A broadband sound field reproduction loudspeaker placement method based on probability maximization

Abstract

The application discloses a wideband sound field reproduction loudspeaker arrangement method based on probability maximization, in the researched wideband range, n frequencies are taken in equal interval and equal mode; then the same loudspeaker arrangement iteration algorithm is used for each frequency in the n frequencies, such as the SA algorithm, the CMP algorithm and the like, for each frequency, L loudspeakers are selected from N candidate position loudspeakers, and the numbers of the L loudspeakers are recorded, so that n*L numbers can be obtained; finally, the first L numbers with the highest appearance probability in the n*L numbers are counted, and the loudspeaker positions corresponding to the L numbers are taken as the final arrangement method. Compared with the traditional arrangement method, the method can obtain a lower microphone average normalized reproduction error in the wideband.

Description

Technical Field

[0001] This invention relates to the field of acoustics, specifically to a method for placing loudspeakers for broadband sound field reproduction based on probability maximization. Background Technology

[0002] Sound Field Reproduction (SFR) is a method that, from a physical implementation perspective, uses a loudspeaker array to reproduce the realistic sound field distribution in a specific environment. In a simulated spatial environment where the sound field needs to be reproduced, a realistic noise field is recreated through the appropriate placement of secondary sound sources (usually loudspeakers, referred to as loudspeakers below). Its applications include 3D auditory experiences in theaters, multi-purpose lecture halls, and home theaters; private audio design for conference rooms, car cabins, and personal audio equipment; acoustic environment assessment of driver's cabs and cockpits; and verification of the effectiveness of vibration reduction and noise reduction methods.

[0003] Pressure matching (PM) is a commonly used sound field reproduction method. Given a loudspeaker layout and monitoring microphone position, a system of linear equations is established to solve for the loudspeaker weight vector in the least squares sense, so that the reproduced sound field can match the desired sound field well. In addition, the PM method has few restrictions on the placement of loudspeakers and monitoring microphones and has high reproduction accuracy at the monitoring microphone position.

[0004] When using PM for sound field reproduction in the frequency domain, once the position of the monitoring microphone array is determined, the number of loudspeakers is often limited due to their high cost. Therefore, it is of great significance to arrange the limited number of loudspeakers as reasonably as possible to obtain a lower reproduction error. Selecting a specified number of loudspeakers from a large pool of candidate locations for sound field reproduction is a common approach to solving this problem. Many existing placement iterative algorithms employ this method, such as Simulated Annealing (SA) and Complementary Matching Pursuit (CMP), which have been proposed and proven to be effective loudspeaker placement iterative algorithms (Baek KH, Elliott S J. Natural algorithms for choosing source locations in active control systems[J]. Journal of Sound & Vibration, 1995, 186(2): 245-267.)(Khalilian, H., Bajiic, IV, and Vaughan, RG. Comparison of loudspeaker placement methods for soundfield reproduction[J]. IEEE International Conference on Acoustics, Speech and Signal Processing, 2016, 24, 1364–1379.).

[0005] For the wideband sound field reproduction requirements widely encountered in real-world scenarios, the speaker positions selected using the same algorithm may differ across different frequencies within the frequency domain, leading to inconsistent speaker placement and making it difficult to achieve a uniform placement across a wide frequency range. The traditional approach to address this problem is to modify the algorithm, adjusting the criterion selected in each iteration from a single frequency to the average of all frequencies. For example, the CMP algorithm changes the speaker selection method from "the speaker whose transfer function most closely approximates the error function at a single frequency" to "the speaker whose transfer function most closely approximates the error function across the entire frequency range"; while the SA algorithm changes "the normalized reproduction error of the monitoring microphone at a single frequency" to "the average normalized reproduction error of the monitoring microphone across the entire frequency range" as the Metropolis criterion function for each iteration, and so on. However, the problem with traditional methods is that using the modified algorithm affects the original algorithm's operating principle and characteristics, and fails to reflect the importance of the selected speakers for sound field reproduction at each frequency. Therefore, the resulting speaker placement may not be optimal across the entire frequency range. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention discloses a broadband sound field reproduction loudspeaker placement method based on probability maximization. The basic principle of this method is as follows: Within the studied broadband range, n frequencies are selected using equal intervals and other methods. Then, for each of these n frequencies, the same loudspeaker placement iterative algorithm is applied, such as the SA algorithm or CMP algorithm mentioned above. For each frequency, L loudspeakers are selected from N candidate locations, and the numbers of these L loudspeakers are recorded, resulting in a total of n×L numbers. Finally, the L loudspeaker positions with the highest probability among these n×L numbers are counted, and the loudspeaker positions corresponding to these L numbers are used as the final placement method.

[0007] The L loudspeaker positions obtained by the iterative algorithm at each frequency are the optimal placement methods calculated by the algorithm at each frequency. The so-called probability maximization means that the loudspeakers at the L positions with the highest probability of occurrence among n frequencies represent that the loudspeakers at these L positions are used most frequently in the entire frequency band under this algorithm, that is, they contribute the most to the entire frequency band. Compared with traditional placement methods, this method can achieve a lower microphone average normalized reproduction error in a wide frequency range.

[0008] The technical solution of this invention is as follows:

[0009] The broadband sound field reproduction loudspeaker placement method based on probability maximization includes the following steps:

[0010] Step 1: For the set wideband, obtain n frequencies and the sound pressure vector of the target sound field at the microphone. The number of microphones is M. The dimension is M×1; and the transfer function matrices G1, G2, ..., G from the loudspeakers at N candidate positions to all microphones are obtained. n G x =[g 1x g 2x … g Nx The dimension of ] is M×N, where g ix Let be the transfer function vector from loudspeaker i to all microphones at the x-th frequency, with a dimension of M×1;

[0011] Step 2: For the x-th frequency, x = 1, 2, ... n, use... and G x Through an iterative deployment algorithm, L loudspeakers are selected from N candidate locations, and their numbers are recorded.

[0012] Step 3: Repeat Step 2 until speaker positions have been selected and numbers recorded for all n frequencies, resulting in n×L numbers. Count the number of times each speaker position number appears to obtain the probability β1, β2, ..., β of each speaker position being used. N From β1,β2,...,β N Select the L largest numbers from the list, denoted as K1, K2, ..., K. L Choose the corresponding location to place the speakers as the final placement method.

[0013] Furthermore, based on the microphone spacing Δx, this method is applicable to a frequency range of f. max Below, where f max = c / 2Δx, where c is the speed of sound in the medium.

[0014] Furthermore, the deployment iteration algorithm employs a constraint tracking matching algorithm, a simulated annealing algorithm, a reproduction error criterion algorithm, or a source strength amplitude criterion algorithm.

[0015] Furthermore, based on the above method, the present invention also proposes a computer-readable storage medium and system.

[0016] One of the computer-readable storage media stores computer-executable instructions, which, when executed, are used to implement the above-described method.

[0017] A computer system includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the above-described method.

[0018] The process of sound field reproduction based on the above-obtained placement method is as follows: Numbered K1, K2, ..., K... L The transfer function vector from the loudspeaker to all microphones Form a new transfer function matrix G′ x For each of the n frequencies, the least squares method is used to calculate the corresponding loudspeaker weight vector S1, S2, ..., S. n ,in S in sequence i Weights in a vector Input into the corresponding numbers K1, K2, ... K L In a loudspeaker, sound field reproduction is performed to obtain the sound pressure vector of the reproduced sound field at the microphone at the i-th frequency. Iterate through i = 1, 2, ..., n to obtain the sound pressure vector of the reproduced sound field at the microphone for each frequency.

[0019] This invention uses the sound pressure matching method for loudspeaker placement in broadband sound field reproduction. It can guide the selection of a specified number of loudspeakers from candidate locations when realizing broadband sound field reproduction in different scenarios, so as to minimize the average normalized reproduction error at the observation point on the research frequency band.

[0020] Beneficial effects

[0021] This invention proposes a broadband sound field reproduction loudspeaker placement method based on probability maximization. This method can probabilistically select the L loudspeakers that contribute the most to the entire frequency band from N candidate loudspeaker positions. Compared with traditional placement methods, it can achieve a lower microphone average normalized reproduction error over a wide frequency range.

[0022] 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. Attached Figure Description

[0023] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0024] Figure 1 The location of the microphone array, loudspeaker array, and sound source;

[0025] Figure 2 The probabilities of using 30 numbered loudspeakers obtained by different iterative algorithms using the method proposed in this invention: (a) Constraint Matching Pursuit Algorithm, (b) Simulated Annealing Algorithm (SA), (c) Reproduction Error Criterion Algorithm, (d) Source Strength Amplitude Criterion Algorithm.

[0026] Figure 3 Error reduction values ​​for different algorithms;

[0027] Figure 4 The result of changing the sound absorption coefficient α of the wall;

[0028] Figure 5 The result of changing the number of speakers L selected;

[0029] Figure 6 Results of changing the calculated frequency interval Δf under low reverberation (α=0.8);

[0030] Figure 7 The result of changing the calculated frequency interval Δf under high reverberation (α=0.3). Detailed Implementation

[0031] To address the shortcomings of existing technologies, this invention proposes a loudspeaker placement method based on probability maximization for wideband PM frequency domain sound field reproduction. This method probabilistically selects the L loudspeakers from N candidate positions that contribute the most to the entire frequency band. The invention also provides the implementation process of this method. It should be noted that the upper frequency limit for sound field reproduction using the PM method is f. max = c / 2Δx, where c is the speed of sound in the fluid medium and Δx is the distance between the microphones. The applicable frequency range of this invention should be within f. max the following.

[0032] Assume we already have the sound pressure vectors of the target sound field at the microphone for n frequencies within a wide frequency band. And the transfer function matrices G1, G2, ..., G from the loudspeakers at N candidate locations to all microphones. n If the number of microphones is M, then The dimension is M×1, G x =[g 1x g 2x ... g Nx The dimension of (x = 1, 2, ..., n) is M × N (where g ix (i = 1, 2, ..., N) represents the transfer function vector from loudspeaker numbered i to all microphones at the x-th frequency (with dimensions M × 1). The required L loudspeaker positions are obtained according to the following process:

[0033] Number the speakers at the N candidate locations from 1 to N.

[0034] use And G1, using some iterative algorithm, selects L speakers from N candidate speaker positions and records their numbers.

[0035] Will And G1 changed and G x (x = 1, 2, ... n), repeat step 2 until all n frequencies have been selected and their numbers recorded. At this point, n × L numbers can be obtained.

[0036] Count the number of times each number 1 to N appears in an n×L set of numbers, then divide by n to obtain the probability β1, β2, ..., β of each number being used. N From β1,β2,...,β N Select the L largest numbers from the list, denoted as K1, K2, ..., K. L Choose the speakers corresponding to their locations as the final placement method.

[0037] Numbered K1, K2, ..., K L The transfer function vector from the loudspeaker to all microphones (with dimensions M×1) form a new transfer function matrix G′ x (x = 1, 2, ..., n) (dimension M × L), the speaker weight vector S1, S2, ..., S is calculated for each of the n frequencies using the least squares method. n ,in S in sequence i Weights in a vector Enter the corresponding number (K1, K2, ... K) L In a loudspeaker, sound field reproduction is performed to obtain the sound pressure vector of the reproduced sound field at the microphone at the i-th frequency. Iterate through i = 1, 2, ..., n to obtain the sound pressure vector of the reproduced sound field at the microphone for each frequency.

[0038] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0039] Figure 1In the sound field reproduction scenario of this embodiment, the space size is 4.7m × 4.1m. The black dots represent N = 30 candidate loudspeakers, evenly arranged on a circle with a radius of 1.5m, with the center point located at the center of the space. The blue dots represent M = 36 microphones, arranged in a square array, with an adjacent microphone spacing of 0.2m, and the center point is also located at the center of the space. The target sound field is generated by a monopole point sound source located in the [2m, 1.5m] area. Figure 1 The sound field is represented by red dots. The loudspeaker is modeled as a monopole point source, and the sound absorption coefficient α of the wall is set to 0.8. Assuming the spatial medium is air, and the speed of sound in air is c = 340 m / s, the maximum frequency f of the sound field reproduction using the PM method can be calculated based on the microphone spacing. max =850Hz.

[0040] Through simulation calculations (or experimental measurements), the sound pressure vector of the target sound field at the microphone is obtained at n = 170 frequencies within the range of 0 Hz to 850 Hz, with a frequency interval of Δf = 5 Hz. And the transfer function matrices G1, G2, ..., G from the loudspeakers at the 30 candidate positions to all microphones. 170 The required number of speakers (L=5 positions) can be obtained by following these steps:

[0041] Step 1: Number the speakers in the 30 candidate locations from 1 to 30.

[0042] Step 2: Utilize And G1, using some iterative algorithm, selects 5 speakers from 30 candidate speaker positions and records their numbers.

[0043] Step 3: Put And G1 changed and G x (x = 1, 2, ... 170), repeat step 2 until all 170 frequencies have been selected and their numbers recorded. At this point, you will have 170 × 5 = 850 numbers.

[0044] Step 4: Count the number of times each of the 850 numbers 1 through 30 appears, then divide by 170 to obtain the probability β1, β2, ..., β of each number being used. 30 .

[0045] Step 5: From β1, β2, ..., β 30 Select the top 5 numbers with the largest values, denoted as K1, K2, ..., K5, and choose the speakers at their corresponding positions as the final placement method.

[0046] The transfer function vector from the loudspeakers numbered K1, K2, ..., K5 to all microphones. (with dimensions of 36×1) form a new transfer function matrix G′ x (x = 1, 2, ..., 170) (dimension 36 × 5), the speaker weight vector S1, S2, ..., S is calculated for each of the 170 frequencies using the least squares method. 170 Using S1, S2, ..., S 170 To reproduce the sound field, the sound pressure vector at the microphone for each frequency of the reproduced sound field is obtained.

[0047] To illustrate the effectiveness of this invention, the main performance evaluation index used here is the microphone mean normalized reproduction error (MSE), and the specific calculation formula is as follows.

[0048]

[0049] In the formula, ||·||2 is the vector 2-norm, and n is the number of frequencies. Let be the sound pressure vector of the target sound field at the microphone for the i-th frequency. Let MSE be the sound pressure vector at the microphone for the reproduced sound field at the i-th frequency, with dimensions M×1. The value of MSE reflects the average reproduction accuracy at the microphone when the selected loudspeaker reproduces the sound field at all n frequency points. The lower the MSE, the higher the average reproduction accuracy across the entire frequency band.

[0050] The average normalized reproduction error (MSE) of the microphones used for sound field reproduction by the placement method of the present invention is calculated using equation (1). new Similarly, Equation (1) is used to calculate the MSE of the sound field reproduction obtained by the traditional method for the placement method. old

[0051] This embodiment selects four commonly used typical iterative algorithms (Complementary Matching Pursuit (CMP), Simulated Annealing (SA), Reproduction Error Criterion (REC), and Source Strength Magnitude Criterion (SSMC)) as the "a certain iterative algorithm" in step two. The differences between the traditional method and the method proposed in this invention are compared through the above implementation process to illustrate the beneficial effects of this invention, thereby extending it to any iterative algorithm used for loudspeaker deployment.

[0052] And define the error reduction value ΔMSE:

[0053] ΔMSE=MSEold -MSE new (2) Used for comparison with traditional methods, where MSE old MSE is calculated using traditional methods. new The MSE is calculated using the method of this invention. ΔMSE reflects how much the proposed method can further reduce the MSE compared to traditional methods. A larger ΔMSE indicates that the deployment method proposed in this invention is superior.

[0054] Compared to traditional methods, the method proposed in this invention theoretically uses an iterative algorithm to obtain L loudspeaker positions at each frequency, representing the optimal placement method calculated by the algorithm at each frequency. The L loudspeaker positions with the highest probability of occurrence across n frequencies represent those loudspeakers that are used most frequently throughout the entire frequency band under this algorithm, thus contributing the most to the overall frequency band. This placement method is more probabilistically reasonable, resulting in a lower average normalized reproduction error for the microphones compared to traditional methods.

[0055] Figure 2 The probability of using 30 numbered loudspeakers obtained by different iterative algorithms using the method proposed in this invention is shown. The red-marked numbers represent loudspeakers selected using the traditional method. It can be seen that the loudspeakers selected by the method proposed in this invention are different from those selected by the traditional method. Figure 3 The error reduction value ΔMSE for different algorithms reveals that, except for the SSMC algorithm which uses the same speaker numbers in both methods and thus has the same MSE, the placement method of this invention outperforms the traditional method in the other four algorithms. To verify the versatility of the method proposed in this invention, the wall absorption coefficient α and the required number of speakers L in the embodiments were changed respectively. Figure 4 With the other conditions remaining unchanged for the example, ΔMSE was obtained with α being 0.8, 0.5, 0.3, and 0.1 respectively. It can be found that the wall sound absorption coefficient does not limit the effect of the method proposed in this invention. In most cases, the method proposed in this invention is superior to the traditional method. Figure 5 With the remaining conditions unchanged in the embodiments, and L being 3, 5, and 8 respectively, ΔMSE can be obtained. It can be seen that the number of speakers required does not limit the effect of the method proposed in this invention. In fact, from Figure 5 It can be observed that when the number of candidate loudspeakers N is much larger than the required number of loudspeakers L, within a certain range, the larger L is, the larger the ΔMSE is, and the better the proposed method is. Furthermore, since the method proposed in this invention is based on probability statistics, to examine the influence of the number of frequencies n, the calculated interval frequency Δf is changed to 5Hz, 10Hz, 25Hz, and 50Hz, corresponding to n of 170, 85, 34, and 17 respectively. The obtained ΔMSE is as follows: Figure 6 and Figure 7 As shown, where Figure 6 This is the result under low reverberation (α = 0.8). Figure 7 This is the result under high reverberation (α = 0.2). Comparison Figure 6 and Figure 7 It can be observed that under low reverberation, Δf has little effect on ΔMSE, while under high reverberation, as Δf increases, the ΔMSE of some iterative algorithms decreases. Further reducing n may cause ΔMSE to become negative, meaning the method proposed in this invention may...

[0056] The proposed method will perform worse than traditional methods, therefore, under permissible conditions, the smaller Δf and the larger n are, the better the proposed method will be. In summary, compared with traditional deployment methods, the probability-based deployment method proposed in this invention can achieve reproduction results that are no worse than traditional methods over a wide frequency range, and in most cases, it is better than traditional methods (the larger the number of frequencies n, the better). At the same time, it has wide applicability and can be applied to a variety of reproduction scenarios.

[0057] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for placing broadband sound field reproduction loudspeakers based on probability maximization, characterized in that: Includes the following steps: Step 1: For the set wideband frequency band, obtain the frequency information. The frequencies and the sound pressure vector of the target sound field at the microphone. The number of microphones is , The dimension is ; and obtain Transfer function matrix from loudspeakers at candidate locations to all microphones , The dimension is ,in For the first At each frequency, number The transfer function vector from the loudspeaker to all microphones, with dimension . ; Step 2: For the first One frequency, ,use and Through a deployment iterative algorithm, from Selecting from the speaker locations of the candidate positions Identify and record the number of each speaker in each location; Step 3: Repeat step 2 until the condition is met. Each frequency has completed speaker position selection and recorded its number; at this point, we obtain... One number; Count the number of times each speaker location number appears to obtain the probability that each speaker location is used. ; from Select the one with the largest value. Each number is denoted as... Choose the corresponding location to place the speakers as the final placement method.

2. The method for placing broadband sound field reproduction loudspeakers based on probability maximization according to claim 1, characterized in that: According to the spacing of the microphones The frequency range applicable to this method is within The following, among which , The velocity of sound in the medium.

3. The method for placing broadband sound field reproduction loudspeakers based on probability maximization according to claim 1, characterized in that: The deployment iteration algorithm employs a constraint pursuit matching algorithm, a simulated annealing algorithm, a reproduction error criterion algorithm, or a source strength amplitude criterion algorithm.

4. A computer-readable storage medium, characterized in that: The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

5. A computer system, characterized in that: The device includes one or more processors and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

6. A sound field reproduction method based on the placement method described in claim 1, characterized in that: Number The transfer function vector from the loudspeaker to all microphones Form a new transfer function matrix ;right The speaker weight vector for each of the frequencies is calculated using the least squares method. ,in ; in sequence Weights in a vector Enter the corresponding number In the loudspeaker, the sound field is reproduced to obtain the first... The sound pressure vector at the microphone of the reproduced sound field at each frequency ; Traversal This yields the sound pressure vector at the microphone for the reproduced sound field at each frequency. .

Images