Float glass is a fundamental material for architecture, automotive applications, electronic displays and photovoltaics, and its quality stability directly affects downstream processing efficiency and end-use performance. In continuous float glass production, defects such as bubbles, knots, stones and point defects reduce product grade, increase cutting losses and rework costs, and disturb stable operation. Existing online defect inspection systems usually identify defects after they have already formed, so they cannot provide sufficient support for feed-forward adjustment of furnace thermal conditions, combustion state, glass level or tin-bath atmosphere. The melting and forming process is a highly nonlinear, strongly coupled, and long-lag industrial thermal process. Process disturbances are transmitted through the temperature field, pressure field, atmosphere field and glass flow field, and their influence may appear at the inspection end only after tens of minutes or longer. Therefore, this study focuses on short-term prediction of four types of defects with 10 levels in float glass and proposes a lag-aware variable-coupled TimeMixer model, named LVC-TimeMixer, to establish a dynamic mapping from historical process states and defect sequences to future defect trends.

Historical records from a float glass production line were used to construct the prediction dataset. The input data consisted of 31 process variables covering furnace thermal state, pressure and liquid level, combustion and atmosphere, tin-bath protective gas, feeding and control settings, together with 40 historical defect labels corresponding to Bubble, Knot, Stone and PDefect at ten levels. The raw 10 s records were sorted by timestamp and resampled to a 1 min interval. Window averaging was applied to process variables to suppress high-frequency noise, while defect labels were aggregated by counts in each window; short missing values were treated using forward filling and linear interpolation. Supervised samples were generated by a sliding-window strategy, with a 360 min historical input window and a 30 min prediction horizon. On the basis of the original TimeMixer framework, LVC-TimeMixer introduces a lag-aware encoder and a variable-coupled mixer before the multiscale mixing backbone. The lag-aware encoder explicitly extracts delayed representations under candidate lag scales of 5, 10, 30, 60, 120 min and 240 min and uses a gating mechanism to adaptively select effective lag information. The variable-coupled mixer groups variables according to process semantics, including temperature, pressure, flow, atmosphere and historical defects, and then learns intra-group representations and inter-group coupling relationships. The encoded representation is subsequently fed into the TimeMixer backbone, where multiscale decomposition, Past-Decomposable-Mixing and Future-Multipredictor-Mixing are used to predict the multi-step defect sequence.

The proposed model was compared with DLinear, PatchTST, iTransformer, the original TimeMixer and WPMixer under the same data split, input window, prediction horizon and evaluation metrics. The results show that LVC-TimeMixer achieved the best overall performance in MAE, RMSE, R² and 30 min cumulative defect MAE, with corresponding values of 10.525, 30.368, 0.616 and 5 194.10, respectively. Although its sMAPE and severe-defect F1 were not the best among all models, they remained close to the leading level, indicating that the proposed lag-aware and variable-coupled structures improve trend fitting and cumulative risk estimation while maintaining competitive severe-defect warning capability. At prediction horizons of 5, 10, 15, 20 min and 30 min, LVC-TimeMixer consistently maintained the lowest MAE and a relatively high R², demonstrating stable short- and medium-term prediction capabilities.

For different defect categories, the optimal model varied because Bubble, Knot, Stone and PDefect have different temporal patterns and process response mechanisms. LVC-TimeMixer did not achieve the best MAE for every single defect type, but its errors for all four defect categories were close to those of the corresponding optimal models, and its overall defect prediction and 30 min cumulative risk estimation were superior. Rolling prediction curves and predicted-vs.-true scatter distributions further indicate that LVC-TimeMixer can better track the rise, fall and local peaks of total defects on chronological test data. Ablation experiments confirm that the lag-aware encoder improves prediction by aligning process disturbances with delayed defect responses, whereas the variable-coupled mixer used alone may be limited when lag alignment is absent. When both modules were introduced simultaneously, the MAE and 30 min cumulative defect MAE were further reduced by 21.22% and 16.60%, respectively, compared with TimeMixer-Lag, proving the synergistic effect between lag-aware encoding and variable-group coupling. Engineering evaluation showed that the average and maximum inference times for a single prediction window were 11.6 ms and 21.3 ms, respectively, on a computing platform equipped with custom 2 × 24 GB VRAM NVIDIA GeForce RTX 4090 GPUs, which is far below the 1 min rolling warning threshold in industrial applications.

In this study, an LVC-TimeMixer model was proposed for short-term multiclass defect prediction in the float glass melting-forming process. By embedding a lag-aware encoder and a variable-coupled mixer into the TimeMixer multiscale trend-fluctuation modeling framework, the model explicitly describes both the delayed relationship between process disturbances and defect responses and the coupling relationship among temperature, pressure, flow, atmosphere and historical defect variables. The comparative experiments, prediction-curve analysis and ablation study demonstrate that the proposed model improves overall prediction accuracy, cumulative risk estimation and prediction stability. The model can provide data-driven support for rolling defect early warning, furnace operating-condition optimization and intelligent quality control in float glass production. However, further research is still required to improve generalization under extreme operating conditions, to verify long-term real-time deployment, and to integrate synchronized stripe-image diagnosis or other multi-source visual information.