  Existing structural analysis methods may fail to find all hidden constraints
for a system of differential-algebraic equations with parameters if the system
is structurally unamenable for certain values of the parameters.
  In this paper, for polynomial systems of differential-algebraic equations,
numerical methods are given to solve such cases using numerical real algebraic
geometry. First, we propose an embedding method that for a given real analytic
system constructs an equivalent system with a full-rank Jacobian matrix.
Secondly, we introduce a witness point method, which can help to detect
degeneration on all components of constraints of such systems. Thirdly, the two
methods above lead to a numerical global structural analysis method for
structurally unamenable differential-algebraic equations on all components of
constraints.
