Numerical Methods for mapping band-type resonance in insect flight
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2025
Författare
Zhang, Congxiao
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Insect flight is a highly complex and energy-intensive process. Flapping-wing insects employ a
unique muscle contraction mechanism that enables high-frequency wing beats, with metabolic rates
reaching several times those at rest. Their remarkable endurance during flight highlights the
importance of understanding the energy optimization involved. This thesis focuses on developing
numerical methods to map band-type resonance, which serves as a benchmark for assessing
whether a system achieves an energy-optimal state. We describe the mapping of band-type
resonance as an optimization problem and propose two primary numerical methods: particle swarm
optimization and numerical continuation. We evaluate the accuracy of the numerical solutions via
the solution work loops and power waveforms and compare them with analytical approximations to
the space of band-type resonant states. Our findings reveal that while the standalone particle swarm
method can provide a relatively complete set of estimated solutions, the solution space lacks
continuity. The numerical continuation method sacrifices some completeness in finding solution
sets to ensure better continuity in the corresponding domain of the output solution set.
After comparing these methods' performance in identifying potential solutions for simple cases, we
improve them and propose a compound numerical method for solving more complex problems,
such as higher harmonic and nonlinear oscillators. Notably, this compound algorithm performs well
not only on simple linear cases with known analytical solutions but also on complex problems
lacking analytical solutions, offering a valuable numerical tool for estimating the mapping zone of
band-type resonance when analytical methods are not feasible.
Comparing the results of mapping zones of band-type resonance with wingbeat frequency
modulation behaviour observed in actual insect species suggests that such behaviour may be
consistent with sustained resonant energy savings by exploiting band-type resonance.
This report is written in English.
Beskrivning
Ämne/nyckelord
Insect flight motor, energy efficiency, band-type resonance, particle swarm optimization, numerical continuation, work loop