A method for predicting performance limit of underwater acoustic source depth binary identification

Abstract

This invention discloses a method for predicting the performance limit of underwater sound source depth binary identification, comprising the following steps: reading in depth binary identification statistical sequences calculated based on the radiated noise signals from surface and underwater sound sources; fitting the probability density functions of the depth binary identification statistical sequences corresponding to surface and underwater sound sources respectively using kernel density estimation; calculating the confusion estimate between the probability density functions of the depth binary identification statistical sequences corresponding to surface and underwater sound sources using numerical integration; mapping the confusion estimate to obtain predicted values ​​of the lower and upper bounds of the sound source depth binary identification accuracy, wherein the predicted values ​​of the lower and upper bounds together constitute the predicted value of the performance limit of underwater sound source depth binary identification. The method proposed in this invention can achieve quantitative prediction of the performance of underwater sound source depth binary identification, providing theoretical support and evaluation benchmarks for the analysis and optimization of the performance of underwater acoustic target depth binary identification algorithms.

Description

Technical Field

[0001] This invention relates to a method for predicting the performance limitations of depth binary identification of underwater sound sources, belonging to the field of feature extraction and identification of underwater acoustic target radiated noise signals. Background Technology

[0002] Target depth is a crucial factor in distinguishing between surface and underwater targets. In shallow-water waveguide environments, sound wave propagation is strongly constrained by the sea surface and seabed boundaries, exhibiting a multipath effect related to target depth. Traditional passive sonar depth identification techniques can be broadly categorized into two types based on signal frequency band characteristics: depth identification techniques based on broadband feature information and depth identification techniques based on narrowband feature information.

[0003] For a long time, methods based on broadband feature information have been the mainstream research in the field of underwater acoustic target depth identification. These methods retrieve target depth by analyzing the continuous and modulation spectra of the target's radiated noise, or by employing broadband matched-field processing techniques. However, with the rapid development of modern ship vibration reduction and noise reduction technologies, the radiated noise level of targets has significantly decreased, leading to a substantial drop in the signal-to-noise ratio (SNR) of broadband features. Furthermore, broadband signals suffer significant propagation losses at high frequencies, and broadband matched-field processing is extremely sensitive to mismatches in marine environmental parameters. In long-range detection or low SNR environments, broadband features are often difficult to extract effectively, significantly impacting the robustness of depth discrimination and drastically reducing accuracy.

[0004] Given this, depth identification techniques based on narrowband feature information have gradually become a research hotspot. Compared to broadband continuous spectrum, narrowband line spectrum components in target radiated noise have significant advantages such as high power spectral density, strong stability, and long propagation distance. According to normal mode theory, sound sources at different depths have varying abilities to excite different modes of normal waves in ocean waveguides, and this depth modulation creates observable physical differences in the sound field. Therefore, existing identification research based on narrowband feature information typically transforms line spectrum source depth identification into a binary hypothesis testing problem. This involves extracting differences in amplitude, phase, or energy distribution from received signals from sound sources at different depths to construct decision statistics, and setting corresponding decision thresholds to achieve binary classification of surface and underwater targets.

[0005] However, despite the promising application prospects of methods based on narrowband feature information, current research on the performance evaluation of decision statistics themselves remains significantly insufficient. Existing techniques mostly focus on constructing new feature quantities and verifying algorithm performance by calculating the recognition accuracy under specific classifiers through Monte Carlo simulations. This evaluation method often couples feature extraction with classifier design, making it difficult to isolate and evaluate the intrinsic discriminative power of decision statistics. Further research is needed on how to quantitatively describe the overlap of statistical distributions corresponding to water surface and underwater sound sources in the feature space, i.e., quantitatively assessing the separability of decision statistics for the two types of targets without being affected by the specific classifier threshold selection.

[0006] This invention proposes a method for predicting the performance limit of underwater sound source depth binary identification. The input is a sequence of depth binary identification statistics calculated from surface and underwater sound source radiated noise signals, and the output is the predicted performance limit of underwater sound source depth binary identification. This method can objectively characterize the depth identification capability of the depth binary identification statistics, providing theoretical support and evaluation benchmarks for the evaluation and optimization of underwater acoustic target depth binary identification algorithms.

[0007] The retrieved prior art documents and their comparison with this patent are listed below:

[0008] I. Technical Comparison with Patent CN111914641A "A Target Depth Identification Method and System Based on Modal Intensity Matching Analysis"

[0009] 1. Patent CN111914641A primarily extracts the normal mode intensity characteristics of the target's radiated noise and performs correlation analysis with the mode intensity of the surface platform's radiated noise. Based on the correlation coefficient, it determines the depth attributes of surface and underwater targets. This patent is mainly based on the idea of ​​matched field processing, relying on the correlation calculation between the copy vector of the physical sound field model and the received data. In contrast, the method disclosed in this invention reads in a pre-calculated sequence of depth binary identification statistics, uses kernel density estimation to fit the probability density function, calculates the confusion estimate, and maps the confusion estimate to obtain a predicted value for the identification performance limit. This invention is based on hypothesis testing theory and combines the statistical characteristics of the depth binary identification statistics to predict the identification performance. Therefore, the two methods rely on different existing theoretical foundations and employ different technical approaches.

[0010] 2. The core of patent CN111914641A lies in using physical features based on modal intensity to construct specific statistics and directly outputting identification results using a matching algorithm, aiming to achieve a specific target depth identification process. In contrast, the method disclosed in this invention maps the confusion estimate corresponding to the statistics to predict identification performance, focusing more on evaluating the depth identification capability of the constructed statistics themselves. This invention does not directly perform real-time target depth determination, but rather aims to quantitatively predict and evaluate the performance boundaries of the identification algorithm. Therefore, it is clear that the two address different technical problems and have different objectives.

[0011] II. Technical Comparison with Patent CN111708007A "Target Depth Identification Method and System Based on Modal Scintillation Index Matching Analysis"

[0012] 1. The input in patent CN111708007A relies on array received data acquired by a horizontal towed linear array, and the radiated noise data of the water surface platform needs to be acquired simultaneously as a matching benchmark during the identification process. Its technical implementation is highly dependent on a specific array configuration and an external reference platform. In contrast, the method disclosed in this invention uses a sequence of depth-binary identification statistics corresponding to the radiated noise signal of a single array element or single beam as input, does not rely on complex array manifold processing, and can perform analysis using only a single received data stream. Therefore, the data input requirements and applicable system scenarios of the two methods are different.

[0013] 2. Patent CN111708007A extracts the first-order modal intensity scintillation index of the target as a feature quantity. It uses matching analysis with the modal component scintillation index corresponding to the radiated noise from the water surface platform to determine the sound source depth attribute, focusing on the construction of the depth binary identification statistics and the real-time discrimination process of specific target depth attributes. In contrast, this invention uses numerical integration to calculate the confusion estimate between the probability density functions of the statistical sequences corresponding to water surface and underwater sound sources. By mapping this confusion estimate, it predicts the identification performance, aiming to establish a general statistical evaluation framework that does not rely on the selection of a specific classifier threshold. It focuses more on quantitatively evaluating and predicting the depth identification capability boundary of the constructed statistics for water surface and underwater targets, providing an evaluation benchmark for various statistical quantities. Therefore, it is evident that the two inventions differ significantly in their technical focus.

[0014] III. Technical Comparison with Patent CN112034440A "A Target Depth Identification Method and System Based on Wavenumber Spectrum Energy Cumulative Distribution"

[0015] 1. Patent CN112034440A processes signals received by a horizontally towed array. Its technical approach starts from the physical level, using modal domain beamforming to calculate the radiated noise of the water surface platform and the modal wavenumber spectrum of the target to be determined. It then extracts the energy accumulation value at one-third of the wavenumber spectrum as a physical feature to construct a depth binary identification statistic. In contrast, this invention processes a sequence of statistics with already extracted features. It no longer focuses on the underlying acoustic field physical model or the specific processing of the original received signal, but directly reads in existing depth binary identification statistical data. Therefore, patent CN112034440A belongs to the target feature extraction and specific depth identification process implementation stage, while this invention belongs to the statistical analysis and performance evaluation stage after feature extraction. Their input objects and processing stages are different.

[0016] 2. The core of patent CN112034440A lies in constructing specific classification criteria, that is, by comparing the difference in the cumulative energy distribution of the wavenumber spectrum between the target to be judged and the reference source, it outputs the discrimination result of the target attribute, aiming to solve the specific binary identification problem of target depth. The core of this invention lies in establishing a general performance prediction model, using kernel density estimation to fit the probability density function of the binary statistics of the depths corresponding to surface and underwater targets, and calculating the confusion estimate through numerical integration, ultimately mapping the confusion estimate to the upper and lower bound prediction values ​​of the identification accuracy. This invention does not directly perform real-time depth determination, but aims to quantitatively predict the theoretically achievable identification capability boundary under the current statistical distribution, aiming to solve the problem of prediction and evaluation of identification capability. Therefore, it is evident that the core processing logic and technical objectives of the two are significantly different. Summary of the Invention

[0017] The purpose of this invention is to address the performance prediction problem of depth binary identification statistics based on the line spectrum fluctuation characteristics of single-element or single-beam target radiated noise signals, and to provide a method for predicting the performance limit of depth binary identification of underwater sound sources. The method takes as input sequences of depth binary identification statistics calculated from surface and underwater sound source radiated noise signals; uses kernel density estimation to fit probability density functions of the depth binary identification statistics sequences corresponding to surface and underwater sound sources respectively; calculates the confusion estimate between the probability density functions using numerical integration; and outputs the predicted performance limit of the depth binary identification of underwater sound sources after mapping the confusion estimate. This prediction result can be used to quantitatively evaluate the depth identification capability boundary of binary identification statistics for surface and underwater targets.

[0018] To achieve the above objectives, the method employed in this invention is: a method for predicting the performance limitations of underwater sound source depth binary identification, comprising the following steps:

[0019] (1) Read in the depth binary identification statistics sequence calculated based on the radiated noise signals from the water surface and underwater sound sources, wherein the statistics sequence includes the δ statistics sequence or the A 1,4 Statistical series;

[0020] (2) Using the kernel density estimation method, the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources are fitted respectively;

[0021] (3) Calculate the confusion estimate between the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources by numerical integration;

[0022] (4) The confusion estimate is mapped to obtain the predicted values ​​of the lower and upper bounds of the sound source depth binary identification accuracy, and the predicted values ​​of the lower and upper bounds together constitute the predicted value of the performance limit of the underwater sound source depth binary identification.

[0023] As a further improvement of the present invention, step (1) specifically includes the following steps:

[0024] Read in the depth binary identification statistics sequence U, calculated from the noise signals radiated from the water surface and underwater sound sources, respectively. sur (v) and U sub (v), v = 0, 1,…, V – 1, where V is the total length of the deep binary identification statistics sequence.

[0025] As a further improvement of the present invention, step (2) specifically includes the following steps:

[0026] (2.1) Let sequence U sur The maximum and minimum values ​​in (v) are U and U, respectively. sur max with U sur min Sequence U sub The maximum and minimum values ​​of (v) are U and U, respectively. sub max with U sub min U max For U sur max and U sub max The maximum of the two, U min For U sur min and U sub min The minimum of the two, in [U min U max Within the interval, samples are taken at equal intervals to generate a resampled sequence x = {x1, x2, ..., x...} containing L observation points.L}; where the step size d between adjacent observation points satisfies d = (U max - U min ) / (L -1), x l = U min + (l - 1)d;

[0027] (2.2) The Gaussian kernel function is selected as the kernel function, and the kernel density estimation method is used to fit the statistical sequence U of the water surface sound source. sur The probability density function f of (v) U_sur (x) and the underwater sound source statistics sequence U sub The probability density function f of (v) U_sub (x).

[0028] As a further improvement of the present invention, step (3) specifically includes the following steps:

[0029] (3.1) Let CD be the confusion degree between the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources. U :

[0030] ;

[0031] (3.2) Regarding the aforementioned confusion level CD U The estimated value was calculated using numerical integration. :

[0032] .

[0033] As a further improvement to the present invention, step 4 specifically includes the following steps:

[0034] The estimated value of the degree of confusion By performing linear and nonlinear mappings, the accuracy A of binary sound source depth identification is obtained respectively. p The lower bound prediction value A p L Compared with the upper bound prediction value A p U :

[0035] ;

[0036] Where p0 and p1 are the prior probabilities of the surface sound source and the underwater sound source, respectively;

[0037] From the A p L With A p U Together they constitute the predicted value of the depth binary identification performance limit of underwater sound sources [A] pL A p U ].

[0038] This invention discloses a method for predicting the performance limit of underwater sound source depth binary identification. The method takes as input a sequence of depth binary identification statistics calculated from the radiated noise signals of surface and underwater sound sources; uses kernel density estimation to fit the probability density functions of the depth binary identification statistics sequences corresponding to surface and underwater sound sources respectively; calculates the estimated value of the confusion degree of the above probability density functions using numerical integration; and maps the estimated value of the confusion degree to obtain the predicted value of the performance limit of underwater sound source depth binary identification. The method proposed in this invention provides a quantitative analytical means for measuring the depth identification performance of depth binary statistics.

[0039] Beneficial effects:

[0040] Compared with existing technologies, the method disclosed in this invention has the following advantages: Existing depth identification evaluation systems based on narrowband features typically rely on specific classifier designs, making it difficult to independently evaluate the effectiveness of the decision statistics themselves without determining the decision threshold. The method proposed in this invention establishes a confusion model between the probability density functions of the binary identification statistics sequence. By mapping the estimated values ​​of confusion, it predicts the performance limit of the statistical identification, providing theoretical support and evaluation benchmarks for the evaluation and optimization of binary depth identification algorithms for underwater acoustic targets. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0042] Figure 2 This is the sequence of depth binary identification statistics corresponding to the surface and underwater sound sources under low overlap conditions in Example 1;

[0043] Figure 3 This is the sequence of depth binary identification statistics corresponding to the water surface and underwater sound sources under the overlapping condition in Example 1;

[0044] Figure 4 This is the sequence of depth binary identification statistics corresponding to the surface and underwater sound sources under high overlap conditions in Example 1;

[0045] Figure 5 This is the probability density function fitted under the low overlap condition in Example 1;

[0046] Figure 6 This is the probability density function fitted under the overlapping condition in Example 1;

[0047] Figure 7 This is the probability density function after fitting in the case of high overlap in Example 1. Detailed Implementation

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0049] This invention proposes a method for predicting the performance limit of depth binary identification of underwater sound sources, realizing the quantitative prediction and analysis of the depth identification performance of depth binary identification statistics.

[0050] Example 1:

[0051] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0052] This embodiment presents a method for predicting the performance limitations of depth-based binary sound source identification in underwater environments. Figure 1 As shown, it includes the following steps:

[0053] Step 1 is as follows:

[0054] (1.1) Setting statistical distribution parameters: To simulate scenarios with low, medium and high overlap, the depth binary identification statistic U of the underwater sound source is set. sub Follows a Gaussian distribution (0,4); Set the depth binary identification statistic U for the water surface sound source. sur They respectively follow Gaussian distributions (10,4) (low overlap) (5,4) (middle overlap) and (1,4) (high overlap). Based on the above distribution, generate the corresponding deep binary identification statistic sequence U. sur (v) and U sub (v), where the total length of the sequence is V = 1500 points, and v = 0, 1, ..., V – 1. The statistical sequences U under low, medium, and high overlap are... sur (v) and U sub (v) respectively as Figure 2 , Figure 3 and Figure 4 As shown.

[0055] Step 2 is as follows:

[0056] (2.1) Let sequence U sur The maximum and minimum values ​​in (v) are U and U, respectively. sur max with U sur min Sequence U sub The maximum and minimum values ​​of (v) are U and U, respectively. sub max with U sub min U max For Usur max and U sub max The maximum of the two, U min For U sur min and U sub min The minimum of the two, in [U min U max Equal-interval sampling is performed within the interval to generate a resampled sequence x = {x1, x2, ..., x} containing L = 2000 observation points. L}; where the step size d between adjacent observation points satisfies d = (U max - U min ) / (L - 1), x l = U min + (l - 1)d;

[0057] (2.2) The Gaussian kernel function is selected as the kernel function, and the kernel density estimation method is used to fit the statistical sequence U of the water surface sound source. sur The probability density function f of (v) U_sur (x) and the underwater sound source statistics sequence U sub The probability density function f of (v) U_sub (x). The probability density functions obtained by fitting under low, medium, and high overlap levels are respectively as follows: Figure 5 , Figure 6 and Figure 7 As shown.

[0058] Step 3 specifically involves:

[0059] (3.1) Let CD be the confusion degree between the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources. U :

[0060] ;

[0061] (3.2) Regarding the aforementioned confusion level CD U The estimated value was calculated using numerical integration. :

[0062] ;

[0063] The calculated confusion estimates were obtained under three levels of overlap: low, medium, and high. As shown in Table 1, the values ​​are 0.0363, 0.4864, and 0.9590, respectively. The results show that the confusion degree is positively correlated with the overlap degree, indicating that the defined confusion degree can effectively quantitatively characterize the degree of overlap in the distribution of the decision statistics of surface and underwater target radiated noise in the feature space.

[0064] Step 4 is as follows:

[0065] (4.1) Estimated value of the aforementioned confusion By performing linear and nonlinear mappings, the accuracy A of binary sound source depth identification is obtained respectively. p The lower bound prediction value A p L Compared with the upper bound prediction value A p U :

[0066] ;

[0067] Where p0 and p1 are the prior probabilities of the surface sound source and the underwater sound source, respectively;

[0068] From the A p L With A p U Together they constitute the predicted value of the depth binary identification performance limit of underwater sound sources [A] p L A p U ].

[0069] Under the prior conditions of surface water source and underwater water source (p0 = p1 = 1 / 2), targeting Figure 5 (Low overlap) Figure 6 (Middle overlap) Figure 7 The performance limits for underwater sound source depth identification calculated under three conditions (high overlap) are shown in Table 1, which are [98.18%, 99.97%], [75.68%, 93.69%], and [52.05%, 64.17%], respectively. Based on the Bayesian minimum error criterion, the depth binary identification statistic sequence U corresponding to surface and underwater sound sources is determined. sur (v) and U sub (v) is the decision threshold, and the target depth binary recognition accuracy A under this threshold is calculated. b In the three overlapping cases mentioned above, the calculated A b As shown in Table 1, the percentages are 99.53%, 88.43%, and 61.67%, respectively. The results indicate that A... b All fall within the confusion estimate The predicted sound source depth binary identification performance is within the predicted value range, and A b and The results show a negative correlation. These results indicate that the confusion level is highly consistent with the actual feature separation degree, and the prediction method for the identification performance limit proposed in this invention can objectively and effectively quantify the identification performance of deep binary identification statistics.

[0070] Table 1. Underwater sound source depth binary identification performance under different overlap levels

[0071]

[0072] The above embodiments demonstrate that the method proposed in this invention can effectively achieve quantitative prediction of the depth binary identification performance of underwater acoustic sources, providing theoretical support and evaluation benchmark for the analysis and optimization of underwater acoustic target depth binary identification algorithms.

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting the performance limitations of underwater sound source depth binary identification, characterized in that, Includes the following steps: (1) Read in the depth binary identification statistics sequence calculated based on the noise signals radiated from the water surface and underwater sound sources; (2) Using the kernel density estimation method, the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources are fitted respectively; (3) Calculate the confusion estimate between the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources by numerical integration; (4) The confusion estimate is mapped to obtain the predicted values ​​of the lower and upper bounds of the sound source depth binary identification accuracy, and the predicted values ​​of the lower and upper bounds together constitute the predicted value of the performance limit of the underwater sound source depth binary identification.

2. The method for predicting the performance limitations of underwater sound source depth binary identification according to claim 1, characterized in that, Step (3) specifically includes the following steps: (3.1) Let CD be the confusion degree between the probability density functions of the depth binary identification statistics sequences corresponding to the water surface and underwater sound sources. U : ； Among them, f U_sur (x) is the probability density function of the statistical sequence of water surface sound sources, f U_sub (x) is the probability density function of the underwater sound source statistics sequence; (3.2) Regarding the aforementioned confusion level CD U The estimated value was calculated using numerical integration. : ； Where L is the number of observation points.

3. The method for predicting the performance limitations of underwater sound source depth binary identification according to claim 2, characterized in that, Step (4) specifically includes the following steps: The estimated value of the degree of confusion By performing linear and nonlinear mappings, the accuracy A of binary sound source depth identification is obtained respectively. p The lower bound prediction value A p L Compared with the upper bound prediction value A p U : ； Where p0 and p1 are the prior probabilities of the surface sound source and the underwater sound source, respectively; The lower bound prediction value A p L Compared with the upper bound prediction value A p U Together they constitute the predicted value of the depth binary identification performance limit of underwater sound sources [A] p L A p U ].

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