  Identification of complicated quantum environments lies in the core of
quantum engineering, which systematically constructs an environment model with
the aim of accurate control of quantum systems. In this paper, we present an
inverse-system method to identify damping rate functions which describe
non-Markovian environments in time-convolution-less master equations. To access
information on the environment, we couple a finite-level quantum system to the
environment and measure time traces of local observables of the system. By
using sufficient measurement results, an algorithm is designed, which can
simultaneously estimate multiple damping rate functions for different
dissipative channels. Further, we show that identifiability for the damping
rate functions corresponds to the invertibility of the system and a necessary
condition for identifiability is also given. The effectiveness of our method is
shown in examples of an atom and three-spin-chain non-Markovian systems.
