  We present a general framework for constructing trans-scale \emph{discrete
Boltzmann models} (DBMs) for high-speed compressible flows ranging from
continuum to transition regime. This is achieved by designing a higher-order
discrete equilibrium distribution function which satisfies additional
nonhydrodynamic kinetic moments. In order to characterize the \emph{%
thermodynamic non-equilibrium} (TNE) effects and estimate the condition under
which the DBMs at various levels should be used, two novel measures are
presented: (i) the relative TNE strength, describing the relative strength of
the ($N+1$)-th order TNE effects to the $N$-th order one; (ii) the TNE
discrepancy between DBM simulation and relevant theoretical analysis. Whether
or not the higher-order TNE effects should be taken into account in the
modeling and which level of DBM should be adopted, is best described by the
relative TNE intensity and/or the discrepancy, rather than by the value of the
Knudsen number. As a model example, a two-dimensional DBM with $26$ discrete
velocities at Burnett level is formulated, verified, and validated.
