We assume that the measured data are noise-free,
and therefore do not directly use the general Tikhonov-like regularization
though we could use it for the underdetermined system to have a unique solution.
For the basic studies, however,
we address the benefits for solving the load updating problems
using the relative measurement method,
the fewer four-noded beam elements,
polynomials of lower order,
and richer measured data, smoothing,
and enforcing C0continuity to reduce the relative model order to the extent
that an overdetermined inverse problem is obtained.