  In the era of time-domain, multi-messenger astronomy, the detection of
transient events on the high-energy electromagnetic sky has become more
important than ever. Previous attempts to systematically search for
onboard-untriggered events in the data of Fermi-GBM have been limited to
short-duration signals with variability time scales smaller than ~1 min due to
the dominance of background variations on longer timescales. In this study, we
aim at the detection of slowly rising or long-duration transient events with
high sensitivity and full coverage of the GBM spectrum. We make use of our
earlier developed physical background model, propose a novel trigger algorithm
with a fully automatic data analysis pipeline. The results from extensive
simulations demonstrate that the developed trigger algorithm is sensitive down
to sub-Crab intensities, and has a near-optimal detection performance. During a
two month test run on real Fermi-GBM data, the pipeline detected more than 300
untriggered transient signals. For one of these transient detections we verify
that it originated from a known astrophysical source, namely the Vela X-1
pulsar, showing pulsed emission for more than seven hours. More generally, this
method enables a systematic search for weak and/or long-duration transients.
