ARO model is a novel intelligent multi-objective optimization strategy inspired by the group behaviors observed in the survival and evolution of rabbit populations (Wang et al., 2022). During their survival, rabbits primarily engage in two strategies: detouring foraging (exploration) and random digging (hiding). The transition between these strategies is mainly influenced by the rabbit’s energy factor (Formula 1). When the energy factor is high, rabbits have more stamina and are more likely to adopt exploration strategies. Conversely, when the energy factor is low, they are more inclined to adopt hiding strategies to avoid predators. A t = 4 1 − t T ln 1 r (1)

In this context, A(t) represents the energy factor, which is a function that oscillates and gradually decreases over time t. T represents the total number of iterations of the algorithm, and r is a random number between 0 and 1.

The ARO algorithm simulates the survival and evolution process of a rabbit population to seek the optimal solution in a multi-dimensional space. Assume there is a rabbit population of N rabbits in a D-dimensional space, where the position of the ith rabbit can be represented as: R i = R i 1 , R i 2 , R i 3 , · · · , R i D . During the iteration process of the population, the positions of the rabbits will continuously change. The mathematical model of the exploration strategy can be represented by Formula 2, and the mathematical model of the hiding strategy can be represented by Formula 3. v i t + 1 = x j t + e − e t − 1 T 2 ⋅ sin 2 π r 2 ⋅ c ⋅ x i t − x j t + r o u n d 0.5 ⋅ 0.5 + r 1 ⋅ n 1 (2) v i t + 1 = x i t + e − e t − 1 T 2 ⋅ sin 2 π r 2 ⋅ c ⋅ r 3 ⋅ x i t + T − t + 1 T ⋅ r 4 ⋅ g r ⋅ x i t − x i t (3) where v i t + 1 represents the position of the ith rabbit at time t+1, and x j t represents the position of the jth rabbit at time t; c and g _r represent sequences in the D-dimensional space where the mth position is 1 and all other positions are 0. n ₁ follows a standard normal distribution, and r ₁,r ₂,r ₃,r ₄ are random numbers between 0 and 1.

LightGBM is a high-performance ensemble learning algorithm based on gradient boosting trees (Ke et al., 2017). Its core idea is to iteratively train multiple weak classifiers, where each iteration generates a new decision tree to correct the prediction errors of all previous trees, thereby gradually improving the overall predictive performance of the model. The objective function of LightGBM is as follows (Formula 4): O b j t = ∑ i = 1 n L y i , f t − 1 x j + ∑ k = 1 T Ω f k (4) where O b j t represents the loss function at the tth iteration, ∑ i = 1 n L y i , f t − 1 x j represents the prediction error up to the (t-1)-th iteration, and ∑ k = 1 T Ω f k represents the regularization term.

To improve training speed, LightGBM also employs the histogram-based optimization algorithm and the leaf-wise growth strategy. The histogram-based optimization algorithm reduces computational complexity by grouping continuous feature values into discrete bins, thereby decreasing the amount of computation required during the splitting of decision trees and more effectively determining the optimal split points. The leaf-wise growth strategy selects the leaf node with the maximum gain for splitting at each iteration. Compared to the traditional level-wise growth strategy, leaf-wise can quickly find good split nodes, effectively reducing the depth of the tree and speeding up model training. Additionally, the leaf-wise strategy can handle feature imbalance more flexibly, giving the model better generalization ability.

During exploration, there is a significant imbalance in the number of lithological types in rock thin sections. Such severe sample imbalance can cause machine learning models to overly focus on the majority class samples and ignore the characteristics of the minority class samples during the learning process (Deng et al., 2023). To address this issue, sampling algorithms are needed to balance the number of samples of different lithologies, thereby enhancing the machine learning model’s ability to analyze minority class samples. ST is a combined sampling algorithm that integrates Smote oversampling with Tomek link undersampling techniques (Pereira et al., 2020; Devi and Purkayastha, 2017). It has shown good effectiveness in addressing the problem of sample imbalance in datasets. Compared to single sampling methods, Smote-Tomek compensates for the limitations of the Smote oversampling method, which tends to focus only on the minority class samples, leading to further overlap of different types of samples and low-quality data synthesis. The specific implementation steps are as follows:

(1) For the minority class samples, calculate the distance between the minority class samples and other class samples.

The training effectiveness of a machine learning model primarily depends on the quality of the dataset and the configuration of model parameters (Probst et al., 2019). This paper first uses the ST model to perform combined sampling on the lithological dataset in the study area, generating a new dataset. Then, the ARO multi-objective optimization strategy is used to adjust the hyperparameters of the LightGBM model, enhancing its lithological identification capability. The steps to establish the ST-ARO-LightGBM model are as follows, with the flowchart shown in Figure 1.

1. Use the ST method on the collected imbalanced lithological dataset to generate a new dataset, making the number of different lithological samples relatively balanced.

In classification tasks, the confusion matrix is commonly used to reflect the relationship between true classes and predicted classes (Sun Y. et al., 2020). For example, in binary classification tasks as shown in Table 1, the number of samples where the true class is predicted as the true class is defined as True Positive (TP). Similarly, False Negative (FN), False Positive (FP), and True Negative (TN) are defined accordingly. Based on this, four model evaluation metrics can be defined, as shown in Formula 5: Accuracy, Recall, Precision, and F1-score. Accuracy reflects the overall performance of the model, while F1-score is the harmonic mean of Recall and Precision. Higher values of these evaluation metrics indicate better classification performance of the model. Accuracy = TP + TN TP + FN + FP + TN Precision = TP TP + FP Recall = TP TP + FN F 1 − score = 2 × Precision × Recall Precision + Recall (5)

The data of rock slices used in this paper are from Jimusaer Depression, as shown in Figure 2. The Jimusaer Depression is located in the eastern part of the Junggar Basin and overall presents a west-low east-high, west-faulted east-overlapping graben feature Lucaogou Formation in Jimusaer Depression is rich in tight oil and shale oil resources, and its shale formations are developed in two oil-bearing systems, the upper and the lower, which are characterized by the integration of source and reservoir, thin layer superposition, large thickness, whole oil-bearing and continuous distribution. Influenced by multi-source mixing and frequent changes in water bodies, the lithology of the Permian Lucaogou Formation in the study area exhibits complex and diverse characteristics (Zha, 2022; Xiong et al., 2023). As shown in Figure 3. Based on thin section and core sample data, the lithology of the Permian Lucaogou Formation is divided into four categories according to grain size and mineral composition: mudstone, cloud-bearing sandstone, siltstone, and detrital-bearing dolomite. These categories are the subjects of this study, with sample proportions of 39.49%, 38.03%, 16.00%, and 6.49%, respectively.

The ratio of the majority class, mudstone, to the minority class, detrital-bearing dolomite, is close to 7:1, indicating a serious imbalance in the dataset. This imbalance can cause the model to overlook the feature extraction of the detrital-bearing dolomite class during training, thereby affecting the model’s performance. This issue will be addressed in Section 4.1.

The logging response characteristics of different rock types exhibit certain differences. Conventional logging curves are a comprehensive response to the mineral composition of rocks, the nature of pore fluids, and physical properties, while nuclear magnetic resonance (NMR) logging data can reflect physical factors such as the specific surface area and shape of rock pores (Singh and Maheswar, 2022; Mitchell, 2020). Therefore, combining conventional logging curves with NMR logging data after thin section correlation, eight curves were selected to establish the lithological dataset: Acoustic travel time (AC), Compensated Neutron Log (CNL), Density log (DEN), Natural Gamma Ray (GR), Deep Resistivity (RT), Shallow Resistivity (RXO), T2 geometric mean (T_2LM), and Total Porosity from NMR (POR).

The study of the distribution of logging response parameters for different lithologies is fundamental for lithological identification. Therefore, it is necessary to statistically analyze the logging parameters of different lithologies within the study area, as shown in Table 2.

As shown in Figure 4, the box diagram can better describe the distribution range of logging parameters for each lithology. The lower boundary of the box represents the first quartile, i.e. 25% of the data is less than or equal to this value, the upper boundary represents the third quartile, and the black line in the middle of the box represents the median. The box plots of logging parameters for different lithologies indicate that mudstone exhibits characteristics of medium-high DEN, medium-high GR, medium-low RT, and medium-low POR. Cloud-bearing sandstone shows characteristics of medium AC, medium-low GR, medium-high RXO, and medium-high POR. Siltstone displays low AC, medium-high GR, medium-low RXO, and medium-high T_2LM. Detrital-bearing dolomite exhibits medium-low GR, medium-high RT, medium-low T_2LM, and medium-low POR. Different logging parameters reflect different physical information of the rocks (Sebtosheikh et al., 2015). However, there is no distinct separation between different lithologies based on single logging parameters alone. Therefore, it is necessary to integrate multiple logging parameters and use multidimensional, multi-scale machine learning methods for efficient data analysis to classify lithologies.

In this study, a total of 895 core thin section samples were collected, including 353 mudstone samples, 341 cloud-bearing sandstone samples, 143 siltstone samples, and 58 detrital-bearing dolomite samples. The imbalance in sample numbers can cause the classifier to fail to adequately extract features from minority class samples, thus affecting its ability to classify minority class samples and reducing the model’s generalizability and accuracy. To address this issue, the ST algorithm was employed for comprehensive sampling of the dataset. The sampling results are shown in Figure 5. The number of samples for siltstone and detrital-bearing dolomite increased, introducing new feature information to the dataset. The number of samples for mudstone and cloud-bearing sandstone slightly decreased, removing some redundant features of the majority classes. The overall dataset has now reached a balanced state after sampling.

To verify the impact of ST combined sampling on the performance of the LightGBM model, this study splits the datasets before and after ST combined sampling into training and testing sets in a 7:3 ratio and trains the model using five-fold cross validation. Table 3 shows the comparison of various evaluation metrics of the LightGBM model before and after ST combined sampling. Compared to before ST sampling, the model accuracy improved by 14.17%. The F1 scores for cloud-bearing sandstone, siltstone, and detrital-bearing dolomite increased by 1.31%, 6.92%, and 82.34%, respectively, while the F1 score for mudstone decreased by 7.22%. This decrease is because, before ST sampling, the model overly focused on mudstone samples, lacking sufficient learning of the characteristics of detrital-bearing dolomite. Consequently, the F1 score for mudstone slightly decreased, while the F1 score for detrital-bearing dolomite significantly increased.

The training effectiveness of the LightGBM model depends on the influence of multiple input hyperparameters. Therefore, the ARO algorithm was employed to find the optimal hyperparameter combination for the LightGBM model. The main hyperparameters and their default values are listed in Table 4. This study simultaneously optimized 7 hyperparameters of the model, where the first three parameters affect the ensemble process of the LightGBM model, and the remaining four parameters influence the process of generating weak classifiers. The ARO algorithm was set with a population size of 50, with each “artificial rabbit” containing 7 hyperparameters. The F1 score of the LightGBM model was used as the fitness value, and the maximum number of iterations was set to 50.

Figure 6 shows the change in F1 score during the iteration process with the blue line, while the yellow baseline represents the F1 score trained with default parameters. After 21 iterations, the F1 score stabilized at 81.06%, which is a 3.08% improvement compared to the baseline. After the iteration, the optimal hyperparameter combination of the model is found, and the global optimal solution is shown in the last column of Table 4. At this point, the optimal model contains 97 decision trees, the maximum depth of the trees is 17, the minimum weight to control the splitting of leaf nodes is 0.03, the minimum sample number is 10, and the maximum number of leaf nodes in each decision tree is 89. The proportion of training samples is 0.61, and the learning rate of the model is 0.3.

After dividing the dataset following ST sampling into training and testing sets in a 7:3 ratio, the ST-ARO-LightGBM lithology recognition model was established using AC, CNL, DEN, GR, RT, RXO, T_2LM, POR eight curves, and the optimal hyperparameter combination as inputs. Table 5 shows the classification performance of the proposed model on different lithologies. The classification accuracy on the test set is 81.25%, with F1 scores for the four lithologies being 70.21%, 79.35%, 87.62%, and 87.10% respectively, averaging 81.07%. Compared to the untuned ST-LightGBM model (Table 3), precision, recall, F1 score, and accuracy have improved by 2.99%, 3.15%, 3.09%, and 6.41%, respectively, demonstrating that the ARO algorithm effectively enhances various evaluation metrics of the LightGBM model.

To verify the lithological classification capabilities of different machine learning models for the Permian shale reservoirs in Jimusar. KNN, DT, XGBoost, GBDT, and RF are several classical machine learning models that have been applied in lithology identification by predecessors (Guo et al., 2003; Ren et al., 2023; Dev and Eden, 2019; Sun Z. et al., 2020; Ahmed and Ali, 2024), but different algorithms have different application effects in different research areas. Therefore, these five algorithms are selected in this paper for comparison.

Table 6 presents a comparison of the classification accuracy and F1 scores of different models before and after ST comprehensive sampling. Before ST sampling, the models achieved an accuracy of 50.56%–72.12% and F1 scores of 36.01%–62.1%. This was because the imbalanced dataset caused the models to overly rely on features from the majority class samples, resulting in low recognition ability for minority class samples and thus weakening the models’ ability to identify lithology.

After ST comprehensive sampling, the dataset introduced new feature information, leading to a more balanced distribution of samples across various categories. The models could effectively extract features from minority class samples, resulting in an improvement in accuracy by 5.29%–15.06% and F1 scores by 11.18%–29.13%. The LightGBM model performed particularly well with an accuracy of 78.13% and an F1 score of 77.98%. ST comprehensive sampling effectively addressed the issue of dataset imbalance and significantly enhanced the lithological recognition performance of various classifiers, thereby increasing the models’ robustness and applicability.

Due to the overall poor classification performance of the model before ST composite sampling, the ST-ARO-LightGBM model was compared with different models established after sampling. Figure 7 shows the confusion matrices calculated for different models on the test set, visually reflecting the models’ ability to identify various lithologies. The horizontal axis is the true lithology of the sample, the vertical axis is the predicted lithology, and the integer represents the number of samples classified, and the percentage is the corresponding proportion. The darker the color on the main diagonal of the confusion matrix, the better the classification effect on lithology. The ST-ARO-LightGBM model demonstrated the best lithology classification performance, with recognition rates of over 90% for siltstone and detrital-bearing dolomite, and a resolution of 76.84% for cloud-bearing sandstone. However, the resolution for mudstone was relatively low at only 66.67%. This low resolution is due to the interference of logging feature ambiguities, which obscure the differences between mudstone and other lithologies. Other models also exhibited similar characteristics, with the lowest performance seen in the ST-DT model, which had a classification accuracy of only 43.43% for mudstone. This indicates that the proposed ST-ARO-LightGBM model can effectively reduce the interference of weak differences in logging features between different lithologies. To address the issue of low recognition accuracy for mudstone, future research should include more samples to explore the differences between mudstone and other lithologies.

Table 7 presents the accuracy, precision, recall, and F1 score of the ST-ARO-LightGBM model and six other models. Through comparative analysis, the ST-ARO-LightGBM model proposed in this study outperforms the other six models in all metrics, consistently achieving over 80%. Combined with Table 7 and Figure 7, the ST-ARO-LightGBM model demonstrates high accuracy and stability in predicting four different lithologies. Compared to traditional machine learning algorithms, it exhibits better robustness and application prospects.

The results show that the prediction result of integrated machine learning model (such as LightGBM) is better than that of single machine learning model (such as DT and KNN). In addition, the LightGBM model can achieve higher accuracy after being optimized by ARO algorithm, and the performance of machine learning model can be deeply explored, but the iteration time is increased. In the actual modeling process, attention should be paid to the balance between accuracy and computing power, and iteration can be ended in advance within the acceptable accuracy range to achieve the highest accuracy as possible.

To verify the application of the ST-ARO-LightGBM model in the study area, predictions were made for well sections containing different lithologies, as shown in Figures 8, 9. In these figures, the first panel displays depth, the second to fourth panels show input parameters for the model, the fifth panel presents lithological information from rock thin sections not used in model building, the sixth panel shows the lithology predictions and errors of the ST-ARO-LightGBM model, and the seventh to twelfth panels compare the lithology predictions and errors of other models.

Figure 8 illustrates the prediction results for well section A17X from 3,272 to 3,300 m, where mudstone and cloud-bearing sandstone are predominantly developed, with lesser occurrences of siltstone and detrital-bearing dolomite. Through comparison with actual rock thin section lithologies, the ST-ARO-LightGBM model significantly outperforms the six comparison models, accurately reflecting the complex interactions between different lithologies in the actual formations. Errors in the proposed model mainly occur in thin mudstone layers, consistent with the results in Table 5 and Figure 7.

Figure 9 displays the prediction results for well section A32X from 3,724 to 3,736 m, where siltstone and mudstone are primarily developed. The predictions of the ST-ARO-LightGBM model closely match the actual rock thin section lithologies, whereas the comparison models generally capture the variation trends in lithology within the well section but with higher errors.