## 4 Quantitative Analysis of the Effect of Various Factors
### SVR-DSWA Parameterization Setting  
The SVR-DSWA [37] algorithm is a method used for predicting time series data. It integrates SVR and DSWA techniques. The SVR is utilized to establish a regression model for time series data. The DSWA is applied for data processing. Specifically, the algorithm divides time series data into multiple windows, and each contains a certain number of consecutive time points. Then, within each window, SVR is used to construct a regression model for predicting the value of the next time point. Finally, the predicted results from each window are aggregated to obtain the overall prediction results for the entire time series. The SVR-DSWA algorithm is advantageous in its ability to process nonlinear time series data. It also can adaptively adjust the window size to accommodate the changing patterns within the time series data. This enables the algorithm to function well in many time series prediction tasks. To analyze the effect weight of various factors on the stability of the skid-and-mud-return line, this paper conducts a weight analysis based on the SVR-DSWA algorithm. The principle of the derivative significance weight analysis (DSWA) algorithm is shown as follows. The derivative significance analysis method based on SVR can be used to analyze the effect weight of input values on the desired output. The decision-making function can only be constructed using training samples corresponding to non-zero coefficients (\(a_{i}-a_{i}^{*}\)). Therefore, the decision-making function can be represented as follows [37]:  
\[f(x_{i})=\sum\limits_{j=1}^{Ns}{(a_{j}-a  
Substituting Equations (7) and (8) into Equation (9) yields the weight of the feature input:  
\[C(k)=\frac{\sum\limits_{i=1}^{N}\left|-2\gamma\sum\limits_{j=1}^{Ns}{(\alpha_{j}- \alpha_{j}^{*})(x_{ik}-x_{jk})\exp\left[-\gamma\sum\limits_{l=1}^{N}{(x_{il}-x_ {jl})^{2}}\right]}\right|}{\sum\limits_{k=1}^{K}\sum\limits_{i=1}^{N}\left|-2 \gamma\sum\limits_{j=1}^{Ns}{(\alpha_{j}-\alpha_{j}^{*})(x_{ik}-x_{jk})\exp \left[-\gamma\sum\limits_{l=1}^{N}{(x_{il}-x_{jl})^{2}}\right]}\right|} \tag{10}\]  
Based on the SVR-DSWA algorithm, the steps for calculating the weight of each parameter on the maximum displacement are shown in Figure 11.  
Step 1: The training and testing sets are constructed. From the given n data samples, N data samples are selected as the training set. The remaining (n-N) test samples are used as the testing set. Figure 11: SVR-DSWA algorithm flowchart. Step 2: The data samples are normalized. The \"mapminmax\" function is used to normalize the data samples at a range of \([-1,1]\) to improve the convergence speed and accuracy of SVR. Step 3: The parameters are optimized. The Gaussian radial basis kernel function is used for training and prediction. The grid search method combined with ten-fold cross-validation is employed to find the optimal penalty factor c and the kernel parameter \(\gamma\). The training set is randomly divided into ten subsets, among which nine subsets are used as the training set and one subset as the validation set. The training sets and the validation set are alternately iterated for ten rounds. In each iteration, the \"svmtrain\" function is used to train the prediction model, and the RMSE\(e_{i}\) of the prediction model is recorded. The average value, \(E_{i}=\frac{1}{10}\sum\limits_{i=1}^{10}e_{i}\), is calculated. Next, the parameters are changed, the grid is traversed to train the model for m rounds, and the average RMSE of each round of training is obtained. the minimum value is obtained, and the optimal parameters of the model are determined. Next, the parameters are modified, and the grid is traversed to train the model for m rounds to obtain the average RMSE for each round of training. The minimum E\({}_{\text{m}}\) value is obtained, which determines the optimal parameters for the model. Step 4: The predicted results are then found.