Probabilistic prediction of unconfined compressive strength for deep cement mixing piles using multi-head attention and convolutional neural networks

Various factors influence the unconfined compressive strength (UCS) of deep cement-mixed (DCM) piles, and standard core tests to measure UCS are both time-consuming and costly. Constructing predictive models can markedly improve testing efficiency and underpin real-time quality control. However, traditional machine-learning approaches often deliver suboptimal accuracy, while single deep-learning architectures lack uncertainty quantification and automated hyperparameter tuning. To date, existing UCS prediction studies have either focused on single-source inputs or deterministic outputs, and none has offered a unified probabilistic framework coupling multi-source data fusion with automatic hyperparameter optimization. In this study, we develop a unified hybrid framework that integrates six key multi-source features with a multi-head self-attention module to capture global dependencies across construction, survey, and detection data; three-layers convolutional neural network (CNN) for hierarchical local feature extraction; adaptive-bandwidth kernel density estimation to quantify predictive uncertainty via 95% confidence intervals; and the Differentiated Creative Search algorithm for global hyperparameter optimization (learning rate, hidden-node count, and regularization coefficient). We benchmark DCS-MSACK against mainstream machine-learning models each tuned via randomized search and five-fold cross-validation on three large-scale engineering datasets. Experimental results demonstrate that DCS-MSACK achieves an R 2 of 0.858 (improving by 28.3% and 31.0% respectively over optimized SVM and BP models), a MAPE of 14.25% (reducing error by 35.6% and 38.2%), confirming its efficacy for accurate, well-calibrated UCS forecasting in complex DCM construction scenarios.