Geotechnical engineering settlement prediction method

Abstract

The invention provides a geotechnical engineering settlement prediction method which comprises the following steps: S1, performing settlement prediction by adopting a traditional regression analysis method to obtain a regression curve; s2, calculating a historical regression value on each historical time node and a historical deviation value of the monitoring data; the historical regression value is a value of a regression curve on a historical time node; s3, based on the historical deviation value of each historical time node, performing Kriging interpolation on a future time node, and calculating a regression prediction deviation value; s4, the regression prediction deviation value on the future time node obtained through interpolation and the regression prediction value on the future time node are added, a final settlement prediction value is obtained, and the regression prediction value is the value on the regression curve on the future time node. Optimization is carried out on the basis of a traditional regression analysis method, and the settlement prediction precision is effectively improved.

Description

Technical Field

[0001] The invention relates to the field of geotechnical engineering, in particular to a method for predicting geotechnical engineering settlement. Background Art

[0002] Settlement prediction is an important technical link in geotechnical engineering, which is usually used in engineering practices such as engineering monitoring, foundation treatment, and tunnel construction. Therefore, the geotechnical engineering community has been committed to developing accurate settlement prediction technology.

[0003] Traditional settlement prediction methods rely on regression analysis theory, including hyperbola method, shallow hill method, exponential curve method and gray model method, etc. By performing regression analysis on existing data, a mathematical model between settlement and related factors is established to predict future settlement. However, the traditional regression analysis method has relatively low prediction accuracy, especially in complex engineering situations, and may not accurately reflect the actual settlement situation; and it has limited adaptability to data and is difficult to process data with strong nonlinear relationships.

[0004] With the development of artificial intelligence technology, machine learning models have been gradually applied to the field of settlement prediction, such as using advanced algorithms such as feedforward neural networks, decision trees, and support vector machines; by learning and processing a large number of training samples, complex models are established to predict settlement; these models provide new ideas and methods for settlement prediction with their powerful data learning and processing capabilities. Nevertheless, the superior performance of machine learning models is often based on sufficient and diverse training samples, and has high requirements on the quantity and quality of training samples. For the limited sample size common in engineering practice, its performance may not be as good as traditional regression analysis methods. In addition, the model is relatively complex, making it difficult for engineers to understand and apply it, and its acceptance in actual engineering operations is relatively low.

[0005] Since traditional regression analysis methods have the characteristics of simple model structure and convenient operation, they are easier for engineers to understand and apply, and enjoy a high degree of acceptance in actual engineering operations. Therefore, how to improve the accuracy of its prediction results based on traditional regression analysis methods is a technical problem that needs to be solved urgently.

[0006] In view of this, the present invention proposes a geotechnical engineering settlement prediction method to optimize the accuracy of the traditional regression analysis method. Summary of the invention

[0007] The purpose of the present invention is to propose a method for predicting geotechnical engineering settlement, which is dedicated to optimizing the prediction accuracy based on the traditional regression analysis method. Compared with the machine learning model method, the method of the present invention has a low reliance on samples and strong engineering applicability.

[0008] To achieve the above object, the technical solution of the present invention is: a method for predicting geotechnical engineering settlement, comprising the following steps:

[0009] S1: Use traditional regression analysis method to predict settlement and obtain regression curve;

[0010] S2: Calculate the historical regression value at each historical time node and the historical deviation value of the monitoring data; the historical regression value is the value of the regression curve at the historical time node;

[0011] S3: Based on the historical deviation value at each historical time node, Kriging interpolation is performed on the future time nodes to calculate the regression prediction deviation value;

[0012] S4: Add the regression prediction deviation value at the future time node obtained by interpolation to the regression prediction value at the future time node to obtain a final settlement prediction value, where the regression prediction value is the value on the regression curve at the future time node.

[0013] Preferably, the traditional regression analysis method includes any one of a hyperbola method, a shallow slope method, an exponential curve method, and a grayscale model method.

[0014] Preferably, S2 specifically includes: splitting the historical monitoring data into historical regression values ​​and historical deviation values:

[0015] z(t)=μ(t)+ε(t) (1)

[0016] Wherein, z(t) represents the monitoring data value at time t; μ(t) represents the historical regression value at time t, which is obtained by performing settlement prediction through traditional regression analysis method; ε(t) represents the historical deviation value at time t, and the historical deviation value ε(t) at time t is the difference between the monitoring data value z(t) at time t and the historical regression value μ(t) at time t.

[0017] Preferably, S3 comprises the following steps:

[0018] S3.1: Perform Box-Cox transformation to make the interpolated data closer to normal distribution:

[0019]

[0020] In the formula, ε represents a vector containing all historical deviation values; λ represents a vector whose elements are all λ1, where λ1 is the minimum value of the sum of squares of ε; λ2 is a constant introduced to ensure that ε(t)+λ2>0; ε trans (t) represents the historical deviation value after transformation; gm(.) represents the geometric mean of the vector ε+λ;

[0021] S3.2: Calculate the autocorrelation function of the data based on the Matérn equation and maximum likelihood estimation method;

[0022] S3.3: Perform Kriging interpolation on the historical deviation values ​​to calculate the regression prediction deviation values:

[0023]

[0024] ε(t)=[ε(t)] T β (6)

[0025] p,trans p trans

[0026] Where t represents the historical time point of the monitoring data; t p Indicates the future time point that needs to be predicted; ε p,trans (t p ) represents the regression prediction deviation value in the Box-Cox transformation space; β is a vector containing interpolation weights; l represents a unit vector; λ0 represents the Lagrange multiplier; V0 and V c Respectively represent the covariance matrix between historical time points and the covariance matrix between historical time points and future time points. The covariance matrix is ​​calculated by the autocorrelation function of S3.2; V c (k) represents the future time t p The corresponding k-th column vector;

[0027] S3.4: Regression prediction bias ε p,trans (t p ) performs the inverse transformation of the Box-Cox transformation to obtain the final regression prediction deviation value ε p (t p ).

[0028] Preferably, S3.2 is specifically:

[0029] Matérn equation:

[0030]

[0031] In the formula, h ij Represents the interval between two monitoring time points; R(h ij ) represents the autocorrelation function of two time nodes; ν is the factor that controls the smoothness of the model; r represents the range parameter; Γ(ν) represents the Gamma equation of ν; K ν represents the Bessel equation of the second kind of order ν; in this formula ν and r are parameters that control the flexibility of the function;

[0032] Maximum likelihood estimation method:

[0033]

[0034] Where X is a matrix containing time nodes; V0 represents the covariance matrix between historical time points, which is obtained based on Formula 3; θ = [ν, r] contains the parameters in the Matérn equation; I is the unit matrix; n represents the number of historical time points; p represents the number of elements in θ, p = 2; W and Q are both intermediate calculations, and W = X T V0 -1 X, Q = I - XW -1 X T V0 -1 ; y = (IX (X T X) - 1 X T )×ε trans (t), this formula is used to filter the trend component in the data.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) Both accuracy and adaptability. The present invention is optimized on the basis of the traditional regression analysis method, which effectively improves the prediction accuracy. It overcomes the disadvantage of relatively low prediction accuracy of the traditional regression analysis method, and can more accurately predict the settlement in geotechnical engineering, providing a more reliable basis for engineering practices such as engineering monitoring, foundation treatment, and tunnel construction. At the same time, the present invention does not need to rely on sufficient and diverse training samples, and can better adapt to the limited sample size that is common in engineering practice, which is in sharp contrast to the machine learning model. Although the machine learning model has powerful data learning and processing capabilities, it performs poorly when the sample size is limited, while the present invention can ensure prediction accuracy under different data conditions.

[0037] (2) Good engineering applicability. Compared with machine learning models, the present invention has significant advantages in engineering applications. Machine learning models are relatively complex, difficult to understand and apply, and relatively low in acceptance in actual engineering operations. The present invention inherits the characteristics of simple model structure and convenient operation of traditional regression analysis methods, which engineers can easily understand and apply. In engineering practice, engineers do not need to spend a lot of time learning complex model architectures and operating procedures, and can use the present invention to make accurate settlement predictions. In summary, the present invention far exceeds machine learning models in terms of engineering applicability, and provides a more practical solution for geotechnical engineering settlement prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0039] The following is combined with Figure 1, the technical solution of the present invention is specifically described.

[0040] The present invention proposes a method for predicting geotechnical engineering settlement, which improves the prediction accuracy of the traditional regression method based on regression kriging interpolation technology, and includes the following steps:

[0041] S1: Use traditional regression analysis methods, such as hyperbola method, shallow hill method, exponential curve method and gray model method, to predict settlement and obtain regression curve;

[0042] S2: Calculate the deviation between the value of the regression curve at each historical time node (i.e., historical regression value) and the monitoring data (i.e., historical deviation value);

[0043] S3: Based on the historical deviation value at each historical time node, perform Kriging interpolation on the future time nodes, calculate the regression prediction deviation value, and take the deviation into account in the prediction value of each future time node;

[0044] S4: adding the regression prediction deviation value at the future time node obtained by interpolation to the regression prediction value at the future time node to obtain the final settlement prediction value;

[0045] The present invention utilizes the technical advantages of unbiased interpolation of the Kriging interpolation method and takes into account the autocorrelation characteristics of the data, and takes the deviation between the regression curve and the monitoring data in the regression analysis into account in the final settlement prediction result, which can significantly improve the accuracy of the settlement regression prediction method.

[0046] Each step is described in detail below.

[0047] S1: Use the traditional regression prediction method to predict the settlement and obtain the regression equation μ(t). The methods that can be used include: hyperbola method, shallow hill method, exponential curve method and gray model method, etc. The present invention does not limit the regression prediction method used.

[0048] Step S1 combines the traditional methods in the prior art and lays the foundation for subsequent optimization.

[0049] S2: Split the historical monitoring data into historical regression values ​​and historical deviation values ​​(Formula 1):

[0050] z(t)=μ(t)+ε(t) (1)

[0051] In formula 1, z(t) represents the monitoring data value at time t; μ(t) represents the historical regression value at time t. μ(t) can be calculated using a variety of settlement prediction methods, such as the hyperbola method, the shallow hill method, the exponential curve method, and the grayscale model method. The present invention does not limit the calculation method of μ(t); ε(t) represents the historical deviation value at time t.

[0052] Step S2 provides a specific direction for further optimization by clarifying the deviation.

[0053] S3: Calculate the regression prediction deviation value based on the historical deviation value; this step involves the following sub-steps:

[0054] S3.1: The Box-Cox transformation makes the interpolated data closer to the normal distribution (Formula 2):

[0055]

[0056] In formula 2, ε represents a vector containing all historical deviation values; λ represents a vector whose elements are all λ1, where λ1 is the minimum value of the sum of squares of ε; λ2 is a constant introduced to ensure that ε(t)+λ2>0; ε trans (t) represents the historical deviation value after transformation; gm(.) represents the geometric mean of the vector ε+λ;.

[0057] S3.2: Calculate the autocorrelation function of the data based on the Matérn equation (Formula 3) and the maximum likelihood estimation method (Formula 4):

[0058] Matérn equation:

[0059]

[0060] In formula 3, h ij Represents the interval between two monitoring time points; R(h ij ) represents the autocorrelation function of two time nodes; the value range of ν is 0 to positive infinity, which is used as a factor to control the smoothness of the model; r represents the range parameter; Γ(ν) represents the Gamma equation of ν; K ν Represents the second-order Bessel equation of order ν. In this formula, ν and r are parameters that control the flexibility of the function, so the Matérn equation is a highly flexible, data-driven autocorrelation function model.

[0061] The two parameters r and ν of the Matérn equation are determined by the maximum likelihood estimation method:

[0062]

[0063] In the above formula, X is a matrix containing time nodes; V0 represents the covariance matrix between historical time points, which is obtained based on Formula 3; θ = [ν, r] contains the parameters in the Matérn equation; I is the unit matrix; n represents the number of historical time points; p represents the number of elements in θ, p = 2; W and Q are both intermediate calculations, and W = X T V0 -1 X, Q = I - XW -1 XT V0 -1 ; y = (IX (X T X) -1 X T )×ε trans (t), this formula is used to filter the trend component in the data.

[0064] S3.2: Perform Kriging interpolation (unbiased interpolation) on the historical deviation values ​​to calculate the regression prediction deviation values ​​(Formulas 5 and 6)

[0065]

[0066] ε(t)=[ε(t)] T β (6)

[0067] p,trans p trans

[0068] In the above formula, t represents the historical time point of the monitoring data; t p Indicates the future time point that needs to be predicted; ε p,trans (t p ) represents the regression prediction deviation value in the Box-Cox transformation space; β is a vector containing interpolation weights; l represents a unit vector; λ0 represents the Lagrange multiplier; V0 and V c They represent the covariance matrix between historical time points and the covariance matrix between historical time points and future time points respectively. The covariance matrix is ​​the autocorrelation function obtained by formula 3; V c (k) represents the future time t p The corresponding k-th column vector is obtained by R(h ij ) for calculation.

[0069] S3.4: Regression prediction bias ε p,trans (t p ) performs the inverse transformation of the Box-Cox transformation (Formula 2) to obtain the final regression prediction deviation value ε p (t p ).

[0070] S4: Add the regression prediction value and the regression prediction deviation value to obtain the final settlement prediction value (Formula 7).

[0071] z p (t p )=μ(t p )+ε p (t p ) (7)

[0072] where z p (t p) represents the final settlement prediction value; μ(t p ) represents the regression prediction value.

[0073] Step S3 predicts the regression deviation value at the future moment based on the traditional regression analysis method, and then obtains the final settlement prediction value through step S4, which effectively improves the accuracy and reliability of the prediction compared with the traditional regression analysis method.

[0074] The present invention introduces regression kriging interpolation technology, fully utilizes the technical advantages of unbiased interpolation of the kriging interpolation method and takes into account the autocorrelation characteristics of data, optimizes the traditional regression method, and can significantly improve the accuracy of the settlement regression prediction method, which has a vital impact on achieving the purpose of the invention.

[0075] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A method for predicting geotechnical engineering settlement, characterized in that: The following steps are involved: S1: Use traditional regression analysis method to predict settlement and obtain regression curve; S2: Calculate the historical regression value at each historical time node and the historical deviation value of the monitoring data; the historical regression value is the value of the regression curve at the historical time node; S3: Based on the historical deviation value at each historical time node, Kriging interpolation is performed on the future time nodes to calculate the regression prediction deviation value; S4: Add the regression prediction deviation value at the future time node obtained by interpolation to the regression prediction value at the future time node to obtain a final settlement prediction value, where the regression prediction value is the value on the regression curve at the future time node.

2. A method for predicting geotechnical engineering settlement according to claim 1, characterized in that: The traditional regression analysis method includes any one of a hyperbola method, a shallow hill method, an exponential curve method, and a grayscale model method.

3. A method for predicting geotechnical engineering settlement according to claim 1, characterized in that: The S2 is specifically: splitting the historical monitoring data into historical regression values ​​and historical deviation values: z(t)=μ(t)+ε(t) (1) Wherein, z(t) represents the monitoring data value at time t; μ(t) represents the historical regression value at time t, which is obtained by performing settlement prediction through traditional regression analysis method; ε(t) represents the historical deviation value at time t, and the historical deviation value ε(t) at time t is the difference between the monitoring data value z(t) at time t and the historical regression value μ(t) at time t.

4. A method for predicting geotechnical engineering settlement according to claim 3, characterized in that: The S3 comprises the following steps: S3.1: Perform Box-Cox transformation to make the interpolated data closer to normal distribution: In the formula, ε represents a vector containing all historical deviation values; λ represents a vector whose elements are all λ1, where λ1 is the minimum value of the sum of squares of ε; λ2 is a constant introduced to ensure that ε(t)+λ2>0; ε trans (t) represents the historical deviation value after transformation; gm(.) represents the geometric mean of the vector ε+λ; S3.2: Calculate the autocorrelation function of the data based on the Matérn equation and maximum likelihood estimation method; S3.3: Perform Kriging interpolation on the historical deviation values ​​to calculate the regression prediction deviation values: ε (t)=[ε (t)] T b (6) p,trans p trans Where t represents the historical time point of the monitoring data; t p Indicates the future time point that needs to be predicted; ε p,trans (t p ) represents the regression prediction deviation value in the Box-Cox transformation space; β is a vector containing interpolation weights; l represents a unit vector; λ0 represents the Lagrange multiplier; V0 and V c Respectively represent the covariance matrix between historical time points and the covariance matrix between historical time points and future time points. The covariance matrix is ​​calculated by the autocorrelation function of S3.2; V c (k) represents the future time t p The corresponding k-th column vector; S3.4: Regression prediction bias ε p,trans (t p ) performs the inverse transformation of the Box-Cox transformation to obtain the final regression prediction deviation value ε p (t p ).

5. A method for predicting geotechnical engineering settlement according to claim 4, characterized in that: The S3.2 is specifically: Matérn equation: In the formula, h ij Represents the interval between two monitoring time points; R(h ij ) represents the autocorrelation function of two time nodes; ν is the factor that controls the smoothness of the model; r represents the range parameter; Γ(ν) represents the Gamma equation of ν; K ν represents the Bessel equation of the second kind of order ν; in this formula ν and r are parameters that control the flexibility of the function; Maximum likelihood estimation method: Where X is a matrix containing time nodes; V0 represents the covariance matrix between historical time points, which is obtained based on Formula 3; θ = [ν, r] contains the parameters in the Matérn equation; I is the unit matrix; n represents the number of historical time points; p represents the number of elements in θ, p = 2; W and Q are both intermediate calculations, and W = X T V0 -1 X, Q = I - XW -1 X T V0 -1 ; y = (IX (X T X) -1 X T )×ε trans (t), this formula is used to filter the trend component in the data.

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