CN116976229A - Array design method for turbulence boundary layer pulsating pressure two-dimensional measurement array - Google Patents
Array design method for turbulence boundary layer pulsating pressure two-dimensional measurement array Download PDFInfo
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- 230000015572 biosynthetic process Effects 0.000 abstract 1
- 239000004973 liquid crystal related substance Substances 0.000 description 8
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- 238000009530 blood pressure measurement Methods 0.000 description 4
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
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- G06F30/20—Design optimisation, verification or simulation
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- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
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Abstract
The invention discloses a two-dimensional measurement array type design method for turbulent boundary layer pulsating pressure, which is based on a particle swarm optimization algorithm, and can design and complete optimized spiral array type distribution according to the measurement requirement of a wave number domain wave number formation measurement technology on the turbulent boundary layer pulsating pressure, thereby greatly improving the measurement capacity of a turbulent boundary layer pulsating pressure test.
Description
Technical Field
The invention relates to the field of wind tunnel tests, in particular to a design method of a turbulence boundary layer pulsating pressure two-dimensional measurement array.
Background
The turbulent boundary layer pulsating pressure is a very focused problem in the field of fluid mechanics, on one hand, noise can be directly radiated outwards, and on the other hand, wall surface structure flow excitation vibration can be caused to form a secondary sound source, so that the turbulent boundary layer pulsating pressure is highly focused in the field of engineering practice of airplanes, high-speed rails, submarines and the like. Wind tunnel model test is one of the most main means for obtaining turbulent boundary layer pulsation pressure characteristics, and the current main methods comprise a single-point method, a one-dimensional line array method and a two-dimensional array method. The single-point method is the main stream method at present, namely, a single pulse pressure sensor which is common in the market is adopted, and the pulse pressure measurement is carried out in a wind tunnel by being installed on the surface of a model. However, the single-point method has the problems that a plurality of sensors are required to be installed on the surface of a model, the distance is large, the number of measuring points is small, and time-space coherence coefficient and wave number-frequency spectrum analysis are not easy to realize. The one-dimensional linear array method adopts a plurality of continuous MEMS sensors to carry out high-density linear integration, thereby realizing the high-precision measurement of the turbulent boundary layer pulsating pressure on the surface of the wind tunnel model. Compared with a single-point method, the method can realize flow direction wave number-frequency spectrum analysis and has greater advantages. However, since the model surface pulsating pressure has a spatial two-dimensional distribution characteristic, a one-dimensional line array cannot realize two-dimensional measurement, and thus has a limitation. In contrast, the two-dimensional array method can overcome the problem and realize the measurement of the two-dimensional spatial distribution of the surface of the model.
The two-dimensional array method is used as an optimal scheme for measuring the pulsating pressure of the turbulent boundary layer, and one of key technologies is array design. The traditional conventional array, namely M rows and N columns of arrays, can meet the measurement requirement, but aiming at wave number-frequency spectrum measurement, on the premise of a certain number of measurement array points, the conventional array transverse, longitudinal distances DeltaX and DeltaY are required to be designed according to the measurement requirements of different wave number regions, and the applicability of the whole wave number range is weak. In order to improve the applicability to the whole wave number segment, a wave number domain beam forming technology is developed, the technology uses a time domain or frequency domain beam forming sound source positioning algorithm used by the research of the acoustic field, and the algorithm is expanded to pulse pressure wave number domain measurement and analysis. The wave number domain beam forming technique has stronger applicability to the full wave number range of the systolic pressure measurement under the condition of equally measuring the number of the array points.
However, there is still a lack of an array design method specifically for wave number domain beamforming, so that the wave number domain beamforming technology cannot exert the maximum performance, and has limitations.
Disclosure of Invention
The invention aims to specifically design a two-dimensional measurement array design method facing wave number domain wave beam forming measurement technology aiming at the measurement requirement of turbulent boundary layer pulsation pressure. The method is based on a particle swarm optimization algorithm, can form measurement technology measurement requirements aiming at wave number domain wave numbers, and designs and completes optimized spiral array distribution.
The scheme adopted is a turbulence boundary layer pulsating pressure two-dimensional measurement array design method, which comprises the following steps:
step one: determining an fitness function;
step two: constructing an optimization target for a two-dimensional pulsating pressure array;
step three: initializing a particle swarm comprises setting particle swarm population parameters and generating an initial population;
step four: calculating the fitness of each particle;
step five: updating the individual history optimal position and the group history optimal position according to the fitness, updating the particle position speed, carrying out boundary processing on the particle position speed, judging constraint conditions, and repeating the second step;
step six: and (3) circularly repeating the step four and the step five until the maximum iteration times or the global optimal position meets the minimum limit.
In the above technical solution, in step one, a functional form of a two-dimensional array sensor layout is obtained by a bessel function,
.wherein: m, N is a finite integer, m and n are natural numbers representing the bit sequence of the array element, < >>Is a zero-order bessel function,maximum wave number>Is the minimum wave number>Is the array element spacing.
In the technical scheme, the multi-arm spiral array is used as an optimization object, and the two-dimensional pulse pressure sensor array element optimal layout is realized when the fitness function takes the minimum value after the boundary condition establishment is completed.
In the above technical solution, the outer diameter D of the spiral array is determined by the minimum wave number of the measured target signal,，
the maximum wave number of the measured target signal is determined by the frequency of the flow field signalAnd the propagation velocity v is determined,。
in the above technical solution, when the number of microphones on each arm is the same and the arrangement positions are the same, the optimal array layout expression is:
wherein: m is the total number of microphones in the array, +.>For the number of arms of the array, +.>For the number of microphones on each arm, < > for each arm>For the smallest inner diameter of the array, +.>For the maximum inner diameter of the array,is a mathematical special symbology representing the presence,/->Minimum particle positionBoundary (S)>Is the maximum boundary of the particle position.
In the above technical solution, the particle velocity and coordinate update expression in the particle swarm is:
wherein: />For a set maximum number of iterations, +.>For particle velocity after the t-th iteration, < >>For the particle coordinate position after the t-th iteration, < >>The inertia factor for the t-th iteration, d is the dimension,>is the local optimum of the nth particle, < >>Is the global optimum, < >>、/>For learning factors->Are random numbers between (0, 1), respectively>Is the maximum inertia factor, +.>Is the minimum inertia factor.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
the fitness function of the two-dimensional pulsation pressure measurement array matrix design is provided, boundary conditions are defined, an optimization objective function is established, and a theoretical basis is provided for the two-dimensional pulsation pressure measurement array matrix design. Meanwhile, the particle swarm optimization algorithm is utilized to solve the optimization objective function, so that the final array element coordinates are obtained, the number of array elements can be effectively reduced, the processing difficulty is reduced, and the wave number domain-wave beam forming algorithm can be provided for turbulent boundary layer measurement.
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The invention will now be described by way of example and with reference to the accompanying drawings in which:
FIG. 1 is a schematic flow chart of a design method.
Description of the embodiments
All of the features disclosed in this specification, or all of the steps in a method or process disclosed, may be combined in any combination, except for mutually exclusive features and/or steps.
Any feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise. That is, each feature is one example only of a generic series of equivalent or similar features, unless expressly stated otherwise.
The method of the embodiment is shown in fig. 1, and the specific flow is as follows:
step one: an fitness function is determined.
Assuming that the incident plane wave received by the sensor has an amplitude of 1, the amplitude does not decay with propagation distance, and time is not considered, the received pulsating pressure signal can be written as:
wherein the method comprises the steps ofRespectively isx、yVector wave number of directionx，y) Is the coordinates of the sensor. The delay and sum calculation is carried out on the signals received by each sensor by a beam forming algorithm, and the following steps are obtained:
wherein the method comprises the steps ofAs vector wavenumbers of signals, the above formula can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,Was a smooth function of pore diameter
An ideal two-dimensional array of pulsed pressure sensors should have the aperture smoothing function satisfy the following relationship:
with a limited number of sensors, it can be seen from the equation that N is a limited integer and that the equation cannot be satisfied. So whenMaximum->The value represents the side lobe size, the two-dimensional pulse pressure sensor array is designed to be as small as possible, and the value can be used as an optimization target in optimization calculation to obtain the minimum value, so that the optimal two-dimensional pulse pressure sensor array distribution is obtained. Taking the sensor position as an unknown number, establishing the following equation:
wherein, the liquid crystal display device comprises a liquid crystal display device,and->Depending on the design requirements of the two-dimensional array of pulsed pressure sensors, < >>Depending on the diameter of the sensor array, +.>Depending on the maximum frequency of array identification. In the calculation, since the minimum frequency (maximum wavelength) of the signal which can be measured by the array is determined by the array aperture, the wave number is inversely proportional to the wavelength, the minimum wave number is inversely proportional to the array aperture, and the relation between the wave number and the frequency shows that the higher the frequency is, the larger the wave number is, so the ratio of the wave number to the wave number can be increased>And->The values are as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,Din order to be a sensor array diameter,f max v is the wave propagation velocity, which is the maximum frequency measured. The combination type can be rewritten as
Wherein the method comprises the steps of
Using the bessel function, we can find:
wherein, the liquid crystal display device comprises a liquid crystal display device,J 0 as a zero-order Bessel function, can be used as a functional form of sensor layout optimization, and corresponds to the minimum value when the sensor layout optimization is achievedx n A kind of electronic device with high-pressure air-conditioning systemy n The required sensor position coordinates are obtained, and the coordinate values are solved through the subsequent steps.
Step two: and constructing an optimization target for the two-dimensional pulsating pressure array type.
The embodiment is mainly designed and optimized for the two-dimensional pulsation pressure array type of the multi-arm spiral type, and the resolution can be guaranteed to be in a good level because the multi-arm spiral type is a periodic array, so that only the dynamic range is optimized below. The following optimization is to take a multi-arm spiral array as an optimization object, the minimum inner diameter and the maximum outer diameter of the array are regulated during optimization, the number of microphones on each arm is the same, the arrangement positions are the same, the optimal array arrangement mode is searched under the condition of the same number of microphones, and the optimal design can be expressed as the following formula.
Where M is the total number of microphones in the array,lfor the number of arms of the array, a is the number of microphones on each arm,r min and (3) withr max The minimum and maximum inner diameters of the array, respectively.
And after the boundary condition is established, obtaining the optimal layout of the two-dimensional impulse pressure sensor array elements when the fitness function in the first step takes the minimum value.
Step three: initializing a population of particles includes setting population parameters of the population of particles and generating an initial population
Setting the number N of population, the space dimension D and the maximum iteration timesNumber, position boundary, velocity boundary, inertial weight w, self-learning factor c 1 Group learning factor c 2 . Generating an initial population, randomly generating an initial population position, randomly generating a population initial position, initializing an individual history optimal position and an individual history optimal fitness, and finally initializing a population history optimal position and a population history optimal fitness.
The particle group is represented by X, whereinRepresenting the nth particle, each representing an array pattern of a microphone array, which successively approximates the optimal array pattern by an iterative algorithm.
Step four: the fitness of each particle is calculated. Bringing the initial state of the particles generated in the third step into fitness function calculation, and updating the individual historical optimal position (p nd ) And the group history best position (g) d ）。
P is the optimum of the individual, represents the optimum value of each particle in the iterative process, and represents the optimum of the population, g represents that all the particle coordinates are the same as the optimum particle coordinates in the population.
Step five: updating p according to fitness nd 、g d The particle position velocity is updated. And D, updating the speed and the position according to the updated pbest and gbest of the step two, carrying out boundary processing on the updated pbest and gbest, judging constraint conditions, and repeating the step two.
The particle velocity and coordinate update formula in the particle swarm is as follows:
wherein the method comprises the steps ofT is the set maximum number of iterations, < ->And->The particle velocity and the particle coordinate position after the t-th iteration.
Step six: and obtaining final matrix coordinates.
And (3) through continuous iteration, repeating the step four and the step five in a circulating way, if the maximum iteration number does not reach the convergence condition, continuing to iterate by taking the result of the last iteration as an initial value until the maximum iteration number is reached or the global optimal position meets the minimum limit, and obtaining the final matrix type each point coordinate.
The invention is not limited to the specific embodiments described above. The invention extends to any novel one, or any novel combination, of the features disclosed in this specification, as well as to any novel one, or any novel combination, of the steps of the method or process disclosed.
Claims (4)
1. A turbulence boundary layer pulsating pressure two-dimensional measurement array design method is characterized by comprising the following steps:
step one: determining an fitness function;
step two: constructing an optimization target for a two-dimensional pulsating pressure array;
step three: initializing a particle swarm comprises setting particle swarm population parameters and generating an initial population;
step four: calculating the fitness of each particle;
step five: updating the individual history optimal position and the group history optimal position according to the fitness, updating the particle position speed,
wherein: />For a set maximum number of iterations, +.>For particle velocity after the t-th iteration, < >>For the particle coordinate position after the t-th iteration, < >>The inertia factor for the t-th iteration, d is the dimension,>is the local optimum of the nth particle, < >>Is the global optimum, < >>、/>For learning factors->Are random numbers between (0, 1), respectively>As a result of the maximum inertia factor,is the minimum inertia factor;
and the boundary processing is carried out on the same,
wherein: m is the total number of microphones in the array, +.>For the number of arms of the array, +.>For the number of microphones on each arm, < > for each arm>For the smallest inner diameter of the array, +.>For the maximum inner diameter of the array, +.>Is a mathematical special symbology representing the presence,/->Is the minimum boundary of particle position->Is the maximum boundary of the particle position;
judging constraint conditions, if the maximum iteration number does not reach a convergence condition, continuing iteration by taking the last iteration result as an initial value, and repeating the second step;
step six: and (3) circularly repeating the step four and the step five until the maximum iteration times or the global optimal position meets the minimum limit.
2. The method of claim 1, wherein in the first step, a function form of a two-dimensional array sensor layout is obtained by Bessel function,
wherein: m, N is a finite integer, m and n are natural number representation arraysThe bit sequence of the element,/->Is a zero order Bessel function, +.>Maximum wave number>Is the minimum wave number>Is the array element spacing.
3. The method for designing the array of the two-dimensional measurement array of the pulsating pressure of the turbulent boundary layer according to claim 2, wherein the multi-arm spiral array is used as an optimization object, and the two-dimensional pulsating pressure sensor array elements are optimally arranged when the fitness function takes the minimum value after the completion of establishment when the number of microphones on each arm is the same and the arrangement positions are the same.
4. A turbulent boundary layer pulsating pressure two-dimensional measurement array matrix design method according to claim 3, characterized in that:
the outer diameter D of the spiral array is determined by the minimum wave number of the measured target signal,，
the maximum wave number of the measured target signal is determined by the frequency of the flow field signalAnd the propagation velocity v is determined,。
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