Kalman Filter and Model-Free Adaptive Control Theory Applied to the Unsteady Flow State Estimation of Product Pipelines

The accurate online estimation of unsteady flow state provides important operation information for product pipelines real-time scheduling. In practice, affected by the parameter drift and observation noises, traditional estimation methods based on the first principle can hardly provide accurate results within acceptable time. The nonlinear and fast transient characteristics of pipeline flow make it difficult to realize on-line adaptive modification of model parameters. In order to meet the requirements of computational efficiency and accuracy simultaneously, this paper proposes a methodology with two-level adaptive adjustment to realize the digital twin of pipeline nonlinear transient flow process by using simplified linear flow model. In terms of improving computing efficiency, the linear flow model based on frequency response and difference transforming is established to process the on-line state estimation of transient flow. To reduce the deviation between the actual observed value and the linear model estimation, we first introduce mode-free adaptive control method as linear compensation of the reduced order unsteady flow model. The compact form dynamic linearization method has been adopted to design the virtual input of the linear flow model. To further improve the adaptability of the linear model, the model parameters are online adjusted by using the recursive least squares with forgetting factor method. The uncertainty of the model and the interference of observation noise is eliminated by adopting Kalman filter to the state space model based on modified linear model. The effectiveness of the proposed methodology is evaluated by applying to the digital twin process of a product pipeline transient pressure in a multistation pipeline. The results show that the proposed method can make transient pressure estimation of second-order linear model agree well with the value of nonlinear flow model even under unforeseen conditions and noise interference. The performance of the proposed method is better than model-based linear method, data-driven linear method and nonlinear method.