  Block-spin transformation of topological defects is applied to the violation
of the non-Abelian Bianchi identity (VMABI) on lattice defined as Abelian
monopoles. To get rid of lattice artifacts, we introduce various techniques
smoothing the vacuum. The effective action can be determined by adopting the
inverse Monte-Carlo method. The coupling constants $F(i)$ of the effective
action depend on the coupling of the lattice action $\beta$ and the number of
the blocking step $n$. But it is found that $F(i)$ satisfy a beautiful scaling,
that is, they are a function of the product $b=na(\beta)$ alone for lattice
coupling constants $3.0\le\beta\le3.9$ and the steps of blocking $1\le n\le
12$. The effective action showing the scaling behavior can be regarded as an
almost perfect action corresponding to the continuum limit, since $a\to 0$ as
$n\to\infty$ for fixed $b$. The almost perfect action showing the scaling is
found to be independent of the smooth gauges adopted here. Then we compare the
results with those obtained by the analytic blocking method of topological
defects from the continuum. The infrared monopole action can be transformed
into that of the string model. The physical string tension and the lowest
glueball mass can be evaluated \textit{analytically} by the strong-coupling
expansion of the string model. We get $\sqrt{\sigma}\simeq
1.3\sqrt{\sigma_{phys}}$ for $b\ge 1.0\ \ (\sigma_{phys}^{-1/2})$, whereas the
scalar glueball mass is kept to be near $M(0^{++})\sim
3.7\sqrt{\sigma_{phys}}$. Also we can almost reproduce \textit{analytically}
the scaling function of the squared monopole density determined numerically for
large $b$ region $b>1.2\ (\sigma_{phys}^{-1/2})$.
