CN114373477B - Active source lean secondary path modeling method based on sound field reconstruction - Google Patents
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Abstract
The invention provides a modeling method of an active source sub-path based on sound field reconstruction, which adopts a linear microphone array in a closed space to sample the sound field and realizes accurate reconstruction of a time domain sound pressure signal in a head motion area; according to the invention, when the secondary path is modeled, an additional microphone is not required to be placed at the human ear to directly acquire the noise signal, and the noise signal at the human ear is indirectly acquired through sound field reconstruction, so that the effect of virtual error sensing is achieved; the invention avoids repeated modeling and storage work of the secondary path before control, carries out secondary path modeling before each control through sound field reconstruction, does not need to establish secondary path models of all preset points in a preparation stage, and releases the storage space of the controller; according to the invention, accurate modeling can be realized at each head movement point, the situation that effective model data cannot be called because no secondary channel model is established at gaps among preset point positions is avoided, and the problem of difficult secondary channel modeling under head movement is solved.
Description
Technical Field
The invention belongs to the technical application field of sound field reconstruction, and particularly relates to a method for reconstructing a time domain low-frequency sound field in a small range by using sound pressure signals measured by a linear microphone array in a closed space.
Background
Estimating sound field information at an unknown location in an indoor space is valuable in practical engineering applications, and if sound field information at other unknown locations in space can be numerically predicted by some inverse calculation method, this method can provide more research value for indoor sound field reconstruction, sound field analysis, sound field control, and indoor reverberation compensation for audio reconstruction. In room acoustics, sound field information of the whole space can be predicted and estimated through sound pressure values measured by a limited number of microphones, which is called sound field reconstruction (Sound Field Reconstruction, SRF).
In the low frequency range, near field acoustic holography (NEARFIELD ACOUSTIC HOLOGRAPHY, NAH) proposed by e.g. williams and j.d. maynard et al is an important sound field reconstruction method, and the basic idea is to collect sound field information on a surface close to a sound source by using a microphone array in a certain form, and then calculate sound pressure, particle vibration velocity, sound intensity and other distributions of the sound source and the whole sound field through spatial sound field transformation. However, this method requires the transfer characteristics (spatial green's function) of the sound field to be predicted, however, only a regular closed-space green's function has a clear expression, so if the closed space is irregular, it will be difficult to achieve sound field reconstruction. Another sound field reconstruction method is a method based on superposition of basis functions, and the implementation flow is as follows: firstly decomposing a sound field under a basis function and solving expansion coefficients of the sound field, and then reconstructing sound pressures at other positions of the sound field by utilizing linear superposition of products of the basis function and the expansion coefficients of the basis function. According to the difference of the basis functions, the method can be divided into plane waves, circular harmonic functions, cylindrical harmonic functions, spherical harmonic functions and the like, then the number of expansion terms and corresponding expansion coefficients are determined, and the predicted sound field is close to the real sound field step by step through the continuous superposition of the number of expansion terms. This method does not require a prediction of the spatial transfer characteristics, and also has various decomposition methods, which are more suitable for practical engineering applications.
Active noise control (Active Noise Control, ANC for short, active noise control) is a technology for outputting sound waves with the same amplitude and opposite phase as the original noise sound waves to play a role in mutual cancellation of the sound waves, so that noise reduction is realized.
Active source rest (ACTIVE HEADREST) is a technology for realizing local (near human ear) dead zone by using active noise control technology, and can generate dead zone at human ear to obtain comfort when working or resting. The practical application of active source is based on an active source algorithm, the earliest active source algorithm can be traced to virtual microphone placement (Virtual Microphone Arrangement, VMA) technology proposed by Elliott and David in 1992, the implementation process of the method is that a virtual microphone is supposed to be placed at an observation point, a physical microphone is used for observing noise signals at the virtual microphone (human ear), and the assumption is based on the fact that primary noise signals at the positions of the two microphones are the same. Subsequently, roure and Albarrazin first proposed remote microphone technology (Remote Microphone Technology, RMT) in 2000, the principle of which is to model the transfer function between physical microphone and virtual microphone, and estimate the noise signal at the virtual microphone position by using the noise signal at the physical microphone position, which is more accurate than VMA, so as to achieve better control effect. An essential step in the application of RMT technology is to obtain a transfer function model between the error microphone and the physical microphone, and the accuracy of the transfer function model between the two microphones affects the final noise control effect. In addition, accurately establishing a secondary path model between a secondary sound source and an error point is also a key link of control.
In general, secondary path modeling is a transfer function model between a position where noise reduction is required and a secondary sound source, and secondary path modeling is a particularly critical link in an active noise control technology, and without the secondary path model, active noise control cannot achieve an expected effect. In the active source rest, as no actual microphone exists near the human ear, the secondary channel model cannot be built after the active noise reduction system is started, the secondary channel model is built in advance in the existing active source rest research, and then noise control is performed. In the existing research, a general method for establishing a secondary path model is to set a microphone at the human ear in advance and then model by using a modeling method of a secondary sound source and additive noise. However, each time the head position changes, the secondary path needs to be re-estimated, which in turn will require re-positioning of the microphone at the human ear to build the secondary path model. Therefore, previous studies required a number of sub-path models corresponding to different positions of the human head to be measured and stored in advance for later control phase invocation.
This presents several problems. On the one hand, the preparation work in the early stage is tedious, a considerable number of secondary path models are required to be measured and stored, and an additional microphone is required to be arranged at the human ear during modeling; on the other hand, in any design, the point locations are divided at a certain interval in the head movement range, and then the secondary path models of the point locations are measured. Since all the sub-path models in the head movement range cannot be measured, the control performance is degraded when the head moves to a point where the sub-path model is not stored. Therefore, the problem of modeling the secondary path caused by the movement of the head needs to be solved.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides an active source lean secondary path modeling method based on sound field reconstruction by utilizing a sound field reconstruction technology. Studies have shown that sound fields can be reconstructed more accurately within a certain range around a linear microphone array. If the microphone array is used in active head rest to reconstruct the sound field in a certain range around the head, the noise signal near the human ear can be reconstructed when the head moves to any point, so that the effect similar to that of the virtual error sensing technology is realized. The invention has the advantages that no additional microphone is needed to be placed at the human ear to directly acquire the noise signal when the secondary path is modeled, because the noise signal at the human ear can be indirectly acquired through sound field reconstruction; in addition, repeated modeling and storage work of the secondary path before control are avoided, because the secondary path modeling can be carried out before each control through sound field reconstruction, and the model of all preset points does not need to be built at one time; finally, because of the application of sound field reconstruction, each head movement point position can be accurately modeled, and the situation that gaps among preset point positions in the prior study cannot establish a secondary channel model is avoided.
The specific steps of the invention are shown in figure 1:
step 1: in the closed space omega, determining a two-dimensional area A to be reconstructed and simultaneously determining the position of a linear microphone array; assuming that the linear microphone array contains M microphones;
step 2: establishing a space rectangular coordinate system, and determining the position coordinates of the microphone array and the space coordinates of the reconstruction area; the position vector at the M-th microphone position is denoted as r m＝(xm,ym,zm), m=1, 2, …, M, sampling the original sound field with the M microphones set;
Step 3: measuring and obtaining a time domain sound pressure signal of the original sound field at the position of the microphone;
Step 4: performing Fourier transform (FFT) on the time-domain sound pressure signals, and calculating to obtain original sound field frequency domain sound pressure vectors p (k, r) = [ p 1(k,r)p2(k,r)…pM(k,r)]∈CM×1 ] at M microphones, wherein k=2pi f/C represents wave numbers at a certain frequency f, C is sound velocity, and C represents complex sets;
step 5: obtaining a plane wave vector on a spherical surface with the radius of k according to an approximately uniform sampling method, and ensuring the randomness and representativeness of the plane wave vector;
step 6: determining N total plane wave directions, and decomposing sound pressure measured by each measuring point into superposition of plane waves with different directions and amplitudes on the basis of the N total plane wave directions; the plane wave direction is determined by a wave number vector k n＝xni+ynj+zn k, where n=1, 2, …, N, i, j and k represent unit vectors in the rectangular coordinate system X, Y and Z directions, respectively, and the coordinates of a position r in space are represented by r= (x, y, Z);
step 7: obtaining a perception matrix (or a transfer matrix) H epsilon C M×N formed by plane wave items in different directions:
Where k n denotes the wave vector in a certain direction and r m denotes the position coordinates of the microphone array, all of which have been explained in step 6. In addition, in the case of the optical fiber, Represents imaginary units, and e represents natural base.
Step 8: solving forWherein "|·| 2" represents l 2 norm, ε is an estimate of the noise upper bound, and x is the complex amplitude vector of the plane wave to be solved;
step 9: solving a plane wave complex amplitude vector x by using an iterative re-weighted least square method (ITERATIVE REWEIGHTED LEAST square, IRLS);
Step 10: using the complex amplitude vector x of plane wave obtained by solving according to Predicting and estimating a frequency domain sound pressure signal of a sound field to be reconstructed, wherein/>A perception matrix for sound field point positions to be reconstructed;
Step 11: obtaining a real number sequence through inverse Fourier transform (IFFT) by utilizing a frequency spectrum constructing method, so as to obtain a time domain sound pressure signal of a reconstructed sound field;
step 12: and taking the time domain sound pressure signal at the reconstruction point as a desired signal of the modeling system, taking the secondary sound source signal as an input signal, and establishing a secondary path model between the secondary sound source and the reconstruction point.
Further, in step 5, in the spatial pitch angle θ n ε [0, pi ], the horizontal angleThe plane wave vector is obtained in a range, wherein the specific sampling method of the space pitch angle and the horizontal angle comprises the following steps:
knz＝kcosθn
kn＝knxi+knyj+knzk。
further, in step 5, spherical surface approximate uniform sampling is used to obtain wave vectors in N directions.
Further, the specific process of solving the complex amplitude vector x of the plane wave by using the IRLS in the step 9 is as follows:
Step 9.1: setting an original sound field frequency domain sound pressure matrix p epsilon C M×1, a perception matrix H epsilon C M×N and an initial weight matrix W epsilon C N×N, wherein the initial weight matrix W is an N-order identity matrix:
step 9.2: setting iteration solving input parameters: the method comprises the steps of normalizing regularization parameters beta, the maximum iteration times I MAX and solving the minimum error delta x min by two times of iteration; wherein Δχ i+1 from the (i+1) th iteration is defined as:
step 9.3: setting a cyclic solving step:
Gi＝AWi
si＝svd{Gi}
βi＝β×max{si}2
xi＝WiGT{(GGT+βiIM)\p}
Wi+1＝diag(wi)
Wherein svd {. Cndot. } represents solving the singular value of the matrix and returning the value, max {. Cndot. } represents solving the maximum value and returning the value, |cndot./represents solving the absolute value and returning the value, diag (&) represents constructing a diagonal matrix based on the elements in (&);
Step 9.4: setting an iteration solution termination condition: on one hand, the method meets the requirement that the error delta x is smaller than delta x min in the two iterative solutions, and on the other hand, the total iterative solution times are larger than I MAX; and (3) meeting the two conditions, ending the iteration, finishing the calculation, outputting the complex amplitude value x of the plane wave, and otherwise, repeating the step 9.3.
Advantageous effects
(1) According to the invention, the linear microphone array in the closed space is adopted to sample the sound field, so that accurate reconstruction of the time domain sound pressure signal is realized in the assumed head movement region, and meanwhile, the whole preset sound field can also have higher reconstruction precision, thereby being suitable for practical application.
(2) According to the invention, an additional microphone is not required to be placed at the position of the human ear to directly acquire the noise signal when the secondary path is modeled, and the noise signal at the position of the human ear can be indirectly acquired through sound field reconstruction, so that the effect of virtual error sensing is achieved.
(3) The invention avoids repeated modeling and storage work of the secondary path before control, because the secondary path modeling can be carried out before each control through sound field reconstruction, and the secondary path model of all preset points is not required to be established in the preparation stage, thereby releasing the storage space of the controller.
(4) According to the invention, accurate modeling can be realized at each head movement point, the situation that effective model data cannot be called because no secondary channel model is established at intervals among preset points in the previous study is avoided, and the problem that the secondary channel modeling is difficult under head movement is solved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of an active source-by-secondary path modeling technique based on closed space acoustic field reconstruction;
Fig. 2 is a schematic plan view of a linear microphone array in an enclosed space;
FIG. 3 is a schematic diagram of an original time domain sound pressure signal, a reconstructed time domain sound pressure signal, and an error signal thereof at coordinates (-0.15,0,0);
FIG. 4 is a schematic illustration of an original sound field at a point in time sampled at a reconstruction plane;
FIG. 5 is a schematic diagram of a reconstructed sound field at a point in time taken at a reconstruction plane;
FIG. 6 is a schematic diagram of a time-averaged mean square error of a reconstruction plane;
FIG. 7 is a schematic diagram of three acoustic paths used in active source arm;
FIG. 8 is a graph of secondary path modeling results between secondary acoustic sources and estimated points.
Detailed Description
The following describes an active source-by-secondary path modeling method based on closed space acoustic field reconstruction with reference to the drawings and examples, including but not limited to the following examples.
The invention comprises the following detailed steps:
1. Given a rectangular enclosure with a wall sound absorption coefficient of 0.2, the dimensions of which are 3.2m x 5.72m x 4m, an obstacle and a hypothetical head are placed in the enclosure, which to some extent simulates the actual situation of an active source in use, as shown in fig. 2. M=12 microphones are arranged in total, and divided into 4 columns, and the microphone intervals are 0.04M, so as to form a linear microphone array. A point sound source is set at the positions (1.6 m,4.9m,1.55 m) and the sound source signal is set to 0.01×sin (2pi×200×t) m 3/s, so as to generate a sound field to be reconstructed.
2. In the embodiment, the center of the head is taken as an origin, a space rectangular coordinate system is established, and then the coordinates of each microphone under the space coordinate system are determined. The original sound field was sampled with 12 microphones set, giving a plan view of the specific set-up as shown in fig. 3. A two-dimensional area of 0.5m multiplied by 0.3m to be reconstructed is determined around the linear microphone array, 50 multiplied by 50 points (head part is removed) are uniformly selected in the area to be used as reconstruction points, and signals of the points are collected to be used as original sound field signals.
3. The time domain sound pressure signal vector p (t, r) of the original sound field at 12 microphone positions is measured.
4. And carrying out Fourier transform on the time domain sound pressure signals to calculate and obtain frequency domain sound pressure vectors p (k, r) epsilon C 14×1 of the original sound field at 12 microphones.
5. On a sphere with radius of k=2pi×200, in the space pitch angle theta n epsilon [0, pi ], horizontal angleAnd obtaining a plane wave vector in the range. According to the approximately uniform sampling method, N=400 plane wave directions are determined, and sound pressures measured by 12 measuring points are decomposed into N=400 plane waves with different directions and amplitudes.
6. Obtaining a perception matrix (or a transfer matrix) H epsilon C 12×400 formed by plane wave items in different directions:
Where k n denotes a wave vector in a certain direction, r m denotes a coordinate vector of the microphone array, and furthermore, Represents imaginary units, and e represents natural base.
7. Constructing and solvingWhere "|·| 2" denotes the l 2 norm, ε is an estimate of the noise upper bound, and x is the complex amplitude vector of the plane wave to be solved.
8. The problem in 7 is solved by using an iterative re-weighted least Squares method (ITERATIVE REWEIGHTED LEAST square, IRLS), and then the plane wave complex amplitude vector x is solved. The specific process is as follows:
(1) Constructing an original sound field frequency domain sound pressure matrix p epsilon C 12×1, a perception matrix H epsilon C 12×400 and an initial weight matrix W epsilon C 400×400, wherein the initial weight matrix W is an N=400-order identity matrix:
(2) Setting iteration solving input parameters: in this example, a normalized regularization parameter β=10 -4, a maximum iteration number I MAX＝103, and two previous and subsequent iterations are set to solve for a minimum error Δx min＝10-3. Where deltax i+1 from the (i+1) th iteration is defined as,
(3) And respectively carrying out iterative solution according to the cyclic solution step:
Gi＝AWi
si＝svd{Gi}
βi＝β×max{si}2
xi＝WiGT{(GGT+βiIM)\p}
Wi+1＝diag(wi)
wherein svd {. Cndot. Is used to solve for the singular value of the matrix and return the value, max {. Cndot. Is used to solve for the maximum value and return the value, |cndot. Is used to solve for the absolute value and return the value, diag (&) is used to construct a diagonal matrix based on the elements in (&).
(4) Setting an iteration solution termination condition: meanwhile, the method meets the requirements that the error delta x is smaller than delta x min in the previous and later iterative solution processes, and the total number of iterative solution is larger than I MAX. And (5) meeting the two conditions, ending the iteration, finishing the calculation, outputting the complex amplitude value x of the plane wave, and otherwise, repeating the iteration solution.
9. Using the complex amplitude vector x of plane wave obtained by solving according toPredicting and estimating frequency domain sound pressure signal/>, of sound field to be reconstructedWherein/>Is a perception matrix of sound field points to be reconstructed.
10. Obtaining a real number sequence after inverse Fourier transform by using a construction spectrum method, thereby obtaining a time domain sound pressure signal of the reconstructed sound field
11. And carrying out secondary path modeling by using a system identification method based on an LMS algorithm by using the time domain sound pressure signal and the sound source signal at the reconstructed point obtained by reconstruction to obtain a path model of the FIR filter structure between the two, so as to be called in a subsequent control stage.
The original time domain sound pressure signal, the reconstructed time domain sound pressure signal and the error signal thereof at (-0.15,0,0) are shown as shown in figure 4, and the original signal and the reconstructed signal are almost consistent at the point, so that the reconstruction accuracy is high, and the invention can accurately realize the reconstruction of the sound field signal in the time domain.
The original sound field and the reconstructed sound field at a certain moment are shown in fig. 4 and 5, respectively. As can be seen by comparing the two, the original sound field and the reconstructed sound field are almost identical, except for the head. To further quantify the accuracy of sound field reconstruction, an evaluation index is given as follows:
reconstruction point time average mean square error E r (r)
Wherein the method comprises the steps ofAnd p (t k, r) represent the reconstructed time domain sound pressure and the original time domain sound pressure, respectively, t k represents the kth discrete point in time, and 600 consecutive points in time are selected for subsequent calculations in this example.
Fig. 6 shows the time-averaged mean square error of all reconstruction points in a reconstruction plane selected around the microphone array in this example arrangement. The time average mean square error is below-20 dB in a quite large part of area around the microphone array, particularly in the area around the head, and the invention has a relatively accurate reconstruction effect, so that the time domain sound pressure signal can be accurately reconstructed in a certain range around the array and the head.
Fig. 7 shows a schematic diagram of the three acoustic path models applied in the active source algorithm, using the microphone signal, the acoustic signal at the estimated point and the secondary acoustic source signal, under the present example. While figure 8 shows the modeling of the acoustic path between the secondary acoustic source and the estimated point (-0.15,0,0). The method achieves the effect of arranging the microphones without actually arranging the virtual microphones, and further establishes a secondary path model between the secondary sound source and the virtual microphones.
While the above examples have shown the advantages of the present invention, the foregoing is illustrative and not to be construed as limiting the invention, and that modifications, substitutions and variations may be made by those of ordinary skill in the art without departing from the spirit and principles of the invention.
Claims (5)
1. A modeling method of an active source secondary path based on sound field reconstruction is characterized by comprising the following steps: the method comprises the following steps:
step 1: setting a sound source in a closed space omega, determining a two-dimensional area A to be reconstructed, and simultaneously determining the position of a linear microphone array; the linear microphone array includes M microphones;
Step 2: establishing a space rectangular coordinate system, and determining the position coordinates of the microphone array and the space coordinates of the reconstruction area; the position vector at the M-th microphone position is denoted as r m＝(xm,ym,zm), m=1, 2, …, M, sampling the original sound field with the M microphones set;
Step 3: measuring and obtaining a time domain sound pressure signal of the original sound field at the position of the microphone;
Step 4: performing Fourier transform (FFT) on the time-domain sound pressure signals, and calculating to obtain original sound field frequency domain sound pressure vectors p (k, r) = [ p 1(k,r) p2(k,r)…pM(k,r)]∈CM×1 ] at M microphones, wherein k=2pi f/C represents wave numbers at a certain frequency f, C is sound velocity, and C represents complex sets;
Step 5: obtaining plane wave vectors on a spherical surface with the radius of k according to an approximately uniform sampling method, determining N total plane wave directions, and decomposing sound pressure measured by each measuring point into superposition of plane waves with different directions and amplitudes; the plane wave direction is determined by a wave number vector k n＝xni+ynj+zn k, where n=1, 2, …, N, i, j and k represent unit vectors in the rectangular coordinate system X, Y and Z directions, respectively, and the coordinates of a position r in space are represented by r= (x, y, Z);
step 6: obtaining a perception matrix H epsilon C M×N composed of plane wave items in different directions:
Where k n denotes a wave vector in a certain direction, r m denotes a position coordinate of the microphone array, Representing imaginary units, e representing natural base numbers;
step 7: solving for Subject to Hx-p 2 < ε, where "| 2" represents l 2 norm, ε is an estimate of the upper bound of the noise, and x is the complex magnitude vector of the plane wave to be solved;
Step 8: solving a plane wave complex amplitude vector x;
Step 9: using the complex amplitude vector x of plane wave obtained by solving according to Predicting and estimating a frequency domain sound pressure signal of a sound field to be reconstructed, wherein/>A perception matrix for sound field point positions to be reconstructed;
Step 10: obtaining a real number sequence after inverse Fourier transform by using a construction frequency spectrum method, thereby obtaining a time domain sound pressure signal of a reconstructed sound field;
Step 11: and taking the time domain sound pressure signal at the reconstruction point as a desired signal of the modeling system, taking the secondary sound source signal as an input signal, and establishing a secondary path model between the secondary sound source and the reconstruction point.
2. The method for modeling an active source side secondary path based on sound field reconstruction according to claim 1, wherein the method comprises the following steps: in step 5, in the spatial pitch angle theta n epsilon [0, pi ], the horizontal angleThe plane wave vector is obtained in a range, wherein the specific sampling method of the space pitch angle and the horizontal angle comprises the following steps:
knz＝kcosθn
kn＝knxi+knyj+knzk。
3. the method for modeling an active source side-by-side path based on sound field reconstruction according to claim 2, wherein the method comprises the following steps: in step 5, spherical surface approximate uniform sampling is used to obtain wave vectors in N directions.
4. The method for modeling an active source side secondary path based on sound field reconstruction according to claim 1, wherein the method comprises the following steps: in the step 8, the specific process of solving the complex amplitude vector x of the plane wave by using the iterative re-weighted least square method is as follows:
Step 8.1: setting an original sound field frequency domain sound pressure matrix p epsilon C M×1, a perception matrix H epsilon C M×N and an initial weight matrix W epsilon C N×N, wherein the initial weight matrix W is an N-order identity matrix:
step 8.2: setting iteration solving input parameters: the method comprises the steps of normalizing regularization parameters beta, the maximum iteration times I MAX and solving the minimum error delta x min by two times of iteration; wherein Δχ i+1 from the (i+1) th iteration is defined as:
Step 8.3: setting a cyclic solving step:
Gi＝AWi
si＝svd{Gi}
βi＝β×max{si}2
xi＝WiGT{(GGT+βiIM)\p}
Wi+1＝diag(wi)
Wherein svd {. Cndot. } represents solving the singular value of the matrix and returning the value, max {. Cndot. } represents solving the maximum value and returning the value, |cndot./represents solving the absolute value and returning the value, diag (&) represents constructing a diagonal matrix based on the elements in (&);
Step 8.4: setting an iteration solution termination condition: on one hand, the method meets the requirement that the error delta x is smaller than delta x min in the two iterative solutions, and on the other hand, the total iterative solution times are larger than I MAX; and (3) meeting the two conditions, ending the iteration, finishing the calculation, outputting the complex amplitude value x of the plane wave, and otherwise, repeating the step 8.3.
5. The method for modeling an active source side secondary path based on sound field reconstruction according to claim 1, wherein the method comprises the following steps: in step 11, a system identification method based on an LMS algorithm is used for carrying out secondary path modeling, and a path model of the FIR filter structure between the two is obtained.
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