  Gravitational wave echoes may provide a smoking gun signal for new physics in
the immediate vicinity of black holes. As a quasiperiodic signal in time,
echoes are characterized by the nearly constant time delay, and its precise
measurement can help reveal a Planck-scale deviation outside of the would-be
horizon. Different search methods have been developed for this quasiperiodic
signal, while the searches suffer from large theoretical uncertainties of the
echo waveform associated with the near-horizon physics. On the other hand, a
coherent combination of a large number of pulses gives rise to a generic narrow
resonance structure for the echo amplitude in frequency. The quasiperiodic
resonance structure sets a complementary search target for echoes, and the time
delay is inversely related to the average resonance spacing. A uniform comb has
been proposed to look for the resonance structure in a rather model-independent
way. In this paper, we develop a Bayesian algorithm to search for the resonance
structure based on combs, where a phase-marginalized likelihood plays an
essential role. The algorithm is validated with signal injections in detector
noise from Advanced LIGO. With special treatments of the non-Gaussian
artifacts, the noise outliers of the log Bayes factor distribution are properly
removed. An echo signal not significantly below noise is detectable, and the
time delay can be determined to very high precision. We perform the proposed
search on real gravitational wave strain data of the first observing run of
Advanced LIGO. We find no clear evidence of a comblike structure for GW150914
and GW151012.
