## 4 Conclusions  
Unlike the extensive traditional study of transformation models based on empirical evidence, data-driven ensemble learning methods combined with traditional empirical models have received limited research attention in geotechnical engineering. Moreover, the comprehensive use of Bayesian theory for probabilistic characterization of soil parameter uncertainties and algorithmic optimization problems has not been fully leveraged in a systematic and coherent manner. To address the above challenges, the following study has been conducted. Under the Bayesian framework, the CatBoost algorithm (CatBoost-Bayesian) based on Bayesian optimization algorithm was developed to obtain the feature importance level of soil parameters affecting the undrained shear strength of clay, so as to adaptively couple the theoretical equation of undrained shear strength of \(K_{0}\) consolidated clay, which was derived from the modified Cambridge model, and then the theoretical equation of undrained shear strength of isotropically consolidated clay was established from the critical state of clay parameters, and the calculation results were verified later. 1. From the feature importance ranking of the CatBoost-Bayesian hybrid model, parameters with high importance and ease of measurement were selected; the overconsolidation ratio (\(OCR\)) and the effective overburden pressure (\(\sigma_{\text{tr}}^{\prime}\)) could reasonably explain the model and indirectly estimate the undrained shear strength of the clay. 2. The equation parameter \(\gamma\) of the clay in the overconsolidated state was affected by \((1-C_{s}/C_{c}),\gamma=m=0.88\cdot(1-C_{s}/C_{c})\pm 0.06\cdot SD\), and the equation parameter \(\alpha\) was affected by the plasticity index, \(\alpha=2+0.5\cdot I_{p}\). For the measured parameters of clay that were difficult to obtain, it was recommended that when the clay depth is \(1.9m<D<17m\), the calculation parameters of undrained shear strength should be computed according to the following recommended values \((\alpha)_{\text{OCI}}=2.246\), \((\beta)_{\text{OCI}}=0.490\) and \((\gamma)_{\text{OCI}}=0.770\). The theoretical equation was \((S_{u})_{\text{OCI}}=2.246\cdot\left(\sigma_{\text{tr}}^{\prime}\right)^{0.49 0}\cdot\left(OCR\right)^{0.770}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**R\({}^{2}\)\_Mean**} & \multicolumn{2}{c}{**Evar\_Mean**} & \multicolumn{2}{c}{**RMSE\_Mean**} & \multicolumn{2}{c}{**MAE\_Mean**} \\ \hline  & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline UCL\_Su & - & 0.88 & - & 0.88 & - & 0.19 & - & 0.04 \\ NCI\_Su & - & 0.90 & - & 0.90 & - & 0.16 & - & 0.03 \\ OCI\_Su & - & 0.97 & - & 0.97 & - & 0.22 & - & 0.02 \\ CatBoost–Bayesian & 0.91 & 0.86 & 0.91 & 0.86 & 0.30 & 0.37 & 0.12 & 0.20 \\ LightGBM-Bayesian & 0.99 & 0.81 & 0.99 & 0.81 & 0.14 & 0.48 & 0.08 & 0.23 \\ XGBoost-Bayesian & 0.94 & 0.81 & 0.94 & 0.82 & 0.24 & 0.41 & 0.16 & 0.24 \\ RandomForest-Bayesian & 0.95 & 0.80 & 0.95 & 0.80 & 0.99 & 0.98 & 0.46 & 0.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation performance comparison of four hybrid models. When the undrained shear strength of clay in the normally consolidated state was estimated at a depth of \(1.9m<D<22m\), the recommended theoretical equation was \(\left(S_{u}\right)_{\text{NCI}}=1.376\cdot\left(\sigma_{vz}^{\prime}\right)^{0.7 03}\cdot\left(OCR\right)^{-0.342}\); when the undrained shear strength of clay in the underconsolidated state was estimated at a depth of \(1.9m<D<22m\), the recommended theoretical equation was \(\left(S_{u}\right)_{\text{UCI}}=1.793\cdot\left(\sigma_{vz}^{\prime}\right)^{ 0.581}\cdot\left(OCR\right)^{-0.423}\). 4. Compared with the calculation results of [PERSON] and [PERSON] et al., it was found that the theoretical equation in this study can well estimate the undrained shear strength of isotropically consolidated clay.