The free lime (f-CaO) content in cement clinker is a key indicator for evaluating calcination quality and process stability, directly influencing cement soundness and mechanical performance. Efficient and accurate real-time prediction of f-CaO content is essential for achieving stable cement quality control. In actual production, process parameter data are sampled at approximately 1-second intervals, while f-CaO content is typically measured once per hour, resulting in a severe scarcity of labeled data. This asynchronous sampling and data heterogeneity constrain both the scale and diversity of data available for supervised learning models, thereby reducing prediction accuracy and generalization capability. To address this challenge, this study proposes a method based on a semi-supervised generative adversarial network (SSGAN) to enhance the diversity and representativeness of the training dataset. Through evaluating its impact on the downstream f-CaO prediction task and conducting ablation studies, the research explores the feasibility of applying GANs to address the issue of asynchronous sampling between process parameters and offline measurement data.

This study proposes a data augmentation model based on a semi-supervised generative adversarial network (SSGAN), which generates virtual data resembling the actual data distribution to expand the training dataset and effectively enhance the model's learning capability under conditions of limited labeled data. The model consists of three main components: an encoder, a generator network, and a discriminator network. The encoder first extracts features from a small amount of process parameter data with real labels, which are then used as conditional inputs. The generator learns the latent features of the true label distribution through adversarial training and generates corresponding label values based on unlabeled process parameter data. The discriminator distinguishes between real and generated labels, guiding the generator to continuously optimize its generation strategy. As adversarial training progresses, the generator produces synthetic label data that closely resemble actual production data, while the discriminator continuously improves its understanding of the true data distribution and label characteristics.

When the SSGAN model is trained to approximately 10 000 iterations, both the discriminator loss and the generator loss converge to near zero and remain stable, indicating that a balance has been achieved between the generator and discriminator, and the model has effectively learned the latent distribution features within the process parameters. Further analysis of the distribution of generated label values shows that they exhibit a distribution trend generally similar to that of the real labels. The model demonstrates strong learning and fitting capability within the primary range of label values, and the generated data are reliable. After introducing SSGAN for data augmentation, the MAE, MSE, and RMSE of the downstream GRU (Gate Recurrent Unit) model for f-CaO content prediction decreased from 0.24, 0.08, and 0.29 to 0.19, 0.06, and 0.24, respectively, indicating an improvement in the model's ability to predict outliers and extreme samples. Ablation studies revealed that removing the encoder, the GRU module, or introducing random noise led to significantly higher prediction errors, highlighting the critical role of temporal information and deep features embedded in the process parameters for generating high-quality label data. In particular, the encoder and its internal GRU module are essential for capturing long-range temporal dependencies and dynamic variation patterns.

To address the issue of label scarcity caused by the mismatch in sampling intervals between process parameters and f-CaO content measurements, this study proposes a data augmentation method based on SSGAN. By using an encoder to extract high-dimensional features and a generator to learn the latent distribution of true labels, the approach constructs a more diverse and representative training dataset. Ablation experiments were conducted to evaluate the effectiveness of each key module. The main conclusions are as follows: The introduction of the SSGAN-based data augmentation strategy effectively expanded the training dataset. The distribution of the generated label values closely matched that of the true labels, verifying the reliability of the synthetic data. The application of the SSGAN method significantly improved the accuracy of the downstream f-CaO content prediction task, with MAE on the test set decreasing from 0.24 to 0.19, MSE from 0.08 to 0.06, and RMSE from 0.29 to 0.24. Ablation experiments further revealed that introducing random noise, removing the encoder, or omitting the GRU module led to significantly increased prediction errors. This highlights the critical role of temporal information and deep features embedded in process parameters for generating high-quality label data. In particular, the encoder and its internal GRU module are essential for capturing long-range temporal dependencies and dynamic variation patterns.