Joint inversion method for static and dynamic parameters of Yangtze river diffuse beach phase soft soil based on inverse Nataf transformation theory

Abstract

The invention relates to the technical field of geotechnical engineering parameter inversion, in particular to an inverse Nataf transformation theory-based joint inversion method for static and dynamic parameters of soft soil in the diffuse beach facies of the Yangtze River, and belongs to the related technical field of random stratum simulation. Comprising the following steps that a system collects and arranges silty clay samples of typical sites of the Yangtze River Beach, and key static parameters (c, phi, e, Es, w, IP and IL) and in-situ test SPT-N values of the silty clay samples of the typical sites of the Yangtze River Beach are obtained; a mixed edge distribution model (normal, logarithmic normal, Weibull, Gamma distribution) is adopted to flexibly represent the non-Gaussian statistical characteristics of each parameter; the method comprises the following steps: in a Nataf transformation system, quantifying correlation among parameters by using a Pearson correlation coefficient matrix, and constructing a joint probability distribution model of the Pearson correlation coefficient matrix; establishing an inversion model from random normal distribution of independent variable parameters to consideration of parameter distribution characteristics and parameter correlation conditions and a corresponding database through inverse Nataf transformation; and under the condition of parameter missing, intelligently recommending an optimal missing parameter value from the database based on known parameters by means of a nearest neighbor algorithm.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering parameter inversion technology, specifically to a method for joint inversion of static and dynamic parameters of soft soil in the Yangtze River floodplain based on the inverse Nataf transform theory. Background Technology

[0002] Soft soil sites in the Yangtze River floodplain are widely distributed along the Yangtze River in central and eastern my country. Their complex engineering geological conditions are characterized by low soil strength, high compressibility, high water content, and significant spatial variability and rheological properties. These soft soils are mainly composed of saturated silty clay and silty mud, and are common unsuitable foundations for various infrastructure projects. A key challenge in constructing projects on these sites is accurately obtaining their critical mechanical parameters to precisely assess foundation bearing capacity, settlement deformation, and seismic liquefaction potential. However, traditional laboratory tests are easily affected by soil sample disturbance, while single field tests (such as the Standard Penetration Test, SPT) can reflect the overall soil resistance but cannot directly provide static parameters (such as cohesion c, internal friction angle φ, and compression modulus E) for stability and deformation analysis. s Therefore, how to indirectly and reliably infer a series of static parameters through convenient in-situ testing, and quantify their uncertainty, has become a key scientific problem in the reliability design and analysis of geotechnical engineering.

[0003] For a long time, scholars at home and abroad have been committed to establishing empirical relationships between static and dynamic parameters of soil. Early studies mostly used univariate or multivariate linear regression methods to establish the relationship between the SPT blow count (SPT-N) and individual static parameters (such as c, φ, E) in specific regions. s The deterministic conversion formula for parameters is used. While these methods are simple and practical, they fail to fully consider the inherent spatial variability, nonlinear correlation, and probability distribution characteristics of parameters. In recent years, with the development of neural networks and reliability engineering and probabilistic geotechnical mechanics, researchers have gradually recognized the importance of considering parameter uncertainty and related structures. Some scholars have begun to use neural networks or random field theory to characterize the cross-correlation between soil parameters and combine multi-source test data with methods such as Bayesian updates. However, existing studies, when dealing with the joint distribution of dynamic and static parameters, mostly assume that they follow a Gaussian distribution or only consider a limited number of parameter types. For soft soils like the Yangtze River floodplain facies, which have significant non-Gaussian and nonlinear characteristics, their applicability is still insufficient. Therefore, how to construct a joint probability inversion model that can simultaneously accommodate multiple distribution types and effectively characterize complex correlations remains a challenge in current research. Summary of the Invention

[0004] The purpose of this invention is to provide a non-Gaussian probability inversion framework based on inverse Nataf transform, which integrates standard penetration test (SPT) and laboratory test data to achieve high-precision joint inversion of dynamic and static parameters of silty clay in the Yangtze River floodplain, thereby solving the problems mentioned in the background art.

[0005] The objective of this invention is achieved as follows: A joint inversion method for static and dynamic parameters of soft soil in the Yangtze River floodplain based on the inverse Nataf transform theory, comprising the following steps: Step S1. Collect soil samples and test to obtain the static parameter set C={c, φ, e, E}. s , w, IP, IL} and dynamic parameters SPT-N; Step S2. Fit the statistical characteristics of each parameter using a mixed marginal distribution model, and select the optimal distribution type using the Kolmogorov-Smirnov test; Step S3. Calculate the Pearson correlation coefficient matrix R to quantify the linear correlation between parameters; Step S4. Construct a joint probability distribution model using the inverse Nataf transform to generate a synthetic parameter sample library that conforms to actual statistical laws; Step S5. When parameters are missing, the optimal missing value is retrieved from the sample library and predicted based on the known parameters using the K nearest neighbor algorithm.

[0006] Preferably, in step S2, a mixed marginal distribution model is used to fit the statistical characteristics of each parameter. The Kolmogorov-Smirnov test is used to select the optimal distribution type. Since soil parameters (such as SPT-N, c, φ, etc.) typically exhibit non-Gaussianity (e.g., skewness, boundedness), directly using the normal assumption would lead to unreasonable physical meaning and model distortion. Fitting the marginal distributions of each parameter using mixed distributions (such as normal, log-normal, Weibull, etc.) can accurately reflect their statistical regularity, providing qualified input for subsequent joint distribution modeling. More importantly, in correlation structure modeling based on Nataf transform, the accuracy of the marginal distribution directly affects the quantification results of the correlation between variables and the effectiveness of inversion prediction. Only by establishing a reasonable marginal distribution can the final static-dynamic parameter joint probability model and SPT-N inversion results be guaranteed to have both mathematical rationality and engineering practicality.

[0007] Preferably, in step S3, the Pearson correlation coefficient matrix R is calculated to quantify the linear correlation between parameters. The Pearson correlation coefficient measures the strength of the linear relationship between two continuous variables, and its value ranges from -1 to 1. The closer the value is to 1 or -1, the stronger the correlation between the two parameters. A negative value indicates a negative correlation, and a positive value indicates a positive correlation.

[0008] Assuming the two variables are x and y, the calculation formula is as follows: Preferably, in step S4, a joint probability distribution model is constructed using the inverse Nataf transform to generate a synthetic parameter sample library that conforms to actual statistical laws. That is, an inversion model and corresponding database are established from random normally distributed independent variable parameters to parameters considering the distribution characteristics and correlation conditions of the parameters through the inverse Nataf transform. Randomly generate coefficient a i (i=1,2,......8) Independent standard normal random vectors with absolute values ​​of (i=1,2,......8) , with matrix express: Establish coefficient a i (i=1,2,......8) The matrix R of correlation between absolute values; transform R into an equivalent correlation coefficient matrix Ri using the given correction factor F. e ,R e = F . R. Regarding R e Perform Cholesky decomposition: In the formula, L and L T These are the lower triangular matrix and its transpose, respectively.

[0009] matrix The independent standard normal random vectors in the data are transformed into correlated standard normal random vectors. , with matrix express: Will The relevant standard normal random vector The marginal distribution is transformed into the corresponding log-normal random vector. On the marginal distribution, a correlated log-normal random vector is obtained. : In the formula, Indicates to Perform equal probability transformation, for The marginal cumulative distribution function. At this point, we obtain numerous sample values ​​of the parameters. The inversion is now complete.

[0010] Preferably, in step S5, the optimal missing value is retrieved and predicted from the sample database using the K-nearest neighbor algorithm. The specific process is as follows: Feature selection and vectorization: The known parameters of the input (existing partial parameter values) are defined as the coordinates of a point in a multidimensional space, which we call the query point. Similarly, each row of samples in the database is also represented as a point with the same dimensions (containing all parameter values).

[0011] Data standardization: This is to avoid distance distortion caused by differences in dimensions (e.g., compressibility modulus E). s The value of (which is much larger than the porosity e, and would dominate distance calculation if not processed) requires prior Z-score standardization of all data. This transforms all parameters into dimensionless data with a mean of 0 and a standard deviation of 1, ensuring that each parameter has equal weight in distance calculation. The Z-score calculation formula is: In the formula: x i It is the original data value; μ i σ is the mean of the data. i It is the standard deviation of the data.

[0012] Similarity Measurement and Nearest Neighbor Search: In a subspace spanned by known parameters, the Euclidean distance between the query point and every sample in the database is calculated. The shorter the Euclidean distance, the higher the similarity between the two samples. The system then sorts all samples in the database according to the distance from smallest to largest and selects the top K most similar samples (here, 5 are selected), called the "nearest neighbor" sample set. The calculation formula is as follows: Where, x i,known It is the i-th known parameter value input by the user, x i,db It is the parameter value corresponding to a certain sample in the database.

[0013] Preferably, step S6 involves parameter inversion testing under multiple operating conditions. The testing method is as follows: 40 sets of complete parameter samples are randomly selected from the constructed parameter database. For each missing operating condition, specified parameters are artificially masked to simulate actual data loss scenarios. Then, the remaining parameters are used as input, and the system is used to predict the missing values. The test sets four operating conditions with 4, 3, 2, and 1 missing parameters, respectively.

[0014] Beneficial effects The system collects and organizes silty clay samples from typical sites along the Yangtze River floodplain, obtaining key static parameters (c, φ, e, Es, w, IP, IL) and in-situ SPT-N values. A hybrid marginal distribution model (normal, log-normal, Weibull, Gamma distribution) is used to flexibly characterize the non-Gaussian statistical features of each parameter. Under the Nataf transform framework, the Pearson correlation coefficient matrix is ​​used to quantify the correlation between parameters, constructing their joint probability distribution model. An inverse model and corresponding database are established from randomly normally distributed independent variable parameters to a model considering parameter distribution characteristics and correlation conditions through inverse Nataf transform. In the case of missing parameters, the nearest neighbor algorithm is used to intelligently recommend optimal missing parameter values ​​from the database based on known parameters. Attached Figure Description

[0015] Figure 1 This is the overall flowchart of the present invention.

[0016] Figure 2 For parameters SPT QQ plot.

[0017] Figure 3 For parameter c, QQ graph.

[0018] Figure 4 The parameter φ is the QQ diagram.

[0019] Figure 5 For parameter e, QQ graph.

[0020] Figure 6 For parameter E s QQ image.

[0021] Figure 7 For parameter w, QQ graph.

[0022] Figure 8 For parameters IP QQ graph.

[0023] Figure 9 For the parameter IL QQ graph.

[0024] Figure 10 This describes the distribution of each parameter and their correlations.

[0025] Figure 11 The parameter distribution and correlation are obtained through the inverse Nataf transform.

[0026] Figure 12 This is a comparison of the measured parameters and the predicted values ​​of the missing parameters. Detailed Implementation

[0027] The invention will be further summarized below with reference to the accompanying drawings.

[0028] like Figure 1 As shown, an improved conditional random field simulation method includes the following steps: Step S1. Collect soil samples and test to obtain the static parameter set C={c, φ, e, E}. s , w, IP, IL} and dynamic parameters SPT-N; Step S2. A mixed marginal distribution model is used to fit the statistical characteristics of each parameter, and the optimal distribution type is selected through the Kolmogorov-Smirnov test. In step S2, the mixed marginal distribution model is used to fit the statistical characteristics of each parameter, and the optimal distribution type is selected through the Kolmogorov-Smirnov test. Since soil parameters (such as SPT-N, c, φ, etc.) usually exhibit non-Gaussianity (e.g., skewness, boundedness), directly using the normal assumption will lead to unreasonable physical meaning and model distortion. Fitting the marginal distribution of each parameter using mixed distributions (such as normal, log-normal, Weibull, etc.) can truly reflect their statistical regularity and provide qualified input for subsequent joint distribution modeling. More importantly, in correlation structure modeling based on inverse Nataf transform, the accuracy of the marginal distribution directly affects the quantification results of the correlation between variables and the effectiveness of inversion prediction. Only by establishing a reasonable marginal distribution can the final static-dynamic parameter joint probability model and SPT-N inversion results be guaranteed to have both mathematical rationality and engineering practicality. Silty clay is the most common soil layer in the Yangtze River floodplain facies, and it is used as an example for this study. Figure 2-9 This is a distribution fit of 8 parameters for silty clay.

[0029] Step S3. Calculate the Pearson correlation coefficient matrix R to quantify the linear correlation between parameters; Step S3 involves calculating the Pearson correlation coefficient matrix R to quantify the linear correlation between parameters; the Pearson correlation coefficient measures the strength of the linear relationship between two continuous variables, with a value range of [-1, 1]. The closer the value is to 1 or -1, the stronger the correlation between the two parameters. A negative value indicates a negative correlation, and a positive value indicates a positive correlation.

[0030] Assuming the two variables are x and y, the calculation formula is as follows: The results and distribution of the Pearson correlation coefficient matrix established for the eight parameters proposed in this invention are as follows: Figure 10 As shown in the figure. All parameters passed the significance test at 0.01. The relationship between SPT and E can be seen from the graph. s It showed a relatively strong positive correlation with e, w, and IL, and a relatively strong negative correlation with them. Moisture content and liquid limit index showed a strong correlation, consistent with actual conditions. Among these, E showed the highest correlation. sIn practical engineering, when SPT operating conditions are lacking, E can be referenced. s Make reasonable predictions based on the indoor test results of e.

[0031] Step S4. Construct a joint probability distribution model using the inverse Nataf transform to generate a synthetic parameter sample library that conforms to actual statistical laws; that is, establish an inversion model and corresponding database from random normally distributed independent variable parameters to parameters considering distribution characteristics and correlation conditions through the inverse Nataf transform. Randomly generate coefficient a i (i=1,2,......8) Independent standard normal random vectors with absolute values ​​of (i=1,2,......8) , with matrix express: Establish coefficient a i (i=1,2,......8) The matrix R of correlation between absolute values; transform R into an equivalent correlation coefficient matrix Ri using the given correction factor F. e ,R e = F . R. Regarding R e Perform Cholesky decomposition: In the formula, L and L T These are the lower triangular matrix and its transpose, respectively.

[0032] matrix The independent standard normal random vectors in the data are transformed into correlated standard normal random vectors. , with matrix express: Will The relevant standard normal random vector The marginal distribution is transformed into the corresponding log-normal random vector. On the marginal distribution, a correlated log-normal random vector is obtained. : In the formula, Indicates to Perform equal probability transformation, for The marginal cumulative distribution function. At this point, we obtain numerous sample values ​​of the parameters. The inversion is now complete. The results are as follows: Figure 11 As shown, comparison Figure 10It can be observed that the inversion parameters obtained through the inverse Nataf transform match the distribution of actual parameters and the correlation between parameters very well. This indicates that this method can effectively expand the sample library, and when a certain soil parameter is missing, the missing parameter can be directly compared with other parameters of the soil in the sample library to obtain a more reasonable value for the missing parameter.

[0033] Step S5. When parameters are missing, the optimal missing value is retrieved from the sample library and predicted based on the known parameters using the K nearest neighbor algorithm.

[0034] The optimal missing value is retrieved and predicted from the sample database using the K-nearest neighbor algorithm. The specific process is as follows: Feature selection and vectorization: The known parameters of the input (existing partial parameter values) are defined as the coordinates of a point in a multidimensional space, which we call the query point. Similarly, each row of samples in the database is also represented as a point with the same dimensions (containing all parameter values).

[0035] Data standardization: This is to avoid distance distortion caused by differences in dimensions (e.g., compressibility modulus E). s The value of (which is much larger than the porosity e, and would dominate distance calculation if not processed) requires prior Z-score standardization of all data. This transforms all parameters into dimensionless data with a mean of 0 and a standard deviation of 1, ensuring that each parameter has equal weight in distance calculation. The Z-score calculation formula is: In the formula: x i It is the original data value; μ i σ is the mean of the data. i It is the standard deviation of the data.

[0036] Similarity Measurement and Nearest Neighbor Search: In a subspace spanned by known parameters, the Euclidean distance between the query point and every sample in the database is calculated. The shorter the Euclidean distance, the higher the similarity between the two samples. The system then sorts all samples in the database according to the distance from smallest to largest and selects the top K most similar samples (here, 5 are selected), called the "nearest neighbor" sample set. The calculation formula is as follows: Where, x i,known It is the i-th known parameter value input by the user, x i,db It is the parameter value corresponding to a certain sample in the database.

[0037] To verify the effectiveness and reliability of the constructed intelligent prediction system, this invention designed a parameter inversion test under multiple operating conditions. The test method is as follows: 40 sets of complete parameter samples were randomly selected from the constructed parameter database. For each missing operating condition, specified parameters were artificially masked to simulate actual data loss scenarios. Then, the remaining parameters were used as input, and the system was used to predict the missing values. Four operating conditions were set up for the test, with the number of missing parameters being 4, 3, 2, and 1, respectively. The specific configuration is shown in Table 1.

[0038] Table 1 Predictive Parameter Operating Condition Settings Comparative analysis of predicted results and measured values, as follows: Figure 12 As shown in the figure. It can be seen that when the number of missing parameters is 4 ( Figure 12 a) The prediction results show the largest relative deviation, but the ratio of most predicted values ​​to measured values ​​is still concentrated in the range of 0.85 to 1.15, indicating that the system still has good inference ability even with limited input information. As the number of missing parameters decreases and the known information becomes more complete, the prediction accuracy is significantly improved. Figure 12 (b) and Figure 12 (c) shows that the ratio of predicted values ​​to measured values ​​is becoming more concentrated, and the normal distribution contour of the scatter plot is becoming steeper, indicating that the prediction error has been significantly reduced.

[0039] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for joint inversion of parameters of soft soil in the Yangtze River floodplain, characterized in that... The method includes the following steps: Step S1. Collect soil samples and test to obtain static parameters c, φ, e, E s w, IP, IL, and standard penetration test dynamic parameters SPT-N; c is cohesion, φ is the internal friction angle, e is the void ratio, E s Where is the compression modulus, w is the moisture content, IP is the liquid index, and IL is the plasticity index; Step S2. Fit the statistical characteristics of each parameter using a mixed marginal distribution model, and select the optimal distribution type using the Kolmogorov-Smirnov test; Step S3. Calculate the Pearson correlation coefficient matrix R to quantify the linear correlation between parameters; Step S4. Construct a joint probability distribution model using the inverse Nataf transform to generate a synthetic parameter sample library that conforms to actual statistical laws; Step S5. When parameters are missing, the optimal missing value is retrieved from the sample library and predicted based on the known parameters using the K nearest neighbor algorithm.

2. The method for joint inversion of parameters of soft soil in the Yangtze River floodplain according to claim 1, characterized in that... The system collects and organizes silty clay samples from typical sites along the Yangtze River floodplain, obtaining their key static parameters and in-situ SPT-N values.

3. The method for joint inversion of parameters of soft soil in the Yangtze River floodplain according to claim 1, characterized in that... Studying the marginal distributions of dynamic / static parameters is the foundation of the entire probabilistic inversion modeling. Its purpose is to accurately characterize the distribution type of each parameter. Since soil parameters usually exhibit non-Gaussianity, directly adopting the normality assumption will lead to unreasonable physical meaning and model distortion. By fitting the marginal distributions of each parameter separately through a mixture distribution, we can truly reflect their statistical regularity and provide qualified input for subsequent joint distribution modeling. More importantly, in the correlation structure modeling based on Nataf transform, the accuracy of the marginal distribution directly affects the quantification results of the correlation between variables and the effectiveness of the inversion prediction. Only by establishing a reasonable marginal distribution can we ensure that the final static and dynamic parameter joint probability model and SPT-N inversion results have both mathematical rationality and engineering practicality.

4. The method for joint inversion of parameters of soft soil in the Yangtze River floodplain according to claim 1, characterized in that... To construct the parameter correlation matrix, the Pearson correlation coefficient is used. The Pearson correlation coefficient measures the strength of the linear relationship between two continuous variables, with a value ranging from -1 to 1. The closer the value is to 1 or -1, the stronger the correlation between the two parameters. Negative values ​​indicate a negative correlation, and positive values ​​indicate a positive correlation. Assuming the two variables are x and y, the calculation formula is as follows: In the formula, x and y are hypothesized variables, and r is the Pearson correlation coefficient of variables x and y.

5. The method for joint inversion of parameters of soft soil in the Yangtze River floodplain according to claim 1, characterized in that... : Establish an inversion model and corresponding database based on the parameters of a random normally distributed independent variable, considering the distribution characteristics and correlation conditions of the parameters, through inverse Nataf transform; Step 5-1: Randomly generate coefficient a i (i=1,2,......8) Independent standard normal random vectors with absolute values ​​of (i=1,2,......8) , with matrix express: Step 5-2: Establish coefficient a i (i=1,2,......8) The matrix R of correlation between absolute values; transform R into an equivalent correlation coefficient matrix Ri using the given correction factor F. e ,R e = F . R, for R e Perform Cholesky decomposition: In the formula, L and L T These are the lower triangular matrix and its transpose, respectively. Step 5-3: Convert the matrix Transform independent standard normal random vectors into correlated standard normal random vectors. , with matrix express: Step 5-4: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The relevant standard normal random vector The marginal distribution is transformed into the corresponding log-normal random vector. On the marginal distribution, a correlated log-normal random vector is obtained. : In the formula, Indicates to Perform equal probability transformation, for The marginal cumulative distribution function is obtained, and at this point, we get many sample values ​​of the parameters, thus ending the inversion.

6. The method for joint inversion of parameters of soft soil in the Yangtze River floodplain according to claim 1, characterized in that... In the case of missing parameters, this study aims to provide a scientific and reliable method for uncertainty quantification and parameter inference for floodplain soft soil sites by using the nearest neighbor algorithm to intelligently recommend the optimal missing parameter values ​​from the database based on known parameters. The constructed database and retrieval mechanism significantly reduce the workload of experimental testing and provide a theoretical basis for subsequent reliability-based geotechnical engineering design. Step 6-1: Feature Selection and Vectorization: Define the known input parameters as the coordinates of a point in a multidimensional space, called the query point. Similarly, each row of samples in the database is also represented as a point with the same dimension. Step 6-2: Data Standardization: To avoid distance distortion caused by differences in dimensions, all data must be pre-standardized using Z-score, converting all parameters into dimensionless data with a mean of 0 and a standard deviation of 1. This ensures that each parameter has equal weight in the distance calculation. The Z-score calculation formula is: In the formula: x i It is the original data value; μ i It is the mean of the data; σ i It is the standard deviation of the data; Step 6-3: Similarity Measurement and Nearest Neighbor Search: In the subspace spanned by known parameters, calculate the Euclidean distance between the query point and every sample in the database. The shorter the Euclidean distance, the higher the similarity between the two samples. The system then sorts all samples in the database according to the distance from smallest to largest and selects the top K most similar samples, called the "nearest neighbor" sample set. The calculation formula is as follows: Where, x i,known It is the i-th known parameter value input by the user, x i,db It is the parameter value corresponding to a specific sample in the database; Step 6-4: Parameter inversion test under multiple working conditions. The test method is as follows: 40 sets of complete parameter samples are randomly selected from the constructed parameter database. For each missing working condition, the specified parameters are manually masked to simulate the actual data missing scenario. Then, the remaining parameters are used as input, and the missing values ​​are predicted using this system. The test sets four working conditions with the number of missing parameters being 4, 3, 2, and 1, respectively.

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