Sandstone type uranium mine logging data lithology automatic identification method based on artificial intelligence
By employing an AI-based method for automatic lithology identification of sandstone-type uranium deposit logging data, and utilizing models such as random forest, NRS+AdaBoost, and PSO+BP neural networks, this method addresses the issues of low efficiency and reliance on the interpreter in traditional uranium exploration, achieving efficient and accurate lithology identification and optimized data processing workflows.
Patent Information
- Application Number
- CN202511495167.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-20
- Publication Date
- 2026-02-17
AI Technical Summary
Traditional uranium exploration relies on manual fitting for interpreting logging data, resulting in a large workload and the accuracy of the results depending on the interpreter's skill level. The identification rate of thin-layer lithology is not high, and artificial intelligence algorithms are not optimized sufficiently.
An AI-based method for automatic lithology identification of sandstone-type uranium deposit logging data is adopted, including logging data preparation, feature engineering, model selection and training, model testing and optimization, and lithology identification. It utilizes models such as random forest, NRS+AdaBoost, and PSO+BP neural networks, combined with feature engineering and data processing techniques, such as outlier handling, median filtering, normalization, automatic stratification, and feature selection.
It significantly improves the efficiency and accuracy of lithology identification in sandstone-type uranium deposit logging data, optimizes data processing procedures, reduces labor costs, and promotes the digital transformation of the uranium exploration field.
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Figure CN121542901A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of well logging in sandstone-type uranium deposits, and more specifically to an artificial intelligence-based method for automatic lithology identification of well logging data in sandstone-type uranium deposits. Background Technology
[0002] With the deepening of the construction of the "digital nuclear industry", the traditional uranium exploration industry is facing the situation that the work efficiency and quality are relatively lagging behind due to the surge in workload and the shortage of personnel. Therefore, it is urgent to upgrade and update the new generation of digital exploration systems to ensure the efficient and high-quality completion of exploration tasks.
[0003] Well logging data interpretation is a crucial technical means of obtaining geological information within boreholes during uranium exploration. Well logging data interpretation is typically conducted based on the sensitivity and characteristic variations of different logging curves to different lithologies. Traditional well logging interpretation methods rely on manual fitting or subjective expert judgment. Besides being labor-intensive, manual interpretation suffers from inconsistent accuracy depending on the interpreter's skill level, affecting the acquisition of correct results. Currently, artificial intelligence technology is developing rapidly and has been effectively applied in various fields. Previous experiments using an intelligent lithology identification system for sandstone well logging data have preliminarily explored the possibilities of AI-based sandstone well logging identification, but challenges remain, including low recognition rates for thin-layer lithology and the need for further algorithm optimization. Summary of the Invention
[0004] To address the problems of existing technologies, this invention provides an automatic lithology identification method for sandstone-type uranium deposit logging data based on artificial intelligence.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] An AI-based method for automatic lithology identification from well logging data in sandstone-type uranium deposits includes the following steps:
[0007] Well logging data preparation: Collect well logging data from sandstone-type uranium deposits under different regions and geological conditions, and perform data cleaning; Well logging data analysis and processing: Perform outlier handling, median filtering, and normalization on the data.
[0008] Feature engineering: Dimensionality reduction algorithms are used to extract and select features from well logging features, and features that have a significant impact on lithology identification are screened.
[0009] Model selection and training: Random Forest, NRS+AdaBoost, and PSO+BP neural network models were selected and trained using the training dataset;
[0010] Model testing and optimization: The accuracy, generalization ability and operational efficiency of the model in the lithology identification task are evaluated through the test set, and the optimal model is selected.
[0011] Lithology identification: Input the well logging data to be identified into the optimal model and output the automatic identification results of lithology and lithofacies.
[0012] The aforementioned artificial intelligence-based automatic lithology identification method for sandstone-type uranium deposit logging data includes the following logging data analysis and processing steps:
[0013] Outlier handling employs either the Grobbs test or the Dixon test, and replacements are made using the average of neighboring data.
[0014] Median filtering uses a sliding window method to smooth the logging curves in order to eliminate spike interference;
[0015] The normalization process uses the maximum-minimum normalization method to unify the dimensions of different logging curves to the [0, 1] interval;
[0016] The normalization formula is:
[0017]
[0018] In the formula, x i x is the logging value corresponding to a certain depth on the logging curve. max and x min These are the maximum and minimum values in the well logging curve, respectively; x i ' is the normalized value of the logging curve at that depth.
[0019] The aforementioned artificial intelligence-based method for automatic lithology identification of sandstone-type uranium deposit logging data further includes an automatic stratification processing step, specifically including:
[0020] The logging curves are automatically stratified using analysis of variance or comparison of adjacent boreholes.
[0021] The layered results are merged at the layer interfaces, and the layer logging values are calculated using methods such as taking the peak value, the center mean, the weighted value, or the surrounding rock value.
[0022] The aforementioned artificial intelligence-based method for automatic lithology identification of sandstone-type uranium deposit logging data, assuming x ij For the j-th data point in the i-th stratum, the following formula can be used:
[0023] x ij =μ+α i +e ij
[0024] in:
[0025] μ—Overall mean
[0026] α i—Systematic error. Represents the overall influence of the i-th stratum (i.e., the influence of the electrical properties of the rocks in that stratum).
[0027] e ij —The combined random error of the j-th observation in the i-th layer.
[0028] The aforementioned artificial intelligence-based automatic lithology identification method for sandstone-type uranium deposit logging data assumes the following for the studied well section: k is the total number of layers; n1 is the number of observation data in the i-th layer. The overall average is... Let be the average of the i-th layer; N be the total number of observations.
[0029] Therefore, the following formula is derived:
[0030]
[0031]
[0032] The aforementioned artificial intelligence-based automatic lithology identification method for sandstone-type uranium deposit logging data calculates the sum of squares of the differences between the observed data and the overall mean.
[0033]
[0034] If we let the first term be Q1 and the second term be Q2, then we have:
[0035] Q = Q1 + Q2
[0036] As can be seen from the above formula, the variance Q of each observation value and the overall mean can be divided into two parts: Q1 is the sum of squares of the differences between each observation value and the mean of its corresponding stratum, called the within-group variance sum of squares. Q2 is the sum of squares of the differences between the mean of each stratum observation value and the overall mean.
[0037] If the within-group variance is W and the between-group variance is B, then:
[0038]
[0039]
[0040] From the two formulas above, the ratio of the two equations can be obtained as:
[0041] .
[0042] The formula for calculating the R statistic in the artificial intelligence-based automatic lithology identification method for sandstone-type uranium deposit logging data is as follows:
[0043] The R-statistic and the F-statistic are consistent and can be written as:
[0044] The change of R has the following relationship with stratification:
[0045] ① If there are no significant differences in the strata (i.e., the same layer), the between-group variance and within-group variance should be very close, or B = W. At this time, R is very close to 0 or = 0.
[0046] ② If there are significant differences in the strata (i.e., different layers), there are two situations for the between-group variance and within-group variance:
[0047] Situation 1: B≠0, W = 0, and B >> W. At this time, R = 1 or very close to 1.
[0048] Situation 2: In actual situations, there will be a situation where B < W, that is, R < 0. This is because the random factor fluctuations are relatively large, resulting in the group variance exceeding the between-group variance. At this time, it is inferred as the same layer.
[0049] Compared with the prior art, the beneficial effects of the invention are as follows: The invention not only significantly improves the efficiency and accuracy of lithology identification of logging data for sandstone-type uranium ore, but also optimizes the data processing process through a systematic and modular technical architecture, reduces labor costs, and strongly promotes the digital transformation in the field of uranium ore exploration, having important practical application value and industry promotion significance. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Other features, objects, and advantages of the present invention will become more apparent by reading the detailed description of the non-limiting embodiments with reference to the following drawings.
[0051] Figure 1 It is a schematic diagram of the confusion matrix of the prediction results of the BP neural network and PSO+BP neural network models of the present invention.
[0052] Figure 2 It is a schematic diagram of the confusion matrix of NRS+AdaBoost of the present invention.
[0053] Figure 3 It is a schematic diagram of the technical route of the PSO+BP neural network model of the present invention.
[0054] Figure 4 It is a schematic diagram of the technical route of the NRS+AdaBoost model of the present invention.
[0055] Figure 5 It is a scatter plot of the concentrated distribution of lithology sensitivity of the present invention.
[0056] Figure 6 It is a schematic diagram of the technical route of intelligent interpretation of logging data of the present invention.
[0057] Figure 7 It is a flow chart of the present invention.
[0058] Figure 8 This is a flowchart of the median filtering process of this invention.
[0059] Figure 9 This is a three-layered example diagram of the present invention.
[0060] Figure 10 This is the flowchart of the lithology classification module of the present invention.
[0061] Figure 11 This is a diagram of the document selection interface for this invention.
[0062] Figure 12 This is a diagram of the data display interface of the present invention.
[0063] Figure 13 This is a diagram of the interface for adding models in this invention.
[0064] Figure 14 This is a diagram of the interface for adding models in this invention.
[0065] Figure 15 This is an interface diagram of the lithology identification results of the present invention. Detailed Implementation
[0066] The present invention will be further described in detail below through embodiments. These embodiments are only used to illustrate the present invention and do not limit the scope of the present invention.
[0067] An AI-based method for automatic lithology identification from well logging data in sandstone-type uranium deposits is presented, involving model optimization: four models—BP neural network, SVM, random forest, and NRS+AdaBoost—were trained and optimized. The preliminary performance of each model is as follows:
[0068] 1. Backpropagation (BP) neural network
[0069] Neural network models are among the earliest machine learning algorithms applied in lithology identification. However, BP neural networks have inherent drawbacks, including susceptibility to local minima, slow convergence, inconsistent model structure, and overfitting. Recent research suggests using the t-SNE algorithm to reduce the dimensionality of the original data, using the resulting feature matrix as model input, and employing the PSO (Particle Swarm Optimization) algorithm to calculate the optimal initial parameters for the BP neural network. The optimized initial parameters obtained after PSO are: 15 hidden layers, a learning rate of 0.6789, and a momentum factor of 3.532. When the feature-selected data is used for training and testing, the BP neural network, due to its inherent limitations and the complexity of well logging data, not only performs poorly in computational performance and time complexity, requiring numerous network parameters and exhibiting slow convergence, but also suffers from severe overfitting and performs poorly on new data. A comparative experiment was conducted between the BP neural network and the PSO+BP neural network models. Figure 1 Ultimately, the PSO+BP neural network outperformed the simple BP neural network.
[0070] 2.SVM
[0071] SVM requires finding the optimal hyperplane for the feature space data. During computation, it uses an inner product kernel function instead of a nonlinear mapping to a higher-dimensional space, resulting in high time complexity. The space consumption of SVM mainly involves storing training samples and the kernel matrix, and solving for support vectors using quadratic programming. Solving quadratic programming involves calculating an m-order matrix, which, due to the large sample size of well logging data, requires significant machine memory and computation time. Furthermore, classic support vector machines only provide algorithms for binary classification problems. For lithology identification with multiple lithology categories, only one-to-one or one-to-many models can be chosen, which is difficult to apply effectively to large datasets in the field of lithology identification. Therefore, this model was excluded.
[0072] 3. Random Forest
[0073] Random Forest (RF) is an ensemble learning model that integrates multiple decision trees using the Bagging approach. When training each tree, a dataset of size N with possible duplicates is selected from all training samples for training. At each node, a subset of all features is randomly selected to compute the optimal split. RF can handle high-dimensional logging features and returns feature importance information after training. Furthermore, RF has a fast training speed and low time complexity. It uses a normalized, feature-selected, and equalized dataset as input to the model, selects appropriate decision tree parameters through grid search, and then trains the decision tree model based on the data. While RF achieves good accuracy in lithology identification of single-hole logging data, it exhibits insufficient generalization performance when testing with multi-hole models.
[0074] 4. NRS+AdaBoost model
[0075] The basic principle of the AdaBoost algorithm is to combine multiple weak classifiers (generally single-layer decision trees) into a single strong classifier. AdaBoost employs an iterative approach, training only one weak classifier per iteration. This trained weak classifier is then used in the next iteration. In other words, in the Nth iteration, there are N weak classifiers, of which N-1 are previously trained with unchanged parameters, and the Nth classifier is trained in this iteration. The relationship between the weak classifiers is that the Nth classifier is more likely to correctly classify the data that the previous N-1 classifiers have not correctly classified. The final classification output depends on the combined performance of these N classifiers. Compared to Random Forest, AdaBoost incorporates weighting factors in the result voting process. For different lithologies, weights are assigned based on their importance, thickness, etc., which positively impacts the final lithology classification. AdaBoost offers higher classification accuracy than Random Forest and is less prone to overfitting. Using normalized and balanced data as model input, the model is trained, and the results are as follows... Figure 2 .
[0076] Model testing:
[0077] 1. PSO+BP Neural Network Model
[0078] (1) Technical methods
[0079] The lithological classification of the study area is compiled using well logging data. Production data is converted into data suitable for input into the algorithm. Data cleaning and preprocessing are then performed, including missing value imputation, imbalanced data equalization, and normalization. Feature engineering studies, such as feature extraction, can be conducted if necessary. The processed sample data is then used to learn and train the model. A particle swarm optimization algorithm is used to iteratively search for the optimal initial value of the network to prevent it from falling into local optima and to accelerate network learning. After the network learning and training are complete, evaluation samples are fed into the model, and the neural network output is compared with actual core observation data to determine the consistency rate. Once the consistency rate reaches a satisfactory value, the model is then used for lithological identification of unknown well sections.
[0080] (2) Model parameters
[0081] The experiment constructed a neural network based on the Neural network models module in the scikit-learn library. Through multiple experiments, a 16*64*16*11 four-layer neural network model was adopted: the first layer was the input layer, containing 16 neurons, corresponding to 16 well logging features; the second and third layers were hidden layers, with 64 and 16 neurons respectively; the output layer had 11 neurons, corresponding to 11 lithologies. The hidden layers used the ReLU activation function, and the output layer used the softmax activation function to map the results to probabilities of 0 to 1, thus supporting multi-class classification.
[0082] (3) Test results
[0083] With a particle swarm size of 20 particles, 15 iterations, and an acceleration factor of 1.49, and trained using a backpropagation neural network, 1112 out of 1448 test data points were correctly identified, resulting in an accuracy rate of 76.80%.
[0084] 2. NRS+AdaBoost model
[0085] (1) Technical methods
[0086] The original data is normalized after handling missing values and removing outliers. The normalized data is then input into the NRS algorithm for attribute reduction. The reduced result is used as the model input for training and testing. Targeted model pruning and regularization are performed to reduce overfitting. Neighborhood Rough Set (NRS) can handle continuous data. It discretizes the original data using the neighborhood radius and can reduce existing logging features using attribute importance, thereby removing logging features with low importance for lithology label classification. The following improvements are made to traditional NRS: First, to address the issue of neighborhood radius value, mutual information is introduced. By calculating the mutual information of two logging features, the contribution of each feature to the calculation of the neighborhood radius is obtained, and this contribution is used as the weight of the feature variance to calculate the final neighborhood radius. Second, neighborhood knowledge granularity is added to the calculation of attribute importance, enhancing the ability to distinguish knowledge. AdaBoost, as a boosting method, combines multiple weak classifiers into a strong classifier. Its basic principle is that the weights of samples misclassified by a previous weak classifier are strengthened, and these weighted samples are then used to train the next new weak classifier. In each training round, a new weak classifier is trained using the overall dataset, generating new sample weights, until a predetermined error rate or a specified number of iterations is reached. AdaBoost offers high classification accuracy and is well-suited for binary or multi-class classification problems.
[0087] (2) Model parameters
[0088] The development, improvement, and debugging of the NRS algorithm were implemented using the PyCharm platform. The MyNrs module was imported, and the GetNRSFeatureSelection method within the module was called. This method takes three main parameters: a list of feature sets (C) to be reduced, a subset of baseline features (D) for reduction, and a Pandas.DataFrame table. The AdaBoost algorithm utilizes sklearn.ensemble.AdaBoostClassifier for model building and parameter tuning. Through multiple experiments, it was found that the NRS algorithm uses the entire feature set as the first parameter, SCXDY as the baseline feature subset, and importing the entire table as a Pandas.DataFrame as the last parameter to complete the attribute reduction. In the AdaBoost algorithm, DecisionTreeClassifier is used as the base classifier.
[0089] The parameters of the base classifier are set using grid search:
[0090] max_depth=7,max_features=6,min_samples_split=20,min_samples_leaf=7,algorithm="SAMME",n_estimators=200,learning_rate=0.5.
[0091] (3) Test results
[0092] In single-hole tests, the model outperformed random forests in accuracy. In multi-hole tests, out of 11,190 data points, 8,834 predictions were correct, achieving an accuracy of 78.95%.
[0093] Specific content: (I) Data aspect: Collect well logging data under different regions and geological conditions to reduce the problem of poor data sensitivity analysis under the same geological conditions. Figure 5 This avoids the identification bias problem in the data learning process caused by the centralized distribution of the dataset.
[0094] (ii) Algorithm aspect: Introduce new machine learning algorithms such as CNN (Convolutional Neural Network) and RNN (Recurrent Neural Network), conduct application experiments and comparative analysis, and determine the optimal processing scheme.
[0095] CNN (Convolutional Neural Network): A convolutional neural network processes labeled data by setting up an input layer, convolutional layer, ReLU layer, pooling layer, and fully connected layer, setting activation functions, neuron weights, and biases. Based on the local features of the data, it simulates the global data to fill in missing values under the current conditions, thereby effectively fitting well logging curve data and calculating the root mean square.
[0096] RNN (Recurrent Neural Network): RNNs describe the relationship between the current output and previous outputs of a sequence. They are widely used to process long sequences of data. By remembering important information from previous moments, they influence the output of subsequent neurons, establishing rules for attribute changes between sequence changes and attribute changes. Based on these rules, they fill in missing data. RNNs mainly include two variants: GRU and LSTM. Currently, LSTM (Long Short-Term Neural Network) can effectively fill in some missing data with high efficiency. It can effectively learn the rate of change of curves, showing good consistency between peaks and troughs, which is sufficient for initial data applications. To further improve the model's recognition efficiency and accuracy in filling in missing values, a corresponding technical roadmap is developed. Figure 6 ).
[0097] According to the technology roadmap, the initial learning rate and learning parameters are first set based on the pre-trained model, and an initial Long Short-Term Memory (LSTM) neural network model is built based on TensorFlow. The model parameters, gating layers, and tanh layers are determined to establish a preliminary network model. At the same time, the well logging data is preprocessed to standardize and normalize the dataset, determine the correlation between different attributes, and fit the correlation through multivariate attribute analysis. Then, the generated regression analysis parameters and cell parameters are analyzed together to establish an initial cell model, and the model is optimized through a self-attention mechanism. Finally, the model is used to process the well logging data and compared with GAN and GRU algorithms. The cell forgetting rate is adjusted according to the root mean square error of the recognition results until the root mean square error tends to match, and the final recognition result is determined.
[0098] (III) Program aspects: Based on the Juypter platform and saved in ipy mode. Juypter does not support visual development, so visual design is carried out on the PyCharm platform, including the operation interface and the visualization curves of the recognition process, lithology categories, fitting curves, etc.
[0099] (IV) Specific Scheme: The research on integrated well logging data interpretation technology for sandstone-type uranium deposits based on artificial intelligence is aimed at addressing the problems of long cycles, low accuracy, and significant subjective influence on logging results in the context of geological exploration informatization. It proposes to adopt a relatively mature artificial intelligence machine learning model to deeply develop and learn from a large amount of accumulated sandstone-type uranium deposit borehole logging data, establish a well logging data interpretation model, and achieve automatic identification of borehole lithology and lithofacies through intelligent analysis. The main technical processes of this scheme include: well logging data preparation, well logging data analysis and processing, feature engineering, model selection, model optimization and testing. Figure 7 ).
[0100] An AI-based method for automatic lithology identification from well logging data in sandstone-type uranium deposits includes the following steps:
[0101] Well logging data preparation: Collect well logging data from sandstone-type uranium deposits in different regions and under different geological conditions, and perform data cleaning. Due to limitations of logging instruments or environmental influences, the well logging data may contain inherent problems. During the well logging data preparation stage, it is necessary to understand and analyze the physical meaning of the original well logging data. Consult with geophysical experts to understand the physical meaning of each well logging characteristic and the sensitivity of various logging curves to different lithologies. Furthermore, well logging data itself may contain mechanical or human errors. These errors manifest in the data as differences in the extent of the same logging characteristic in different boreholes with the same lithology. It is necessary to understand whether these differences are caused by inherent differences in lithology or external environmental interference. More importantly, it is essential to select high-quality logging curves to eliminate the negative impact of inaccurate well logging data caused by problems with the quality of the logging instruments.
[0102] Well logging data analysis and processing: This involves outlier handling, median filtering, and normalization, as well as addressing data imbalance. Data quality directly determines the predictive and generalization capabilities of the model. It involves many factors, including accuracy, completeness, consistency, timeliness, reliability, and interpretability. Real-world data may contain numerous missing values, significant noise, and outliers due to human error, which is detrimental to algorithm training. Therefore, data processing is necessary, including missing value imputation, imbalance correction, and normalization. Different methods should be used for correcting and normalizing different well logging parameters based on their properties. Data cleaning involves processing various types of dirty data to obtain standardized, clean, and continuous data for use in data statistics and data mining. Data Analysis: Well logging data is characterized by its large volume, numerous feature values, and diverse label types. A large data volume can increase the accuracy of machine learning in lithology identification, better fitting the features of the training sample set. However, due to data similarity, overfitting may occur, reducing the classifier's generalization ability and thus hindering the classification of unknown data. The large number of feature values, to some extent, ensures the learner can more accurately fit the dataset's features during the learning process. However, the strong correlation between different features increases the time complexity and difficulty of training, leading to problems in some machine learning algorithms, such as the local minima problem during neural network training. The diverse label types dictate that the algorithm structure for this project must be able to solve multi-class problems, which are more complex than binary classification problems. Furthermore, geophysical methods generally suffer from geological ambiguity. For example, the same gravity anomaly curve may correspond to a high-density metal deposit or a high-density strata or rock mass. In well logging data, even with similar feature values, the resulting label (lithology category) can show significant differences. This geological ambiguity may also affect the predicted classification results.
[0103] Data processing: For most machine learning algorithms, such as ANN, KNN, and SVM, extensive data processing is required before model training. Data preprocessing includes dimensionless processing, missing value handling, and data equalization.
[0104] ① A commonly used dimensionless processing method is data normalization. Normalization scales the original data range to between 0 and 1, so that different data have the same value range without changing the distribution of the data. The most commonly used method is maximum and minimum value normalization (Formula 1). X corresponds to the original feature vector, min(x) is the minimum value of the original feature vector, and max(x) is the maximum value of the feature vector.
[0105] X = (x - min(x)) / (max(x) - min(x)) (Formula 1)
[0106] In addition, data standardization is also an important method in dimensionless processing. Data standardization involves subtracting the mean from each data point and then dividing by the variance, which makes the processed data more consistent with a standard normal distribution (Formula 2). X is the feature vector of the original data, μ is the mean of each feature vector, and σ is the variance of the feature vector.
[0107] X=(x-μ) / σ (Formula 2)
[0108] ② There are several methods for handling missing values in data. Simpler methods include mean imputation, median imputation, mode imputation, and specified value imputation. Choosing the right imputation method requires observing the data characteristics and the operator having a certain understanding of the data. Alternatively, missing values can be imputed using algorithms, such as the random forest algorithm. The advantage of this method is that it doesn't require considering or understanding the actual meaning of the data; it imputes missing values appropriately based on the relationships and internal patterns within the data itself—essentially imputing missing values through classification.
[0109] ③ Imbalanced data has a significant impact on model training and classification accuracy in multi-class classification problems. Commonly used methods for addressing imbalanced data include undersampling, oversampling, and cost-sensitive learning. Undersampling reduces the number of samples in the majority class by random sampling, achieving balance between the majority and minority classes. Common undersampling algorithms include EasyEnsemble and BalanceCascade. Oversampling increases the number of samples in the rare class by repeatedly sampling from it. A typical oversampling method involves multiple random samplings of the rare class until the required number of samples is reached. However, this can lead to the same sample being sampled multiple times, making the resulting sample set unable to reflect the characteristics of the rare class. Common algorithms to address this problem include SMOTE and Borderline-SMOTE. Cost-sensitive learning assigns larger weights to the less likely to be misclassified rare classes, thus highlighting their importance. Common algorithms include the AdaCost algorithm.
[0110] Feature engineering involves using dimensionality reduction algorithms (such as PCA or t-SNE) to extract and select features from well logging data, screening for features that significantly impact lithology identification. Features are information extracted from data that is useful for predicting results; they can be text or data. Feature engineering is the process of using specialized background knowledge and skills to process data so that features can play a better role in machine learning algorithms. The process includes modules such as feature extraction, feature construction, and feature selection. The goal of feature engineering is to select better features and obtain better training data. Because good features are more flexible, they can be trained with simpler models and yield better results.
[0111] Feature extraction: Feature extraction involves extracting information from unstructured data such as text, images, and sound, transforming the raw data into a set of features with clear physical meaning (e.g., Gabor, geometric features, texture features) or statistical significance. Commonly used methods include dimensionality reduction (PCA, ICA, LDA, etc.), image-based methods such as SIFT, Gabor, and HOG, and text-based methods such as bag-of-words models and word embedding models. For lithology identification of well logging data, dimensionality reduction is a crucial feature engineering method, especially for computationally intensive models like SVM and ANN. Reducing the dimensionality of processed information while minimizing information loss can effectively improve model training time and increase learning efficiency. Common dimensionality reduction methods include Principal Component Analysis (PCA) and the t-distribution-based SNE algorithm (t-SNE).
[0112] Feature construction: Feature construction combines or inter-computes existing features to obtain new features. For example, if one feature is speed and another is distance, we can create a new feature by dividing the two: the time taken to travel a certain distance.
[0113] Feature selection: To address the curse of dimensionality caused by an excessive number of attributes or features, important features can be selected, allowing the model to be built using only a subset of features. This significantly alleviates the curse of dimensionality. In this sense, feature selection and dimensionality reduction techniques share similar motivations; in fact, they are two mainstream techniques for handling high-dimensional data. Feature selection chooses meaningful features from all available features that are helpful to the model, avoiding the need to import all features for training. The most important aspect of feature selection is ensuring that important features are not lost; otherwise, a poorly performing model will be impossible due to a lack of crucial information. Without any prior knowledge, i.e., domain knowledge, the only way to select a subset of features containing all important information from the initial feature set is to iterate through all possible feature combinations. Commonly used feature selection methods in the field of lithology identification for well logging data include: variance filtering, correlation filtering, F-test, mutual information method, embedded embedding method, and wrapper method.
[0114] Model selection and training: Select artificial intelligence models including but not limited to random forest, NRS+AdaBoost, PSO+BP neural network, etc., and train the models using training datasets; Model selection: Machine learning, as an important form of artificial intelligence, has been effectively applied to the problem of lithology identification. In 2005, Professor Li Hongqi's team at China University of Petroleum began focusing on the application of artificial intelligence and pattern recognition methods (KNN, ICA, decision trees, etc.) in water-flooded layer identification, conglomerate identification, and sedimentary rock microfacies mapping. In 2007, Saumen and Maiti et al. proposed a novel method for lithology identification using a super-adaptive backpropagation neural network, and experimental results showed that this method had high identification accuracy. In 2010, researchers at the Johns Hopkins University Applied Physics Laboratory conducted research on lithology identification using multi-agent framework multi-machine joint learning, and the results showed that multi-machine joint learning was significantly better than single machine learning. In 2012, Mathemy and J. Cracknell et al. used the R programming language to train and evaluate RF (random forest) and SVM (support vector machine) classification models, and evaluated and identified lithological contact zones from an uncertain perspective. In 2015, researchers at China University of Petroleum conducted research on lithology identification using kernel Fischer discriminant analysis (KFD) for well logging curves. In 2016, Stephen... Kuhn et al. used RF to identify lithology in the prospective environment of orogenic gold deposits in the eastern Australian gold mining area. A total of 55,995 samples were divided into 8 lithology categories, and the overall accuracy of the identification results was about 76%. In 2018, Vikrant A. Dev used AdaBoost and LogitBoost algorithms based on decision trees and RF to conduct lithology identification research. According to the experimental results, the LogitBoost algorithm based on RF has higher performance indicators.
[0115] Currently, the most widely used and effective artificial intelligence methods for lithology identification of well logging data include Random Forest, KNN, decision trees, support vector machines optimized with various algorithms, artificial neural networks and their improved algorithms, and various ensemble learning methods. Considering the data characteristics, model applicability, and technological maturity of the lithology identification problem in uranium well logging data, we initially selected Random Forest, decision trees, support vector machines based on genetic algorithms, and AdaBooost based on parameter optimization to construct a lithology identification model for uranium well logging data. The applicability of the model was then tested using specific data to select the final optimal model.
[0116] Model Testing and Optimization: The accuracy, generalization ability, and operational efficiency of the model in lithology identification tasks are evaluated using a test set to select the optimal model. Although many artificial intelligence methods are available, the performance of well logging data from the exploration area on different models needs to be tested with specific well logging data. Based on the data preprocessing and feature engineering methods described above, the raw well logging data is first subjected to missing value imputation, imbalance processing, and normalization. Then, based on the experience of geophysical experts, well logging features sensitive to different lithologies are selected, and interfering features are eliminated. For complex models such as support vector machines, dimensionality reduction is also performed using PCA to reduce the computational complexity of the model and increase training efficiency. Finally, the processed data is input into different models for testing.
[0117] During testing, it is necessary to determine the model's hyperparameters, which can be optimized through grid search, learning curves, and experimental methods. Then, validation set data is input into the model for testing, and the test results are compared. The comparison focuses on: the model's classification accuracy, computation time, and generalization performance (i.e., the model's classification accuracy on location data). The above evaluation is applied to the four pre-selected models, selecting those with high classification accuracy, low computation time cost, low computational complexity, and strong generalization performance. For models with high validation accuracy but poor generalization performance, the model parameters need to be adjusted and the model retrained, or overfitting needs to be reduced through technical means. If the generalization ability still fails to meet the expected requirements, it may indicate that the model is unsuitable for solving multi-label, multi-class lithology identification problems, and a different model is needed.
[0118] Lithology identification: Input the well logging data to be identified into the optimal model and output the automatic identification results of lithology and lithofacies.
[0119] Specific implementation algorithm and key functions
[0120] From a practical and effective perspective, this paper proposes steps and multiple calculation models for automatic stratification of well logging curves. To address disturbances in the raw measurement data caused by instrumentation, methods for outlier handling, median filtering, and normalization are proposed. These methods can be used to eliminate spikes in the well logging curves and standardize their scale and dimensions. Regarding the determination of well logging values after stratification, the model proposes several methods for automatic calculation, primarily: taking the peak value, taking the center mean, taking the weighted value, and taking the surrounding rock value.
[0121] In the well logging data analysis and processing steps:
[0122] Outlier handling employs the Grobbs test or Dixon test, and replaces outliers using the mean of neighboring data. Specifically, outlier handling involves identifying any data that significantly deviates from the mean. The decision to include or exclude outliers must be based on statistical methods, typically using the Grobbs test: The original data set {xi} = {x1, x2, x3, ..., xi, ..., xn} is arranged in ascending order to obtain a new data set {yi} = {y1, y2, y3, ..., yi, ..., yn}. Assuming {yi} follows a normal distribution, the statistic can be...
[0123]
[0124] This is used to verify whether the data contains outliers. In the formula: U is a statistic in the form of extreme values minus the mean; , is the average value, and
[0125]
[0126] When U > Un, a, y(i) is an outlier. Here, Un, a represents the critical value of different significance levels a at different n. Un, a can be found in relevant manuals.
[0127] For questionable data, the Dixon test, Wilks' statistic test, and Chauvent's test can be used. It is best to use multiple tests simultaneously for questionable points to compare and avoid misjudgments. When a questionable point is confirmed as an outlier, the cause of the distortion should be investigated, and retesting should be performed if conditions permit. Because outliers not only interfere with valid data but also affect subsequent data processing such as normalization, they negatively impact the accuracy of computer-processed geological interpretation results. Therefore, outliers should not be discarded arbitrarily but must be carefully handled. We use the nearest neighbor average method to handle these outliers.
[0128] Median filtering uses a sliding window approach to smooth logging curves and eliminate spike interference. Assuming a data sample sequence xi (i=1, 2, ..., N), and the filtering window is 2n+1, the steps of median filtering are as follows:
[0129] ① Take 2n+1 data points centered at the i-th data point and sort them (either in order or in reverse order);
[0130] ② Take the middle value after sorting, that is, the (n+1)th data, as the filter value of the i-th point;
[0131] ③ Iteratively calculate each point on the discrete curve from top to bottom.
[0132] The value of n in the filtering window depends on different purposes. When n = 0, the filter fails; when n is small (e.g., n = 1), the amplitude value of the curve can be maintained; when n is large, only the changing trend of the curve can be maintained.
[0133] When processing the first and last n values, that is, when i < n or i > N - n, let n be equal to i - 1 and N - i respectively, so as to ensure that the number of samples N before and after filtering is equal.
[0134] The non-linear median filtering has the following characteristics:
[0135] ① It can eliminate the spike interference of the curve;
[0136] ② It can pass the step function and keep the step position unchanged;
[0137] ③ It can pass the ramp function and keep both the position and slope unchanged.
[0138] Characteristic ③ is difficult to achieve by other filtering methods. As part of the preprocessing work, median filtering is essential.
[0139] The normalization process uses the maximum-minimum normalization method to unify the dimensions of different logging curves to the interval [0, 1]. Since the scales and dimensions of different logging curves are different, when using multiple curves for automatic layer division, it is necessary to normalize the logging curves to [0, 1] respectively to eliminate the influence caused by scales and dimensions. The normalization formula is:
[0140]
[0141] In the formula, xi is the logging value corresponding to a certain depth on the logging curve; x max and x min are the maximum and minimum values in the logging curve respectively; xi' is the normalized value of the logging curve at this depth.
[0142] The feature engineering steps also include:
[0143] Using the Neighborhood Rough Set (NRS) algorithm to perform attribute reduction on logging features and eliminate redundant or low-importance features;
[0144] Introducing the mutual information weighting method to calculate the neighborhood radius and enhance the feature discrimination ability.
[0145] In the model selection and training steps:
[0146] The NRS + AdaBoost model uses decision trees as weak classifiers and optimizes the parameters of the base classifier through grid search;
[0147] The PSO + BP neural network model uses the particle swarm algorithm to optimize the initial parameters of the network, including the number of hidden layers, learning rate, and momentum factor.
[0148] An AI-based method for automatic lithology identification of sandstone-type uranium deposit logging data also includes an automatic stratification process, specifically comprising:
[0149] The logging curves are automatically stratified using analysis of variance or comparison of adjacent boreholes.
[0150] The stratification results are merged at the layer interfaces, and layer logging values are calculated using methods such as peak value, center mean, weighted value, or surrounding rock value. Specific automatic stratification model calculations include:
[0151] (1) Adjacent borehole comparison layering method
[0152] The principle is as follows: lithological identification is performed by referring to the known stratification information of the boreholes around the borehole to be identified and the specific data of each layer. The stratification thickness of the borehole to be identified is calculated by averaging or weighting the thickness of similar boreholes.
[0153] (2) Analysis of variance
[0154] 1) Theoretical basis of analysis of variance
[0155] Variance is a characteristic number in mathematical statistics that reflects the degree of concentration or dispersion of a random variable around its mean. Assume a sample has n observations x1, x2, ..., xn; its mean is... ,formula:
[0156]
[0157] This is called the sample variance. The magnitude of the variance reflects the volatility of the data; the larger the S², the greater the data volatility; the smaller the S², the smaller the data volatility.
[0158] Assuming we extract segment AB of the electrical measurement curve, ρ k The curve is a curve that varies with depth; ρ varies at different depths. k It has different values. ρ k The difference in values is the result of the combined effects of strata, mud, and various other accidental factors.
[0159] Let x ij Let j be the j-th data point of the i-th stratum. It is not the true resistivity of the stratum, but rather includes various error components, and can be expressed by the following formula:
[0160] x ij =μ+α i +e ij
[0161] in:
[0162] μ—Overall mean
[0163] α i —Systematic error. Represents the overall influence of the i-th stratum (i.e., the influence of the electrical properties of the rocks in that stratum).
[0164] e ij —The combined random error of the j-th observation in the i-th layer.
[0165] α i This is caused by differences in the electrical properties of different geological strata, and is generally significant; ij It is caused by unavoidable random errors, and is generally more than α. i The systematic error is much smaller. The purpose of this is to separate and compare systematic and random errors. If the systematic error significantly exceeds the random error, it is considered to be caused by different strata, and the interface of the rock strata can be determined through calculation. This mathematical model is the theoretical basis for using analysis of variance to divide strata. The requirement for using this method is that the random variable must follow a normal distribution.
[0166] 2) Basic principles of layering
[0167] Taking the electrical measurement curve of segment AB as an example, the curve is first "discretized" to obtain three sets of data as follows (Table 1):
[0168] Table 1
[0169]
[0170] To simplify the problem, we assume that the differences between the random factors at each level are negligible, i.e., σ1=σ2=σ3. Therefore, the problem of determining whether A1, A2, and A3 belong to the same level is reduced to testing the expected value α. i The question is whether they are equal. That is, whether α1=α2=α3 holds true. If it holds true, then A1, A2, and A3 are indistinguishable and belong to the same stratum; if it does not hold true, then it is inferred that the strata are significantly different, indicating that A1, A2, and A3 are different strata.
[0171] Assume the following for the well section under study: k is the total number of layers; n1 is the number of observation data in the i-th layer. The overall average is... Let N be the average of the i-th layer; N is the total number of observations. Therefore, the following formula is derived:
[0172]
[0173]
[0174] The sum of squares of the differences between the observed data and the overall mean is obtained by calculating:
[0175]
[0176] If the first term is Q1 and the second term is Q2, then we have:
[0177] Q = Q1 + Q2
[0178] As can be seen from the above formula, the variance sum Q of each observation value and the total average can be divided into two parts: Q1 is the sum of squares of the differences between each observation value and the average of its corresponding layer, called the within-group sum of squares of differences. Q2 is the sum of squares of the differences between the averages of each layer's observation values and the total average.
[0179] Guided by the theory of mathematical statistics, the within-group variance and between-group variance can be calculated using the within-group sum of squares of differences and the between-group sum of squares of differences. If the within-group variance is denoted as W and the between-group variance is denoted as B, then we have:
[0180]
[0181]
[0182] From the above two formulas, the ratio of the two formulas can be obtained as:
[0183]
[0184] Since using the F statistic for stratification analysis is very cumbersome, the R statistic is introduced as the standard for stratification. The calculation formula for the R statistic is:
[0185] The R statistic is consistent with the F statistic and can be written as
[0186] The relationship between the change of R and stratification is as follows:
[0187] ① If there is no significant difference in the strata (i.e., the same layer), then the between-group variance and the within-group variance should be very close, or B = W. At this time, R is very close to 0 or = 0.
[0188] ② If there are significant differences in the strata (i.e., different layers), then there are two cases for the between-group variance and the within-group variance: ① B ≠ 0, W = 0, ② B >> W. At this time, R = 1 or very close to 1.
[0189] ③ In actual situations, there will be cases where B < W, that is, R < 0. This is because the random factor fluctuations are large, resulting in the within-group variance exceeding the between-group variance. At this time, it is inferred as the same layer. Therefore, when R < 0 appears, it is replaced with R = 0, so that the R value is restricted to vary between 0 and 1.
[0190] When using the R index for stratification, the method adopted is the "iterative search" method, that is, finding the maximum R problem in each stratification calculation.
[0191] It is discussed in the following several cases:
[0192] a. In each layer calculation, the interface of the layer is at the point where the maximum R value is selected. The maximum R must correspond to the maximum B and the minimum W, that is, above and below this point, the lithological difference is the most significant. For example, when making a two-layer division, calculate the R value for each possible interface (if there are n observation points for a two-layer division (k = 2), n - 1 R values can be calculated). Then select the maximum R value as the interface for layer division.
[0193] b. When calculating the three-layer division, first fix the lower segment of the two-layer division result and perform the three-layer calculation on the upper segment. Let the maximum value calculated be R'3. Then fix the upper segment and perform the three-layer division on the lower segment, and the maximum value R"3 can be obtained. If R'3 > R"3, it means that the difference between the three segments A', B', C' divided by R'3 is greater than that of the three segments A", B", C" divided by R"3. Therefore, it is reasonable to use the interface at R'3. On the contrary, if R'3 < R"3, then use the interface at R"3. Similarly, in each layer division above the three-layer division, the interface at the maximum R is the best layer division interface.
[0194] c. The post-layer division index R n and the pre-layer division index R n-1 comparison. If R3 > R2, this indicates that it is necessary to continue with the three-layer division after the two-layer division. If R3 < R2, this means that the difference between the three intervals divided by R3 is not as large as that of the two intervals divided by R2, or that the lithology of the A and B intervals is basically similar and there is no significant difference. Of course, a corresponding layer division index R can also be given as the basis for judging the final layer division.
[0195] There are two schemes for the computer to calculate and control R for layer division: one is to stop the operation until no maximum value of R appears, that is, stop the operation when the R of the post-layer division is smaller than that of the pre-layer division. The other is controlled by the value of R. When R is less than a certain specified value, for example, 0.7, the operation stops.
[0196] 3. Post-processing of automatic layer division
[0197] (1) Merging of layer interfaces
[0198] In the pre-processing, necessary median filtering is adopted, but median filtering cannot guarantee filtering out all the spikes generated by instrument measurement errors, which will result in some unnecessary small thin layers being divided in the layer calculation. At this time, it is necessary to eliminate them by merging the thin layer interfaces.
[0199] The merging of thin layers generally adopts the method of scanning and iteration. The curve is regarded as a depth sequence, and the depth difference between two adjacent points is:
[0200]
[0201] For the given minimum layer thickness H min , when Δy i < Hmin When this occurs, the layer is merged into the adjacent top layer (or adjacent bottom layer). After merging thin layers, it is generally necessary to perform trend merging, that is, to merge curve segments (adjacent sampling segments) with the same change properties (increasing, decreasing).
[0202] (2) Calculate the logging values of the layer
[0203] After determining the formation interface, the next step is to calculate the formation logging value. This involves determining a single logging value that reflects the physical characteristics of a formation from the logging values of multiple sampling points within that formation. Several methods are generally used:
[0204] ① Take the peak value. This is often used for layer-by-layer value taking induction logging. If the trend in a layer is increasing, take the maximum logging value x within that layer. max As the layer logging value; if the trend of this layer is decreasing, take the minimum logging value x within the layer. min As a layer logging value.
[0205] ② Take the average value at the center. After removing some logging values from the top and bottom boundaries of this layer, calculate the average logging value of the middle part as the logging value of this layer.
[0206] ③ Take weighted values. Find the n extreme values x within the layer. i (i=1,2,3,…,n), using the distance (thickness) Hi between extreme values as the weight, a weighted average is performed, i.e. Take x as the logging value for this layer.
[0207] ④ Take the surrounding rock value. Scan the smooth points within the layer from top to bottom, that is, among a series of consecutive points centered on that point, the difference between adjacent points should not exceed the characteristic value. Take the logging value of the smooth point as the logging value of this layer. Which method to use to calculate the logging value depends on the specific situation; generally, the latter two calculation methods are better.
[0208] The main workflow includes data import, well logging data preprocessing, automatic lithology stratification, automatic well logging value calculation, lithology identification, and data export. The main task of well logging data preprocessing is to eliminate measurement data disturbances caused by instrumentation using data filtering methods. Automatic lithology stratification is the core of automatic stratification; the system employs two stratification methods: similar borehole comparison stratification and variance analysis. Automatic well logging value calculation is achieved by merging layer interfaces to calculate layer well logging values, making the automatic stratification results clearer and more practical. Lithology identification utilizes algorithms such as random forests to identify the data obtained from the automatic lithology stratification. Data export involves exporting the identified data according to corresponding rules. Figure 10 As shown.
[0209] An AI-based sandstone-type uranium deposit logging data interpretation system allows users to open and import Excel or database files, with basic data selection effects as shown below. Figure 11 As shown, the selected file is read into the display area and displayed. The basic data display effect is as follows. Figure 12 , Figure 13 , Figure 14 As shown:
[0210] Depth detection mainly involves determining the reasonableness of the depth range of imported data, detecting whether the depth is legal, recommending data for illegal depth ranges, and determining reasonable data ranges.
[0211] Lithology identification primarily involves determining the lithology of depth-detected data using a chosen deep learning method. Based on the input depth range, the corresponding lithology is calculated, and the results are displayed in a dialog box, achieving the desired effect. Figure 15 As shown.
[0212] Specifically, an artificial intelligence-based well logging data interpretation system for sandstone-type uranium deposits includes:
[0213] Data import module: Used to import well logging data in Excel or database format;
[0214] Data preprocessing module: performs outlier handling, median filtering, and normalization.
[0215] Feature engineering module: Implements feature extraction, dimensionality reduction, and selection;
[0216] Model training and optimization module: Supports the training, testing, and comparison of various artificial intelligence models;
[0217] Lithology identification module: Automatically identifies lithology from well logging data based on an optimal model;
[0218] The results visualization and export module displays the identification results in the form of line graphs, lithology columnar charts, etc., and supports data export. The system also includes:
[0219] Depth detection module: Used to detect the validity of depth ranges in imported data and recommend reasonable ranges;
[0220] Model management module: Supports adding, training, saving, and loading multiple recognition models.
Claims
1. An artificial intelligence-based automatic lithology identification method for sandstone-type uranium mine logging data, characterized in that, The method comprises the following steps: Logging data preparation: collecting logging data of sandstone type uranium mines under different regional and geological environmental conditions, and performing data cleaning; Logging data analysis and processing: performing abnormal point processing, median filtering and normalization processing on the data, Feature engineering: performing feature extraction and selection on the logging features using dimension reduction algorithms, and screening features that have a significant impact on lithology identification; Model selection and training: selecting random forest, NRS+AdaBoost and PSO+BP neural network models, and training the models using the training data set; Model testing and optimization: evaluating the accuracy, generalization ability and running efficiency of the model in the lithology identification task through the test set, and selecting the optimal model; 2. The artificial intelligence-based sandstone-type uranium mine logging data lithology automatic identification method according to claim 1, characterized in that, Lithology identification: inputting the logging data to be identified into the optimal model, and outputting the automatic identification result of the lithology and facies. In the logging data analysis and processing step: The Grubbs test method or the Dixon test method is used for abnormal point processing, and the average value of the adjacent data is used for replacement; The median filtering adopts a sliding window method to smooth the logging curve to eliminate peak interference; 3. The artificial intelligence-based sandstone-type uranium mine logging data lithology automatic identification method according to claim 1, characterized in that, The maximum and minimum value normalization method is used for normalization processing to unify the dimensions of different logging curves to the [0, 1] interval. It also includes an automatic layering processing step, which specifically includes: The variance analysis method or the adjacent borehole comparison method is used to automatically layer the logging curve; 4. The artificial intelligence-based automatic lithology identification method for sandstone-type uranium mine logging data according to claim 1, characterized in that, Let x ij For the i-th stratum and the j-th data, the following equation is used: x ij = μ + α i + e ij The layer interface merging result is calculated by using the peak value, center mean value, weighted value or surrounding rock value method. Wherein: a i — system error; represents the overall effect of the i-th formation; e ij — the combined random error of the i-th layer j-th observation.
5. The artificial intelligence-based automatic lithology identification method for sandstone-type uranium mine logging data according to claim 3, characterized in that, Assume that the total number of layers is k, and the number of observation data of the i-th layer is n1, is the total average, is the average of the i-th layer, and N is the total number of observations, Thus, the following formula is obtained: 。 μ—total mean 6. Calculate the total sum of squares of the difference between the observed data and the total mean: If the first term is Q1 and the second term is Q2, then: Q=Q1+Q2 7. The artificial intelligence-based automatic lithology identification method for sandstone-type uranium mine logging data according to claim 5, characterized in that, From the above formula, the variance of each observation value and the total mean Q can be divided into two parts: Q1 is the sum of squares of the difference between each observation value and the average number of its corresponding layer, which is called the intra-group difference sum of squares; Q2 is the sum of squares of the difference between the average number of each layer observation value and the total average. If the intra-group variance is W and the inter-group variance is B, then: 。 8. The artificial intelligence-based automatic lithology identification method for sandstone-type uranium mine logging data according to claim 6, characterized in that, From the above two formulas, the ratio of the two formulas is: The R-statistic is identical to the F-statistic, written as wherein the variation of R has the following relationship with delamination: The calculation formula of R statistic is: ① If there is no significant difference in the stratum, the inter-group variance and the intra-group variance should be very close, or B=W; at this time, R is very close to 0 or =0; ② If the stratum has significant differences, the inter-group variance and the intra-group variance have two cases: Case one: B≠0, W=0, ② B>>W; at this time, R=1 or very close to 1; Case two: In actual situations, B<W, that is, R<0, which is due to the large fluctuation of random factors, which leads to the group variance exceeding the inter-group variance; at this time, it is inferred as the same layer.