Saturation coral sand damping ratio prediction method based on explainable artificial intelligence
Through a deep learning model based on explainable artificial intelligence, using the CNN-BiLSTM combined neural network and SHAP analysis, the accuracy and complexity problems of coral sand damping ratio prediction were solved, and efficient and accurate prediction of coral sand damping ratio was achieved.
Patent Information
- Application Number
- CN202510028355.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-08
- Publication Date
- 2025-10-10
- Estimated Expiration
- 2045-01-08
AI Technical Summary
Existing technologies lack a mathematical formula for predicting the damping ratio that can quickly and effectively analyze large amounts of data and comprehensively reflect the nonlinearity and sedimentation depth variability of coral sand. In addition, the empirical relationship for quartz sand is not applicable to coral sand, making it difficult to ensure the safety of engineering construction.
A deep learning model based on explainable artificial intelligence was adopted, and a CNN-BiLSTM combined neural network was used to establish a saturated coral sand damping ratio prediction model. The interpretability of the model was analyzed through SHAP to optimize the prediction results.
Accurate prediction of the coral sand damping ratio was achieved, with R2 of the training set and test set reaching 0.975 and 0.959 respectively, which improved the accuracy and robustness of the prediction and solved the error and complexity problems of the traditional model.
Smart Images
Figure CN119943197B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of coral sand performance research and digital modeling, and particularly relates to a saturated coral sand damping ratio prediction method based on explainable artificial intelligence. BACKGROUND
[0002] Coral sand is a carbonate sediment that is formed by long-term biological accumulation and geological action. The main components of coral sand are the skeletal remains of marine organisms such as corals, high-magnesium calcite, and aragonite minerals, and it contains more than 90% calcium carbonate. The special formation conditions of coral sand make it have the characteristics of irregular particles, a large number of pores inside the particles, a rough surface, and easy breakage. The particle characteristics of coral sand make it prone to liquefaction when subjected to cyclic loads related to earthquakes, leading to tilting and collapse of engineering buildings. So far, in the evaluation of seismic influence and the seismic fortification of engineering structures, the engineering site conditions are usually considered as the most important factor affecting the seismic effect, and the dynamic characteristics of the site soil are the primary factor in the site conditions. Therefore, the study of the dynamic characteristics of coral sand has become the focus of researchers.
[0003] The dynamic characteristics of soil mainly reflect nonlinearity, hysteresis, and strain accumulation. In order to more accurately reflect the energy dissipation and viscous performance indicators of soil under dynamic load, damping ratio λ is considered as the most basic dynamic parameter to characterize the nonlinear, hysteresis, and other viscoelastic-plastic characteristics of soil in various dynamic strain ranges. In order to study the influencing factors of damping ratio, scholars have conducted a large number of experimental studies. Different types and regions of sand have different dynamic characteristics, and current experimental studies are mostly focused on quartz sand, while the study of coral sand is relatively less. The empirical relationship of quartz sand is not applicable to coral sand. Therefore, in order to ensure the safety of island reef buildings, it is necessary to distinguish and compare with quartz sand, and it is necessary to study the dynamic characteristics of coral sand.
[0004] Resonant column test and dynamic triaxial test are the main methods for measuring damping ratio. However, the measurement methods of the two tests are different, and the orders of magnitude of the measured damping ratios are different. The damping ratio of a single test cannot fully reflect the mechanical properties of soil, and the common method is to complement each other with the results of resonant column test and dynamic triaxial test. However, the combination of multiple tests will produce a large amount of data, and the test data will also differ due to different test methods, which makes the research work complex and tedious. At the same time, the dynamic characteristics of soil are not only affected by the single factor of shear strain, but also closely related to other factors such as the initial effective confining pressure of the soil sample.
[0005] At present, a large number of researches are object-specific, damping ratio prediction mathematical formula application working conditions are single and multi-parameter dependent, and an ideal mathematical formula that can comprehensively reflect the nonlinearity of the original site soil and the variability of the deposition depth has not been formed. Therefore, how to establish an optimized model capable of quickly and effectively analyzing a large amount of data and predicting model data is a technical problem to be solved at present. SUMMARY
[0006] In order to solve the problems in the prior art, the application provides a saturated coral sand damping ratio prediction method based on explainable artificial intelligence, proposes an explainable deep learning model, and realizes accurate prediction of the saturated coral sand damping ratio.
[0007] The embodiments of the application provide the following scheme:
[0008] The embodiments of the application provide a saturated coral sand damping ratio prediction method based on explainable artificial intelligence, and the method comprises the following steps:
[0009] Step one, preparing a saturated coral sand sample;
[0010] Step two, performing a test by using the saturated coral sand sample to generate a data set, wherein the influence factors of each sample in the data set include relative density, confining pressure, fine particle content and strain, and the influence target is the damping ratio;
[0011] Step three, establishing a saturated coral sand damping ratio prediction model by using a CNN-BiLSTM (Convolutional Neural Networks-Bidirectional Long Short Term Memory) combined neural network;
[0012] Step four, inputting the data set into the saturated coral sand damping ratio prediction model for training, optimizing the parameters of the saturated coral sand damping ratio prediction model, and obtaining an optimized saturated coral sand damping ratio prediction model;
[0013] Step five, performing explainable analysis on the optimized saturated coral sand damping ratio prediction model by using a SHAP (SHapley Additive exPlanation) method.
[0014] In an optional embodiment, the preparation of the saturated coral sand sample in step one comprises: packing the coral sand, performing saturation treatment on the packed sample by using a method combining CO2 replacement, air-free water injection and staged back pressure saturation, performing step-by-step isostatic consolidation treatment on the sample when the pore pressure coefficient B is greater than or equal to 0.97, and obtaining the saturated coral sand sample.
[0015] In an alternative embodiment, the step two utilizes the saturated coral sand sample to perform the test, including the following process: the saturated coral sand sample is subjected to the resonance column test by using the excitation device, and the damping ratio corresponding to different relative densities, different confining pressures, different fine particle contents and different strains is obtained.
[0016] In an alternative embodiment, the saturated coral sand damping ratio prediction model comprises, in sequence from input to output, an input layer, a CNN (Convolutional Neural Networks) layer, a BiLSTM (Bidirectional Long Short Term Memory) layer, a full connection layer and an output layer.
[0017] In an alternative embodiment, the CNN layer comprises one convolution layer and one pooling layer; and the BiLSTM layer comprises one bidirectional LSTM layer.
[0018] In an alternative embodiment, the processing flow of the saturated coral sand damping ratio prediction model is as follows:
[0019] S3.1, the influencing factors in the data set are taken as input variables, and the convolution and pooling processing are sequentially performed through the CNN layer to extract feature values;
[0020] S3.2, the extracted feature values are subjected to dimension adjustment, input into the BiLSTM layer, the dependency relationship between different input variables is captured, and deep features are extracted;
[0021] S3.3, the extracted deep features are mapped to the output space through the full connection layer to generate a prediction result.
[0022] In an alternative embodiment, in the data set, 80% of the samples are taken as training data set, and the remaining 20% of the samples are taken as test data set.
[0023] In an alternative embodiment, the explanatory analysis of step five comprises global explanatory analysis, feature interaction analysis and interaction analysis between input variables.
[0024] The application based on the technical scheme has the beneficial effects that:
[0025] (1) The application firstly utilizes the saturated coral sand to perform the test, records the change of the saturated coral sand damping ratio under different material parameters, obtains the preliminary conclusion between various influencing factors, then establishes the CNN-BiLSTM hybrid deep learning model, realizes the extraction of feature information and the prediction, finally uses the SHAP to analyze the relationship between the input parameters and the output values of each feature, and expands the application of artificial intelligence in the field of coral sand dynamic deformation characteristics.
[0026] (2) The CNN-BiLSTM model established by the application can accurately predict the damping ratio of saturated coral sand, and the R 2 respectively reach 0.975 and 0.959, which are higher in accuracy and lower in error than single CNN (Convolutional Neural Networks), LSTM (Long Short Term Memory), BiLSTM (Bidirectional Long Short Term Memory) and CNN-LSTM (Convolutional Neural Networks-Long Short Term Memory). The model combines the feature extraction capability of the CNN model and the accurate prediction capability and strong robustness of the prediction result of the BiLSTM model, and has superiority in the prediction of the damping ratio of saturated coral sand.
[0027] (3) The application uses SHAP analysis to solve the black box problem of the deep learning model and obtain the influence law of each feature on the output variable. BRIEF DESCRIPTION OF DRAWINGS
[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present specification or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present specification, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.
[0029] Figure 1 It is a flowchart of a saturated coral sand damping ratio prediction method based on explainable artificial intelligence.
[0030] Figure 2 It is a Pearson correlation matrix diagram of sample space distribution.
[0031] Figure 3 It is a saturated coral sand damping ratio prediction model structure diagram.
[0032] Figure 4 It is the prediction result of the training sample.
[0033] Figure 5 It is the prediction result of the test sample.
[0034] Figure 6 It is a regression distribution diagram of the predicted value and the true value.
[0035] Figure 7 For global SHAP value swarm and feature importance chart.
[0036] Figure 8 For SHAP interaction value chart and heat map.
[0037] Figure 9 For the schematic diagram of the mutual influence relationship of different feature parameters.
[0038] Figure 10 For the schematic diagram of different prediction models. DETAILED DESCRIPTION
[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art belong to the scope of protection of the embodiments of the present application.
[0040] The embodiment provides a saturation coral sand damping ratio prediction method based on explainable artificial intelligence, referring to Figure 1 , the method comprises:
[0041] Step one, prepare the saturated coral sand sample by the following process: sample the coral sand, use CO2 replacement, air-free water and fractional back pressure saturation method to saturate the sample, when the pore pressure coefficient B is greater than or equal to 0.97, the sample is treated by step-by-step isostatic consolidation to obtain the saturated coral sand sample.
[0042] Step two, use the saturated coral sand sample to perform the test, i.e. use the excitation device to perform the resonance column test on the saturated coral sand sample, and obtain the damping ratio corresponding to different relative densities, different confining pressures, different fine particle contents and different strains. Generate a data set, the influence factors of each sample in the data set include relative density, confining pressure, fine particle content and strain, and the influence target is damping ratio.
[0043] In the embodiment, 659 groups of data are collected, and the influence factors, i.e. input variables, are four kinds, which are relative density (kg / m 3 ), confining pressure (kPa), fine particle content (%) and strain, as shown in the following table:
[0044]
[0045] The Pearson correlation coefficient matrix of the sample space distribution for the CNN-BiLSTM model training is as follows: Figure 2The highest correlation coefficient of the input variables is only-0.13, indicating that the correlation between any two variables is very low, thereby verifying the high independence of each variable. This result means that the constructed saturated coral sand design parameter database has good feature independence, providing a reasonable and reliable data basis for developing and training artificial intelligence models.
[0046] Step three, using a CNN-BiLSTM combined neural network to establish a saturated coral sand damping ratio prediction model.
[0047] Referring to Figure 3 , the saturated coral sand damping ratio prediction model comprises, in sequence from input to output, an input layer, a CNN layer, a BiLSTM layer, a fully connected layer, and an output layer. The convolutional layer contains 64 filters, the size of the convolution kernel is 3, the size of the pooling layer is 2, and the bidirectional LSTM layer is set to 256 neurons. The number of training rounds of the trained model is set to 170 rounds. The structure of the CNN-BiLSTM prediction model is as shown in Figure 10 . In the figure, x t is the input value, h t and h t are the output vectors of the bidirectional LSTM, σ is the vector obtained by splicing the output vectors, y t is the value formed by mapping the spliced vector through the Softmax Layer.
[0048] The processing flow of the saturated coral sand damping ratio prediction model is as follows:
[0049] S3.1, taking the influencing factors in the data set as input variables, and performing convolution and pooling processing in sequence through the CNN layer to extract feature values;
[0050] S3.2, adjusting the dimensions of the extracted feature values, inputting them into the BiLSTM layer, capturing the dependency between different input variables, and extracting deep features;
[0051] S3.3, mapping the extracted deep features to the output space through the fully connected layer to generate a prediction result.
[0052] Step four, using the data set to input the saturated coral sand damping ratio prediction model for training. During the model training process, 80% of the samples are set as the training set, and the remaining 20% of the samples are set as the test set. The parameters of the saturated coral sand damping ratio prediction model are optimized to obtain an optimized saturated coral sand damping ratio prediction model. The prediction results of the training samples and the test samples are as shown in Figure 4 and Figure 5 . The result analysis is shown in the following table:
[0053]
[0054] The regression distribution diagram of predicted values and true values is shown in FIG. 3. Figure 6 As can be seen from the figure, most of the data points of the training set and the test set fall within the 95% confidence interval, further proving that the prediction result is accurate and reliable.
[0055] Step five, using SHAP method to explain the optimized saturated coral sand damping ratio prediction model, including global explanatory analysis, feature interaction analysis and interaction analysis between input variables.
[0056] (1) Global explanatory analysis
[0057] Figure 7 is the SHAP summary chart and feature importance bar chart of all features related to saturated coral sand damping ratio, which is used to visualize the global feature importance. Figure 7 Each point in the figure represents a data sample, and the redder the color, the higher the value of the feature parameter, and the bluer the lower. The positive and negative signs of the SHAP value on the horizontal axis represent the positive or negative influence of the feature on the output result, and the absolute value of the SHAP value reflects the strength of the influence, the larger the absolute value, the more significant the influence of the feature on the model output. The bar chart represents the importance of the feature parameter to the contribution of the saturated coral sand damping ratio, and the importance decreases from top to bottom.
[0058] As can be seen from FIG. 4, Figure 7 Strain is the most important parameter affecting damping ratio, and as strain increases, the corresponding positive SHAP value also increases, indicating that strain has a significant positive contribution to damping ratio. The SHAP value gradually changes to positive as the relative density value increases, indicating that the relative density also has a positive contribution to the damping ratio. The SHAP value of the fine particle content tends to be more negative as the parameter value increases, indicating that there is a negative correlation between the fine particle content and the damping ratio. The SHAP value changes from negative to positive as the confining pressure increases.
[0059] (2) Feature interaction analysis
[0060] Feature interaction analysis can consider the interaction between features. As shown in the left SHAP interaction value chart, Figure 8 The diagonal line is the main influence of the feature, which represents the independent contribution of the feature to the model prediction value; the non-diagonal line is the two-way interaction between the feature and other features, which represents the contribution excluding the independent contribution, and only reflects the gain or loss of synergy. In each small chart, each point represents a data sample, and the horizontal axis is the SHAP value. The color of the point represents the size of the feature value parameter, the redder the color, the higher the value, and the bluer the lower. In order to evaluate the influence of each feature on the model prediction of a single sample, and at the same time view the reaction of the model prediction to a single feature, further draw Figure 8The right heat map is used to visualize these relationships. The horizontal axis of the heat map is each instance, and the left y-axis is the feature importance ranking, with importance decreasing from top to bottom, corresponding to the right bar chart, where longer bars represent higher importance. The right y-axis is the visualization of SHAP values, with red representing positive values and blue representing negative values. The darker the color, the larger the absolute value of SHAP. The top curve is the model's prediction result under the corresponding feature parameter. The heat map can visually demonstrate the influence of features on model prediction, enhancing the explainability of the prediction model.
[0061] From Figure 8 It can be seen that the main influence of strain and relative density on damping ratio is positive. Under the action of strain and relative density alone, the damping ratio increases with the increase of strain and relative density. Under the interaction of strain and relative density, the SHAP value becomes positive, and the damping ratio of saturated coral sand increases. Through the data of step two, it is known that there is a negative correlation between fine particle content and damping ratio, and the SHAP value changes from negative to positive with the increase of confining pressure. Figure 8 The left subgraph shows no obvious change in the SHAP value of these two features, which requires further analysis. From Figure 8 The right heat map shows that high prediction (high value in the left f(x)) is related to high relative density and high strain (red). Low prediction (low value in the left f(x)) is related to low strain and low relative density (blue). The SHAP interaction value graph is consistent with the results shown in the SHAP heat map.
[0062] (3) Interaction analysis between input variables
[0063] In order to understand the influence of feature parameters on the damping ratio of saturated coral sand more thoroughly, the dependence graph of each feature parameter should be drawn, as shown in Figure 9 The SHAP dependence graph can more detailedly show the influence of the interaction between two features on the SHAP value, which can be used as a supplement to the SHAP interaction value graph. The x-axis of the dependence graph represents the feature parameter, the left y-axis represents the SHAP value corresponding to the feature on the x-axis, and the right y-axis is another feature parameter. The redder the color, the higher the value, and the bluer the color, the lower the value. From Figure 9 The mutual influence relationship between different features can be further analyzed. From Figure 9 (a) and Figure 9 (d), it can be seen that as the relative density and strain increase, the corresponding SHAP value also increases. However, when the relative density is 70 kg / m3, i.e. in the case of high relative density, the increase of strain will cause the SHAP value of relative density to increase. From 9(b), it can be seen that when the confining pressure is 300 KPa, the SHAP value of confining pressure increases with the increase of fine particle content, indicating that when the confining pressure is relatively high, the increase of fine particle content will increase the damping ratio of saturated coral sand. From Figure 9(c) It can be seen that when the fine particle content is high, the increase in strain will make the SHAP value smaller, and the damping ratio of saturated coral sand will decrease.
[0064] Based on the test data of step two, strain and relative density have the greatest impact on the damping ratio of saturated coral sand, which is significantly greater than the impact of confining pressure and relative density on confining pressure, and there is a negative correlation between fine particle content and damping ratio. Therefore, combined with the analysis of the dependence diagram, the following conclusions can be drawn: increasing the values of relative density and strain and reducing the fine particle content can effectively improve the damping ratio of saturated coral sand when the confining pressure is 100 KP.
[0065] To further verify the effectiveness of the CNN-BiLSTM prediction model used in the invention, the CNN, LSTM, BiLSTM, and CNN-LSTM models are used to predict the damping ratio, and the prediction results of these models are compared with the prediction results of the CNN-BiLSTM model. The following table summarizes the prediction performance of each model on the training set and the test set.
[0066]
[0067] In addition, to more deeply evaluate the prediction performance of the CNN-BiLSTM model, according to the three key performance indicators of the determination coefficient (R 2 ), root mean square error (RMSE), and mean absolute error (MAE) of the five prediction models on the training set, their distribution is shown in the Taylor diagram, as Figure 10 shown.
[0068] From the above comparison, it can be seen that when the CNN-BiLSTM prediction model is tested, the R2 value of the training set reaches 0.975, and the R 2 value of the test set reaches 0.959, which is higher than that of the other four models, and has the highest accuracy. The accuracy of CNN-LSTM is higher than that of CNN and LSTM, because the combination of the feature extraction ability of CNN and the special recurrent neural network LSTM complements each other's advantages and improves the model's prediction ability of features. The accuracy of CNN-BiLSTM is higher than that of CNN-LSTM, because BiLSTM is composed of bidirectional LSTM layers, which can utilize the context information and improve the robustness and generalization ability of the model compared with LSTM. In summary, the CNN-BiLSTM model used in the invention has better performance in data prediction tasks, and the accuracy is significantly improved compared with traditional neural network models.
[0069] Those skilled in the art will appreciate that embodiments of the present application can be devised for a variety of applications. It is intended that the present application be limited only by the scope of the appended claims, and it is intended that various modifications and alterations made by those skilled in the art be considered as within the scope of the present application. The embodiments of the present application will be described with reference to the attached drawings, wherein:
[0070] The present application is described in reference to the drawings using a flowchart illustration and / or a block diagram of the method, apparatus (modules) and / or computer program product according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.
[0071] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.
[0072] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.
[0073] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the embodiments by those skilled in the art once they learn of the basic inventive concepts. Therefore, the appended claims are intended to cover all such modifications and variations as fall within the scope of the present application.
[0074] Obviously, many modifications and variations of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the appended claims and their equivalents, the application can be practiced otherwise than as specifically described.
Claims
1. A method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence, characterized in that: The method comprises: Step 1: Prepare saturated coral sand sample; Step 2: Conduct experiments using saturated coral sand samples to generate a data set. The influencing factors of each sample in the data set include relative density, confining pressure, fine particle content, and strain, and the influencing target is the damping ratio. Step 3: Using the CNN-BiLSTM combined neural network to establish a saturated coral sand damping ratio prediction model; the saturated coral sand damping ratio prediction model includes an input layer, a CNN layer, a BiLSTM layer, a fully connected layer, and an output layer from input to output; the CNN layer includes one convolutional layer and one pooling layer; the BiLSTM layer includes one bidirectional LSTM layer; Step 4: Using the data set to input the saturated coral sand damping ratio prediction model for training, optimizing the parameters of the saturated coral sand damping ratio prediction model to obtain an optimized saturated coral sand damping ratio prediction model; Step 5: Use the SHAP method to perform explanatory analysis on the optimized saturated coral sand damping ratio prediction model.
2. The method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence according to claim 1, characterized in that: The preparation of the saturated coral sand sample described in step 1 includes loading the coral sand, saturating the loaded sample using a combination of CO2 replacement, introduction of airless water, and graded back-pressure saturation methods, and when the pore pressure coefficient B is greater than or equal to 0.97, subjecting the sample to stepwise isobaric consolidation to obtain a saturated coral sand sample.
3. The method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence according to claim 1, characterized in that: The test using the saturated coral sand sample described in step 2 includes the following process: using an excitation device to perform a resonant column test on the saturated coral sand sample to obtain damping ratios corresponding to different relative densities, different confining pressures, different fine particle contents, and different strains.
4. The method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence according to claim 1, wherein: The processing flow of the saturated coral sand damping ratio prediction model is as follows: S3.
1. Take the influencing factors in the dataset as input variables, perform convolution and pooling processing in sequence through the CNN layer, and extract the feature values; S3.
2. The extracted feature values are dimensionally adjusted and input into the BiLSTM layer to capture the dependencies between different input variables and extract deep features. S3.
3. Map the extracted deep features to the output space through the fully connected layer to generate the prediction results.
5. The method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence according to claim 1, characterized in that: In the data set, 80% of the samples are used as training data sets, and the remaining 20% of the samples are used as testing data sets.
6. The method for predicting the damping ratio of saturated coral sand based on explainable artificial intelligence according to claim 1, characterized in that: The explanatory analysis described in step five includes global explanatory analysis, feature interaction analysis, and interaction analysis between input variables.