A Low Frequency Noise Source Localization and Identification Method Based on a Virtual Open Spherical Vector Microphone Array
Round 1
Reviewer 1 Report
Please check my comments in the attachement
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1 Comments （Please see the attachment）
Point 1: Some notations used in the equations are not explained. Specifically, there are no explanations for and in equation (2), L in comments after (5), in (6) and (7), c in (12).
Response: It has been revised item by item according to the reviewer's comments. See equation (2), line 88-91, 109 and 119.
Point 2: It is not clear what the statement “randomly and uniformly distributed microphones" means. This phrase is used both in the description of simulation (section 4) and in the experimental section (section 5). At first look, the microphone positions should be known accurately for data processing. So, what does word “randomly” mean? This issue should be clarified.
Response: The simulation and experimental object used in this paper is a 64 element open spherical array. The array element position is determined by a random and uniform distribution. Therefore, the positions of open spherical array elements in simulation and experiment are known. However, the distribution of array elements (microphones) is random and uniformly distributed on the sphere.
Point 3: When I look at the experiment results for double sound source (section 5.2.), the advantage of 'p+v' joint processing method is not obvious. Moreover, I would say that virtual SMA processing method gives even better resolution. This result contradicts to simulation, which clearly shows better resolution for 'p+v' method. I think, this should be discussed in the manuscript and authors opinion related to this results would be of interest for readers.
Response: From equation 15 and 16, it can be seen that . The radius of the virtual open SMA in simulation and experimental data processing is 0.45m. That is to ensure that the two virtual SMA used for comparison have the same radius, . At this time, , . Therefore, the element error of the radius of a virtual spherical array with a radius of is greater than that of a virtual spherical array with a radius of . At the same time, as can be seen from Figure 3 (b), as the frequency of the sound source increases, the error of the virtual spherical array also increases. In addition, in actual measurement, due to the impact of the measurement process and environment, there are also errors, which ultimately leads to significant errors in the velocity calculation results. Thereby affecting the final noise source localization and identification results. This has led to a decline in the advantages of 'p+v' joint processing methods.
Author Response File: Author Response.pdf
Reviewer 2 Report
This study describes a method for localizing and identifying low-frequency noise sources based on virtual-vector open SMA (’p+v’ joint processing method of pressure and velocity). The method involves obtaining a virtual open SMA with a larger aperture using a virtual array extrapolation method. This is a relevant and very interesting problem. The paper is well-written and effectively communicates its ideas. That's why I suggest that the paper be accepted with a minor revision for publication
1 - Line 1 of introduction: The first time the acronym SMA is used, a definition is needed.
2 - After equation (1) is needed to define k.
3 - Please note that a space must separate the number and unit.
Author Response
Response to Reviewer 2 Comments
Point 1: Line 1 of introduction: The first time the acronym SMA is used, a definition is needed.
Response: It has been revised item by item according to the reviewer's comments. (Beamforming technology with spherical microphone arrays (SMAs) is widely used in localizing and identifying noise sources in the mid–high-frequency range because of its small size, full space directivity, and good resolution in medium and high frequencies.) See line 20.
Point 2: After equation (1) is needed to define k.
Response: It has been revised item by item according to the reviewer's comments. (where k is wavenumber, and k=ω/c, ω represents angular frequency, c is sound speed in the air.) See line 88-89.
Point 3: Please note that a space must separate the number and unit.
Response: It has been revised item by item according to the reviewer's comments. See Figure 3(a), Figure 5-Figure 8, Figure 10- Figure13. In addition, there are numbers and units marked in yellow in the manuscript.
Author Response File: Author Response.pdf
