Sound field reconstruction and ghost suppression method based on PSO-MVDR
Technical Field
The invention relates to a sound field reconstruction and ghost suppression method, which can effectively suppress interference caused by grating lobes and side lobes in the sound field reconstruction process and improve the precision of the sound field reconstruction under the conditions of limited space and limited number of microphones.
Background
Beamforming (Beamforming) is an important task of array signal processing, and its main functions include: forming the directivity of the array receiving system; performing spatial filtering, suppressing spatial interference and environmental noise, and improving the signal-to-noise ratio; estimating the arrival direction of the signal, creating conditions for signal source positioning and the like. Through the beam forming processing, the sound source of the sound field can be reconstructed and positioned.
The sound source identification process is to disperse the reconstructed sound field space into a series of reconstruction points, calculate the reconstructed sound pressure value of the reconstruction points by using a beam forming algorithm, draw a sound pressure cloud picture and judge the sound source position according to the position of a hot point in the picture. The sound source identification effect of the microphone array and the structural shape, the number of array elements, a processing algorithm and other factors are determined. An appropriate microphone array can inhibit grating lobes and side lobes, improve the identification precision of a sound source and improve the reconstruction quality of a sound field. In the research of sound field reconstruction based on microphone arrays, predecessors built some arrays with equal spacing such as grid arrays, cross arrays, circular arrays and the like to perform sound field actual measurement and analysis. However, the equidistant array has inherent defects that: in order to ensure a smaller main lobe width and improve the sound field reconstruction resolution, a larger array size needs to be maintained, so that the distance between adjacent array elements is increased, grating lobes occur, and the sound field reconstruction capability of the array is greatly weakened. In response to the defect of equal-pitch array reconstruction capability, some researchers have proposed a method for sound field reconstruction using an unequal-pitch array. The method is usually based on an equally spaced arrayAnd optimally designing the coordinate distribution of the array elements by using an optimization algorithm to obtain an optimized unequal space array. Unequal-spacing array capable of restraining grating lobes[8]The quality of sound field reconstruction can be improved to a certain extent. However, the larger side lobe amplitude in the array still interferes with the correct identification of the real sound source. Aiming at the problems, if the grating lobes can be inhibited through array optimization, an effective algorithm is applied to inhibit the generation of larger side lobes on the basis, an accurate sound field reconstruction cloud picture is obtained, and ghost inhibition is realized. The present invention has been made to achieve this object.
2012-09-19: CN102680071A, title: the inventors of the noise source identification method using vibration velocity measurement and local near-field acoustic holography: yandsen (R). The invention provides a noise source identification method adopting vibration velocity measurement and a local near-field acoustic holography method. And measuring the vibration velocity of normal mass points on the limited aperture measuring surface of the near field, performing zero filling expansion on the vibration velocity, and finally calculating to obtain the sound pressure and the vibration velocity of the normal mass points on the sound source surface. The method has the characteristics that the normal particle vibration speed is used as an input quantity to carry out sound field reconstruction, and compared with the traditional iteration local near-field acoustic holography method, the method is simple in calculation and high in efficiency.
2013-01-30: CN102901950A, title: in a method for recognizing three-dimensional coordinates of a sound source by a planar array, the inventors: is wonderful; plum spring dawn; jinjiang Ming; butane and Hao; mei is very tall and erect. The invention provides a method for identifying and positioning three-dimensional coordinates of a sound source by adopting a planar array. Based on a spherical wave sound field model, a beam forming method is adopted, the grid intersection points after three-dimensional space gridding are used as reconstruction points, plane sound field reconstruction with different distances is carried out, output values of beam formers with different reconstruction surfaces in the distance direction (namely the z direction) are compared, and the z-axis coordinate corresponding to the maximum output value is determined as the distance of a sound source. And finally, determining the coordinates of the sound source in the x axis and the y axis according to the maximum value point output by the beam former on the reconstruction surface corresponding to the sound source distance. The invention has the advantages that the three-dimensional coordinates of the sound source can be identified by using a two-dimensional planar array, the method can be directly applied to the existing planar array acoustic holography equipment which can only identify the two-dimensional coordinates of the sound source, and the effectiveness and the reliability of the scheme of the invention are verified by experiments.
The invention is different from the prior invention patents in that: the PSO particle swarm algorithm and the MVDR beam forming algorithm are combined, so that ghosting in sound field reconstruction can be restrained, and sound field reconstruction accuracy is improved. Specifically, the method comprises two steps: firstly, optimizing the layout of a cross equidistant microphone array by utilizing a PSO algorithm to obtain an unequal-pitch array with optimal array element position layout; on the basis, MVDR beam forming operation is carried out on the signals collected by each array element, and a sound field reconstruction cloud picture is obtained. The method combines the advantage that the unequal-spacing array suppressed grating lobe and the MVDR beam forming algorithm have stronger spatial filtering characteristics, and can realize ghost suppression in sound field reconstruction by using the microphone array with less array elements.
Disclosure of Invention
The invention aims to provide a method capable of effectively inhibiting ghost phenomenon in sound field reconstruction. The method can effectively avoid the existence of grating lobes and side lobes in the sound field reconstruction cloud picture under the conditions of limited space and limited number of microphones, improve the sound source identification precision of the sound field reconstruction and realize the suppression of ghost.
The technical scheme of the invention is as follows: a sound field reconstruction and ghost suppression method based on PSO-MVDR is characterized in that on the basis of optimizing an equidistant cross microphone array, an MVDR beam forming method is adopted to reconstruct the sound field to obtain a sound pressure cloud picture. The method specifically comprises the following steps:
step 1, searching the optimal combination of the moving distances of each array element by using a PSO particle swarm algorithm of an equidistant cross microphone array containing a certain array element to obtain an unequal-interval cross array without grating lobes and with the minimum side lobe influence. After obtaining an optimized non-equidistant cross by the PSO algorithm, the grating lobes of the array have been suppressed as much as possible and have degenerated into side lobes;
and 2, in order to further weaken the influence of the side lobe on the sound field reconstruction, the sound field is reconstructed by using an MVDR beam forming algorithm on the basis of obtaining the optimized unequal-spacing cross array, and the influence of the side lobe on the sound field reconstruction is reduced to the maximum extent by using the stronger spatial filtering characteristic of the MVDR algorithm, so that the accuracy of the sound field reconstruction is improved.
Preferably, the PSO particle swarm algorithm for the equidistant cross microphone array including a certain array element in step 1 includes: firstly, determining a final target of array optimization, namely searching an optimal combination of moving distances of each array element on the premise of keeping the shape of the cross array unchanged, so that the maximum side lobe level SL of sound field reconstruction under the condition of the unequal-spacing array is minimum; and then initializing the particle swarm, performing iterative operation for multiple times, wherein each iterative operation needs to update the global optimal solution of the particle swarm algorithm, and recording the maximum side lobe value of the global optimal solution. And when the maximum side lobe value SL tends to be converged, the algorithm iteration is ended to obtain a group of optimal array element position coordinate solutions.
Further, the particle swarm optimization algorithm based on the equidistant cross array in the step 1 specifically includes the following steps:
firstly, the size of the maximum side lobe level SL in the sound field reconstruction result is used as an optimization target, so that the optimization effect of the array is measured. Under the condition that the number of microphone array elements is limited, in order to ensure that the reconstructed sound field cloud picture has enough spatial resolution, a cross microphone array is selected for optimizing the position. To maintain the cross shape of the array, the array element positions at the cross intersections remain unchanged after optimization. From the above analysis, the goal of array optimization is: and finding the optimal combination of the moving distances of the array elements to minimize the maximum side lobe level SL of the sound field reconstruction under the condition of the unequal-spacing array.
Then, initialization and iterative operation of the algorithm are performed.
Is provided with Zi={zi1,zi2,…,zij,…zi13Is one possibilityArray element position coordinate solution, namely ZiIs a particle, wherein ZijIndicating the coordinate position of the jth array element in the ith particle. M particles form a group Z ═ Z1,Z2,…Zi…,ZmAnd initializing the particle swarm.
In the iterative operation, the velocity of each particle, denoted Vi={vi1,vi2,…vid…vi13In which v isidIndicating the velocity of the d-th array element coordinate in the i-th particle. In each iteration, each particle may update the velocity according to equation (1):
vid(t+1)=wvid(t)+η1rand()(pid-zid(t))+η2rand()(pgd-zid(t)) (1)
in the formula (1), vid(t) represents the speed of the ith particle's d array element coordinate in the t iteration, zid(t) represents the coordinate solution of the d array element in the ith particle after the t iteration, w is the inertial weight, η1、η2For the acceleration constant, rand () is a random number between 0 and 1. p is a radical ofidAnd pgdRespectively representing the optimal coordinate solution searched by each particle and the whole particle swarm after t iterations from the beginning of the search. On the basis of updating the particle velocity, the coordinate solution z of the d array element in the ith particle after the (t +1) th iteration can be obtainedid(t+1):
zid(t+1)=zid(t)+vid(t+1) (2)
And after the particles are updated, calculating the maximum side lobe level of each particle, comparing the maximum side lobe level with the maximum side lobe level of the existing optimal coordinate solution of each particle and the whole particle swarm so as to update the optimal coordinate solution of each particle and the whole particle swarm, and continuing the next iterative operation.
And finally, when the maximum side lobe level SL reaches the minimum and tends to converge, the iteration of the whole algorithm is finished, and a group of optimal array element position coordinate solutions can be obtained.
In summary, in order to reduce the grating lobe value in the sound field reconstruction and also reduce the increment of the original side lobe value, the PSO algorithm is used to optimize the position of the unequal-spacing cross array under the condition that the number of array elements is limited, and the maximum side lobe level SL is used as the optimization target to finally obtain the optimal arrangement scheme of the array, thereby laying a foundation for the suppression of ghost.
Further, as described in step 2, the MVDR beamforming method for the unequal-spacing cross array has the following principle:
in the beamforming algorithm, the acoustic pressure response p of the array is:
wherein w is a weight vectorx is the signal [ x ] of each channel1,x2,…xM]TWhereinm=1、2…M。
in the MVDR algorithm, the weighting vector w is of the form:
(4) wherein,for sound sources just from the reconstruction directionArray manifold vector at incidence, ρnIs the covariance matrix of the interfering signal. In practical application, due to the connectionCovariance matrix rho of interference signal in received datanIs not estimated, often by means of a cross-power spectral matrix R of the received dataxInstead of:
Rx=E{x(θ)xH(θ)} (5)
thus, formula (4) is converted to formula (6)
If the incident direction angle theta of the sound source is set to a constant value theta0And substituting the formula (6) into the formula (1), obtaining a sound field reconstruction response formula based on the MVDR algorithm:
acoustic pressure response to facilitate solving arraysWhere the computation is performed by MVDR beam output power. The MVDR beam output power spectrum is:
the binding formula (4), formula (7) or formula (9) can be obtained
Is obtained by the formula (9)
In the actual calculation process, a certain sound field plane is dispersed into a plurality of coordinate points, the sound field plane is called a reconstruction plane, and the reconstructed sound pressure at each coordinate point in the reconstruction area can be calculated according to the formula (10), so that the reconstructed sound pressure cloud image is obtained.
The advantages of the invention are as follows: (1) the optimized unequal-spacing array obtained through the PSO algorithm can inhibit not only grating lobes but also the increase of side lobe values, and is favorable for obtaining a more accurate sound source identification result; (2) compared with the conventional beam forming algorithm, the beam forming algorithm based on MVDR has stronger spatial filtering characteristics, can further improve the identification precision of a sound source, and ensures the reconstruction quality of the sound field.
Drawings
FIG. 1 is a flow chart of the PSO-MVDR algorithm;
FIG. 2 is a graph of the position distribution of an original equally spaced cross microphone array;
FIG. 3 is a graph of experimental parameter settings;
FIG. 4 is a coordinate diagram of an optimized unequal interval array element;
FIG. 5 is a diagram of an optimized array element position distribution;
FIG. 6 is a schematic view of a total anechoic laboratory test environment;
fig. 7 to 10 are sound pressure reconstruction cloud charts without using the PSO-MVDR algorithm and without using the PSO-MVDR algorithm under 2000hz, 4000hz, 6000hz, 8000hz, respectively.
Detailed Description
To verify the feasibility and correctness of the invention, experimental verification was performed in a total anechoic room. FIG. 1 is a flow chart of the PSO-MVDR algorithm; the flow chart according to fig. 1 is implemented as follows:
firstly, a sound field measurement and reconstruction device is built in a full-silencing room, fig. 6 is a schematic diagram of an experimental device, the distance between a plane where an equidistant cross microphone array is located and a sound source reconstruction surface is 1m, the side length of a square reconstruction surface is 1.4m, the selected sound source is a medium-high frequency volume sound source, the sound production frequency range is 200Hz to 10000Hz, and the sound production frequency range can be similar to a point sound source. The frequencies of the sounds used in the experiments were 2000Hz, 4000Hz, 6000Hz and 8000Hz pure tones. The microphone is a free-field microphone, is omnidirectional and has high sensitivity. The arranged microphone arrays are respectively 13 array elements of equidistant cross arrays and optimized unequal-spacing cross arrays. The acquisition equipment is a PXI-e bus-based data acquisition system, can realize multichannel high-speed synchronous data acquisition, and has the sampling frequency of 44100 Hz. The reconstitution experimental parameters are shown in figure 3.
The following details the implementation of the present invention for sound field reconstruction and ghost suppression.
At present, a PSO particle swarm algorithm is utilized to optimize the equidistant cross array of 13 array elements in FIG. 2. The initial array element interval is d is 0.1m, and the initial position coordinates of array elements from 1 to 13 are respectively as follows: (0.1,0),(0,0.1),(-0.1,0),(0, -0.1),(0.2,0),(0,0.2),(-0.2,0),(0, -0.2),(0.3,0),(0,0.3),(-0.3,0),(0,0).
To maintain the cross shape of the array, the position of array element number 13 at the cross intersection remains unchanged after optimization. After optimization processing, the array element coordinates from No. 1 to No. 12 are sequentially changed into: (0.1+Δd1,0),(0,0.1+Δd2),(-0.1+Δd3,0),(0,-0.1+Δd4),(0.2+Δd5,0),(0,0.2+Δd6),(-0.2+Δd7,0),(0,-0.2+Δd8),(0.3+Δd9,0),(0,0.3+Δd10),(-0.3+Δd11,0),(0,-0.3+Δd12). And (3) in combination with a PSO algorithm principle, taking the maximum side lobe value SL as a fitness function, and searching the optimal combination of the moving distances of each array element to ensure that the maximum side lobe level SL of the sound field reconstruction under the condition of unequal-spacing arrays is the maximumSmall, that is, equation (1) holds:
min{SL(Δd1,Δd2…Δd12)} (1)
in the formula (1), SL is the maximum side lobe level,Δd1,Δd2…Δd12is the distance that each array element moves,Δd1,Δd3,Δd5…Δd11is the horizontal displacement of array elements No. 1, 3 and 5 … 11,Δd2,Δd4,Δd6…Δd12vertical displacement of array element No. 2, 4, 6 … 12. Is provided with Zi={zi1,zi2,…,zij,…zi13Is a possible coordinate solution of array element position, called ZiIs a particle, wherein zijIndicating the coordinate position of the jth array element in the ith particle. 20 particles form a group Z ═ Z1,Z2,…Zi…,Zm}. The velocity of each particle, denoted Vi={vi1,vi2,…vid…vi13In which v isidIndicating the velocity of the d-th array element coordinate in the i-th particle. In each iteration, each particle may update the velocity according to equation (2):
vid(t+1)=wvid(t)+η1rand()(pid-zid(t))+η2rand()(pgd-zid(t)) (2)
in the formula (2), vid(t) represents the speed of the ith particle's d array element coordinate in the t iteration, zid(t) represents the coordinate solution of the d array element in the ith particle after the t iteration, w is the inertial weight, η1、η2For the acceleration constant, rand () is a random number between 0 and 1. p is a radical ofidAnd pgdRespectively representing the optimal coordinate solution searched by each particle and the whole particle swarm after t iterations from the beginning of the search. On the basis of the updated particle velocity, thenObtaining the coordinate solution z of the d array element in the ith particle after the (t +1) th iterationid(t+1):
zid(t+1)=zid(t)+vid(t+1) (3)
When the maximum side lobe value SL reaches the minimum value and tends to converge, the whole algorithm iteration is finished, a set of optimal array element position coordinate solutions shown in fig. 4 can be obtained, and finally, the optimal distribution result of each array element is shown in fig. 5.
Then, in order to further weaken the influence of the side lobe on the sound field reconstruction, better suppress the ghost and improve the accuracy of the sound field reconstruction, the sound field reconstruction needs to be performed by means of an MVDR algorithm.
In the beamforming algorithm, the acoustic pressure response p of the array is:
wherein w is a weight vectorx is the signal [ x ] of each channel1,x2,…xM]TWhereinm=1、2…M。
in the MVDR algorithm, the weighting vector w is of the form:
(5) wherein,for sound sources just from the reconstruction directionArray manifold vector at incidence, ρnIs the covariance matrix of the interfering signal. In practical applications, however, the covariance matrix ρ of the interference signal in the received data is usednIs not estimated, often by means of a cross-power spectral matrix R of the received dataxInstead of:
Rx=E{x(θ)xH(θ)} (6)
thus, formula (5) is converted to formula (7)
MVDR beam output power spectrum:
the binding formula (4), formula (7) or formula (9) can be obtained
Is obtained by the formula (9)
In the actual calculation process, a certain sound field plane is dispersed into a plurality of coordinate points, the sound field plane is called a reconstruction surface, the reconstruction sound pressure at each coordinate point in the reconstruction surface area can be calculated according to the formula (10), and then the reconstruction sound pressure cloud image is obtained.
7-10 are reconstructed sound pressure contour line cloud charts obtained by reconstruction under the sound environment of a full anechoic chamber. The numbers in the figure represent the sound pressure values at the corresponding hot spot locations of the cloud. Fig. 7 and 8 are contour cloud plots of reconstructed sound pressures obtained by the original equidistant matrix conventional beamforming method and the PSO-MVDR method at 2000Hz and 4000Hz, respectively. Because grating lobes do not occur when the frequency is low, ghost images caused by the grating lobes do not occur, and in fig. 7(b) and 8(b), the PSO-MVDR method can weaken the influence of side lobes, so that the reconstructed sound source hot spot is more prominent and the position is more accurate.
Fig. 9 and 10 are contour cloud plots of reconstructed sound pressures obtained by the original equidistant matrix conventional beamforming method and the PSO-MVDR method at 6000Hz and 8000Hz, respectively. In the equidistant array reconstruction cloud images of fig. 9(a) and fig. 10(a), the midpoints and corners of four sides of the reconstruction surface generate ghost images due to the existence of grating lobes; in the reconstructed cloud images of the optimized unequal-pitch arrays as shown in fig. 9(b) and fig. 10(b), the amplitudes of the ghost areas are all significantly reduced due to the suppression of the grating lobes, meanwhile, the interference of the side lobes is also effectively suppressed, and the sound source positioning is more accurate and clear. The PSO-MVDR not only has the inhibiting effect on grating lobes, but also degrades the grating lobes into side lobes; meanwhile, the algorithm has strong spatial filtering characteristics, the grating lobe is suppressed, output values of the array in different directions are prevented from being interfered by side lobes, and the output values can be output as undistorted as possible, so that a good ghost suppression effect can be obtained.
In summary, in the sound field reconstruction of the total anechoic chamber, the PSO-MVDR method provided herein can effectively suppress ghosting from low frequency to high frequency, and improve the accuracy of the sound field reconstruction.