ZHANG zengqi (1991-), male, Ph.D. Professor. E-mail: zhangzq@ustb.edu.cn
Ultra-high-performance concrete (UHPC) is widely applied in bridges, prefabricated structures, and advanced construction owing to its high strength, dense microstructure, and excellent durability performance. Its performance is strongly governed by the type and dosage of supplementary cementitious materials (SCMs), including silica fume (SF), ground granulated blast-furnace slag (GGBS), superfine GGBS (sGGBS), fly ash (FA), and fly ash microspheres (sFA), as well as polycarboxylate superplasticizer (PCE) dosage and curing age (CA). However, the relationships among mixture parameters, water distribution, hydration, and strength development are highly nonlinear, and conventional empirical models often fail to provide accurate predictions.
Water film thickness (WFT) is a key microscopic parameter reflecting the free water covering the surfaces of solid particles, directly influencing particle lubrication, dispersion, and fresh-state behaviour in high-solid-volume UHPC systems. Compressive strength (CS) is another essential index for mechanical evaluation. Accurate prediction of both WFT and CS is crucial for mixture design and performance optimization. Nevertheless, UHPC experiments are costly and time-consuming, leading to limited datasets. To overcome this small-sample challenge, this study proposes an integrated framework combining conditional tabular generative adversarial network (CTGAN) for data augmentation, Bayesian optimization (BO)-based eXtreme Gradient Boosting (XGBoost) for predictive modelling, and interpretable machine-learning methods (SHAP and PDPs) for mechanism analysis.
A total of 160 experimental data points were obtained from binary, ternary, and quaternary cementitious systems. The input variables included cement content, PCE dosage, SF, GGBS, sGGBS, FA, sFA, and CA, while the output variables were WFT and CS. P·I 42.5 cement was used as the reference cement, and quartz sand with particle sizes of 0.84-2.00 mm was used as the aggregate. In the binary systems, one mineral admixture was used to replace cement by volume at replacement levels of 0%, 5%, 10%, 15%, and 20%. In the ternary systems, the SF content was fixed at 10%. In the quaternary systems, the GGBS content was fixed at 20% based on the ternary system. WFT was calculated using the wet packing method, and CS was measured after curing for 3, 7, 28 d, and 90 d.
CTGAN was used for data augmentation to expand the original small dataset. The model learned the joint distribution of the real experimental data through adversarial training between the generator and discriminator. After optimization, 1000 synthetic samples were generated for WFT prediction, and 900 synthetic samples were generated for CS prediction. The quality of the synthetic data was evaluated by comparing histograms, cumulative distribution curves, and correlation matrices between real and synthetic datasets.
The synthetic datasets were used to train XGBoost regression models. BO was applied to optimize hyperparameters, including tree depth, learning rate, number of estimators, subsample ratio, column-sampling ratio, minimum child weight, and regularization. Model performance was evaluated by R2, MAPE, RMSE, and MAE. SHAP and PDPs were employed to interpret feature contributions and nonlinear effects.
The comparison between real and synthetic datasets showed that CTGAN effectively preserved the main distributional characteristics of the original data. The generated samples had value ranges and distribution patterns similar to those of the real samples. The cumulative distribution curves also showed good consistency between real and synthetic datasets. In addition, the correlation matrices indicated that CTGAN captured not only the marginal distribution of individual variables but also the correlation structure among key variables. Therefore, the generated data could provide a reliable data basis for BO-XGBoost model training under small-sample conditions.
The BO-XGBoost model exhibited excellent prediction performance. For WFT, test R2 reached 0.986, with training and test RMSE values of 0.909 3 nm and 0.387 6 nm, respectively. For CS, test R2 was 0.976, with RMSE values of 5.244 8 MPa and 3.837 9 MPa. Predicted values clustered around the 45° ideal line, with most samples within ±10% error. Residuals were concentrated and symmetric, indicating no systematic bias, and loss curves showed stable convergence without overfitting. These results demonstrate that CTGAN augmentation effectively improved the ability of XGBoost to capture complex nonlinear relationships under small-sample conditions.
The SHAP and PDP analyses further revealed the influence mechanisms of different variables. For WFT, sFA showed a strong positive contribution, mainly because its fine and spherical particles improved particle dispersion and increased effective water-film formation. SF had a positive effect at low-to-medium dosages, but excessive SF could reduce WFT because of its high specific surface area. GGBS and sGGBS tended to show negative effects at high dosages, which may be related to denser particle packing and compression of effective water-film space. PCE showed a nonmonotonic effect: moderate PCE improved WFT, while excessive PCE could weaken the stability of the water-film structure.
For CS, CA was the most important factor and showed a strong positive contribution, reflecting continuous hydration and microstructure densification with curing time. sGGBS, SF, and sFA generally promoted strength development. sGGBS contributed to strength through microfilling and potential pozzolanic activity, while SF improved strength through pore refinement and matrix densification. In contrast, GGBS and FA showed negative effects at high dosages because excessive cement replacement reduced clinker content and limited the availability of calcium hydroxide (Ca(OH)2) for secondary reactions. These results demonstrate that different mineral admixtures have dosage-dependent and material-specific effects on UHPC performance.
This study establishes a multi-response prediction and interpretation framework integrating CTGAN, BO-XGBoost, SHAP, and PDPs for UHPC under small-sample conditions. CTGAN effectively generated high-quality synthetic data while preserving original distribution and correlation characteristics. The optimized BO-XGBoost model achieved outstanding predictive accuracy and generalization, with test R2 of 0.986 for WFT and 0.976 for CS. The interpretability analysis demonstrated that the effects of mineral admixtures on WFT and CS are highly dependent on material type and dosage: sFA and SF are beneficial for WFT within suitable ranges, whereas sGGBS, SF, and sFA promote CS; excessive GGBS and FA impair CS due to limited reaction activity. The proposed framework offers an effective data-driven approach for UHPC mixture design, performance prediction, and mechanism interpretation when only limited experimental data are available.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |