  We have studied the evolution of the Low Frequency Quasi-Periodic
Oscillations (LFQPOs) during the rising phase of seven outbursts of the neutron
star Soft X-ray Transient (SXT) Aql X$-$1 observed with the \textit{Rossi X-ray
Timing Explorer (RXTE)}. The frequency correlation between the low frequency
break and the LFQPO sampled on the time scale of $\sim$2 days was seen. Except
for the peculiar 2001 outburst, the frequency of the LFQPOs increased with time
before the hard-to-soft state transition up to a maximum $\nu_{max}$ at
$\sim$31 Hz, a factor of $\sim$5 higher than those seen in black hole
transients such as GX 339$-$4, making the maximum QPO frequency a likely
indicator of the mass of the central compact object. The characteristic
frequencies increased by around ten percent per day in the early rising phase
and accelerated to nearly one hundred percent per day since $\sim$2 days before
the hard-to-soft state transition. We examined the dependence of the frequency
$\nu_{LF}$ on the source flux $f$ and found an anti-correlation between the
maximum frequency of the LFQPOs and the corresponding X-ray luminosity of the
hard-to-soft transition (or outburst peak luminosity) among the outbursts. We
suggest that X-ray evaporation process can not be the only mechanism that
drives the variation of the inner disk radius if either of the twin kHz QPO
corresponds to the Keplerian frequency at the truncation radius.
