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Demand-response operation of air separation units requires frequent changes in production rate(s), and scheduling calculations must explicitly consider process dynamics to ensure feasibility of the solutions. To this end, scale-bridging models (SBMs) approximate the scheduling-relevant dynamics of a process and its controller in a low-order representation. In contrast to previous works that have employed nonlinear SBMs, this paper proposes linear SBMs, developed using time-series analysis, to facilitate online scheduling computations. Using a year-long industrial dataset, we find that compact linear SBMs are suitable approximations over typical scheduling horizons, but that their accuracies are unpredictable over time. We introduce a strategy for online updating of the SBMs, based on Kalman filtering schemes for online parameter estimation. The approach greatly improves the accuracy of SBM predictions and will enable the use of linear SBM-based demand-response scheduling in the future.