A Method for Optimizing the Design of Surface Array Formations Based on Spatial Virtual Field Sources

Abstract

The present invention discloses a method for optimizing the design of a surface array formation based on a spatial virtual field source. This method uses the traveling wave method to construct a spatial virtual wavenumber-frequency spectrum field source function for the surface array response, and based on the wavenumber domain beamforming processing algorithm or the direct measurement method, a target response function for the virtual field source is established. By taking the improvement of the resolution of the typical wavenumber segment of the formation and the maximization of the measurement accuracy in the full wavenumber segment as the basis, a multi-objective optimization criterion is established, and then the final optimized formation is obtained through continuous iteration. This method provides a virtual excitation source input for the numerical simulation process required for array formation optimization, can effectively support the design of the surface array formation, and greatly improves the test capabilities of the surface array in wind tunnel, water tunnel, flight, underwater and other tests.

Description

Technical Field

[0001] The present invention relates to the field of wind tunnel tests, and particularly to an optimization design method for surface array formation based on a spatial virtual field source. Background Art

[0002] The fluctuating pressure in the turbulent boundary layer is the key excitation source for the fluid-induced vibration and noise problems of various military and civilian equipment. The fluctuating pressure in the turbulent boundary layer results from the unsteady force of vortices of various scales in the turbulent boundary layer acting on the wall. On the one hand, it directly radiates noise outward, and on the other hand, it causes the wall structure to vibrate to form a secondary sound source and lead to structural fatigue. Therefore, the fluid-induced vibration and noise problems induced by the fluctuating pressure in the turbulent boundary layer pose a severe test to the safety, comfort, and acoustic stealth of the equipment. Conducting tests such as wind tunnels, water tunnels, flights, and underwater is the main means to obtain the characteristics of the fluctuating pressure in the turbulent boundary layer. Among them, the application of surface array test technology effectively improves the test ability in this regard and can realize the measurement of the wave number-frequency spectrum of the fluctuating pressure in the turbulent boundary layer. Formation design and optimization play a key role in the development process of surface arrays. By reasonably designing the formation distribution, the measurement ability of the surface array for the wave number-frequency spectrum of the fluctuating pressure can be effectively improved. Formation design and optimization require the input of a virtual excitation source to realize computer simulation response and complete formation iteration calculation and screening. However, there is currently a lack of a virtual source design method specifically for surface arrays, so the formation optimization calculation cannot be completed, restricting the improvement of the measurement ability of the surface array. Summary of the Invention

[0003] The purpose of the present invention is to solve the deficiencies existing in the formation optimization of the current surface array of the fluctuating pressure in the turbulent boundary layer during the design and development process, and propose an optimization design method for the surface array formation based on a spatial virtual field source.

[0004] To achieve the above purpose, the solution adopted by the present invention is as follows:

[0005] An optimization design method for a surface array formation based on spatial virtuality, comprising the following steps:

[0006] Step 1: Use the traveling wave method to construct a spatial virtual wave number-frequency spectrum field source function for the surface array response.

[0007] To realize the simulation of the surface array response by computer, a spatial virtual wave number-frequency spectrum field source needs to be designed. Let the flow direction coordinate be represented as , the spanwise coordinate be represented as , and the two-dimensional position vector in the flow direction and spanwise direction be represented as . For a plane wave propagating arbitrarily in the two-dimensional plane of the flow direction and spanwise direction, its function is expressed as , being the time variable. This plane wave function is composed of NCharacterized by the superposition of sub traveling wave functions, and the amplitude of each sub traveling wave function is , the wave number vector is , the angular frequency is , and the phase is . Note that here is a two-dimensional wave number vector, which only contains the streamwise wave number and the spanwise wave number , that is . The above relationship can be written as:

[0008] (1)

[0009] The scalar form of the above formula can be written as:

[0010] (2)

[0011] Or the complex form:

[0012] (3)

[0013] The selected wave numbers and angular frequencies of the sub traveling wave functions should be representative, and for the related wave number segments, the number of sub traveling waves and the degree of mutual variation can be increased to enhance the analysis weight. It should be noted here that if the spatial virtual wave number-frequency spectrum field source is only a one-dimensional function, that is, it only propagates in the streamwise or spanwise direction, then the wave number and coordinate value in the other direction can be set to zero.

[0014] Step 2: Taking the two-dimensional coordinates of the surface array element distribution as the independent variables of the multivariate function, and based on the wave number domain beamforming processing algorithm or the direct measurement method, establish the target response function for the virtual field source.

[0015] After constructing the spatial virtual wave number-frequency spectrum field source function, taking the wave number domain beamforming algorithm or the direct measurement algorithm of the surface array as the basis, substitute this spatial virtual wave number-frequency spectrum field source function to calculate the response and obtain the target response function.

[0016] Step 3: Based on maximizing the resolution improvement of the typical wave number segment of the array and the measurement accuracy of the full wave number segment, establish a multi-objective optimization criterion

[0017] First of all, taking the improvement of the resolution of the typical wave number segment of the array and the maximization of the measurement accuracy of the full wave number segment as the optimization basis, establish a dual performance index, which lays the foundation for constructing the multi-objective optimization criterion. This index specifically includes:

[0018] The lobe characteristics of the virtual array response: the peak value of the main lobe , the peak values of other (sidelobes) except the main lobe ;

[0019] Differential characteristics between the virtual array response and the field source: Resolution in different wavenumber bands , Measurement error in the full wavenumber band .

[0020] Then, based on these two performance indicators, by increasing the weight factor for gain or suppression, a multi-objective optimization criterion expressed by a fitness function is formed, providing an evaluation and selection basis for the next iteration of the genetic algorithm.

[0021] The expression of the multi-objective optimization criterion (i.e., the genetic algorithm fitness function) is as follows:

[0022] (4)

[0023] It is used to systematically evaluate the response characteristics and performance of the array in different wavenumber bands and the full wavenumber band, enabling the genetic algorithm to select the optimal array configuration with the maximum main lobe gain, minimum side lobe, the highest resolution in a specific wavenumber band, and the smallest error value in the full wavenumber band.

[0024] Step 4: Use the genetic algorithm to carry out iterative optimization of the surface array configuration

[0025] First, take the coordinates of the elements of the basic array configuration as the initial values and randomly generate an initial population of array configurations according to the conditions;

[0026] Then, based on the spatial virtual wavenumber-frequency spectral field source function constructed in Step 1 and the target response function established in Step 2, quantitatively evaluate the two performance indicators of different array configurations under the multi-objective optimization criterion defined in Step 3;

[0027] Secondly, evaluate and screen the initial population of array configurations based on the fitness function to form a better population, and then carry out crossover and mutation iterative calculations;

[0028] Finally, terminate the search when the maximum number of iterations or the threshold condition is reached, forming the optimal array configuration and its fitness function value.

[0029] Step 5: Develop relevant supporting arrays and conduct experimental research.

[0030] Develop and process the MEMS surface array with the optimized high-performance configuration, and conduct necessary hardware calibration, testing, and evaluation on the two MEMS surface arrays; after completion, experiments can be carried out.

[0031] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are as follows:

[0032] Based on the traveling wave method, a spatial virtual wavenumber-frequency spectral field source is constructed, providing a virtual excitation source input for the numerical simulation process required for array formation optimization. It can effectively support the design of surface array formations and significantly improve the testing capabilities of surface arrays in wind tunnels, water tunnels, flight, underwater, and other tests. Brief Description of the Drawings

[0033] The present invention will be described by way of examples with reference to the accompanying drawings, where:

[0034] Figure 1 is the flow schematic diagram of the present solution;

[0035] Figure 2 is a schematic diagram of the spatial virtual wavenumber-frequency spectral field source for surface array response constructed by the traveling wave method;

[0036] Figure 3 is the basic helical formation before optimization;

[0037] Figure 4 is the optimized helical formation after iterative calculation;

[0038] Figure 5 The two-dimensional wavenumber domain beamforming result obtained from the wind tunnel test of the optimized array. Detailed Embodiment

[0039] All features disclosed in this specification, or all steps in the disclosed methods or processes, except for mutually exclusive features and / or steps, can be combined in any manner.

[0040] Any feature disclosed in this specification (including any additional claims, abstract, and drawings), unless specifically stated, can be replaced by other equivalent or similar-purpose alternative features. That is, unless specifically stated, each feature is only an example of a series of equivalent or similar features.

[0041] In this embodiment, in combination with the accompanying drawings, taking the two-dimensional surface array wind tunnel test in a 1.8 m × 1.4 m wind tunnel as an example, the specific implementation manner of the present invention is described.

[0042] The formation optimization process of this embodiment is as Figure 1 shown:

[0043] Step 1: Use the traveling wave method to construct a spatial virtual wavenumber-frequency spectral field source function for surface array response.

[0044] Specifically in the example, such as Figure 2As shown, the constructed spatial virtual wavenumber-frequency spectrum field source function consists of two sub-traveling wave functions. The amplitude of the streamwise sub-wave is 2.7 Pa, the wavenumber is 18 rad / m, and the angular frequency is 12566 rad·Hz; the amplitude of the spanwise sub-wave is 5.2 Pa, the wavenumber is 45 rad / m, and the angular frequency is 3142 rad·Hz. Based on the superposition in Equation (1), this spatial virtual wavenumber-frequency spectrum field source function can be obtained.

[0045] Step 2: Use the wavenumber domain beamforming processing algorithm to calculate the two-dimensional array response, and take this response result as the target response function.

[0046] Specifically in the example, such as Figure 3 shown, it is a two-dimensional basic spiral array with 76 array elements.

[0047] First, conduct virtual wavenumber-frequency field data response and acquisition through computer simulation, with a sampling frequency of 12.8 kHz and a sampling time of 4 s;

[0048] Then, for the 76-channel response data, calculate the cross-spectral matrix of the array response and conduct wavenumber domain beamforming calculation. During the process, a Hanning window is used as the window function for calculation, and the block length is set to 1024 and the overlap rate is 50% to obtain the cross-spectral matrix . Note that a parallel computing method is adopted here to improve the computing efficiency;

[0049] Secondly, calculate the array wavenumber steering vector;

[0050] Finally, calculate the wavenumber domain beamforming results at different angular frequencies . That is, the wavenumber domain beamforming results obtained at the angular frequency of 6200 rad·Hz, where the inside of the white circle near (0,0) is the marked acoustic field region boundary.

[0051] Step 3: Based on maximizing the resolution improvement of the typical wavenumber segment of the array and the measurement accuracy of the full wavenumber segment, establish a multi-objective optimization criterion.

[0052] Specifically in the example, establish an applicable optimization criterion according to Equation (4). First, select the full wavenumber segment range, specifically covering the streamwise range K1 [-20, 1000] rad / m and the spanwise range K3 [-600, 600] rad / m. To focus on the key wavenumber characteristics, determine the typical wavenumber segment range as [0,20] [30,50] [200, 350] rad / m. Then conduct weight combination configuration, where the main lobe weight of the response , the side lobe weight , and the resolution of the specific wavenumber segment weight , the measurement error in the full wave number range weight . Note that it is necessary to standardize the dual performance indicators to eliminate the influence of dimension.

[0053] Step 4: Use the genetic algorithm to carry out iterative optimization of the surface array formation

[0054] First, reasonably configure the core parameters and termination conditions of the genetic algorithm: set the formation population size to 20 individuals, the crossover probability to 0.5 to ensure appropriate gene recombination, and the mutation probability to 0.01 to maintain the genetic diversity of the population. In the termination criterion, the maximum number of iterations is specified as 100 times, which is used as the judgment basis for the algorithm to converge.

[0055] Secondly, introduce the array element coordinate data of the basic formation to generate an initial formation population with different distributions. Input each individual of the generated formation population into the response model (Step 2) to obtain their corresponding response results.

[0056] Then, according to the optimization criterion defined in Step 3, comprehensively evaluate the performance of these formations, and select the formations with better performance from them. For the selected better formations, perform crossover operation and mutation operation to generate a new formation population. After that, repeat Step 2 and Step 3, that is, continuously iterate the process of formation response evaluation, optimization, and generating a new population through genetic operations until the preset termination conditions are met.

[0057] Finally, when the algorithm converges to the termination conditions, output the array element position coordinates of the optimal formation searched during the entire optimization process and its corresponding fitness function value. The new formation is as shown in Figure 4 .

[0058] Step 5: Develop relevant supporting arrays and carry out experimental research.

[0059] After obtaining the optimized array formation, complete the development of the high-performance MEMS surface array according to the process requirements, and perform necessary hardware calibration, testing and evaluation. Then complete the experiment in a 1.8 m × 1.4 m low-speed wind tunnel. The two-dimensional wavenumber domain beamforming result obtained is as shown in Figure 5 .

[0060] The present invention is not limited to the foregoing specific embodiments. The present invention extends to any new feature disclosed in this specification or any new combination, as well as any new method or process step disclosed or any new combination.

Claims

1. A method for optimizing the design of a surface array formation based on a spatial virtual field source, characterized in that It includes the following steps: S1: Construct a spatial virtual wavenumber-frequency spectrum field source function for the surface array response by using the traveling wave method. If the function is only a one-dimensional function propagating in the flow direction or spanwise direction, the wavenumber and coordinate value in the other direction are zero. The expression form of the function is as follows: , The scalar form of the function is as follows: , The plural form of the function is: , Wherein: is the flow direction coordinate, is the spanwise coordinate, is the two-dimensional position vector in the flow direction and spanwise direction, is the time variable, is the amplitude of each sub traveling wave function, is a two-dimensional wave number vector containing the flow direction wave number and the spanwise wave number is the angular frequency, is the phase, where n and N are both natural numbers,​ S2: Take the two-dimensional coordinates of the surface array element distribution as the independent variables of the multivariate function, and establish a target response function for the virtual field source based on the wavenumber domain beamforming processing algorithm or the direct measurement method. S3: Establish a multi-objective optimization criterion based on maximizing the resolution improvement of the typical wavenumber segment of the array pattern and the measurement accuracy in the full wavenumber segment. S4: Use the genetic algorithm to carry out iterative optimization of the surface array pattern. The optimization criterion includes the following steps:

2. The surface array formation optimization design method based on a spatial virtual field source according to claim 1, characterized in that S31: Establish a dual performance index based on maximizing the resolution improvement of the typical wavenumber segment of the array pattern and the measurement accuracy in the full wavenumber segment. S32: Based on the dual performance index, increase or suppress it by adding a weight factor to form a multi-objective optimization criterion expressed by a fitness function. The dual performance index includes the lobe characteristics of the virtual array response and the difference characteristics between the virtual array response and the field source. The fitness function is:

3. The surface array formation optimization design method based on a spatial virtual field source according to claim 2, wherein 4. According to any one of claims 1-3, a surface array pattern optimization design method based on a spatial virtual field source, characterized in that: , Wherein: is the weighting factor, is the main lobe peak value, is the side lobe peak value, is the resolution of different wavenumber bands, is the measurement error of the full wavenumber band. A1: Input the coordinates of the elements of the basic array pattern as the initial values, and randomly generate an initial array pattern population according to the conditions. A2: Quantitatively evaluate the dual performance indexes of different array patterns under the multi-objective optimization criterion defined in S3 based on the spatial virtual wavenumber-frequency spectrum field source function constructed in S1 and the target response function established in S2. A3: Evaluate and screen the initial array pattern population according to the fitness function to form a better population, and then carry out cross and mutation iterative calculations. A4: Terminate the search when the maximum number of iterations or the threshold condition is reached to form the optimal array pattern configuration and its fitness function value. ​

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