Machine learning has been widely applied to various concrete materials tasks, such as macroscopic performance prediction and mix proportion optimization. The performance of machine learning models depends strongly on the quantity and quality of the available datasets. However, constructing large-scale and high-quality concrete mix proportion datasets remains challenging because concrete experiments are time-consuming, costly, and easily affected by material sources, curing conditions, and human operations. At present, small-sample modeling problems are mainly addressed through two strategies: model optimization and data augmentation. Model optimization methods mainly improve the extraction of information from existing small-sample datasets by adjusting model structures or training strategies. However, they do not fundamentally increase the amount of data, and their improvement in prediction accuracy is still limited by the original sample size. Conventional data augmentation methods mainly rely on generative adversarial networks, which learn the real data distribution through adversarial training between a generator and a discriminator, thereby generating virtual samples to expand the original dataset. Nevertheless, when dealing with complex tabular data, generative adversarial networks may encounter unstable training, insufficient sample diversity, and distribution shifts in generated data, resulting in limited consistency between virtual and real data. To address these issues, this study proposes MixDiff, a denoising diffusion probabilistic model (DDPM) for generating virtual concrete mix proportion data under small-sample conditions. This model aims to generate high-quality virtual concrete mix proportion data.

A small-sample dataset containing 100 sets of concrete mix proportions was first established. The input features included water, cement, fly ash, mineral fines, river sand, manufactured sand, coarse aggregate, water-reducing agent, total binder content, water-to-binder ratio, total fine aggregate content, and sand ratio. The target variables included 7 d compressive strength, 28 d compressive strength, slump, expansion degree, initial setting time, and final setting time. MixDiff was developed using a fully connected neural network and a denoising diffusion probabilistic model. The model consisted of a sinusoidal timestep embedding module and four stacked residual fully connected blocks. Each residual block contained fully connected layers, batch normalization layers, and SiLU activation functions. In the forward diffusion process, Gaussian noise was progressively added to the normalized data according to a cosine variance schedule. In the reverse generation process, a neural network was used to predict the noise and progressively reconstruct concrete mix proportion samples with realistic distribution characteristics from standard Gaussian noise. Subsequently, the quality of virtual data generated by MixDiff was quantitatively evaluated from two perspectives: marginal distribution and feature correlation. Under five-fold cross-validation and grid search, several mainstream machine learning models were further used to compare the prediction performance of the baseline mode and the augmentation mode. Finally, 15 mix proportions were selected from the generated virtual dataset for experimental validation to evaluate the engineering plausibility of the generated data.

The quantitative evaluation results showed that the virtual dataset generated by MixDiff showed high similarity to the real dataset. The average Wasserstein distance, K-S statistic, and J-S divergence between the two datasets were 0.019 5, 0.095 2, and 0.120 7, respectively. The Frobenius distance between their Pearson correlation matrices was 0.332 7, indicating that MixDiff effectively preserved the marginal distribution characteristics of the real data and the correlation structure among variables. The machine learning comparison results showed that the prediction performance of all models improved significantly after the introduction of MixDiff-generated data. In the baseline mode, the average R² of the seven models was 0.817 1, and increased to 0.953 7 in the data augmentation mode. Meanwhile, the average RMSE decreased from 14.20 to 7.39, and the average MAE decreased from 8.77 to 4.66. Correspondingly, R² increased by 16.72%, while RMSE and MAE decreased by 47.96% and 46.86%, respectively. Among the machine learning models, the deep neural network achieved the best performance after data augmentation, with R², RMSE, and MAE values of 0.959 4, 7.00, and 4.52, respectively. In addition, the standard deviations of the five-fold cross-validation results were significantly reduced in the data augmentation mode. This indicates that MixDiff-generated data not only improved the prediction accuracy of machine learning models but also enhanced model stability and generalization ability. Experimental validation of 15 virtual mix proportions showed that the data generated by MixDiff had high plausibility in six key performance indicators, including 7 d compressive strength, 28 d compressive strength, slump, expansion degree, initial setting time, and final setting time. The average MAPE of each performance indicator was lower than 5%, and the overall average MAPE was 3.8%.

This study proposed MixDiff, a denoising diffusion probabilistic model for concrete mix proportion data generation. The results show that the virtual data generated by MixDiff were highly consistent with the real data in terms of marginal distribution and feature correlation. The Frobenius distance between the Pearson correlation matrices was only 0.332 7. After introducing MixDiff-generated data, the prediction performance of multiple machine learning models, including RF, SVR, KNN, XGBoost, LightGBM, CatBoost, and DNN, was significantly improved, with R² values of all models increasing above 0.94. Based on the average performance of the seven machine learning models for the six output performance indicators, R² increased by 16.72%, while RMSE and MAE decreased by 47.96% and 46.86%, respectively. Among these models, DNN achieved the highest R² and the lowest RMSE in the data augmentation mode. Experimental validation of 15 virtual mix proportions showed that the generated results were highly consistent with the measured results in terms of 7 d compressive strength, 28 d compressive strength, slump, expansion degree, initial setting time, and final setting time. The MAPE of each performance indicator was below 5%, and the overall average MAPE across the six performance indicators was 3.8%. These results indicate that MixDiff can learn the underlying relationships between concrete mix proportions and macroscopic properties, and it can serve as an effective method for concrete mix proportion data augmentation under small-sample conditions.