Soil-rock interface probability prediction method based on kernel regression

Abstract

The invention belongs to the field of geological engineering, and particularly discloses an earth-rock interface probability prediction method based on kernel regression, which comprises the following steps: firstly, extracting earth-rock interface coordinates from existing engineering drilling data according to an engineering general situation and a corresponding earth-rock classification rule, and then selecting a proper kernel function for a kernel regression equation based on earth-rock interface distribution characteristics, the method comprises the following steps: constructing a kernel regression equation, fitting the constructed kernel regression equation with existing earth-rock interface data, determining hyper-parameters related to the kernel based on cross validation, finally predicting earth-rock interface coordinates of an uninvestigated area by using the constructed kernel regression equation, and quantifying the uncertainty of an earth-rock interface prediction result based on a prediction variance as a probability. According to the method, the precision and reliability of soil-rock interface prediction can be improved, the problems of subjectivity and uncertainty caused by empirical judgment in a traditional method are solved, a more objective interpolation result can be provided, soil-rock interface interpolation result probability prediction can be carried out, effective reference can be provided for civil airport investigation engineering, and the method has good application prospects.

Description

Technical Field

[0001] The present invention relates to the technical fields of civil engineering and geological engineering, and particularly relates to a probability prediction method for soil-rock interfaces based on kernel regression. Background Art

[0002] The soil-rock interface refers to the contact surface between soil layers and bedrock or different rock layers, and its position and properties directly affect various aspects of engineering design (such as airport engineering), such as project cost, construction period, construction machinery scheduling, and engineering safety. Due to limited relevant exploration data, the problem of predicting soil-rock interfaces in uninvestigated areas often arises in engineering. Soil-rock interface investigation methods usually adopt means such as direct measurement, borehole sampling, and seismic exploration. Although these methods can provide accurate soil-rock interface information, because geological exploration data is relatively limited and sparse, it usually can only cover local areas. For example, the most commonly used on-site investigation data such as drilling data is usually carried out at intervals of 30 m or more, especially for large civil engineering projects such as civil airports.

[0003] Various traditional geological spatial interpolation methods have been used to predict soil-rock interfaces in the 20th century, including natural domain interpolation methods, spline interpolation methods, and trend surface analysis. However, these methods are suitable for regular data and are difficult to handle complex geological structures. Some scholars have also used software such as GIS to implement the prediction of soil-rock interfaces based on triangulation interpolation methods and bilinear interpolation methods for grid data. However, the above methods cannot provide any information about prediction errors or uncertainties. The Kriging interpolation method based on regionalized variable theory and considering spatial autocorrelation can provide interpolation uncertainty, but the calculation amount is large, and the variogram needs to be reasonably selected.

[0004] With the development of machine learning and deep learning related technologies, more and more scholars have applied them to the geological field. Starting from the data itself, through specialized processing of these meaningful data, the laws and correlations between data are mined, and new understandings and laws that are difficult to discover by traditional interpolation methods are discovered. In recent years, some scholars have used the BP neural network for predicting the distribution of underground characteristics, achieving "transparency" within 5 km and generating formation distribution maps, but the accuracy is not good. Some scholars have used the random forest algorithm to achieve large-scale prediction of soil positions, but a large amount of data training and learning are required. As people's understanding of computer technology deepens, machine learning algorithms have also shifted from unsupervised to supervised learning algorithms. Some literature has used Logistic regression and neural network methods for underground stratification modeling. Some scholars have successively applied SVM and three data-driven methods (Bayesian, KNN, and neural network classifiers) to geological feature exploration. Some scholars have also used three machine learning methods, KNN, BPNN, and SVM, to predict the underground interface respectively and verified its feasibility. The literature shows that the data requirements of supervised learning algorithms are relatively large and the process is usually complex. The above prediction methods may have the following three problems: 1) The amount of data required for training the model is large; 2) The prediction method steps are cumbersome and the calculation amount is large; 3) The uncertainty of the prediction results cannot be quantified. Therefore, there is an urgent need for a probability prediction method for the soil-rock interface that can solve the above problems. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a probability prediction method for the soil-rock interface based on kernel regression, which solves the problems mentioned in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: A probability prediction method for the soil-rock interface based on kernel regression, comprising the following steps:

[0007] Step S1: According to the project overview, project requirements and relevant specifications, determine the soil-rock classification rules and various lithology data classification standards, and extract the position coordinates of the soil-rock demarcation points from the existing borehole data;

[0008] Step S2: According to the distribution characteristics of the soil-rock interface data extracted in Step S1, select a suitable kernel function to construct a kernel regression prediction equation;

[0009] Step S3: Based on the soil-rock demarcation data in Step S1 and the prediction equation constructed in Step S2, use the cross-validation method to determine the hyperparameters related to the kernel function;

[0010] Step S4: Substitute the hyperparameters determined in Step S3 into the kernel regression equation, and use the prediction variance of the equation as the probability representing the uncertainty of the soil-rock interface interpolation result, and use the predicted mean of the equation as the soil-rock interface coordinates of the uninvestigated area.

[0011] Preferably, in step S1, determining the soil and rock classification rules and various lithologic data classification standards according to the project overview, project requirements, and relevant specifications specifically includes: classifying the soil and rock types and grades of the rock and soil layers involved in the survey range according to the excavation difficulty of soil and rock; or classifying the engineering categories of the rock and soil layers according to the properties of the rock and soil layers; or classifying the engineering fillers of the rock and soil layers according to the filler properties.

[0012] Preferably, the various lithologic data specifically includes, but is not limited to: cohesive plain fill, gravel plain fill, vegetable soil, silty clay, clay, silty clay, siltstone mudstone, dolomite, muddy siltstone, and quartz sandstone.

[0013] Preferably, in step S2, selecting a suitable kernel function specifically includes: 1) When the data is linearly separable in the original space, select a linear kernel function; 2) When dealing with some image classification or pattern recognition tasks, select a polynomial kernel function; 3) When facing data with high-dimensional and complex linear relationships, select a Gaussian radial basis kernel function.

[0014] Preferably, the form of the kernel regression prediction equation is as follows:

[0015]

[0016] where y(x) is the predicted elevation value of the point to be predicted, y(x , ) is the elevation value of the known observation point; k(x, x , ) is the kernel function in the kernel regression, and x and x , respectively represent the horizontal position coordinates of the point to be predicted and the known point.

[0017] Preferably, in step S3, dividing the data set composed of the soil-rock boundary data into a training set and a test set, based on cross-validation, using the mean square error as an index, and using the kernel function selected in step S2 to obtain the optimal hyperparameters of the kernel regression equation on the known data set; including, but not limited to, the number of neighboring points in the inverse distance weighting method IDW and the K-nearest neighbor algorithm KNN, the bandwidth in the equivalent Gaussian kernel function, and the weight index.

[0018] Preferably, in step S4, based on the kernel regression equation, calculate the weight of each observation point and calculate its prediction variance as the probability to characterize its uncertainty; at the same time, use the predicted mean as the prediction result of the unknown point.

[0019] The beneficial effects of the present invention are as follows: the method of the present invention can improve the accuracy and reliability of soil-rock interface prediction, thereby solving the subjectivity and uncertainty problems caused by reliance on empirical judgment in traditional methods, providing more objective interpolation results, and being able to perform probabilistic prediction of soil-rock interface interpolation results, providing an effective reference for civil airport survey engineering, reliability analysis and design, and having good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of the process flow of the soil-rock interface probability prediction method based on kernel regression in Example 1;

[0021] Figure 2 This is a spatial schematic diagram of extracting the soil-rock boundary point in the borehole in Example 2, where the grayscale represents its elevation value. (a) is an XY plane top view, and (b) is a three-dimensional side view;

[0022] Figure 3 Schematic diagram of the soil-rock boundary point space encrypted based on a soil-rock interface probability prediction method based on kernel regression in Example 2, where the grayscale represents its elevation value, (a) is an XY plane top view, and (b) is a three-dimensional side view;

[0023] Figure 4 Schematic diagram of uncertainty quantification of soil-rock boundary points generated by the soil-rock interface probability prediction method based on kernel regression in Example 2, where the grayscale represents its prediction variance, (a) is an XY plane top view, and (b) is a three-dimensional side view. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0025] Example 1

[0026] The present invention provides a technical solution: a soil-rock interface probability prediction method based on kernel regression, such as Figure 1 As shown, the following steps are included:

[0027] Step S1: Determine soil and rock classification rules and various lithology data classification standards based on the project overview, project requirements, and relevant specifications, and extract the location coordinates of the soil and rock boundary points from the existing drilling data;

[0028] Step S2: Select a suitable kernel function to construct a kernel regression prediction equation based on the distribution characteristics of the soil-rock interface data extracted in step S1;

[0029] Step S3: Based on the soil-rock boundary data in Step S1 and the prediction equation constructed in Step S2, use the cross-validation method to determine the hyperparameters related to the kernel function;

[0030] Step S4: Substitute the hyperparameters determined in Step S3 into the kernel regression equation, and use the prediction variance of the equation as the probability characterizing the uncertainty of the soil-rock interface interpolation result. Use this equation to predict the mean value as the soil-rock interface coordinates of the uninvestigated area.

[0031] Preferably, in Step S1, the determination of the soil-rock classification rules and various lithological data classification criteria according to the project overview, project requirements, and relevant specifications specifically includes: dividing the soil and rock layers involved in the investigation scope into soil and rock categories and soil and rock grades according to the difficulty of soil and rock excavation; or dividing the soil and rock layers into engineering categories according to the properties of the soil and rock layers; or classifying the soil and rock layers into engineering fillers according to the properties of the fillers.

[0032] Preferably, the various lithological data specifically includes but is not limited to: cohesive plain fill, gravel plain fill, plant soil, silty clay, clay, silty clay, siltstone mudstone, dolomite, argillaceous siltstone, and quartz sandstone, etc.

[0033] Preferably, in Step S2, the selection of a suitable kernel function specifically includes: 1) When the data is linearly separable in the original space, the linear kernel function is the simplest and most effective choice, and the linear kernel function can be selected; 2) When dealing with some image classification or pattern recognition tasks, select the polynomial kernel function; 3) When facing data with high-dimensional and complex linear relationships, select the Gaussian radial basis kernel function.

[0034] Preferably, the form of the kernel regression prediction equation is as follows:

[0035]

[0036] where \(y(x)\) is the predicted elevation value of the point to be predicted, \(y(x , )\) is the elevation value of the known observation point; \(k(x,x , )\) is the kernel function in the kernel regression and is also the covariance function during the prediction of the regression equation, which is used to describe the similarity between the input point and the known point. \(x\) and \(x , respectively represent the horizontal position coordinates of the point to be predicted and the known point.

[0037] Preferably, in step S3, the data set composed of soil-rock boundary data is divided into a training set and a test set. Based on cross-validation, with the mean square error as the index, using the kernel function selected in step S2, the optimal hyperparameters of the kernel regression equation on the known data set are obtained; including but not limited to the number of neighboring points in the inverse distance weighting (IDW) method and the K-nearest neighbor (KNN) algorithm, the bandwidth in the equivalent Gaussian kernel function, and the weight exponent.

[0038] Preferably, in step S4, based on the kernel regression equation, the weight of each observation point is calculated, and its prediction variance is calculated. As a probability, it characterizes its uncertainty; at the same time, the predicted mean is used as the prediction result of the unknown point. The effects of soil-rock interface prediction and probability prediction can be achieved.

[0039] Example 2 A probability prediction of soil-rock interface based on kernel regression for a "civil airport project"

[0040] The method is as follows: Step 1, for the "civil airport project" undertaken by a certain survey unit, there are many exposed strata in its filling and excavation works. To calculate the soil-rock ratio of the site, the probability prediction method of soil-rock interface based on kernel regression of the present invention is used to determine the soil-rock interface. According to the relevant specification requirements, the rock and soil layers involved in the survey range are classified into soil and rock categories and soil and rock grades according to the difficulty of soil and rock excavation, as shown in Table 1:

[0041] Table 1 Soil-rock division table

[0042]

[0043]

[0044] The spatial distribution of the extracted soil-rock boundary points is as Figure 1 shown, Figure 2 where (a) is the top view of the XY plane and (b) is the three-dimensional side view.

[0045] Step 2, after preprocessing the borehole data, the soil-rock boundary points are extracted. According to the engineering data characteristics, the inverse distance weighting regression algorithm (IDW) is selected for this project, and the weight function in IDW that is inversely proportional to the distance is used as the kernel function of the kernel regression method to determine the kernel regression equation.

[0046] Step 3, through the prediction model, the known point data is divided into a training set and a test set. Based on cross-validation, with the mean square error as the index, the optimal hyperparameters of the kernel regression equation are obtained, the number of neighboring points k = 4, and the weight exponent p = 2.

[0047] Step 4: Based on the kernel regression method, substitute the weight function inversely proportional to the Euclidean distance in the inverse distance interpolation regression algorithm, calculate the predicted variance of the equation as the probability characterizing the uncertainty of the soil-rock interface interpolation result, and calculate its predicted mean as the spatial Z coordinate of the soil-rock demarcation point in the area to be measured, as Figure 3 and Figure 4 shown.

[0048] From the results, it can be seen that the method of the present invention has a good effect in predicting the soil-rock interface, has no specific requirements for the amount of data, and the method proposed by the present invention is very simple, indicating that the method of the present invention has high accuracy and efficiency in predicting the soil-rock interface relying on limited drilling data. At the same time, its predicted variance can be calculated as a probability to characterize its uncertainty, and its predicted mean can be calculated as the predicted value.

[0049] It should be noted that in this article, the terms "including", "comprising" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the element.

[0050] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the" and "said" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms unless the context clearly dictates otherwise.

[0051] It should be understood that the term " / or" used herein is only a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in this article generally represents an "or" relationship between the associated objects before and after.

[0052] Depending on the context, the word "if" as used herein can be interpreted as "when" or "while" or "in response to a determination" or "in response to a detection". Similarly, depending on the context, the phrase "if a determination" or "if a detection (stated condition or event)" can be interpreted as "when a determination is made" or "in response to a determination" or "when a detection (stated condition or event) is made" or "in response to a detection (stated condition or event)".

[0053] The "first / second" mentioned in the embodiments is only used to distinguish similar objects and does not represent a specific order for the objects. It can be understood that the "first / second" can be interchanged in a specific order or sequence when permitted. It should be understood that the objects distinguished by the "first / second" can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0054] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A probability prediction method for soil-rock interface based on kernel regression, characterized in that It includes the following steps: Step S1: According to the project overview, project requirements and relevant specifications, determine the soil and rock classification rules and various lithology data classification standards, and extract the position coordinates of the soil-rock boundary points from the existing borehole data; Step S2: According to the distribution characteristics of the soil-rock interface data extracted in Step S1, select a suitable kernel function to construct a kernel regression prediction equation; Step S3: Based on the soil-rock boundary data in Step S1 and the prediction equation constructed in Step S2, use the cross-validation method to determine the hyperparameters related to the kernel function; Step S4: Substitute the hyperparameters determined in Step S3 into the kernel regression equation, and use the prediction variance of the equation as the probability characterizing the uncertainty of the soil-rock interface interpolation result, and use the predicted mean of the equation as the soil-rock interface coordinates of the uninvestigated area.

2. The probability prediction method for the soil-rock interface based on kernel regression according to claim 1, wherein: In Step S1, the determination of the soil and rock classification rules and various lithology data classification standards according to the project overview, project requirements and relevant specifications specifically includes: classifying the soil and rock types and soil and rock grades of the rock and soil layers involved in the survey range according to the excavation difficulty of soil and rock; or classifying the engineering categories of the rock and soil layers according to the properties of the rock and soil layers; or classifying the engineering fillers of the rock and soil layers according to the filler properties.

3. The probability prediction method for soil-rock interface based on kernel regression according to claim 1, characterized in that: The various lithology data specifically includes, but is not limited to: cohesive plain fill, gravel plain fill, plant soil, silty clay, clay, silty clay, siltstone mudstone, dolomite, muddy siltstone and quartz sandstone.

4. The probability prediction method for the soil-rock interface based on kernel regression according to claim 1, wherein: In Step S2, the selection of a suitable kernel function specifically includes: 1) When the data is linearly separable in the original space, select a linear kernel function; 2) When dealing with some image classification or pattern recognition tasks, select a polynomial kernel function; 3) When facing data with high dimensions and complex linear relationships, select a Gaussian radial basis kernel function.

5. The probability prediction method for the soil-rock interface based on kernel regression according to claim 1, wherein: The form of the kernel regression prediction equation is as follows: Among them, y(x) is the predicted elevation value of the point to be predicted, and y(x , ) is the elevation value of the known observation point; k(x, x , ) is the kernel function in kernel regression, and x and x , represent the horizontal position coordinates of the point to be predicted and the known point respectively.

6. The probability prediction method for soil-rock interface based on kernel regression according to claim 1, characterized in that: In Step S3, divide the data set composed of the soil-rock boundary data into a training set and a test set. Based on cross-validation, with the mean square error as the index, use the kernel function selected in Step S2 to obtain the optimal hyperparameters of the kernel regression equation on the known data set; including but not limited to the number of neighboring points in the inverse distance weighting interpolation method IDW and the K-nearest neighbor algorithm KNN, the bandwidth in the equivalent Gaussian kernel function, and the weight exponent.

7. The probability prediction method for soil-rock interface based on kernel regression according to claim 1, characterized in that: In step S4, based on the kernel regression equation, the weights of each observation point are obtained, and its prediction variance is calculated As a probability to characterize its uncertainty; at the same time, the predicted mean Is used as the prediction result of the unknown point.

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