A seawater sound velocity profile inversion method and device based on an HMC algorithm
By employing an HMC-based method for inverting seawater sound velocity profiles, and utilizing interpolation and empirical orthogonal function decomposition combined with the HMC sampling algorithm, the problem of obtaining seawater sound velocity profiles was solved, achieving efficient and accurate sound velocity profile reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2023-11-07
- Publication Date
- 2026-07-07
AI Technical Summary
In the current technology, it is difficult to obtain the sound velocity profile of seawater. Direct measurement is time-consuming and labor-intensive, while indirect measurement depends on instruments and cannot be applied during navigation.
A seawater sound velocity profile inversion method based on the HMC algorithm is adopted. Through interpolation preprocessing and empirical orthogonal function decomposition, combined with the HMC sampling algorithm, the seawater sound velocity profile is reconstructed by calculating the empirical orthogonal function coefficients.
It achieves efficient and accurate seawater acoustic velocity profile inversion, reduces the number of unknown parameters, and improves inversion efficiency and accuracy.
Smart Images
Figure CN117572431B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of seawater sound velocity profile inversion, and particularly relates to a method and apparatus for seawater sound velocity profile inversion based on the HMC algorithm. Background Technology
[0002] Sound velocity profiles are among the most important parameters of the marine environment. Different sound velocity profiles indicate significant differences in sound propagation in the ocean, and sound velocity profiles are crucial for underwater communication and detection. Therefore, researching how to obtain sound velocity profiles has significant military and civilian value. Generally, seawater sound velocity profiles are obtained through two methods: direct measurement and indirect measurement. Direct measurement involves using a sound velocity profiler to measure sound velocity, but this is time-consuming, labor-intensive, and highly susceptible to external influences. Indirect measurement involves using hydrological instruments, such as temperature, salinity, and depth gauges (TDM), to measure seawater temperature and salinity, and then using empirical formulas to calculate the sound velocity profile using these environmental factors. However, indirect measurement relies on instruments such as TDM and thermal probes, which has drawbacks such as time-consuming and labor-intensive instrument retrieval and inapplicability during transit. Summary of the Invention
[0003] The purpose of this invention is to propose a method and apparatus for inverting seawater sound velocity profiles based on the HMC algorithm, which solves the problem of difficulty in obtaining seawater sound velocity profiles, thereby enabling the efficient acquisition of seawater sound velocity profiles.
[0004] To achieve the above objectives, the present invention adopts the following technical solution.
[0005] A method for inverting seawater acoustic velocity profiles based on the HMC algorithm includes the following steps:
[0006] S1. Based on historical sound velocity profile data, the acquired data is preprocessed by interpolation, and then empirical orthogonal function decomposition is performed to obtain the empirical orthogonal function expression of the sound velocity profile.
[0007] S2. Calculate the time required for sound to propagate to different depths based on the empirical orthogonal function expression of the obtained sound velocity profile;
[0008] S3. Based on the obtained time as observation data, an inversion algorithm model is performed based on the HMC sampling algorithm principle, and then the result dataset is obtained by sampling.
[0009] S4. Calculate the mean and standard deviation of the data based on the obtained dataset. The mean is the empirical orthogonal function value obtained by inversion.
[0010] S5. Use the empirical orthogonal function values obtained by inverting the HMC algorithm to reconstruct the seawater sound speed profile, and finally complete the inversion of the seawater sound speed profile.
[0011] The beneficial effects of this invention are: Based on the HMC sampling algorithm, this invention uses the time taken for sound waves to propagate to different depths to invert the sound velocity profile of seawater, so that the HMC sampling algorithm can accurately calculate the empirical orthogonal function coefficients of the sound velocity profile, thereby completing the inversion of the sound velocity profile of seawater and providing a new method for the inversion of the sound velocity profile of seawater.
[0012] For further improvement or specific implementation of the aforementioned seawater sound velocity profile inversion method based on the HMC algorithm, step S1 includes the following steps:
[0013] S101. Using the raw seawater sound velocity profile data obtained from historical observations as input data, interpolation is performed on the depth at equal intervals of 1 meter. The final dataset contains seawater depths from 0 to N meters, with an interval of 1 meter, corresponding to a total of M historical sound velocity profile data.
[0014] S102. Perform empirical orthogonal function decomposition on the interpolated data, and represent the original data as a matrix C, where N is the number of discrete depths and M is the number of sound velocity profiles, as shown below:
[0015]
[0016] The average sound speed profile can be obtained As shown below:
[0017]
[0018] Where c i (z j ) represents the sound velocity corresponding to the i-th sound velocity profile at sea depth zj.
[0019] The covariance matrix R can be obtained as shown below, where Δc i (z j The ) represents the difference between the observed i-th sound speed profile and the average sound speed profile:
[0020]
[0021] By performing eigenvalue decomposition on the covariance matrix R, we can obtain N mutually orthogonal eigenvectors f. n and the corresponding eigenvalue λ n Then the covariance matrix R can be expressed in the following form:
[0022]
[0023] The N eigenvalues obtained through orthogonal decomposition are arranged in descending order, i.e., λ1>λ2>…>λ nThen, the eigenvectors (i.e., empirical orthogonal functions) corresponding to the first K eigenvalues are selected to represent the sound velocity profile to be inverted. The sound velocity value at any point in the observed sea area can then be expressed in the following form:
[0024]
[0025] Where a k (x, y) are the coefficients of the Kth order empirical orthogonal function, calculated as follows:
[0026]
[0027] S103. The coefficients a1, a2, a3 of the first three empirical orthogonal functions obtained from the calculation are used as unknown parameters to be inverted.
[0028] The beneficial effect of the above-mentioned further scheme is that the present invention reduces the number of unknown parameters that need to be inverted by decomposing the original sound velocity profile data into empirical orthogonal functions and using empirical orthogonal functions to characterize the sound velocity profile, thus enabling the use of the HMC sampling algorithm to better invert the unknown parameters.
[0029] For further improvement or specific implementation of the aforementioned seawater sound velocity profile inversion method based on the HMC algorithm, step S2 includes the following steps:
[0030] S201. Based on the characteristics of the sound velocity profile changing with time, the time taken for sound waves to propagate to different depths is selected as the observation data. Let t1 be the time required for the sound wave to travel from the ocean surface to a discrete point n1, t2 be the time required to travel from the ocean surface to point n2, and so on. The time required for the sound wave to travel from the ocean surface to the nth point can be denoted as t. n ;
[0031] S202, Record the actual observed data as T obs The observation time is the combination of time taken for sound waves to travel to different depths, i.e., T. obs =(t1,t2,…,t n ).
[0032] For further improvement or specific implementation of the aforementioned seawater sound velocity profile inversion method based on the HMC algorithm, step S3 includes the following steps:
[0033] S301. Determine the target parameters to be inverted, namely the prior distribution and initial value q of the first three empirical orthogonal coefficients α = (α1, α2, α3). (0) =α (0) Based on the obtained time observation data, construct the target distribution function;
[0034] S302. Determine the numerical settings of hyperparameters in the HMC algorithm, perform algorithm modeling based on the HMC sampling algorithm, and finally run the algorithm to complete sample sampling.
[0035] S303. Finally, the sample values of the target parameter α = (α1, α2, α3) obtained by the HMC algorithm are processed. The sample values of the combustion period are discarded and the sample mean is calculated as the inversion estimate of the target parameter.
[0036] The beneficial effects of the above-mentioned further scheme are: the present invention uses the HMC algorithm to complete the inversion calculation of the seawater sound velocity profile, which effectively improves the efficiency of inverting the seawater sound velocity profile and provides a new method for the inversion of the seawater sound velocity profile.
[0037] For a further improvement or specific implementation of the aforementioned seawater sound velocity profile inversion method based on the HMC algorithm, the objective likelihood function expression of the HMC sampling algorithm is as follows:
[0038]
[0039] Where q is the target parameter to be inverted, α = (α1, α2, α3), e is the error between the observed value and the model output value, and the error e follows a standard normal distribution N(0, I). σ is the standard deviation of the distribution that the error e follows. The specific expression for the error e is e = T. obs -T cal .
[0040] A seawater acoustic velocity profile inversion device based on the HMC algorithm includes a data processing module, an objective function construction module, and an inversion module;
[0041] The data processing module is used to process the acquired historical ocean sound velocity profile data and calculate the time observation data;
[0042] The objective function construction module constructs the objective parameter distribution based on the obtained time observation data and the prior distribution of the objective parameters;
[0043] The inversion module is used to invert the empirical orthogonal function coefficients of the seawater sound velocity profile.
[0044] The beneficial effects of the aforementioned scheme are: the inversion of seawater sound velocity profile based on the HMC sampling algorithm of this invention can accurately calculate the relationship between parameters using the constructed target distribution function, and efficiently complete the inversion of seawater sound velocity profile using the HMC sampling algorithm, providing a new method for the inversion of seawater sound velocity profile. Attached Figure Description
[0045] Figure 1 This is a flowchart of the HMC sampling algorithm of the present invention for inverting the sound velocity profile of seawater;
[0046] Figure 2 This is a flowchart of the module for inverting the sound velocity profile of seawater using the HMC sampling algorithm of this invention. Detailed Implementation
[0047] The present invention will be described in detail below with reference to specific embodiments.
[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be noted that similar or identical parts are referred to by the same reference numerals in the accompanying drawings or description. Implementations not shown or described in the drawings are forms known to those skilled in the art. The relevant prior art is explained as follows:
[0049] Seawater sound speed profile: refers to the change in sound speed with depth, i.e., the sound speed-depth function relationship.
[0050] HMC sampling algorithm: It is a dynamics-based MCMC algorithm that uses Hamiltonian dynamics to construct Markov chains, thereby efficiently sampling from the constructed target distribution.
[0051] Example 1
[0052] Sound velocity profiles are among the most important parameters of the marine environment. Different sound velocity profiles indicate significant differences in sound propagation in the ocean, and sound velocity profiles are crucial for underwater communication and detection. Therefore, researching how to obtain sound velocity profiles has significant military and civilian value. Generally, seawater sound velocity profiles are obtained through two methods: direct measurement and indirect measurement. Direct measurement involves using a sound velocity profiler to measure sound velocity, but this is time-consuming, labor-intensive, and highly susceptible to external influences. Indirect measurement involves using hydrological instruments, such as temperature, salinity, and depth gauges (TDM), to measure seawater temperature and salinity, and then using empirical formulas to calculate the sound velocity profile using these environmental factors. However, indirect measurement relies on instruments such as TDM and thermal probes, which has drawbacks such as time-consuming and labor-intensive instrument retrieval and inapplicability during transit. Therefore, in recent years, methods for using existing information to inversely deduce sound speed profile parameters—that is, methods for obtaining sound speed profile-related information using inversion methods—have received increasing attention from scholars. Using inversion methods to deduce key parameters of the sound speed profile and then reconstructing the sound speed profile is another approach to obtaining the sound speed profile. Based on inversion theory, exploring and selecting suitable machine learning algorithms to complete the inversion of seawater sound speed profiles is also extremely important. For example... Figure 1 This invention provides a method for retrieving sound velocity profiles based on the HMC sampling algorithm, the implementation of which is as follows:
[0053] S1. Based on historical sound velocity profile data, the acquired data is preprocessed by interpolation, and then empirical orthogonal function decomposition is performed to obtain the empirical orthogonal function expression of the sound velocity profile.
[0054] S101. The raw seawater sound velocity profile data obtained from historical observations is used as input data. Then, the data is interpolated at equal intervals of 1 meter in depth. The final dataset contains seawater depths from 0 to N meters, with an interval of 1 meter, corresponding to a total of M historical sound velocity profile data.
[0055] S102. Perform empirical orthogonal function decomposition on the interpolated data. First, represent the original data as a matrix C, where N is the number of discrete depths and M is the number of sound velocity profiles, as shown below:
[0056]
[0057] The average sound speed profile can be obtained As shown below:
[0058]
[0059] The covariance matrix R can be obtained as shown below, where Δc i (z j The ) represents the difference between the observed i-th sound speed profile and the average sound speed profile:
[0060]
[0061] By performing eigenvalue decomposition on the covariance matrix R, we can obtain N mutually orthogonal eigenvectors f. n and the corresponding eigenvalue λ n Then the covariance matrix R can be expressed in the following form:
[0062]
[0063] The N eigenvalues obtained through orthogonal decomposition are arranged in descending order, i.e., λ1>λ2>…>λ n Then, the eigenvectors (i.e., empirical orthogonal functions) corresponding to the first K eigenvalues are selected to represent the sound speed profile to be inverted. The empirical orthogonal function expression for the sound speed profile over the observed sea area can then be expressed as follows:
[0064]
[0065] Where a k (x, y) are the coefficients of the Kth order empirical orthogonal function, calculated as follows:
[0066]
[0067] S103. The coefficients a1, a2, a3 of the first three empirical orthogonal functions obtained from the calculation are used as unknown parameters to be inverted.
[0068] In this embodiment, the input original historical sound velocity profile data and the interpolated sound velocity profile data are shown in Table 1 and Table 2, respectively, and the values of the coefficients a1, a2, a3 of the first three order empirical orthogonal functions obtained by decomposition are shown in Table 3.
[0069] Serial Number 1 2 3 … 2920 1 1537.45568 1537.5017 1537.5640 … 1536.7984 2 1537.6162 1537.6708 1537.3748 … 1536.9465 3 1537.7767 1537.8309 1537.9011 … 1537.0810 4 151537.9125 1537.9809 1538.0626 … 1537.1845 … … … … … … 50 1531.3747 1531.3753 1531.3750 … 1531.8404
[0070] Table 1
[0071] Serial Number 1 2 3 … 2920 1 1544.3129 1544.3171 1544.3165 … 1544.8125 2 1544.2954 1544.29956 1544.2989 … 1544.7947 3 1544.2777 1544.2819 1544.2813 … 1544.7772 4 1544.2601 1544.2644 1544.2636 … 1544.7596 … … … … … … 5000 1537.3754 1537.7141 1537.4787 … 1536.7243
[0072] Table 2
[0073] <![CDATA[α1]]> <![CDATA[α2]]> <![CDATA[α3]]> <![CDATA[α4]]> <![CDATA[α5]]> <![CDATA[α6]]> 4073.9153 1571.2096 634.2419 317.0166 206.6905 95.434
[0074] Table 3
[0075] S2. Calculate the time required for sound to propagate to different depths based on the empirical orthogonal function expression of the obtained sound velocity profile.
[0076] S201. Based on the characteristics of the sound velocity profile changing with time, the time taken for sound waves to propagate to different depths is selected as the observation data. Let t1 be the time required for the sound wave to travel from the ocean surface to a discrete point n1, t2 be the time required to travel from the ocean surface to point n2, and so on. Thus, the time required for the sound wave to travel from the ocean surface to the nth point can be denoted as t. n .
[0077] S202, Record the actual observed data as T obs The observation time is the combination of time taken for sound waves to travel to different depths, i.e., T. obs =(t1,t2,…,t n ).
[0078] In this embodiment, the obtained observation time data is shown in Table 4.
[0079] Serial Number <![CDATA[T obs ]]> 1 0.0361 2 0.0734 3 0.1142 ... ... 4999 3.3308
[0080] Table 4
[0081] S3. Using the obtained time as input observation data, an inversion algorithm model is performed based on the HMC sampling algorithm principle, and then the result dataset is obtained by sampling.
[0082] S301. Determine the target parameters to be inverted, namely the prior distribution and initial value q of the first three empirical orthogonal coefficients α = (α1, α2, α3). (0) =α (0)Based on the obtained time observation data, a target distribution function is constructed.
[0083] S302. Determine the numerical settings of hyperparameters such as step number L and step size e in the HMC algorithm, then perform algorithm modeling based on the HMC sampling algorithm, and finally run the algorithm to complete sample sampling.
[0084] S303. Finally, the sample values of the target parameter α = (α1, α2, α3) obtained by the HMC algorithm are processed. The sample values of the combustion period are discarded and the sample mean is calculated as the inversion estimate of the target parameter.
[0085] In this embodiment, the objective likelihood function of the HMC sampling algorithm is:
[0086]
[0087] Where q is the target parameter to be inverted, α = (α1, α2, α3), e is the error between the observed value and the model output value, and the error e follows a standard normal distribution N(0, I). σ is the standard deviation of the distribution that the error e follows. The specific expression for the error e is as follows:
[0088] e = T obs -T cal
[0089] S4. Calculate the mean and standard deviation of the data based on the obtained dataset. The mean is the empirical orthogonal function value obtained by inversion.
[0090] In this embodiment, the sample standard deviation of the target parameters to be inverted obtained by the HMC algorithm is calculated.
[0091] The sample standard deviation is used to measure the dispersion of the obtained sample data. The calculation formula is as follows:
[0092]
[0093] This example demonstrates a comparative study of the HMC sampling algorithm through an inversion experiment of seawater sound velocity profiles. The coefficients of the first three orders of empirical orthogonal functions of the sound velocity profile to be inverted are a1 = 4037.9158, a2 = 1571.2096, and a3 = 637.2419.
[0094] The HMC algorithm is more accurate in evaluating all three parameters and has a smaller standard deviation. Although the standard deviation of the sample parameters obtained by the MH and Gibbs algorithms is smaller, the MH and Gibbs algorithms are sensitive to the starting point of the target parameters, while the HMC algorithm is not highly dependent on the starting position of the initial target parameters and uses the fewest iteration steps. Therefore, the HMC algorithm has a strong advantage in seawater sound velocity profile inversion.
[0095] In summary, the method for inverting seawater sound velocity profiles based on the HMC sampling algorithm described in this invention has the following advantages: (1) the accuracy of the inverted parameters is high; (2) the HMC algorithm uses fewer iteration steps and a smaller iteration step size, thus exhibiting higher efficiency in inversion compared to other algorithms that utilize dynamics. Therefore, the method for inverting seawater sound velocity profiles based on the HMC sampling algorithm described in this invention has broad application prospects in sound velocity profile inversion.
[0096] Example 2
[0097] like Figure 2 As shown, the present invention also provides a method for inverting seawater sound velocity profiles based on the HMC sampling algorithm, comprising:
[0098] The data processing module is used to process the acquired historical ocean sound velocity profile data and calculate the time observation data.
[0099] The objective function construction module constructs the objective parameter distribution based on the obtained time observation data and the prior distribution of the objective parameters.
[0100] The inversion module is used to invert the empirical orthogonal function coefficients of the seawater sound velocity profile.
[0101] like Figure 2 The embodiment shown provides a method for inverting seawater sound velocity profiles based on the HMC sampling algorithm. The technical solution shown in the embodiment, which provides a method for inverting seawater sound velocity profiles based on the HMC sampling algorithm, has a similar implementation principle and beneficial effects, and will not be described again here.
[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.
Claims
1. A method for inverting seawater acoustic velocity profiles based on the HMC algorithm, characterized in that, The steps include the following: S1. Based on historical sound velocity profile data, the acquired data undergoes interpolation preprocessing, followed by empirical orthogonal function decomposition to obtain the empirical orthogonal function expression of the sound velocity profile; specifically including the following steps: S101. Using the raw seawater sound velocity profile data obtained from historical observations as input data, interpolation is performed at equal depth intervals of 1 meter. The final dataset contains seawater depths from 0 to... Meters, spaced one meter apart, corresponding to a total of Historical sound velocity profile data; S102. Perform empirical orthogonal function decomposition on the interpolated data to represent the original data as a matrix. ,in For discrete depth numbers, The number of sound velocity profiles is shown in the matrix below: The average sound speed profile can be obtained As shown below: in Represents the first A sound velocity profile at ocean depth The corresponding speed of sound; The covariance matrix can be obtained As shown below, where Indicates the observed first The difference between the single sound velocity profile and the average sound velocity profile: For covariance matrix By performing eigenvalue decomposition, we can obtain eigenvectors that are mutually orthogonal and corresponding eigenvalues Then the covariance matrix It can be represented in the following form: The result obtained through orthogonal decomposition The eigenvalues are arranged in descending order, i.e. Then select the previous one. The eigenvectors corresponding to the eigenvalues are used to represent the sound velocity profile to be inverted; then the sound velocity value at any point in the observed sea area can be expressed in the following form: in For the first The coefficients of the first-order empirical orthogonal function are calculated as follows: S103. Calculate the coefficients of the first three order empirical orthogonal functions. As unknown parameters to be inverted; S2. Calculate the time required for sound to propagate to different depths based on the empirical orthogonal function expression of the obtained sound velocity profile; S3. Based on the obtained time as observation data, an inversion algorithm model is performed based on the principle of HMC sampling algorithm, and then the result dataset is obtained by sampling. S4. Calculate the mean and standard deviation of the data based on the obtained dataset. The mean obtained is the empirical orthogonal function value obtained by inversion. S5. Use the empirical orthogonal function values obtained by inversion using the HMC algorithm to reconstruct the seawater sound speed profile, thereby completing the inversion of the seawater sound speed profile.
2. The seawater acoustic velocity profile inversion method based on the HMC algorithm according to claim 1, characterized in that, Step S2 includes the following steps: S201. Based on the characteristics of sound velocity profile changing with time, the time taken for sound waves to propagate at different depths is selected as the observation data. Assume that the sound wave travels from the ocean horizontal plane to discrete points... The time required is Transmitted from the ocean surface to the point The time required is And so on, transmitting sound waves from the ocean surface to the next... The time required for a point can be recorded as ; S202, Record the actual observation data as The observation time is the combination of time taken for sound waves to travel to different depths, i.e. .
3. The seawater acoustic velocity profile inversion method based on the HMC algorithm according to claim 1, characterized in that, Step S3 includes the following steps: S301. Determine the target parameters to be inverted, namely the first three order empirical orthogonality coefficients. The prior distribution it follows and its initial values Based on the obtained time observation data, construct the target distribution function; S302. Determine the numerical settings of hyperparameters in the HMC algorithm, perform algorithm modeling based on the HMC sampling algorithm, and finally run the algorithm to complete sample sampling. S303, Finally, the target parameters obtained by sampling the HMC algorithm are... The sample values are processed, the sample values of the combustion period are discarded, and the sample mean is calculated as the inversion estimate of the target parameter.
4. The seawater acoustic velocity profile inversion method based on the HMC algorithm according to claim 3, characterized in that, The objective likelihood function expression of the HMC sampling algorithm is as follows: in The target parameters to be inverted , The error is the difference between the observed values and the model output values. Follows a standard normal distribution For error The standard deviation and error of the distribution it follows The specific expression is as follows .
5. A seawater acoustic velocity profile inversion device based on the HMC algorithm for any one of claims 1 to 4, characterized in that, It includes a data processing module, an objective function construction module, and an inversion module; The data processing module is used to process the acquired historical ocean sound velocity profile data and calculate the time observation data; The objective function construction module constructs the objective parameter distribution based on the obtained time observation data and the prior distribution of the objective parameters; The inversion module is used to invert the empirical orthogonal function coefficients of the seawater sound velocity profile.