Transformer-Based Missing Data Imputation in Time Series With Application to Flight Test Data

Accurate imputation of missing data is essential yet challenging in complex engineering systems testing and scientific experiments, as the data are often high-dimensional, nonlinear, dynamic, and difficult or expensive to reproduce. Recent advances in Transformer architectures have demonstrated strong capabilities for modeling long-term dependencies in time-series data, offering new opportunities for accurate dynamic data imputation. The recent success of Transformer models in large language models (LLMs) opens new opportunities for missing data imputation in complex dynamic systems. In this article, a Transformer-based missing-data imputation technique (TransMIT) is proposed to tackle the challenges of dynamic systems testing data. First, we introduce a hybrid imputation strategy that combines reconstruction-based and prediction-based approaches, allowing the model to leverage both temporal dependencies and cross-correlations at each time step. Second, we design a combined attention mechanism to jointly model temporal and feature dependencies by incorporating transposed input representations to capture complex patterns along both the temporal and feature dimensions. The effectiveness of TransMIT is verified on a real-world flight test dataset, which is expensive to collect, as well as on an industrial boiler process dataset. Experimental results are presented to demonstrate that TransMIT achieves the lowest imputation error, with a scaled RMSE of 0.2.