A method for predicting the porosity of marine soil depth profile considering uncertainty

Abstract

This invention provides a method for predicting the porosity of marine soil depth profiles considering uncertainties, comprising the following steps: S1, collecting a large amount of acoustic impedance-porosity data and establishing an acoustic impedance-porosity probability conversion model; S2, collecting acoustic impedance measurement data distributed along the depth direction of the target site; S3, combining the data of the target site, considering uncertainties, and using ensemble Kalman filtering to predict the porosity of the target site along the depth direction. The method provided by this invention accurately predicts the probability distribution of marine soil porosity along the depth direction and quantifies the uncertainty of marine soil porosity, providing a theoretical basis for the selection of marine engineering design parameters and ensuring the safety and reliability of engineering designs.

Description

Technical Field

[0001] This invention belongs to the field of marine engineering technology, and in particular relates to a method for predicting the porosity of marine soil depth profiles that takes into account uncertainties. Background Technology

[0002] To ensure the safety of engineering design, it is essential to investigate the seabed environment and geological structure, and accurately understand the physical and mechanical properties of the soil. Strength parameters, in particular, are crucial as engineering design parameters directly impacting the safety assessment of geotechnical engineering designs. For soil and rock masses, porosity is closely related to soil strength; therefore, accurately understanding the porosity distribution of the soil is helpful in obtaining strength design parameters for marine engineering projects.

[0003] However, current quantitative assessments of marine soil porosity rely almost entirely on in-situ geotechnical tests and laboratory geotechnical tests using samples. Limited by economic, technical, and site conditions, porosity test data for soil in marine geotechnical engineering investigations are extremely limited, exhibiting small sample characteristics, which inevitably increases the uncertainty in engineering design and safety assessment.

[0004] It is generally believed that there is a relationship between soil wave impedance and porosity, and wave impedance data is readily available geophysical survey data. Therefore, in engineering practice, empirical conversion models are often established between wave impedance and porosity to efficiently and extensively obtain soil porosity data.

[0005] Many papers have proposed empirical conversion models between wave impedance and porosity. However, these empirical conversion models do not consider uncertainties, and there is a large difference between the calculated predicted porosity value and the measured value, with the difference exhibiting random fluctuations. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for predicting the porosity of marine soil depth profiles that takes into account uncertainties.

[0007] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0008] A method for predicting the porosity of marine soil depth profiles considering uncertainties, characterized in that the method includes the following steps:

[0009] S1. Collect a large amount of wave impedance-porosity data and establish a wave impedance-porosity probability conversion model.

[0010] S2. Collect wave impedance measurement data distributed along the depth direction of the target site;

[0011] S3. Combining the target site data and considering uncertainties, use ensemble Kalman filtering to predict the porosity of the target site along the depth direction.

[0012] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0013] As a preferred technical solution of the present invention, step S1 specifically includes the following steps:

[0014] S101. Collect and organize a large amount of wave impedance-porosity measurement data from around the world;

[0015] S102. The least squares method is used to perform regression analysis on all the wave impedance-porosity measurement data obtained in step S101 to obtain the wave impedance-porosity empirical conversion model.

[0016] S103. Use the random variable ε to characterize the uncertainty of the transformation model between the empirical transformation model obtained in step S102 and the site measurement data, and calculate the statistical characteristics of the random variable ε.

[0017] S104. By considering the uncertainty ε of the conversion model, a wave impedance-porosity probabilistic conversion model is established.

[0018] As a preferred technical solution of the present invention: in step S101, the collected data are wave impedance measurement data and porosity measurement data at the same spatial location.

[0019] As a preferred technical solution of the present invention: in step S102, the wave impedance-pore empirical conversion model is a deterministic calculation model, which does not consider uncertainty.

[0020] As a preferred technical solution of the present invention: in step S103, the statistical characteristics of the random variable ε are the mean and standard deviation that the uncertainty of the transformation model follows.

[0021] As a preferred technical solution of the present invention: in step S104, the wave impedance-porosity probability conversion model takes into account the uncertainty of the conversion model.

[0022] As a preferred technical solution of the present invention: step S2 preferably collects measured porosity data distributed along the depth direction at a limited location within the target site.

[0023] As a preferred technical solution of the present invention, step S3 specifically includes the following steps:

[0024] S301. Using porosity as the state variable, determine the prior distribution of the initial state variable based on existing engineering experience, including the type of prior distribution and prior statistical characteristic values ​​(such as mean, standard deviation, etc.); generate MC samples of the initial state variable through Monte Carlo (MC) sampling to form the initial set.

[0025] S302. Using a random walk model as the prediction model for state variables (also known as a state transition model), the state variables of the next depth are predicted to obtain a prediction set of state variables.

[0026] S303. If there is wave impedance observation data at the depth predicted in step S302, then the predicted set of state variables is updated using the wave impedance observation data and the wave impedance-porosity probability conversion model established in step S104 to obtain the updated set of state variables, and the state variables at the next depth are predicted based on the updated set of state variables obtained in this step.

[0027] S304. If there is no wave impedance observation data at the depth predicted in step S302, continue to use the random walk model to predict the state variables at the next depth.

[0028] S305. Repeat steps S302 to S304 until all wave impedance observation data are combined.

[0029] As a preferred technical solution of the present invention: the wave impedance measurement data along the depth is used as the model input, the calculated porosity posterior distribution along the depth is used as the model output, and the porosity prediction result is compared with the measured porosity data at a limited location in the target site to verify the reliability of the porosity prediction result.

[0030] This invention provides a method for predicting the porosity of marine soil depth profiles considering uncertainties. Utilizing a large amount of existing acoustic impedance-porosity data, and considering the uncertainty of the predicted porosity values, a acoustic impedance-porosity probabilistic transformation model is established, taking into account the uncertainty of the transformation model. Combining acoustic impedance measurement data from the target site, and based on ensemble Kalman filtering, considering the uncertainty of state transitions, an algorithm for predicting the porosity of marine soil depth profiles based on ensemble Kalman filtering is proposed. This algorithm updates and predicts the porosity of marine soil, thereby accurately predicting the probability distribution of porosity along the depth direction and quantifying the uncertainty of marine soil porosity. This provides a theoretical basis for determining the values ​​of marine engineering design parameters, ensuring the safety and reliability of engineering designs. Attached Figure Description

[0031] Figure 1 A flowchart illustrating the method for predicting the porosity of marine soil depth profiles considering uncertainties, provided by this invention.

[0032] Figure 2 The figures show the target site wave impedance measurement data and the measured porosity data at finite locations in the embodiment.

[0033] Figure 3 The illustration shows the wave impedance-porosity data and empirical conversion model for seven sites worldwide in the example.

[0034] Figure 4 The illustration shows the predicted porosity and the measured porosity in the example. Detailed Implementation

[0035] The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

[0036] Reference Figure 1 As shown, a method for predicting the porosity of marine soil depth profiles considering uncertainties includes:

[0037] S1. Collect a large amount of wave impedance-porosity data and establish a wave impedance-porosity probability conversion model.

[0038] S2. Collect wave impedance measurement data distributed along the depth direction of the target site;

[0039] S3. Combining the target site data and considering uncertainties, use ensemble Kalman filtering to predict the porosity of the target site along the depth direction.

[0040] Step S1 specifically includes the following steps:

[0041] S101. Collect and organize a large amount of wave impedance-porosity measurement data from around the world;

[0042] S102. The least squares method is used to perform regression analysis on the data of all sites to obtain the empirical conversion model of wave impedance-porosity, as shown in Equation (1).

[0043] S103. Use the random variable ε to characterize the uncertainty of the conversion model between the empirical conversion model obtained in step S102 and the site measurement data, and calculate the statistical characteristics of ε, including the mean and standard deviation.

[0044] S104. By considering the uncertainty of the conversion model, a wave impedance-porosity probabilistic conversion model is established. The model equation is shown in equation (2):

[0045] n=n(I) (1)

[0046] n i =n(D i )=n(D i ) * +ε i =n[I(D i)]+ε i (2)

[0047] In the formula, n represents porosity (%), and I represents wave impedance (m / s)·(g / cm). 3 );D i Indicates the i-th depth; n i For depth D i Porosity at ε i It is a random variable characterizing the uncertainty of the transformation model, and its statistical characteristics are calculated in step S103; I(D i ) is in D i Wave impedance measured at depth; n(D) i )* is based on the given I(D i D was calculated using the empirical transformation model (1). i Porosity at depth.

[0048] In step S2, the measurement data of the target site is the wave impedance data of the soil along the depth direction; if conditions permit, the measured porosity data of a limited number of locations in the site can be collected.

[0049] Step S3 specifically includes the following steps:

[0050] S301. Using porosity as the state variable, determine the prior distribution of the initial state variable based on existing engineering experience, including the type of prior distribution and prior statistical characteristic values ​​(such as mean, standard deviation, etc.); generate M MC samples of the initial state variable through MC sampling to form the initial set N(D0), as shown in equation (3):

[0051] N(D0)=[n(D 0,1 ),n(D 0,2 ),...,n(D 0,k ),...,n(D 0,M )] T (3)

[0052] In the formula, 0 represents the initial depth (depth is 0m), N(D0) represents the initial set; n(D 0,k Let be the kth sample of the initial state n(D0), where k = 1, 2, ..., M; and M be the number of samples in the set.

[0053] S302. A predictive model using a random walk model as the state variable (also known as a state transition model) to describe the current state n(D) of porosity. i ) and its previous state n(D) i-1 The relationship between them is shown in equation (4):

[0054] n(D i )=n(D i-1)+ω i (4)

[0055] In the formula, n(D) i ) is in D i Predicted porosity at depth; ω i The mean is 0 and the standard deviation is σ. ω The random variable ω represents the uncertainty of state transitions. In this invention, ω i Standard deviation σ ω The value is taken from the previous state n(D) i-1 The standard deviation of the set of samples at depth D. i The set of state variable predictions at point N(D) i ) f It can be represented as:

[0056] N(D i ) f =[n(D i,1 ) f ,n(D i,2 ) f ,...,n(D i,k ) f ,...,n(D i,M ) f ] T (5)

[0057] In the formula, M is the number of samples in the set; the superscript f indicates prediction.

[0058] S303, if depth D i If wave impedance observation data is available, then the prediction set N(D) of the state variables is updated using the wave impedance observation data and the wave impedance-porosity probability transformation model (2) established in step S104. i ) f The updated set N(D) of the state variables is obtained. i ) u As shown in the following formula:

[0059] N(D i ) u =N(D) i ) f +K i [y i -N(D i ) f (6)

[0060] In the formula, the superscript u indicates update; N(D i ) u Indicates updating the set, N(D) i ) u =[n(D i,1 )u ,n(D i,2 ) u ,...,n(D i,M ) u ] T ;y i The observation vector representing porosity is calculated by substituting the wave impedance data of the target site into the probability transformation model, y i =[y i,1 ,y i,2 ,...,y i,k ,...,y i,M ], y i,k =n(D i )*+ε i,k k = 1, 2, ..., M; K i D i The Kalman gain matrix at depth determines the weights of the predicted state variables and the observed data. Based on the update set N(D) i ) u The random walk model is used to predict the next depth D. i+1 The state variable at point n(D) i+1,k ) f =n(D i,k ) u +ω i k = 1, 2, ..., M.

[0061] S304, if the depth D i Without wave impedance observation data, the random walk model will continue to be used to predict the next depth D. i+1 The state variable, n(D) i+1,k ) f =n(D i,k ) f +ω i k = 1, 2, ..., M.

[0062] S305. Repeat steps S302 to S304 until all wave impedance observation data are combined.

[0063] The following specific example illustrates the process of applying the prediction method provided by this invention:

[0064] This specific embodiment uses a specific site as the target site. Multi-sensor core logging tools at that site are used to collect acoustic impedance measurement data, and the measured porosity data at limited locations within that site are used as the comparison standard for the prediction results. This site has a total of 446 acoustic impedance measurement data points and 12 measured porosity data points, as follows: Figure 2 As shown.

[0065] First, 416 sets of wave impedance-porosity data were collected from 7 different sites worldwide. Combining the data from all sites, a general empirical conversion model of wave impedance-porosity was obtained using the least squares method, as shown in Equation (7).

[0066] n = 5.564 × 10 -6 ·I 2 -5.361×10 -2 ·I+1.613×10 2 (7)

[0067] Secondly, the differences between the empirical conversion model and the collected measured data are analyzed, such as... Figure 3 As shown, Figure 3 The data points in the figure are wave impedance-porosity data from seven different sites worldwide, and the curve is the empirical conversion model represented by equation (7). There is a certain difference between the data points and the empirical conversion model, and the difference fluctuates randomly. This difference comes from the uncertainty of the conversion model. To account for this uncertainty, the random variable ε is used to characterize the uncertainty of the conversion model, combined with... Figure 3 ε can be calculated to be a random variable with a mean of 0 and a standard deviation of 3.517 (%). Based on the empirical conversion model (7), considering ε, the wave impedance-porosity probability conversion model is obtained, as shown in equation (8).

[0068] n i =n(D i )=n(D i ) * +ε i =5.564×10 -6 ·I(D i ) 2 -5.361×10 -2 ·I(D i )+1.613×10 2 +ε i (8)

[0069] Then, based on the obtained observation data and engineering experience, porosity is used as the state variable. The prior distribution of the initial state variable is set to follow a Gaussian distribution with a mean of 72% and a standard deviation of 2%. MC samples of the initial state variable are generated through MC sampling, resulting in an initial set with a set size of M = 100. Combining the prediction model of equation (4), the state variable is predicted once for every 0.001m increase in depth. The M set samples of the i-th state are shown in equation (5). If the depth D i If wave impedance observation data is available at a certain location, then D can be obtained through equation (8). i The observation vector y at depth i Then, the prediction set N(D) of the state variables is updated using equation (6).i ) f The updated set N(D) of the state variables is obtained. i ) u If there is no wave impedance observation data at that depth, the random walk model (4) is used to predict the state variables at the next depth. The prediction and update of the state variables are repeated until all wave impedance observation data are combined.

[0070] Finally, the prediction results are output and compared with the measured porosity data at limited locations in the target site, such as... Figure 4 As shown. From Figure 4 As can be seen from the present invention, the method for predicting the porosity of marine soil depth profiles considering uncertainties successfully predicts the change of porosity along the depth. The trend of the predicted mean curve is consistent with the measured porosity value. The predicted 95% confidence interval covers all measured porosity values, indicating that the method provided by the present invention can accurately predict the distribution of porosity with depth, while reasonably estimating its uncertainty.

[0071] The above specific embodiments are used to explain and illustrate the present invention, and are only preferred embodiments of the present invention, not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for predicting the porosity of marine soil depth profiles considering uncertainties, characterized in that: The method includes the following steps: S1. Collect wave impedance-porosity data and establish a wave impedance-porosity probability conversion model. S2. Collect wave impedance measurement data distributed along the depth direction of the target site; S3. Combining the data of the target site and considering uncertainties, use ensemble Kalman filtering to predict the porosity of the target site along the depth direction. Step S1 specifically includes the following steps: S101. Collect and organize wave impedance-porosity measurement data from around the world; S102. The least squares method is used to perform regression analysis on all the wave impedance-porosity measurement data obtained in step S101 to obtain the wave impedance-porosity empirical conversion model. S103, Using random variables ε The uncertainty of the transformation model between the empirical transformation model obtained in step S102 and the site measurement data is characterized, and random variables are calculated. ε Statistical characteristics; S104, by considering the conversion model uncertainty ε , a wave impedance - porosity probability conversion model is established; In step S103, the statistical characteristic quantity of the random variable ε is the mean and standard deviation of the conversion model uncertainty; Step S3 specifically includes the following steps: S301. Using porosity as the state variable, determine the prior distribution of the initial state variable based on existing engineering experience, including the type of prior distribution and prior statistical characteristic values; generate MC samples of the initial state variable through Monte Carlo sampling to form the initial set; S302. Using a random walk model as the prediction model for state variables, the state variables at the next depth are predicted to obtain a prediction set of state variables. S303. If there is wave impedance observation data at the depth predicted in step S302, then the predicted set of state variables is updated using the wave impedance observation data and the wave impedance-porosity probability conversion model to obtain the updated set of state variables, and the state variables at the next depth are predicted based on the updated set of state variables obtained in this step. S304. If there is no wave impedance observation data at the depth predicted in step S302, continue to use the random walk model to predict the state variables at the next depth. S305. Repeat steps S302 to S304 until all wave impedance observation data are combined.

2. The method for predicting porosity of marine soil depth profile considering uncertainty according to claim 1, characterized in that: In step S101, the collected data are wave impedance measurement data and porosity measurement data at the same spatial location.

3. The method for predicting porosity of marine soil depth profile considering uncertainty according to claim 1, characterized in that: In step S102, the wave impedance-pore empirical conversion model is a deterministic calculation model, which does not consider uncertainties.

4. The method for predicting porosity of marine soil depth profile considering uncertainty according to claim 1, characterized in that: In step S104, the wave impedance-porosity probability conversion model takes into account the uncertainty of the conversion model.

5. The method for predicting the porosity of marine soil depth profiles considering uncertainties according to claim 1, characterized in that: Step S2 preferably involves collecting measured porosity data distributed along the depth direction at a limited number of locations within the target site.

6. The method for predicting porosity of marine soil depth profile considering uncertainty according to claim 1, characterized in that: The wave impedance measurement data along the depth is used as the model input, the calculated posterior distribution of porosity along the depth is used as the model output, and the porosity prediction results are compared with the measured porosity data at limited locations in the target site to verify the reliability of the porosity prediction results.

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