Additive maps preserving semi-Fredholm operators with bounded ascent on $\mathcal{B}(\mathcal{X})$

Let $\mathcal X$ be an infinite-dimensional complex Banach space, and $\mathcal B(\mathcal X)$ the algebra of all bounded linear operators on $\mathcal X$. In this paper, given any positive integer $m$, we characterize the surjective additive maps on $\mathcal B(\mathcal X)$ that preserve semi-Fredholm operators with ascent non-greater than $m$ in both directions, and describe completely the structure of these maps.