In our study, we explore high-order exceptional points (EPs), which are crucial for enhancing the sensitivity of open physical systems to external changes. We utilize the Hilbert−Schmidt speed (HSS), a measure of quantum statistical speed, to accurately identify EPs in non-Hermitian systems. These points are characterized by the simultaneous coalescence of eigenvalues and their associated eigenstates. One of the main benefits of using HSS is that it eliminates the need to diagonalize the evolved density matrix, simplifying the identification process. Our method is shown to be effective even in complex, multi-dimensional and interacting Hamiltonian systems. In certain cases, a generalized evolved state may be employed over the conventional normalized state. This necessitates the use of a metric operator to define the inner product between states, thereby introducing additional complexity. Our research confirms that HSS is a reliable and practical tool for detecting EPs, even in these demanding situations.