Umbrella sampling (US) simulation is a highly effective method for sampling the conformations of a complex system within a small subspace of predefined coordinates. In a typical US stratification strategy, biasing "window" potentials spanning the subspace of interest are introduced to narrow down the range of accessible conformations and accelerate the sampling. The speed of convergence in each biased window simulation may, however, differ. For example, windows that coincide with a large energetic barrier along a coordinate that is orthogonal to the predefined subspace are often plagued by slow relaxation timescales. Here, we design a method that can quantitatively detect this type of issue and gain further insight into the origin of the slow relaxation timescale. Once the problematic windows affected by slow convergence are identified, additional simulations limited to only these windows can be carried out, thereby reducing the overall computational effort. Several possible approaches aimed at performing US simulations adaptively are discussed, and their respective performance is illustrated using a simple model system. Last, simulations of an atomic deca-alanine system are used to demonstrate the efficacy of analyzing US simulation trajectories using the proposed method.