Reliable process monitoring is important for ensuring process safety and product quality. A production process is generally characterized by multiple operation modes

and monitoring these multimodal processes is challenging. Most multimodal monitoring methods rely on the assumption that the modes are independent of each other

which may not be appropriate for practical application. This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring. This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data. This process enables the identified modes to reflect the stability of actual working conditions

improve mode identification accuracy

and enhance monitoring reliability in cases of mode overlap. Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach in multimodal process monitoring with mode overlap.