Brelje 2018a reproduction

headline result

Paper vs reproduced.

Figure 5 (fuel + MTOW/100 objective) contours over mission range and battery specific energy. Paper on the left, omd-run reproduction on the right.

fig 5 · fuel + MTOW/100 · 5x5 grid · paper (left) vs omd Lane B (right). Coarse grid blurs the hybrid/electric boundary but preserves all trends: fuel-heavy designs dominate at low spec energy; battery-heavy dominate at high spec energy; transition is roughly diagonal.

Figure 6 (trip direct operating cost objective). Cost MDO has competing local minima; each cell is warm-started from the fuel-optimized design at the same grid point.

Brelje 2018a Fig 6 paper vs reproduced side-by-side

fig 6 · direct operating cost · 5x5 grid · warm-started from fig 5 optimum per cell. MTOW pins at the 5700 kg upper bound across the middle and lower-right region, matching the paper.

individual panels

Each figure on its own for closer inspection. All cropped consistently between paper and reproduction.

paperfig 5 · Brelje 2018a, AIAA 2018-4979

reproducedfig 5 · omd Lane B, 5x5 grid

paperfig 6 · Brelje 2018a, DOC objective

reproducedfig 6 · omd Lane B, warm-start from fig 5

formulation

MDO problem setup.

Mission, DVs, constraints, and objective match upstream openconcept/examples/HybridTwin.py (lines 372-418) with the plan-level initial-value overrides warm-starting each grid cell.

mission profile

aircraft template	kingair (C90GT)
architecture	twin_series_hybrid
num_nodes	11 (Simpson)
cruise altitude	29,000 ft
mission range	500 nmi (cell)
climb V_eas	124 kt @ 1500 fpm
cruise V_eas	170 kt
descent V_eas	140 kt @ -600 fpm
payload	1000 lb
battery specific energy	450 Wh/kg (cell)

objective & optimizer

objective (fig 5)	mixed_objective
objective (fig 6)	doc_per_nmi
optimizer	SLSQP
maxiter	150
tol	1e-6
nonlinear solver	Newton (inner)
linear solver	DirectSolver
atol / rtol	1e-10 / 1e-10

design variables (10)

ac|weights|MTOW [4000, 5700] kg
ac|geom|wing|S_ref [15, 40] m²
ac|propulsion|engine|rating [1, 3000] hp
ac|propulsion|motor|rating [450, 3000] hp
ac|propulsion|generator|rating [1, 3000] hp
ac|weights|W_battery [20, 2250] kg
ac|weights|W_fuel_max [500, 3000] kg
cruise.hybridization [0.001, 0.999]
climb.hybridization [0.001, 0.999]
descent.hybridization [0.01, 1.0]

constraints (16 rows)

MTOW_margin ≥ 0
rotate.range_final ≤ 1357 m (BFL 4452 ft)
v0v1.Vstall_eas ≤ 42 m/s (~81.6 kt)
descent.SOC_final ≥ 0 (battery not over-drawn)
engineoutclimb.gamma ≥ 0.02 (OEI climb gradient)
climb.throttle ≤ 1.05
component_sizing_margin ≤ 1 (eng1/gen1/batt1 x 4 phases = 11 rows)

decisions

Per-step decision log.

Every plan primitive (solver, DV bounds, constraint, objective, optimizer, result interpretation, convergence assessment) was recorded via omd-cli log-decision during interactive-builder assembly. Verbatim from plans/brelje-fuel-mdo-lane-c/decisions.yaml.

component_selection1 decision

dec-01

Added component mission (ocp/FullMission)

Single ocp/FullMission with kingair template + twin_series_hybrid to reproduce Brelje 2018a Fig 5 at the (500 nmi, 450 Wh/kg) grid cell. num_nodes=11 matches Lane A/B for Simpson integration. Mission params (cruise 29000 ft, climb 1500 fpm @ 124 kn, cruise 170 kn, descent 600 fpm @ 140 kn, 1000 lb payload) copied from upstream HybridTwin example.

solver_selection1 decision

dec-02

Solvers: nonlinear=NewtonSolver, linear=DirectSolver

Newton + DirectSolver with atol/rtol=1e-10 matches Lane A/B for the OCP full-mission analysis. Direct solver is appropriate for the small OCP state vector; Newton converges reliably when initial guesses are reasonable.

dv_setup10 decisions

dec-03

DV ac|weights|MTOW bounds [4000.0, 5700.0] kg

MTOW is the top-level weight DV. Paper bounds [4000, 5700] kg keep the optimizer near the King Air class; the upper bound is active at the Lane A converged optimum.

dec-04

DV ac|geom|wing|S_ref bounds [15.0, 40.0] m²

Wing area DV bounds [15, 40] m² bracket the King Air reference (27.3 m²) while leaving room for the optimizer to trade area against induced drag.

dec-05

DV ac|propulsion|engine|rating bounds [1.0, 3000.0] hp

Engine (turboshaft) rating DV in hp; wide [1, 3000] hp bounds per Brelje paper. Low lower bound lets the optimizer push engine toward zero in electric-leaning designs.

dec-06

DV ac|propulsion|motor|rating bounds [450.0, 3000.0] hp

Motor rating DV in hp; lower bound 450 hp preserves minimum takeoff power; upper bound 3000 hp caps the all-electric extreme.

dec-07

DV ac|propulsion|generator|rating bounds [1.0, 3000.0] hp

Generator rating DV in hp; symmetric to engine bounds since series-hybrid pairs them.

dec-08

DV ac|weights|W_battery bounds [20.0, 2250.0] kg

Battery weight DV; upper bound 2250 kg permits heavily electric designs, lower bound 20 kg permits near-pure conventional.

dec-09

DV ac|weights|W_fuel_max bounds [500.0, 3000.0] kg

Max fuel capacity DV in kg; wide bounds per paper to avoid constraining fuel-heavy designs.

dec-10

DV cruise.hybridization bounds [0.001, 0.999]

Cruise hybridization fraction (motor electric share). Bounds (0.001, 0.999) avoid hard 0/1 endpoints that can trip the series-hybrid power split math.

dec-11

DV climb.hybridization bounds [0.001, 0.999]

Climb hybridization fraction, same bounds rationale as cruise.

dec-12

DV descent.hybridization bounds [0.01, 1.0]

Descent hybridization fraction. Upper bound 1.0 is allowed because idle-descent can realistically run fully electric, matching Brelje paper.

objective_selection1 decision

dec-13

Objective: minimize mixed_objective

Brelje Fig 5 minimizes fuel_burn + MTOW/100 kg. The OCP factory wires mixed_objective automatically for hybrid architectures, so referencing the short name is sufficient and identical to Lane B.

constraint_setup1 decision (16 constraint rows)

dec-14

Added 5 scalar + 11 vector constraints mirroring upstream HybridTwin

MTOW_margin ≥ 0, rotate.range_final ≤ 1357 m (BFL 4452 ft), v0v1.Vstall_eas ≤ 42 m/s (~81.6 kt), descent SOC_final ≥ 0, engine-out climb gradient ≥ 0.02, climb throttle ≤ 1.05, and component_sizing_margin ≤ 1 for eng1/gen1/batt1 on climb/cruise/descent plus batt1 on v0v1.

optimizer_selection1 decision

dec-15

SLSQP with maxiter=150 and tol=1e-6

SLSQP handles the mix of inequality constraints and continuous DVs well on this problem size (10 DVs, 16 constraint rows vectorized). maxiter=150 and tol=1e-6 match Lane A/B settings; the same optimizer converges a single cell in ~60-90 SLSQP iterations for the (500 nmi, 450 Wh/kg) grid point.

problem_definition1 decision

dec-16

Reproduce Brelje 2018a Fig 5 single grid cell (500 nmi, 450 Wh/kg)

Lane C is the agent-interactive-builder counterpart of Lane B. Using the same problem definition lets us verify the interactive builder produces a plan that reaches the same optimum as Lane B (MTOW ~5700 kg, fuel ~176 kg, cruise hyb ~0.69 per Lane A).

result_interpretation1 decision

dec-17

Lane C optimum matches Lane A/B: mixed_objective=233.22

Lane A reports MTOW=5700 kg, fuel ~176 kg, cruise hyb=68.9% for the (500 nmi, 450 Wh/kg) cell; Lane C reproduces these. MTOW and W_fuel_max pinning against their bounds plus a near-zero MTOW_margin (8.7e-6) and SOC_final=-1.2e-8 indicate the optimum sits on three active constraints, consistent with Brelje's Fig 5 pattern for long-range hybrid-heavy designs. Solution accepted.

convergence_assessment1 decision

dec-18

SLSQP reported converged in 57 driver iterations (59 recorded cases)

Key constraint residuals at the optimum: MTOW_margin=8.7e-6 (active), rotate.range_final=1357.0 m (active at BFL bound), v0v1.Vstall_eas=42.0 m/s (active at stall bound), descent.SOC_final=-1.2e-8 (effectively 0, battery depleted), engineoutclimb.gamma=0.0306 > 0.02 (satisfied with margin). All component_sizing_margins ≤ 1. Three bounds-active DVs (MTOW at upper, W_fuel_max at lower, MTOW margin near 0) mean the exit is a constrained optimum sitting on the intersection of BFL, stall, battery-depletion, and MTOW-margin constraints, matching Brelje Fig 5 paper behavior.

known limits

Divergences from the paper.

Documented trade-offs where the reproduction departs from the published result.

where the reproduction differs

grid resolution. The headline result uses 5×5 = 25 cells (~25 min wall time on 4 workers) rather than the paper's 21×12 = 252 cells (~3 h). The coarser grid blurs the hybrid/electric boundary but preserves all qualitative trends.
convergence rate. The paper reports 1/252 failures. In the 5×5 fuel sweep, 6/25 cells exited with SLSQP mode 8 (KKT tolerance hit at a feasible optimum with all constraints active at bounds); those are post-processed to converged after a feasibility check, matching what the fuel grid contour plot renders. The cost sweep had 0/25 raw failures. Better per-cell starting guesses would likely close this gap.
cost warm-starts. The cost objective has competing local minima; the template-default starting point converges at MTOW ~4400 kg, while warm-starting from the fuel-optimized design for the same grid cell finds the true minimum at or near MTOW = 5700 kg. The sweep is therefore run with --warm-from fig5_grid.csv before plotting.
battery energy model. The reproduction approximates E_battery_used = 0.9 × W_battery × spec_energy; upstream OpenConcept integrates actual battery draw over the trajectory. Both use the $36/MWh coefficient for cost.

pipeline

How to re-run this.

The full pipeline is ~45 minutes wall-time on a 4-worker machine. Single cells run in under a minute.

# single-cell sanity check (Lane A, direct Python API) $ uv run python packages/omd/demos/brelje_2018a/lane_a/hybrid_mdo.py \ --range 500 --spec-energy 450 --objective fuel # single-cell Lane B plan (this study's plan format) $ uv run omd-cli run packages/omd/demos/brelje_2018a/lane_b/fuel_mdo/plan.yaml \ --mode optimize # full fuel grid (fig 5) $ uv run python packages/omd/demos/brelje_2018a/sweep.py \ --objective fuel --grid 5x5 --workers 4 $ uv run python packages/omd/demos/brelje_2018a/plotting.py --figure 5 # full cost grid (fig 6) — warm-started from fig 5 optimum per cell $ uv run python packages/omd/demos/brelje_2018a/sweep.py \ --objective cost --grid 5x5 --workers 4 \ --warm-from packages/omd/demos/brelje_2018a/results/fig5_grid.csv $ uv run python packages/omd/demos/brelje_2018a/plotting.py --figure 6 # paper vs reproduced side-by-side $ uv run python packages/omd/demos/brelje_2018a/compare.py --figure 5 $ uv run python packages/omd/demos/brelje_2018a/compare.py --figure 6 # package N2, provenance graph, problem graph, plan detail for this page $ ./deploy/scripts/package-case-study.sh brelje-2018a \ run-20260423T190235-641af06b \ --plan-id brelje-fuel-mdo-lane-c --version 1 # local preview: extract the tarball in-place $ tar -xzf deploy/landing/studies/brelje-2018a.tar.gz \ -C deploy/landing/studies/

Brelje 2018a — figs 5 & 6 reproduction

Paper vs reproduced.

individual panels

Lane-C run output.

MDO problem setup.

mission profile

objective & optimizer

design variables (10)

constraints (16 rows)

Per-step decision log.

Divergences from the paper.

where the reproduction differs

OpenMDAO model structure.

N² diagram

problem graph

W3C PROV-Agent graph & plan detail.

provenance graph

plan detail

How to re-run this.

Paper vs reproduced.

individual panels

Lane-C run output.

MDO problem setup.

mission profile

objective & optimizer

design variables (10)

constraints (16 rows)

Per-step decision log.

Divergences from the paper.

where the reproduction differs

OpenMDAO model structure.

N2 diagram

problem graph

W3C PROV-Agent graph & plan detail.

provenance graph

plan detail

How to re-run this.

N² diagram