Robust Sparse Bayesian Learning Source Localization in an Uncertain Shallow-Water Waveguide

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Since the computation cost and efficiency are important for reader. It is better to compare the computation cost and efficiency of the MPR-SBL and SBL.

2. In Fig.4, It is seen the locations of two sources in during time 35 ~ 50，but in other time, only one source location is seen. How about the performance of the MPR-SBL when there is only one source? or more than two sources? It should be discussed.

 3. How to choose the predictable modes? The influence of the choice is better to be discussed.

Author Response

We would like to thank the editor for his encouraging remarks and the reviewer for his (or her) excellent comments on this manuscript. We have substantially revised the manuscript with reference to comments and suggestions given by the reviewers.

In the following section, we provide a point-by-point answer to each of the reviewer’s comments and the related modifications done in the manuscript. (All the parts differing from the old version are noted in red; our answer for each comment is noted in bold.)

 

Comments 1: Since the computation cost and efficiency are important for reader. It is better to compare the computation cost and efficiency of the MPR-SBL and SBL.

Response 1: The authors greatly appreciate the reviewer for his (or her) remarks. We have included a paragraph in Section 3.3 to provide a more detailed discussion of the computational efficiency issues associated with the proposed method, as follows:

From the perspective of computational efficiency, the average execution time of the Bartlett algorithm is 0.01164 seconds, whereas that of the SBL algorithm is significantly longer at 7.4012 seconds in the case of limited computational resources. Additionally, it should be noted that considering predictable normal modes will further increase both computation and processing time. However, experimental results indicate that the proposed method effectively enhances localization accuracy for weak sources and mitigates issues related to localization misalignment or even complete failure due to environmental mismatches. The trade-off of a modest amount of computing time yields higher and more stable underwater weak source localization accuracy, making this approach feasible for practical ocean exploration applications.

 

Comments 2: In Fig.4, It is seen the locations of two sources in during time 35 ~ 50, but in other time, only one source location is seen. How about the performance of the MPR-SBL when there is only one source? or more than two sources? It should be discussed.

Response 2: The authors greatly appreciate the reviewer for his (or her) remarks. Initially, Figure 4 in the original version has been renumbered as Figure 5 in the revised version. Besides, this paper primarily addresses the issue of weak source localization in the context of environmental mismatch. To facilitate a comprehensive analysis under typical experimental conditions, at least two sources are required for comparison. Consequently, to maintain consistency with the overall experimental framework presented in this study, experiments are conducted using two sources. This approach allows for a thorough consideration of both single-source and multi-source scenarios. Notably, the experimental results also demonstrate that the proposed method is effective for single-source localization as well. Finally, we have revised a paragraph in Section 3.4 to provide a more detailed discussion of the number of located sources, as follows:

By analyzing the positioning results of a source with stronger power, it is evident that while all four processors can approximate the motion trajectory, the trajectory obtained using MPR-SBL is significantly clearer. This indicates that MPR-SBL demonstrates superior positioning performance even in scenarios involving a single source. Therefore, the experiment demonstrates that the MPR-SBL algorithm outperforms the SBL algorithm in identifying and locating weak sound sources as well as single sources when there is a mismatch in the actual environment. In contrast, both the MPR-Bartlett and Bartlett algorithms struggle to effectively identify and locate weak sound sources.

 

 

Comments 3: How to choose the predictable modes? The influence of the choice is better to be discussed.

Response 3: We sincerely apologize for the lack of clarity in our explanation regarding the selection method for the predictable modes. In the latest version, we have thoroughly outlined the mode selection process, which is primarily based on Equations (5) to (10). Additionally, we have included a detailed description of the predictable modes selection process in Section 2.2, as follows:

Based on the variations in the horizontal wave number k_b and the eigenfunctions Z_b of normal modes, it is possible to assess the impact of environmental mismatches on these waves. The predictable modes are identified through normal mode decomposition[18,19], which involves decomposing the acoustic field (as illustrated in Eq. 4) into a predictable subspace and an unpredictable one. This process aims to identify the normal modes that are least affected by environmental mismatches[12].

Reviewer 2 Report

Comments and Suggestions for Authors

1. The paper mentions that conventional MFP is sensitive to environmental mismatch. Quantify the level of environmental uncertainty considered in the simulations and the SWellEx-96 dataset. Specify the types of environmental uncertainties included (e.g., sound speed profile variations, bottom properties, bathymetry uncertainties). Describe how these uncertainties were modeled and incorporated into the simulations and the real-world dataset analysis. A clear characterization of the uncertainty is essential to evaluate the robustness of the proposed method.
2. The MPR-SBL method utilizes two hyperparameters: source powers and noise variance. Describe the methods used for selecting or estimating these hyperparameters. Perform and present a sensitivity analysis to assess the impact of variations in these hyperparameters on the performance of the MPR-SBL algorithm. Demonstrate that the algorithm's performance is relatively insensitive to reasonable variations in the hyperparameters, thereby establishing the robustness of the proposed method.
3. Explain the details of the mode decomposition used to obtain the predictable modes. Specify the type of mode decomposition technique used (e.g., normal mode decomposition, eigenfunction decomposition) and provide a justification for its selection. Analyze the impact of the number of predictable modes selected on the performance of the algorithm. Provide results showing how variations in the number of modes used affect accuracy and computational cost.
4. The paper mentions better performance in a two-source scenario, especially for the weaker source. Provide a detailed quantitative comparison with the Bartlett processor and the original sparse Bayesian learning (SBL) method. Include metrics such as localization accuracy (e.g., root mean square error), resolution, probability of detection, and false alarm rate. Use statistical significance tests (e.g., t-tests, Wilcoxon rank-sum tests) to determine if the observed differences are statistically significant.
5. Discuss the computational complexity of the MPR-SBL algorithm and compare it to the Bartlett processor and the original SBL method. Analyze the computational time required for processing different sized datasets. Assess the feasibility of implementing the MPR-SBL algorithm in real-time applications, considering the computational requirements and the typical data rates involved in acoustic source localization systems. Provide specific runtimes for the algorithm on the datasets used.
6. It is suggested to go through the following papers

·        An amended grey wolf optimization with mutation strategy to diagnose bucket defects in Pelton wheel

 

·        An effective health indicator for the Pelton wheel using a Levy flight mutated genetic algorithm

Author Response

Manuscript : # electronics-3313896 B, “Robust sparse Bayesian learning source localization in an uncertain shallow-water waveguide”, by Bing Zhang, Rui Jin, Longyu Jiang, Lei Yang and Tao Zhang.

We would like to thank the editor for his encouraging remarks and the reviewer for his (or her) excellent comments on this manuscript. We have substantially revised the manuscript with reference to comments and suggestions given by the reviewers.

In the following section, we provide a point-by-point answer to each of the reviewer’s comments and the related modifications done in the manuscript. (All the parts differing from the old version are noted in red; our answer for each comment is noted in bold.)

 

Comments 1: The paper mentions that conventional MFP is sensitive to environmental mismatch. Quantify the level of environmental uncertainty considered in the simulations and the SWellEx-96 dataset. Specify the types of environmental uncertainties included (e.g., sound speed profile variations, bottom properties, bathymetry uncertainties). Describe how these uncertainties were modeled and incorporated into the simulations and the real-world dataset analysis. A clear characterization of the uncertainty is essential to evaluate the robustness of the proposed method.

Response 1: We sincerely apologize for the lack of clarity in our explanation regarding the methods by which the uncertain environment can be modeled and incorporated  into the experimental data. The modeling of environmental parameters will be incorporated into the construction of acoustic field data as outlined in Eq. 4. In the experimental context, KRAKEN software can be utilized to generate acoustic fields that correspond to mismatched environments, thereby integrating environmental parameters into the experimental dataset. In the latest version of the manuscript, we have clarified this in the relevant paragraphs of Section 3, as follows:

the corresponding predictable normal waves are calculated by using Eq. 9. Meanwhile, the acoustic field modeling, when combined with various uncertain environmental parameters simultaneously, can be represented by Eq. 4. In the experiments described in this paper, the acoustic field dataset is generated using KRAKEN [17]. KRAKEN is a specialized software for acoustic field calculations based on mode theory, which accepts all mismatched environmental parameters listed in Table 1 and Table 2 as input. This approach effectively integrates all relevant environmental parameters into the corresponding acoustic field data.

 

Comments 2: The MPR-SBL method utilizes two hyperparameters: source powers and noise variance. Describe the methods used for selecting or estimating these hyperparameters. Perform and present a sensitivity analysis to assess the impact of variations in these hyperparameters on the performance of the MPR-SBL algorithm. Demonstrate that the algorithm's performance is relatively insensitive to reasonable variations in the hyperparameters, thereby establishing the robustness of the proposed method.

Response 2: We sincerely apologize for the lack of clarity in our explanation regarding the hyperparameters γ and σ² . The hyperparameters  γ and  σ² are estimated using a type-II maximum likelihood approach, as outlined in Eq. 14. The specific calculation processes for  γ and σ²  are detailed in Eqs. 16 and 17, respectively. For the MPR-SBL and SBL methods, the localization results are contingent upon the estimated values of these two hyperparameters; thus, the accuracy of their estimation directly influences the precision of source localization. The insensitivity mentioned in the manuscript pertains to parameter K. In the latest version of the manuscript, we have provided further clarification on this matter in Section 2.3, as follows:

The active set M comprises the indices of the nonzero elements of x_l, which can be derived from the K strongest peaks of γ. This information serves as an estimate for the source location.

 

Comments 3: Explain the details of the mode decomposition used to obtain the predictable modes. Specify the type of mode decomposition technique used (e.g., normal mode decomposition, eigenfunction decomposition) and provide a justification for its selection. Analyze the impact of the number of predictable modes selected on the performance of the algorithm. Provide results showing how variations in the number of modes used affect accuracy and computational cost.

Response 3: The authors greatly appreciate the reviewer for his (or her) remarks. This suggestion holds significant importance for both this paper and the whole research group. Analyzing the impact of the number of predictable modes on the decomposition and subsequent positioning process of normal modes is crucial. We will continue to enhance our approach and conduct in-depth research in future studies.  At the same time, we have revised relevant content in Section 2.2 to provide a more detailed discussion of the mode decomposition issues, as follows:

Based on the variations in the horizontal wave number k_b and the eigenfunctions Z_b of normal modes, it is possible to assess the impact of environmental mismatches on these waves. The predictable modes are identified through normal mode decomposition[18,19], which involves decomposing the acoustic field (as illustrated in Eq. 4) into a predictable subspace and an unpredictable one. This process aims to identify the normal modes that are least affected by environmental mismatches[12].

 

Comments 4: The paper mentions better performance in a two-source scenario, especially for the weaker source. Provide a detailed quantitative comparison with the Bartlett processor and the original sparse Bayesian learning (SBL) method. Include metrics such as localization accuracy (e.g., root mean square error), resolution, probability of detection, and false alarm rate. Use statistical significance tests (e.g., t-tests, Wilcoxon rank-sum tests) to determine if the observed differences are statistically significant.

Response 4: The authors greatly appreciate the reviewer for his (or her) remarks. We have included relevant paragraphs in Section 3.3 to provide a more detailed discussion of the quantitative comparison, as follows:

According to quantitative analysis, the PCL values for MPR-SBL, SBL, MPR-Bartlett, and Bartlett processors stabilize at 0.605, 0.507, 0.008, and 0.02 respectively in the genlmis scenario. In the SWellEx-96 scenario, the final stability values are 0.317, 0.315, 0.04, and 0.042 respectively. In other words, even in cases of complete environmental mismatch, both MPR-SBL and SBL demonstrate a certain degree of localization resolution capability; conversely, MPR-Bartlett and Bartlett algorithms nearly lose their localization ability altogether.

In contrast, the RMSE of range for MPR-Bartlett and Bartlett processors is approximately 2 km, while the RMSE of depth exceeds 5 m in the genlmis mismatch scenario. In the SWellEx-96 mismatch scenario, the RMSE of range approaches 2.5 km, and the RMSE of depth is nearly 25 m. These findings illustrate the effectiveness and advancement of MPR-SBL in situations characterized by complete environmental mismatch.

 

Comments 5: Discuss the computational complexity of the MPR-SBL algorithm and compare it to the Bartlett processor and the original SBL method. Analyze the computational time required for processing different sized datasets. Assess the feasibility of implementing the MPR-SBL algorithm in real-time applications, considering the computational requirements and the typical data rates involved in acoustic source localization systems. Provide specific runtimes for the algorithm on the datasets used.

Response 5: The authors greatly appreciate the reviewer for his (or her) remarks. We have included a paragraph in Section 3.3 to provide a more detailed discussion of the computational efficiency issues associated with the proposed method, as follows:

From the perspective of computational efficiency, the average execution time of the Bartlett algorithm is 0.01164 seconds, whereas that of the SBL algorithm is significantly longer at 7.4012 seconds in the case of limited computational resources. Additionally, it should be noted that considering predictable normal modes will further increase both computation and processing time. However, experimental results indicate that the proposed method effectively enhances localization accuracy for weak sources and mitigates issues related to localization misalignment or even complete failure due to environmental mismatches. The trade-off of a modest amount of computing time yields higher and more stable underwater weak source localization accuracy, making this approach feasible for practical ocean exploration applications.

 

Comments 6: It is suggested to go through the following papers:

An amended grey wolf optimization with mutation strategy to diagnose bucket defects in Pelton wheel.

An effective health indicator for the Pelton wheel using a Levy flight mutated genetic algorithm.

Response 6: The authors greatly appreciate the reviewer for his (or her) remarks. These two papers have significantly influenced the research presented in this manuscript. We have provided a summary of their contributions and included them in the reference list, as follows:

18. Vashishtha, Govind, and Rajesh Kumar. "An amended grey wolf optimization with mutation strategy to diagnose bucket defects in Pelton wheel." Measurement 187 (2022): 110272.

19. Vashishtha, Govind, and Rajesh Kumar. "An effective health indicator for the Pelton wheel using a Levy flight mutated genetic algorithm." Measurement Science and Technology 32.9 (2021): 094003.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The current paper is a well-written paper that introduces a novel approach for locating noise sources in shallow water. Its primary objective is to present the results of the "MRP-SBL" approach through simulation.

While I am not an underwater acoustics specialist and cannot fully evaluate the technical approach itself, I will primarily focus on the form rather than the content. That said, I believe the content is well-structured and accessible, allowing non-specialist readers to grasp the purpose of the paper. Although the method is clearly presented, there is room for improvement in the presentation and analysis of the results and their implications.

 

The conclusion is not a conclusion and should be improved.

 

On the form, globally, the paper is well presented. The major point of improvement should be placed in the figures. Here are some improvements to be made :

-          Figure 2, 3, 4 : the scales are not fixed from one subfigure to the other

-          Fig 3 : there are 2 scenarios presenting depth and distance. It should not be presented as subfigures.

-          Fig 2,3,4 : caption presenting the figures have to be rewritten.

o   Example for figure 2 :  Accuracy (PCL) as a function of the SNR, evaluated for 4 different models (four colors in the graphs), on 2 different scenarios : (a) gelmis and (b) SWellEx-96.

-          Fig3 : each subfigure for a same scenario should be labelled as : Distance or Depth

Author Response

Manuscript : # electronics-3313896 B, “Robust sparse Bayesian learning source localization in an uncertain shallow-water waveguide”, by Bing Zhang, Rui Jin, Longyu Jiang, Lei Yang and Tao Zhang.

We would like to thank the editor for his encouraging remarks and the reviewer for his (or her) excellent comments on this manuscript. We have substantially revised the manuscript with reference to comments and suggestions given by the reviewers.

In the following section, we provide a point-by-point answer to each of the reviewer’s comments and the related modifications done in the manuscript. (All the parts differing from the old version are noted in red; our answer for each comment is noted in bold.)

 

The authors greatly appreciate the reviewer for his (or her) remarks. We have seriously modified the manuscript to address all these issues. We have provided individual responses to each of comments from the reviewer. Please find them in the responses to the detailed comments of the reviewer in the following part.

 

Comments 1: The conclusion is not a conclusion and should be improved.

Response 1: The authors greatly appreciate the reviewer for his (or her) remarks. We have revised the paragraph in Section 4 to summarize the work in this paper, as follows:

In this paper, we propose a MPR-SBL algorithm aimed at enhancing the accuracy and stability of underwater source localization, specifically addressing the environmental mismatch problem commonly encountered in traditional MFP. The algorithm integrates a predictable normal mode with sparse Bayesian learning (SBL), leveraging the sparse solution properties of SBL to improve the estimation of weak source locations. Compared to existing MFP algorithms and conventional SBL methods, our proposed algorithm demonstrates superior accuracy and stability in both range and depth estimations of the source.

 

Comments 2: On the form, globally, the paper is well presented. The major point of improvement should be placed in the figures. Here are some improvements to be made :

2.1) Figure 2, 3, 4 : the scales are not fixed from one subfigure to the other

Response 2: We sincerely apologize for the problem of unfixed scale in Figure 2, 3 and 4. In the latest revision, we have standardized the dimensions of all Figures to ensure uniformity. Additionally, to achieve consistency between graphics and text, all instances of "distance" in the manuscript have been revised to "range".

 

2.2) Figure 3: there are 2 scenarios presenting depth and distance. It should not be presented as subfigures.

Response 2: The authors greatly appreciate the reviewer for his (or her) remarks. We have divided the original Figure 3 into two separate figures: Figure 3, which illustrates the "genlmis" scenario, and Figure 4, which depicts the "SwellEX-96" scenario. We have revised the paragraph in Section 3.3 to ensure that the textual descriptions align consistently with the accompanying diagram, as follows:

RMSE of weak source in range and depth is shown in Figure. 3 and Figure. 4, in which Figure. 3 (a) and (b) respectively represent RMSE in range and depth under the scenario of genlmis mismatch, and Figure. 4 (a) and (b) respectively represent RMSE in range and depth under the scenario of SWellEx-96 mismatch. Blue lines represent MFR-Bartlett results, red lines represent MPR-SBL results, yellow lines represent Bartlett results, and green lines represent SBL results. It can be seen from Figure. 3 and Figure. 4 that with the increase of SNR, RMSE decreases continuously and approaches to a constant value. The mean square error of SWellEx-96 in water depth, sound velocity and sediment properties is larger than that of genlmis scene, so the error in depth is close to 5m and in range is close to 1km of the genlmis scene, while the error in depth is close to 20 m and range is close to 2km of the SWellEx-96 scene. In genlmis scene, MPR-SBL is similar to SBL in depth error, but the range error is smaller when SNR is greater than 5dB, which makes the PLC corresponding to MPR-SBL higher; In SWellEx-96 scenario, MPR-SBL has slightly lower errors in depth and range than SBL algorithm, which is consistent with its slightly higher PCL than SBL. In contrast, the RMSE of range for MPR-Bartlett and Bartlett processors is approximately 2 km, while the RMSE of depth exceeds 5 m in the genlmis mismatch scenario. In the SWellEx-96 mismatch scenario, the RMSE of range approaches 2.5 km, and the RMSE of depth is nearly 25 m. These findings illustrate the effectiveness and advancement of MPR-SBL in situations characterized by complete environmental mismatch. Figure. 3 and Figure. 4 basically verifies the results of Figure. 2.

 

2.3) Fig 2,3,4 : caption presenting the figures have to be rewritten. Example for figure 2: Accuracy (PCL) as a function of the SNR, evaluated for 4 different models (four colors in the graphs), on 2 different scenarios : (a) gelmis and (b) SWellEx-96.

Response 2: The authors greatly appreciate the reviewer for his (or her) remarks. We have revised the captions of Figures 2, 3, 4 and 5 in accordance with the provided reference, as follows:

Figures 2: Accuracy (PCL) as a function of the SNR, evaluated for 4 different models (the four markers and colors in the figure), on 2 different scenarios: (a) the gelmis mismatch; (b) the SWellEx-96 mismatch.

Figures 3: Root mean square errors (RMSE) as a function of the SNR, evaluated the error variation trend of weak source in depth and range for 4 different models (the four markers and colors in the figure) under the scenario of a genlmis mismatch: (a)the range; (b)the depth.

Figures 4: Root mean square errors (RMSE) as a function of the SNR, evaluated the error variation trend of weak source in depth and range for 4 different models (the four markers and colors in the figure) under the scenario of a SWellEx-96 mismatch: (a)the range; (b)the depth.

Figures 5: Localization results of 4 different models on the SWellEx-96 dataset for two sources: (a) The MPR-Bartlett; (b) The MPR-SBL; (c) The Bartlett; (d) The SBL.

 

2.4) each subfigure for a same scenario should be labelled as : Distance or Depth

Response 2: The authors greatly appreciate the reviewer for his (or her) remarks. We have labeled the pertinent subfigures as "Range" and "Depth".

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

No further comments