Coursework
Comparing MDO Architectures for Two-Passenger eVTOL Sizing
Implementing and comparing MDF and IDF architectures in OpenMDAO, and quantifying how model fidelity shifts motor selection.
Conceptual sizing of a two-passenger electric multicopter, minimising maximum takeoff weight subject to power and energy feasibility. The coupled powertrain–mass–performance model captures the weight spiral that a 30% structural mass fraction produces: a heavier airframe needs bigger motors, and bigger motors make the airframe heavier again.
MDF versus IDF, in plain terms
Both architectures deal with the same problem: mass and power depend on each other. Total mass sets the power required, power sets how heavy the motors and battery are, and that feeds back into total mass. The difference is when the two are made to agree.
MDF (multidisciplinary feasible): agree at every step. Each time the optimizer proposes a design, an inner loop iterates until mass and power are consistent, and only then is the result handed back.
- Pros: every intermediate design the optimizer sees is physically valid, so stopping at any point still leaves a usable design; there are also fewer optimization variables
- Cons: every step hides an inner loop, so the more expensive the analysis, the slower each step; if the inner loop fails to converge, the whole optimization stalls
IDF (individual discipline feasible): compute separately, reconcile at the end. The optimizer guesses the total mass, each discipline runs once with that guess without waiting on the others, and an equality constraint requires the guess to match the computed mass by the end.
- Pros: no inner loop; the disciplines are decoupled, can run in parallel, and are easier to integrate as separate modules
- Cons: more variables and constraints, and more optimizer iterations; intermediate designs are not physically consistent, and if the constraint is not strict enough the optimizer can exploit the gap — a design that assumes 500 kg but actually computes to 1000 kg
Our results
Both architectures were implemented in OpenMDAO. MDF used a Newton solver to drive the coupling residuals below 10⁻⁹ at every step. IDF was deliberately started from a badly inconsistent point (a 3000 kg guess against roughly 500 kg actual), and its consistency residual converged from 10³ down to 10⁻¹⁰.
Both reached the same optimum, 538.44 kg. The choice between MDF and IDF does not change the answer; it is a trade between computational cost and implementation flexibility — MDF needed fewer optimizer iterations, while IDF made integrating the disciplines simpler. On the optimizer side, gradient-based SLSQP took 14 iterations and gradient-free COBYLA took 19.
Adding a multi-segment mission profile changed the drive motor mass from 16.35 kg to 21.32 kg — a useful measure of how much model fidelity matters at this stage.