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This paper considers the active fault isolation problem for a class of uncertain multimode fault systems with a high-dimensional state-space model. It has been observed that the existing approaches in the literature based on a steady-state active fault isolation method are often accompanied by a large delay in making the correct isolation decision. To reduce such fault isolation latency significantly, this paper proposes a fast online active fault isolation method based on the construction of residual transient-state reachable set and transient-state separating hyperplane. The novelty and benefit of this strategy lies in the embedding of a new component called the set separation indicator, which is designed offline to distinguish the residual transient-state reachable sets of different system configurations at any given moment. Based on the results delivered by the set separation indicator, one can determine the specific moments at which the deterministic isolation is to be implemented during online diagnostics. Meanwhile, some alternative constant inputs can also be evaluated for isolation effects to determine better auxiliary excitation signals with smaller amplitudes and more differentiated separating hyperplanes. The validity of these results is verified by both a numerical comparison and an FPGA-in-loop experiment.