## 2 Methods  
### LSSVM Model for Soft Ground Settlement Prediction  
LSSVM is a method based on statistical learning theory. It is of great significance and good effect to apply LSSVM to the settlement prediction of soft soil, but the choice of model parameters has a great influence on the prediction accuracy. Therefore, on the basis of the fast retention one method, this study intends to minimize the sum of squares of the prediction error of the full sample retention one as the goal and transform the parameter optimization problem of the LSSVM model into the problem of solving nonlinear equations. Meanwhile, the homotopy continuation method is used to solve the nonlinear equations, and the solution results are used as the optimal parameters of the LSSVM model. LSSVM uses the principle of function regression estimation to establish the model based on the monitoring value of soft soil settlement as the training set, and achieves the learning and prediction purpose by accurately monitoring and predicting the settlement of soft soil. Therefore, the training set of soft soil settlement samples must be established before LSSVM is used for learning and prediction. Suppose the training set, \((x_{1},y_{1})\),..., \((x_{i},y_{i})\),..., \((x_{n},y_{n})\), where \(x_{i}\in R^{m}\), \(y_{i}\in R^{n}\), \(i=1\), \(2\),..., \(n\); \(x_{i}\) is the input vector, and in this study, is the cumulative settlement time of soft soil; \(y_{i}\) is the output vector, and in this study, is the cumulative settlement amount of soft soil. The problem of functional regression estimation is to find a function \(f\) after learning the training set, so that \(y_{d}=f(x_{d})\) corresponding to any test sample \(x_{d}\) (cumulative settlement time of soft soil) outside the training set can be found, and the deviation between \(y_{d}\) and its truth value \(y\) (cumulative settlement of soft soil) can be minimized. In its principle, LSSVM uses functions of the following form to perform regression estimation of unknown functions [18]:  
\[y(x)=w^{T}\Phi(x)+b, \tag{1}\]  
where \(\Phi\): \(R^{m}\)\(\rightarrow\)\(H\), \(\Phi\) is the feature mapping, \(H\) is the feature space, \(w\) is the weight vector in space \(H\), and \(b\in R^{n}\) is the offset parameter. LSSVM transforms the above regression estimation problem into risk minimization problem of loss function by introducing loss function. In this study, it is the problem of minimizing the error between the predicted value and the actual value of soft soil settle  
Figure 1: Research ideas and steps. ment, and adopts the structured risk minimization principle to conduct risk minimization analysis, and obtains the following optimization problems and constraints [16; 17],  
\[\min J(w,e)=\frac{1}{2}w^{T}w+\frac{1}{2}C\sum_{i=1}^{n}{e_{k}}^{2}, \tag{2}\]  
\[y_{k}=w^{T}\Phi(x_{k})+b+e_{k}\qquad k=1,2,\cdots,n, \tag{3}\]  
where \(C\) is adjustable regularization parameter and \(e_{k}\) is error variable. As it is difficult to solve Equation (2) directly, LSSVM adopts duality theory to solve and establish Lagrange equation and its optimization conditions [17],  
\[L(w,b,e,\alpha)=\frac{1}{2}w^{T}w+\frac{1}{2}C\sum_{i=1}^{n}{e_{k}}^{2}-\sum_{i =1}^{n}{\alpha_{i}[w^{T}\Phi(x_{i})+b+e_{i}-y_{i}]}, \tag{4}\]  
\[\left\{ \begin{array}{l}\frac{\partial L}{\partial w}=0\\ \frac{\partial L}{\partial a}=0\\ \frac{\partial L}{\partial b}=0\\ \frac{\partial L}{\partial e}=0\end{array} \right., \tag{5}\]  
where \(\alpha\) is the Lagrange multiplier. If the absolute value of the Lagrange multiplier is very small, it makes very little contribution to the regression of the model, and its corresponding samples are called non-support vectors. In other cases, the samples corresponding to the Lagrange multiplier are called support vectors.