AMCT-Former: An Asynchronous Multi-Rate Continuous-Time Transformer for Industrial Soft Sensing

Soft sensors are essential for online prediction of key quality variables in industrial processes. However, practical process data are often affected by asynchronous sensor sampling, delayed laboratory analysis, and heterogeneous update frequencies, resulting in pronounced multi-rate characteristics. Most existing methods rely on interpolation, resampling, or regular discrete-time modeling, which makes it difficult to preserve actual observation times, observation staleness, and continuous dynamics under asynchronous sampling conditions. To address this issue, this paper proposes an asynchronous multi-rate continuous-time Transformer, termed AMCT-Former, for industrial soft sensing. The proposed method first organizes multivariate observations within a historical window into a chronologically ordered event stream and constructs a rectilinear control path to represent time progression, latest observations, and observation staleness. An NCDE-inspired continuous-time encoder is then employed to learn the continuous-time evolution of process states. Furthermore, a variable-wise Transformer is introduced to characterize dynamic cross-variable dependencies, while a target-aware temporal Transformer adaptively aggregates prediction-relevant historical information. In this way, AMCT-Former enables unified modeling of continuous-time dynamics, cross-variable dependencies, and target-related historical features without enforcing explicit time alignment. Case studies on two real-world industrial processes demonstrate the effectiveness and superiority of the proposed method for asynchronous multi-rate soft sensing.