Ducted fan noise circumferential acoustic mode detection method based on genetic algorithm

Abstract

The application provides a duct fan noise circumferential acoustic mode detection method based on a genetic algorithm, utilizes the characteristics of acoustic mode sparsity, solves an inverse problem model of circumferential acoustic mode recognition in a duct, solves an underdetermined equation set through an optimization mode with the aid of measurement values of a small number of sensor measuring points, realizes accurate reconstruction of a main mode order and amplitude under a sub-Nyquist sampling rate condition, solves the problems of a traditional detection method based on a uniform microphone array, such as system complexity and high cost, and improves mode recognition accuracy compared with an l1 norm sparse regularization compressed sensing method.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic noise testing technology for ducted fan propulsion systems, and in particular to a method for circumferential acoustic mode detection of ducted fan noise based on a genetic algorithm. Background Technology

[0002] With the rapid development of civil aviation and urban air mobility (UAM), ducted fans, as a core component of the power system, have been widely used in various aircraft, such as high-bypass turbofan aero engines and ducted propeller units for vertical takeoff and landing unmanned aerial vehicles. However, the fan noise of the propulsion system, especially the single-tone noise generated by the mutual interference between the rotor and stator, dominates the overall noise emissions of the aircraft and has attracted widespread social attention.

[0003] Fan noise often propagates to the outside world in the form of ducted acoustic modes. Since acoustic mode information can directly reflect the noise source mechanism and noise propagation characteristics, it provides guidance for noise reduction design. Therefore, acoustic mode detection methods are very important for the development of low-noise design and evaluation technology for aircraft.

[0004] Ducted acoustic modal detection aims to obtain amplitude information of each mode (especially the dominant mode) to achieve specific testing objectives. Depending on the detection target, it can be divided into circumferential modal detection and radial modal detection, with circumferential modal detection typically providing sufficient sound field information. To conduct circumferential modal detection, a ring of microphones is usually installed flush with the inner wall of the duct along its circumference. The obtained data is then converted to the frequency domain, and the complex sound pressure level at the frequency of interest is extracted. Further spatial Fourier decomposition is then performed to obtain the circumferential modal amplitude at the measurement section. It should be noted that the above detection method must adhere to the Shannon-Nyquist sampling theorem, meaning the number of array elements required for the microphone array must be at least twice the highest-order mode of the mode being tested. However, in actual testing, especially in ground noise experiments on aero-engines, the number of fan blades and exit guide vanes is often large. According to the Taylor-Sofrin selectivity, the resulting circumferential modal orders are generally high. This necessitates the placement of numerous microphones circumferentially within the duct wall, leading to an exceptionally complex circumferential modal detection system and excessively high costs for data acquisition, storage, and processing. Therefore, it is necessary to develop new modal extraction methods from a signal processing perspective.

[0005] To address the aforementioned issues, Chinese Patent Application No. 201710580385.7 proposed a radial acoustic modal detection system and method for pipelines based on compressed sensing theory, and Chinese Patent Application No. 202111648218.4 proposed a method and device for identifying the circumferential acoustic modal of a single tone noise of an aircraft engine fan. Compressed sensing methods based on l1 norm sparse regularization were developed for radial and circumferential modal detection, respectively. However, in practice, it has been found that the compressed sensing method based on l1 norm sparse regularization is not only mathematically complex, but also prone to underestimating modal amplitudes, resulting in insufficient accuracy and low reliability of test results. Therefore, it is necessary to further develop simple and reliable modal detection methods. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a circumferential acoustic mode detection method for ducted fan noise based on a genetic algorithm. Utilizing the sparsity of acoustic modes, it solves the inverse problem model for circumferential acoustic mode identification within the duct. Using measurements from a small number of sensor points, it solves an underdetermined system of equations through optimization, achieving accurate reconstruction of the principal mode order and amplitude under sub-Nyquist sampling conditions. This not only solves the problems of complex systems and high costs associated with traditional detection methods based on uniform microphone arrays, but also improves the accuracy of mode identification compared to the l1-norm sparse regularized compressed sensing method.

[0007] The technical solution of this invention is as follows:

[0008] A method for testing the circumferential acoustic modes of ducted fan noise based on a genetic algorithm includes the following steps:

[0009] Step 1: Establish the duct model: The duct model is a circular cross-section with radius R, represented by a cylindrical coordinate system (x,r,θ), where the sound source plane is located at the x=0 section, and the generated high-order modal sound waves contain S circumferential principal modes, and the modal sound waves propagate in the positive x direction in the duct;

[0010] Step 2: Based on the number of fan rotor blades B and the number of stator blades V, and based on the formula for calculating the circumferential acoustic modal order of fan single-tone noise m=ξB+ζV, determine the range of propagable modal orders, where ξ represents the order of pressure pulsation caused by unsteady aerodynamic forces caused by fan rotor-stator interference, and ζ is an integer;

[0011] Based on the target frequency f for modal identification and the modal cutoff condition, the range of propagable modal orders is determined, thereby obtaining the highest order m of the circumferential acoustic mode of the fan single-tone noise to be observed. max The number of measuring points N ≥ 2m along the circumference of the culvert wall. max ;

[0012] Step 3: A measurement cross-section is set on the duct wall surface of the duct model at the position of x=x0, and N measurement point positions are evenly arranged along the circumferential direction on the measurement cross-section; any H positions are selected from the N measurement point positions to install microphones to form a non-uniform measurement array, where S<H<N; all microphones synchronously collect time-domain data of acoustic signals, the time-domain data is subjected to Fast Fourier Transform to obtain a frequency spectrum, the frequency-domain result (complex sound pressure) of each microphone signal at the target frequency (usually the blade passing frequency) is extracted, and a measurement result vector P is constructed;

[0013] Step 4: Based on the highest order m of the circumferential acoustic mode of the fan tonal noise to be observed determined in Step 2 max and the non-uniform array measurement point positions set in Step 3, a circumferential acoustic mode identification model under H microphones is established, and a transfer matrix φ is constructed;

[0014] Step 5: According to the measurement result vector P obtained in Step 3 and the transfer matrix φ obtained in Step 4, the acoustic mode identification model is solved based on a genetic algorithm to obtain the circumferential principal mode order m j and the amplitude a j , 1≤j≤S;

[0015] Step 6: According to the circumferential principal mode order m obtained in Step 5 j and the amplitude a j , a complete circumferential mode amplitude vector is constructed m j the principal mode is located at the m-th position of vector A max +m j , the element at the corresponding position is set as the mode amplitude a j , and the values of the remaining elements of vector A are set to 0.

[0016] Further, in Step 3, the angles corresponding to the N measurement point positions are θ i =2πj / N, j=1,…,N, H positions are randomly selected therefrom to install microphones, with the installation angles being Θ=[θ1,θ2,…θ H T ; the frequency-domain complex sound pressure of the microphone array at the blade passing frequency f n =nBΩ is taken as P h (f n ), h=1,…,H, and the measurement result vector P=[P1(f n ), P2(f n ), …P H (f n )] T ; where Ω is the rotational frequency of the rotating shaft, and n=1,2,… is the harmonic order of the sound wave.

[0017] ​Furthermore, in step 4, the circumferential acoustic modal recognition model for H measurement points is P = φA, where Let be the circumferential acoustic mode amplitude vector to be estimated. For the transfer matrix

[0018]

[0019] Furthermore, in step 5, the process of solving the acoustic modal recognition model based on the genetic algorithm is as follows:

[0020] Step 5.1: Generate the initial population, which contains N. c Each individual represents a modal amplitude vector A; the population is encoded by transforming each individual from a modal amplitude vector A containing S principal modes into a matrix. In matrix A′, the first column stores the position indices of the S principal modes in vector A, and the second column stores the magnitude a of the principal modes. j ;

[0021] Population size N c Based on experience, if the value is too small, it will affect the speed of hybridization and mutation to produce the best individuals; if the value is too large, it will affect the overall computational efficiency.

[0022] Step 5.2: Calculate the fitness value of each individual in the population;

[0023] Step 5.3: Determine if the termination condition is met: If the termination condition is not met, continue to step 5.4; otherwise, proceed to step 5.6.

[0024] Step 5.4: Through hybridization, mutation, and selection, new individuals are generated to form a new population, and the fitness value of each individual in the new population is calculated;

[0025] The methods of hybridization, mutation, and selection are as follows: New individuals are generated by randomly swapping two rows of two individuals; when mutation occurs, new individuals are generated by randomly changing the value of a certain individual; and individuals with the highest fitness function value are eliminated through the principle of survival of the fittest. Thus, N individuals are selected. c A new population is formed by a group of superior individuals, and the population size remains constant.

[0026] Step 5.5: Determine if the termination condition is met: If the termination condition is met, continue to step 5.6; otherwise, return to step 5.4.

[0027] Step 5.6: Decode the optimal individual that meets the termination condition to obtain the main mode amplitude.

[0028] Decoding is the inverse process of encoding. The first column of A′ is used as the position index of the principal mode in the amplitude vector A, and the second column of A′ is used as the amplitude a corresponding to the position of the principal mode. j Vector elements other than the primary mode can be set to 0, thereby creating the modal magnitude vector A.

[0029] Furthermore, in step 5.2, the fitness function of an individual is defined as:

[0030] J0=‖P-φA‖2+α‖A‖ β

[0031] Where α is the regularization parameter, and the parameter β determines the norm used in the regularization term. The smaller the fitness value J0, the closer the corresponding individual is to the optimal solution.

[0032] Furthermore, in step 5.5, the termination condition is: the fitness of an individual is lower than a preset threshold, or the number of iterations reaches a preset upper limit.

[0033] Beneficial effects

[0034] This invention establishes a genetic algorithm-based method for testing the circumferential acoustic modes of ducted fan noise based on the sparsity of the circumferential modes of single-tone noise in the modal domain. Compared to traditional full-microphone array decomposition of fan noise circumferential modes, this invention's genetic algorithm-based method for duct circumferential acoustic mode recognition employs a non-uniform array with a Sub-Nyquist sampling rate, reducing the originally required large-scale microphone array to an acceptable range while still achieving accurate modal amplitude identification. Compared to traditional detection methods, the proposed method significantly reduces the complexity of hardware layout and the cost of data acquisition, storage, and processing, resulting in a simpler process. Compared to existing l1-norm sparse regularized compressed sensing methods, this invention's genetic algorithm-based method for duct circumferential acoustic mode recognition, by leveraging the principle of survival of the fittest, bypasses complex mathematical convex optimization theory, improving the accuracy of modal amplitude identification. Compared to compressed sensing methods, the proposed method significantly lowers the barrier to entry, is simple in principle, and easy to implement.

[0035] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0036] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0037] Figure 1 This is a schematic diagram of the duct circumferential acoustic modal testing method based on genetic algorithm of the present invention.

[0038] Figure 2 This is a flowchart of the genetic algorithm used in this invention;

[0039] Figure 3 This paper compares the modal test results of the algorithm of this invention with existing constant modal extraction methods and compressed sensing methods under the conditions of main modes m = -4 and 7 and signal-to-noise ratio -10dB. Detailed Implementation

[0040] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0041] like Figure 1 As shown, the pipe is a circular pipe with a uniform cross-section of radius R, represented by a cylindrical coordinate system (x,r,θ). The sound source section of the component that generates high-order modal sound waves is located at the section x=0. The sound wave propagates in the pipe along the positive x direction, and the measurement section is located at the section x=x0.

[0042] The duct circumferential acoustic modal detection system based on genetic algorithm in this embodiment includes: H microphones; based on the highest circumferential modal order m that can be propagated in the duct. max Determine the number N of measuring points to be set along the circumference of the pipe at the measuring section, where N ≥ 2m. max From N measurement points, H microphones are randomly selected at each of the following locations: <N)。

[0043] The duct circumferential acoustic modal detection method based on genetic algorithm in this embodiment includes the following steps:

[0044] Step 1: Establish the duct model: The duct model is a circular shape with a radius R = 0.25m and a uniform cross-section. It is represented by a cylindrical coordinate system (x, r, θ), where the sound source plane (i.e., the fan rotation plane) is located at the x = 0 section position, and the generated high-order mode sound waves propagate in the positive x direction in the duct.

[0045] Step 2: Determine the target frequency for modal detection f = 2100Hz, the number of fan rotor blades B = 7, and the number of stator blades V = 11.

[0046] Based on the formula for calculating the modal order of a single-tone noise mode of an installed fan, m = ξB + ζV, ξ is typically taken as 1 to represent the pressure pulsation order caused by the unsteady aerodynamic force resulting from the fan's rotation-to-stationary interference, which is 1. ζ is taken as an integer, determining the range of propagable modal orders as {…, -4, 7, …}. This is further combined with the modal cutoff / interruption conditions at the target frequency. Determine the maximum circumferential modal order m that can be intercepted (when radial mode n=1). max =7, thus determining the number of measuring points N = 16 to be set along the circumference of the culvert wall. Where σmn J′ m The eigenvalues ​​of J(x) = 0 m Let m represent the m-th order Bessel function.

[0047] Step 3: Set up a measurement section on the wall of the culvert model at a position of x = 2.5m. Distribute 16 measuring points evenly along the circumference of the measurement section. Then, randomly select 6 of these 16 measuring points to install microphones, forming a non-uniform measurement array. In this embodiment, the 1st, 3rd, 7th, 10th, 13th, and 14th sensor positions were selected. All microphones synchronously acquire time-domain data of the sound signal. The time-domain data is then subjected to a Fast Fourier Transform to obtain the spectrum. The frequency domain result P(f) of each microphone signal at the target frequency is extracted, and the measurement result vector P = [P1(f), P2(f), ..., P6(f)] is constructed. T .

[0048] Step 4: Based on the highest order m of the circumferential acoustic mode of the single-tone noise of the fan to be observed, determined in Step 2. max =7 and the non-uniform measurement array positions set in step 3, establish a circumferential acoustic modal recognition model with 6 microphone measurement points, P = φA, where Let be the circumferential acoustic mode amplitude vector to be estimated. To construct the transfer matrix, construct the transfer matrix φ:

[0049]

[0050] Step 5: Based on the measurement result vector P obtained in Step 3 and the transfer matrix φ obtained in Step 4, solve the acoustic modal recognition model using a genetic algorithm to obtain the order m of the circumferential principal modes. j and amplitude a j , 1≤j≤S; the specific steps are as follows:

[0051] Step 5.1: Generate the initial population, which contains 1000 individuals, each representing a modal amplitude vector A. Encode the population to accelerate the computational iteration speed of the genetic algorithm, transforming each individual from a modal amplitude vector A containing two principal modes into a matrix. In matrix A′, the first column stores the index of the principal mode in vector A, and the second column stores the magnitude a of the principal mode. j ;

[0052] Step 5.2: Calculate the fitness value of each individual in the population;

[0053] J0=‖P-φA‖2+α‖A‖0

[0054] Where α is the regularization parameter, and in this embodiment, α = 0.01.

[0055] Step 5.3: Determine if the termination condition is met: If the termination condition is not met, continue to step 5.4; otherwise, proceed to step 5.6. The termination condition is: the fitness J0 of an individual is ≤0.05, or the number of iterations reaches the preset upper limit of 10000.

[0056] Step 5.4: Through hybridization, mutation, and selection, new individuals are generated to form a new population, and the fitness value of each individual in the new population is calculated;

[0057] Step 5.5: Determine if the termination condition is met: If the termination condition is met, continue to step 5.6; otherwise, return to step 5.4.

[0058] Step 5.6: Decode the optimal individual that meets the termination condition to obtain the main mode amplitude.

[0059] Step 6: Based on the circumferential principal mode order m obtained in Step 5 j and amplitude a j Construct a complete circumferential modal magnitude vector m j The principal mode is located at the 8+mth position of vector A. j Position, set the corresponding position element to the modal amplitude a j Set the values ​​of all other elements in vector A to 0.

[0060] This allows us to obtain the final circumferential acoustic mode. Figure 3 The algorithm of this invention is compared with existing conventional methods and compressed sensing methods in modal recognition under a signal-to-noise ratio of -10dB. Compared with compressed sensing methods, the results show that the present invention improves the modal amplitude recognition accuracy, greatly reduces the threshold for use, and is simple in principle and easy to implement.

[0061] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for testing the circumferential acoustic modes of ducted fan noise based on a genetic algorithm, characterized in that: Includes the following steps: Step 1: Establish the duct model: The duct model has a radius of [missing information]. A circular shape with a constant cross section, using a cylindrical coordinate system. This indicates that the sound source plane is located at... The cross-sectional location generates higher-order modal acoustic waves including A circumferential principal mode, the modal acoustic wave travels along the duct. Positive propagation; Step 2: Based on the number of fan rotor blades Number of leaves of the euryptic plant And based on the calculation formula of the circumferential acoustic mode order of fan single-tone noise. Determine the range of propagable modal orders, where This indicates the order of pressure pulsations caused by unsteady aerodynamic forces resulting from the interference of the fan's rotation and stationary motion. It is an integer; Based on the target frequency of modality recognition By combining the modal cutoff condition, the range of propagable modal orders is determined, thereby obtaining the highest order of the circumferential acoustic mode of the fan single-tone noise to be observed. And the number of measuring points set along the circumference of the culvert wall. ; Step 3: Set up a measurement section on the pipe wall of the duct model, located at... The positions are evenly distributed circumferentially along the measuring section. Location of each measuring point; from Any of the measurement points can be selected. A non-uniform measurement array is formed by installing microphones at various locations. ; All microphones synchronously acquire time-domain data of the sound signal. The time-domain data is then subjected to a Fast Fourier Transform to obtain the spectrum. The frequency domain results of each microphone signal at the target frequency are extracted, and a measurement result vector is constructed. ; Step 4: Based on the highest order of the circumferential acoustic mode of the single-tone noise of the fan to be observed, determined in Step 2. And the non-uniform array measurement point positions set in step 3, to establish A circumferential acoustic modal recognition model under one microphone is constructed, and a transfer matrix is ​​built. ; Step 5: Based on the measurement result vector obtained in Step 3 and the transfer matrix obtained in step 4 The acoustic modal recognition model was solved based on a genetic algorithm to obtain the order of the circumferential principal modes. and amplitude , ; Step 6: Based on the circumferential principal mode order obtained in Step 5 and amplitude Construct a complete circumferential modal magnitude vector , The dominant mode is located in the vector No. Position, set the corresponding position element as modal amplitude. ,set up The values ​​of the remaining elements of the vector are .

2. The method for circumferential acoustic modal testing of ducted fan noise based on genetic algorithm according to claim 1, characterized in that: In step 3, The angle corresponding to each measuring point position is Randomly select from them The microphone is installed at one location, with an installation angle of [missing information]. ; Extracting the frequency of the microphone array passing through the blade The frequency domain complex sound pressure is Construct measurement result vector ;in The rotation frequency of the shaft, These are the harmonic orders of the sound wave.

3. The method for testing the circumferential acoustic modes of ducted fan noise based on a genetic algorithm according to claim 2, characterized in that: In step 4, The circumferential acoustic modal recognition model at each measurement point is as follows: ,in Let be the circumferential acoustic mode amplitude vector to be estimated. For the transfer matrix 。 4. The method for testing the circumferential acoustic modes of ducted fan noise based on a genetic algorithm according to claim 1, characterized in that: In step 5, the process of solving the acoustic modal recognition model based on the genetic algorithm is as follows: Step 5.1: Generate the initial population, which includes... Each individual represents a modal magnitude vector. ; Encode the population, and assign individual individuals to the population. Modal amplitude vectors of the principal modes Transform into a matrix , where the matrix First column storage The principal modes in the vector The position index is in the middle, and the second column stores the main mode amplitude. ; Population size Based on experience, if the value is too small, it will affect the speed of hybridization and mutation to produce the best individuals; if the value is too large, it will affect the overall computational efficiency. Step 5.2: Calculate the fitness value of each individual in the population; Step 5.3: Determine if the termination condition is met: If the termination condition is not met, continue to step 5.4; otherwise, proceed to step 5.

6. Step 5.4: Through hybridization, mutation, and selection, new individuals are generated to form a new population, and the fitness value of each individual in the new population is calculated; The methods of hybridization, mutation, and selection are as follows: New individuals are generated by randomly swapping two rows of two individuals; when mutation occurs, new individuals are generated by randomly changing the value of a certain individual; and individuals with the highest fitness function value are eliminated through the principle of survival of the fittest, thus selecting the best individuals. A new population is formed by a group of superior individuals, and the population size remains constant. Step 5.5: Determine if the termination condition is met: If the termination condition is met, continue to step 5.6; otherwise, return to step 5.

4. Step 5.6: Decode the optimal individual that meets the termination condition to obtain the main mode amplitude; Decoding is the reverse process of encoding. The first column of numbers serves as the dominant mode in the amplitude vector. The position index in the middle, The second column of numbers represents the amplitude corresponding to the dominant mode position. ; Vector elements other than the dominant mode are set to 0, and modal magnitude vectors are created accordingly. .

5. The method for circumferential acoustic modal testing of ducted fan noise based on genetic algorithm according to claim 4, characterized in that: In step 5.2, the fitness function of an individual is defined as: in For regularization parameters, the parameters are... The norm and fitness value used in the regularization term are determined. The smaller the value, the closer the corresponding individual is to the optimal solution.

6. The method for testing the circumferential acoustic modes of ducted fan noise based on a genetic algorithm according to claim 4, characterized in that: In step 5.5, the termination condition is: the fitness of an individual is lower than a preset threshold, or the number of iterations reaches a preset upper limit.

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