, a circumferential array is used for pipe acoustic mode recognition measurement (the circumferential microphones are arranged at an angle of 0 ≤ ... <2π, with a pairwise microphone spacing of π / 16 angle), to obtain experimental measurement data for a uniformly distributed microphone array; like Figure 3 As shown, by randomly removing one microphone, the array arrangement becomes non-uniformly spaced, and experimental measurement data of a non-uniformly distributed microphone array can be obtained. The time-domain signal measured by any microphone from 32 microphones (31 after removing one microphone) is: Then we have the cross-correlation function of the noise signals measured by the 32 microphones. Represented as:

[0031] This allows us to obtain the measurement signals from any two microphones. and Cross-power spectrum function of the frequency domain signal after Fourier transform for:

[0032] get, M The cross-spectral matrix of the noise signal measured by each microphone for:

[0033] Step Two: Based on the microphone array experimental measurement data obtained in Step One, the maximum circumferential modal order that can be analyzed is... K =(32-1) / 2=15 (rounded down), thus constructing a model signal with 32 microphones and 15 modes. :

[0034] Furthermore, a cross-spectral matrix of a 15-mode simulation model is constructed. :

[0035] in, Indicates conjugate transpose; ,express k The power spectrum of the first mode.

[0036] Step 3: The ultimate goal is to determine the 15th order circumferential modes of the 32 microphones. B k The value that makes the mean square error between the measured cross-spectral matrix and the simulated model cross-spectral matrix... F ( B Minimum:

[0037] Expanding the above expression into the following form:

[0038] in,

[0039]

[0040]

[0041] In order to The minimum can be set as:

[0042] That is, solving a minimization problem:

[0043] Written in matrix form:

[0044] In the formula: , , , To reduce the impact of background noise, the self-spectral elements in the cross-spectral matrix can be removed. and ), that is, remove U u middle m = n The elements are used to suppress background noise, making the modality recognition results more accurate.

[0045] The calculation example after removing one microphone is the same as the steps above. The maximum recognizable modal order is 15, and the number of microphones is 31. Repeat the above steps to obtain the modal recognition results, which are the values ​​of a total of 31 modal orders and the values ​​of each circumferential mode. B k The value 31 refers to the maximum circumferential mode decomposition order of M microphones. K = (M-1) / 2, the maximum order is 15, that is, -15 to +15, which means that a total of 31 modes are identified.

[0046] Experimental Results: The experimental verification results of engine pipeline acoustic mode identification are as follows: Figure 4 As shown in 5, 6, and 7.

[0047] Figure 4 and Figure 5The results show the modal identification results with 32 microphones in a uniform distribution and with one microphone removed. As can be seen from the figure, removing some microphones does not affect the modal identification results, but it also makes the array non-uniformly distributed. This shows that the new modal identification method is also applicable to non-uniformly distributed microphone arrays.

[0048] Figure 6 The modal identification results for a single frequency of 3600Hz are then displayed, and the figure further illustrates that removing some microphones will not significantly affect the modal identification results.

[0049] Figure 7 This shows the modality identification results after removing autospectral elements, and... Figure 4 The comparison shows that the new method significantly reduces the impact of low-frequency background noise, resulting in clearer modal identification images and more distinct modal boundaries, thus significantly improving the accuracy of modal identification.

[0050] The method of this invention is applicable to measurements of any other circumferential microphone array.

[0051] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying engine duct acoustic modes based on cross-spectral matrix, characterized in that, Includes the following steps: Step 1: Arrange and install [equipment] on the circumferential wall of the pipe to be tested. M One microphone, and M A microphone is arranged at intervals along the axial direction of the pipe under test to form a circumferential sound transmission array; in, M If the value is greater than or equal to 2, and the axial spacing is either equal or non-equal, then... M Maximum circumferential mode decomposition order of each microphone K =( M -1) / 2 rounds down; use M One microphone is used to perform pipe acoustic mode identification measurement, and the obtained noise sound pressure signal is used as a time domain signal, and combined with... M The time difference between the sound signals received by each microphone is obtained. M The cross-correlation function of the noise sound pressure signal measured by each microphone at each noise frequency and the cross-power spectrum function of the Fourier transform of the measured signals from any two microphones are used to obtain... M The cross-spectral matrix of the noise signal measured by each microphone; The Fourier transform is the process of converting a time-domain signal into a frequency-domain signal. Step 2: Establish the frequency settings. M The simulation model of a microphone, since the sound field inside a circular or annular rigid-walled pipe is composed of the linear superposition of waves of different modes, is based on the maximum circumferential modal identification order. K , construct in sequence M Cross-spectral matrix of each microphone and simulation model of different modalities; Step 3: Determine the cross-spectral matrix of the simulation models for different modes. M The circumferential modal amplitudes of each microphone are used to minimize the root mean square error between the measured cross-spectral matrix and the simulated model cross-spectral matrix, thus obtaining the engine pipe acoustic modal identification result. By removing the autospectral elements of the measured cross-spectral matrix and the simulated model cross-spectral matrix during the calculation process, the engine pipe acoustic modal identification result with background noise can be obtained.

2. The engine duct acoustic mode identification method based on cross-spectral matrix as described in claim 1, characterized in that, In step one, the M A microphone is fixed on the circumferential outer wall of the inlet and outlet pipes of the test pipe on the annular blade cascade or aero-engine test bench to realize the pipe acoustic mode recognition measurement in the inlet and outlet directions of the test pipe.

3. The engine duct acoustic mode identification method based on cross-spectral matrix as described in claim 1, characterized in that, In step one, the M The noise sound pressure signals measured by any two of the microphones are: and and the noise sound pressure signal Recorded as the number m The time-domain signal of the noise sound pressure level of each microphone. Recorded as the number n The time-domain signal of the noise sound pressure level of each microphone is then: M Cross-correlation function of noise signals measured by each microphone Represented as: ， In the formula, yes M The time difference between the sound signals received by each microphone t yes M The time it takes for each microphone to receive a sound signal. m and n They represent the first m The and the first n One microphone, M Indicates the total number of microphones; Therefore, the first m The and the first n Noise sound pressure signal measured by one microphone and Cross-power spectrum function after Fourier transform for: ， In the formula, , f Indicates the frequency of the noise; get, M The cross-spectral matrix of the noise signal measured by each microphone for: ， In the formula, M This indicates the total number of microphones.

4. The engine duct acoustic mode identification method based on cross-spectral matrix as described in claim 1, characterized in that, In step two, the constructed M Analog model signal of one microphone for: ， In the formula, k Indicates the modal order; Representing modes k The amplitude; For the first m Analog model signal from one microphone; Indicates the steering vector; m Indicates the first m One microphone; θ m Indicates the first m The circumferential angle of each microphone; Furthermore, the cross-spectral matrix of the simulation models for different modalities was constructed. for: ， in, Indicates conjugate transpose; ,express k The power spectrum of the first mode; m and n They represent the first m The and the first n One microphone, that is M Any two microphones from the microphones. K This represents the order of the maximum circumferential mode identification.

5. The engine duct acoustic mode identification method based on cross-spectral matrix as described in claim 1, characterized in that, Step three specifically involves: Determine the M One microphone k Circumferential mode B k The value of makes the cross-spectral matrix measured Cross-spectral matrix of simulation model The mean square deviation between F ( B Minimum: ， In the formula, k Indicates the modal order; ,express k The power spectrum of the first mode; Indicates conjugate transpose; and Indicates the steering vector; m and n They represent the first m No. and n Microphone; M Indicates the total number of microphones; K The order of the maximum circumferential modal identification; Next, it expands into the following form: ， in, ， ， ， In the formula, m and n They represent the first m The and the first n One microphone; , , , Both represent steering vectors; Indicates conjugate transpose; k and u Indicates the modal order; M Indicates the total number of microphones; In order to F ( B Let the smallest be: ， That is, solving a minimization problem: ， In the formula, k and u Indicates the modal order. B k express k Power spectrum of first mode amplitude; Then, written as a matrix equation: ， In the formula: ， ， ， Solve the matrix equations to obtain the circumferential modes of each order. B k The value of .

6. The engine duct acoustic mode identification method based on cross-spectral matrix as described in claim 5, characterized in that, To reduce the impact of background noise, the autospectral elements in the measured cross-spectral matrix and the simulated model cross-spectral matrix are first removed. and That is, removing the minimization problem U u middle m = n The elements are then used to perform matrix calculations to suppress background noise, resulting in more accurate modal identification and clearer imaging.

7. The engine duct acoustic mode identification method based on cross-spectral matrix as described in any one of claims 1-6, characterized in that, Modal identification calculations are performed at each of the noise frequencies from 0 to 10000 Hz.

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