Pulsating pressure wave number-frequency spectrum two-dimensional surface array data processing method

Abstract

The invention discloses a pulsating pressure wave number-frequency spectrum two-dimensional surface array data processing method, which is based on concepts such as a cross-spectrum matrix and a position difference vector, obtains a corresponding discrete area by defining a plurality of key sets related to a two-dimensional surface array and applying a Worronoi diagram method, and finally obtains the pulsating pressure wave number-frequency spectrum two-dimensional surface array data. And a two-dimensional wave number-frequency spectrum is obtained through a multiplication method. On one hand, the method can adapt to all types of two-dimensional surface array forms, the problem of applicability limitation of a traditional method is thoroughly solved, meanwhile, an analysis result directly corresponds to a TBL pulse pressure wave number-frequency spectrum, and effective measurement of real physical quantities is achieved; and on the other hand, by introducing a parallel computing architecture, the data computing time consumption can be remarkably shortened, the processing efficiency is greatly improved, the universality and high efficiency of two-dimensional pulsating pressure wave number-frequency spectrum data processing are considered, and a better support is provided for engineering landing of related technologies.

Description

Technical Field

[0001] This invention relates to the fields of wind tunnels, water tunnels / tanks, flight tests, and underwater vehicle experiments, specifically to a method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum. Background Technology

[0002] Turbulent boundary layer wall pulsation pressure (TBL pulsation pressure) is induced by vortex structures generated in a fully developed boundary layer near a solid plane or wall. TBL pulsation pressure is not only a key acoustic noise source but can also excite flow-induced vibrations and structural fatigue, leading to indirect noise generation. The wavenumber-frequency spectrum (also known as the wave vector-frequency spectrum) is an important physical quantity characterizing the spatiotemporal properties of TBL pulsation pressure. Surface array technology, as a key experimental technique for conducting TBL pulsation pressure wavenumber-frequency spectrum tests, is widely applicable to various experimental fluid media such as air and water, and can be applied in scenarios such as wind tunnels, water tunnels / tanks, flight tests, and underwater vehicle experiments. Two-dimensional surface arrays can experimentally obtain two-dimensional TBL pulsation pressure wavenumber-frequency spectra containing both flow-direction and spanwise spatial dimensions.

[0003] Currently, there are two main methods for processing two-dimensional surface array data: wavenumber domain beamforming and direct measurement using rotating arrays. Wavenumber domain beamforming originates from frequency domain beamforming technology in the field of far-field acoustic array source localization. Introducing this algorithm into the wavenumber domain can significantly enhance the signal, resulting in more ideal test results. However, while the calculation results of this method are positively correlated with the TBL pulse pressure wavenumber-frequency spectrum, they do not directly correspond to this physical quantity. Direct measurement using rotating arrays obtains an equivalent two-dimensional array by rotating a one-dimensional linear array angle by angle, and calculates the two-dimensional TBL pulse pressure wavenumber-frequency spectrum based on polar coordinates. However, this method does not consider the time asynchrony of the linear array rotation and retesting, and the discretization process in the integration domain is not perfect. Furthermore, current data processing methods do not employ parallel computing algorithm architectures, leading to an exponential increase in computation time as the number of sensor channels increases significantly. Therefore, a dedicated data processing method for the two-dimensional surface array pulse pressure wavenumber-frequency spectrum suitable for parallel computing is still lacking. Summary of the Invention

[0004] This invention addresses the shortcomings of existing TBL pulse pressure two-dimensional surface array data processing methods, such as the lack of direct correspondence between the data and the actual wavenumber-frequency spectrum physical quantities, failure to consider the time asynchrony of linear array rotation retesting, imperfect integral domain discretization process, and weak applicability to parallel computing. It proposes a novel two-dimensional surface array data processing method for pulse pressure wavenumber-frequency spectrum.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum includes the following steps: Step 1: Conduct pulsating pressure experiments on a two-dimensional surface array and complete the calculation of the relevant cross-spectral matrix. A two-dimensional surface array of pulsating pressure sensors is mounted on the model surface. This two-dimensional surface array has a total of M A sensor array of elements was used. Experimental tests were conducted to acquire the pulsating pressure signal detected by each element. , This indicates the coordinate position of a two-dimensional array element in a surface array. Represents the direction of flow coordinates. Represents the direction coordinates, Sampling time.

[0006] The combination of any two array elements is defined as an element pair. The time-space correlation function of the TBL pulse compression of the element pair is calculated as follows: (1) In the formula, This represents the position difference vector between pairs of elements in a surface array. Represents the difference in flow direction location. The difference in the representative exhibition direction; The time delay of the signals measured by the two sensor array elements is given. To represent conjugate complex numbers, This indicates the calculation of the ensemble average.

[0007] Calculate the cross-power spectral density function (referred to as "cross-spectrum") of array element pairs, which is equivalent to performing a time-space correlation function using a time-Fourier transform: (2) Here we use a , b , c , d As array element labels, i.e. a , b , c , d =1, 2, 3… M -1、 M The second element in the two-dimensional array a The, the b The cross spectrum of the array elements composed of each array element is denoted as _ ... or When the position difference vector of the array element pair At that time, that is a = b The cross spectrum is actually the self-power spectral density (self-spectrum) of a single array element, denoted as... or The cross-spectrum matrix (CSM) of this two-dimensional surface array is then expressed as: (3) Parallel computing can be used here to obtain each element of the cross-spectrum matrix, thereby accelerating the computation time.

[0008] Step 2: Calculate the position difference vector of each pair of elements in the two-dimensional surface array, and determine the key set related to the two-dimensional array. Specifically, this includes the set of element pair labels, the set of repeated position difference vector labels, the set of same vector position difference vector labels, the set of non-repeating same vector position difference vector labels, the set of non-equal position difference vector labels, and the set of non-repeating position difference vector labels.

[0009] First, calculate the position difference vector of each element pair in the surface array. ,in: (4) Assemble the labels of all array element pairs into a set: (5) This is called the array element label set.

[0010] Second, determine Neutron set , This is called the set of repeated position difference vector labels. The set of element pair labels containing all element pairs whose position difference vectors are not unique: (6) Third, decomposition For several subsets This subset is collectively referred to as the set of vector labels with the same vector position difference. Array element labels with equal positional difference vectors are divided into several groups based on vector equality, and the corresponding labels form subsets. ,Right now: (7) In the formula, Represents a set The There are subsets, totaling G This subset , indicating the first The values ​​of the position difference vectors are equal.

[0011] Fourth, determine the new set. This is called the set of vector labels for the position difference of the same vector without repetition. From set All subsets Choose any element from the middle to form: (8) In the formula, Represents a set Any element in it.

[0012] Fifth, determine the set of vector labels for vectors with no equidistant positional differences. : (9) Sixth, determine the set of non-repeating position difference vector labels. : (10) Step 3: Based on the set of vector labels with non-repeating position differences The position difference vector corresponding to each element is used to determine the two-dimensional point set, and then the Volonoi diagram of each position difference vector of the two-dimensional surface array is calculated to obtain the corresponding discrete area.

[0013] First, calculate the set of vector labels with no repeating position differences. The position difference vectors corresponding to each element in the set form a two-dimensional point set. When calculating the Voronoi Diagram, the point set needs to be redefined, converting its two-dimensional labels into one-dimensional linear labels. This point set represents the positions of the non-repeating position difference vectors formed by the pairs of elements of the two-dimensional surface array in the vector space.

[0014] Second, the point set Each point is used to construct perpendicular bisectors with the other points, thus trimming the polygon. Taking any point as an example, the equation of the perpendicular bisector is constructed between it and every other point. The area of ​​the trimmed polygon is then determined based on the area of ​​the trimmed polygon, retaining the remaining polygon. This process is repeated iteratively to calculate the perpendicular bisectors between each point and all other points, and the planar region is divided according to the area of ​​the trimmed polygon. This results in several vertices of a Volonoi polygon centered at a single point. Finally, the area of ​​a single Volonoi polygon is calculated using the polygon area formula. .

[0015] Third, iteratively calculate the point set. The Volonoi polygons of each point in the graph are used to form the final Volonoi map, and the area of ​​each polygon is obtained. The corresponding position difference vectors will correspond to the same position difference vector. To obtain the position difference vector for each position The corresponding discrete area of ​​the integration field The loop has a total length of M. 4 This loop can be completed using parallel computing.

[0016] Step 4: Based on the assumption of time stationary and spatially uniformity, multiply and sum the discrete area from Step 3 with the average result of the spatial Fourier transform of the measurement point spectrum of the same vector position difference vector.

[0017] Calculate the mean of the Fourier transform of the spectral space of the points corresponding to the position difference vectors of each group of vectors, multiply it by the corresponding discrete area, and sum the results. ): (11) In the formula, For set subset of The number of elements; For each position difference vector The corresponding discrete area of ​​the Volonoi polygon.

[0018] Step 5: Calculate the discrete space Fourier transform of the spectrum of the measurement points corresponding to the remaining non-equivalent position difference vectors, multiply it by the discrete area corresponding to the vector in Step 3, and sum it with the result of Step 4 above to obtain the final two-dimensional wavenumber-frequency spectrum. Perform a discrete-space Fourier transform summation on the cross spectra corresponding to vectors with no equidistant position differences, and add the summation to the result from step four to obtain the two-dimensional wavenumber-frequency spectrum: (12) Parallel computation can be used when performing discrete space Fourier transform to accelerate computation time.

[0019] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention solves the problem of adapting to all types of two-dimensional surface arrays, completely overcoming the applicability limitations of traditional methods. At the same time, the analysis results directly correspond to the TBL pulse pressure wavenumber-frequency spectrum, realizing the effective measurement of real physical quantities. On the other hand, by introducing a parallel computing architecture, the data calculation time can be significantly shortened, and the processing efficiency can be greatly improved. It takes into account both the universality and efficiency of two-dimensional pulse pressure wavenumber-frequency spectrum data processing, and provides better support for the engineering implementation of related technologies. Attached Figure Description

[0020] The present invention will be described by way of example and with reference to the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating the process of this solution; Figure 2 This is a schematic diagram of the element distribution of a two-dimensional fancy surface array; Figure 3 Volonoitu; Figure 4 Enlarged view of the center of the Volonoj map; Figure 5The TBL pulse pressure wavenumber-frequency spectrum measurement results were obtained at an angular frequency of 7 k rad·Hz. Detailed Implementation

[0021] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0022] Any feature disclosed in this specification (including any appended claims, abstract, and drawings) may be replaced by other equivalent or similar features for a similar purpose, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0023] This embodiment, in conjunction with the accompanying drawings, uses a 1.8m × 1.4m two-dimensional surface array wind tunnel experiment as an example to illustrate the specific implementation of the present invention.

[0024] The specific process of this embodiment is as follows: Figure 1 As shown: Step 1: Conduct a two-dimensional surface array pulsating pressure experiment and complete the relevant cross-spectral matrix calculation.

[0025] Specifically, the experiment was conducted in a closed section of a 1.8m × 1.4m wind tunnel. The experimental model adopted a flat plate structure, with a two-dimensional surface array arranged in the central area. The entire flat plate model was supported by two support plates and erected at the center of the closed section of the wind tunnel. During the experiment, the wind speed in the wind tunnel was set to 50 m / s. The two-dimensional surface array with 76 elements used in the experiment was as follows: Figure 2 As shown. Using a data acquisition system, the sampling frequency was set to 51.2 kHz and the sampling duration to 30 s. The pulsating pressure signal data measured by each array element was obtained. The time-space correlation function of each array element pair was calculated according to equation (1), and the cross-spectral matrix was calculated by performing a time Fourier transform according to equation (2). During the calculation process, a Hanning window was added to the data, and the window length was set to 1024, with an overlap rate of 50%. Parallel computing can be used here to improve the calculation efficiency.

[0026] Step 2: Calculate the position difference vector of each pair of elements in the two-dimensional surface array, and determine the key set related to the two-dimensional array. Specifically, this includes the set of element pair labels, the set of repeated position difference vector labels, the set of same vector position difference vector labels, the set of non-repeating same vector position difference vector labels, the set of non-equal position difference vector labels, and the set of non-repeating position difference vector labels.

[0027] In a specific example, the position difference vector of each element pair is first calculated, and the set of element pair labels is obtained, totaling 76. 2 These elements are not shown here.

[0028] Secondly, determine the set of labels for the repeating position difference vectors; by Figure 3 The set of repeating position difference vector labels that can be obtained from the surface array configuration shown has a total of 84 elements. This set is as follows:

[0029] Third, determine the subset of the set of repeated position difference vector labels, that is, the set of identical vector position difference vector labels and the total number of its subsets. G and the number of elements in each subset Q g ; Depend on Figure 3 The total number of subsets of the set of repeating position difference vector labels that can be obtained from the surface array configuration shown is [number missing]. G =5, of which: , , , , ;and subset , , and Each subset contains 2 elements. Number of elements Q 5 =76.

[0030] Fourth, determine the set of non-repeating identical vector position difference vector labels; the set of non-repeating identical vector position difference vector labels, formed by randomly selecting one element from all subsets of the set of repeated position difference vector labels, is:

[0031] Fifth, for sets and Taking the difference between the sets yields a set of vector labels without equal positional differences; the resulting set of vector labels without equal positional differences contains 76. 2 -84 elements, which are not shown here.

[0032] Finally, for the set and Take the union to obtain the set of unique position difference vector labels. The final set contains a total of 76 elements. 2 -79.

[0033] Step 3: Based on the set of vector labels with non-repeating position differences The position difference vector corresponding to each element in the vector determines the two-dimensional point set. Then, the Volonoi diagram of the difference vector at each position of the two-dimensional surface array is calculated to obtain the corresponding discrete area.

[0034] Specifically, in this example, firstly, the position difference vector corresponding to each element in the set of unique position difference vector labels is calculated, and the point set is redefined. Secondly, perpendicular bisectors are constructed between all points in the point set and the remaining points. Then, the polygons are clipped to obtain the set of Volonoi polygon vertices centered at any point in the point set. Given the polygon area calculation formula, the discrete area of ​​the integration domain corresponding to that point is obtained. Finally, the discrete area of ​​the integration domain corresponding to all points in the point set is calculated iteratively. Equal position difference vectors correspond to the same discrete area, and the discrete area corresponding to each position difference vector is obtained. The Volonoi polygons of each point are then combined to obtain the final Volonoi map, as shown in the following figure. Figure 3 As shown, to further clarify the location of the center of Volonojtu, Figure 4 Given Figure 3 A magnified view of the central area. Note that complex calculations here can be performed in parallel to speed up loop computation time.

[0035] Step 4: Based on the assumption of time stationarity and spatial uniformity, multiply the discrete area from Step 3 by the average result of the spatial Fourier transform of the measurement point spectrum of the same vector position difference vector.

[0036] Specifically, according to equation (11), the mean of the cross-spectral space Fourier transform of each group of same vector position difference vectors is calculated, and the result of multiplying the mean of the corresponding discrete area with the result is accumulated.

[0037] Step 5: Calculate the discrete space Fourier transform result of the spectrum of the measurement point corresponding to the remaining non-equivalent position difference vectors, multiply it by the discrete area of ​​the corresponding step 3, and sum it with the result of step 4 above to obtain the final two-dimensional wavenumber-frequency spectrum.

[0038] Specifically, according to equation (12), the cross spectrum corresponding to the vectors with no equidistant position difference is summed by discrete-space Fourier transform, and then added to the result of step four to obtain the two-dimensional wavenumber-frequency spectrum, as shown in the figure. Figure 5 As shown, since the two-dimensional wavenumber-frequency spectrum is four-dimensional data and cannot be plotted, a slice is displayed at an angular frequency of 7 k rad·Hz. Steps four and five can be completed in parallel.

[0039] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

[0040] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum, characterized in that... Includes the following steps: S1: The relevant cross-spectral matrix was calculated by conducting a two-dimensional surface array pulsating pressure test. S2: Calculate the position difference vector of each element pair in the two-dimensional surface array to determine the key set related to the two-dimensional array; S3: Based on the position difference vector corresponding to each element in the set of non-repeating position difference vector labels, determine the two-dimensional point set, and then calculate the Volonoi diagram of each position difference vector of the two-dimensional surface array to obtain the corresponding discrete area. S4: Based on the assumption of time stationary and spatially uniformity, multiply and sum the discrete areas in S3 with the average result of the spatial Fourier transform of the measurement points of the same vector position difference vector. S5: Calculate the discrete space Fourier transform result of the spectrum of the measurement point corresponding to the remaining equal position difference vectors and multiply it by the discrete area in S3, and sum it with the result in S4 to obtain the final two-dimensional wavenumber-frequency spectrum.

2. The method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum according to claim 1, characterized in that... The key set includes: S21: Calculate the position difference vector of each element pair in the surface array, and form an element pair label set by combining the labels of all element pairs. ; S22: Determine a subset of the array element pair label set that is a set of repeated position difference vector labels, which includes the set of array element pair labels where the position difference vectors of all array element pairs are not unique. ; S23: Decompose the set of repeated position difference vector labels into subsets of several sets of identical position difference vector labels. ; S24: Determine the new set as a set of identical vector position difference vector labels without repetition, composed of any element taken from all subsets of the set of identical vector position difference vector labels. ; S25: Determine the set of vector labels without equal positional differences ; S26: Determine that the set of non-repeating position difference vector labels is the union of the set of non-equal position difference vector labels and the set of non-repeating same vector position difference vector labels; in: a , b , c , d As array element labels , The position difference vector between array element pairs. Let be the natural number representing the subset number, and there are a total of G Subset , Indicates the first The values ​​of equal position difference vectors, Represents a set Any element in it.

3. The method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum according to claim 1, characterized in that... The calculation of the discrete area includes the following steps: S31: Calculate the position difference vector corresponding to each element in the set of non-repeating position difference vector labels, construct a two-dimensional point set from these position difference vectors, and redefine the two-dimensional point set when calculating the Volonoi diagram; S32: Construct perpendicular bisectors between all points in the two-dimensional point set and the remaining points, and trim the polygon. Iteratively calculate the perpendicular bisector between any point and all other points, and divide the planar region according to the reference value. Finally, obtain the set of vertices of the Volonoi polygon centered at the modified point, and calculate the area corresponding to a single Volonoi polygon. S33: Iteratively calculate the Volonoi polygon for each point in the two-dimensional point set to form the final Volonoi map, and obtain the position difference vector corresponding to the area of ​​each Volonoi polygon. Then, assign equal position difference vectors to the area of ​​the same Volonoi polygon to obtain the discrete area of ​​the integral domain corresponding to each position difference vector.

4. The method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum according to claim 2, characterized in that... Calculate the mean of the Fourier transform of the spectral space of the points corresponding to the position difference vectors of the same vector for each group, multiply it by the corresponding discrete area, and sum the results. ， in: A subset of the set of vector labels for repeated position differences The number of elements, The position difference vector of the element pairs in the cross-spectral matrix mutual spectrum, For the flow wave number, For spanwise wavenumber, The distance between array elements along the flow direction. Let be the distance between array element pairs along the spanwise direction. For each position difference vector The corresponding discrete area of ​​the Volonoi polygon. a , b The array element number.

5. The method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum according to claim 4, characterized in that... The two-dimensional wavenumber-frequency spectrum is, ， in: For a set of vector labels with no equal positional difference, ω is the angular frequency.

6. The method for processing two-dimensional surface array data of pulsating pressure wavenumber-frequency spectrum according to claim 1, characterized in that... The calculations in steps S1, S3, and S4 can be performed in parallel.

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