Payload-Based Initial Mass Optimization

This example shows how to use payload= to let OpenTOP optimize the initial mass. When payload is provided, m0 is used only as the initial guess; the actual initial mass is bounded between OEW + payload and the feasible maximum mass.

import warnings

import matplotlib.pyplot as plt
import pandas as pd

import opentop as top

warnings.filterwarnings("ignore", message="Warning: Wave drag is experimental")

Flight Setup

Without payload, m0 fixes the initial mass. With payload, m0 is only an initial guess and the optimizer chooses the initial mass needed for the flight.

actype = "A320"
origin = "EHAM"
destination = "LEMD"

m0 = 0.85
payload = 10_000.0  # kg
nodes = 15
max_iter = 800

def run_case(cls, *, payload=None):
    opt = cls(actype, origin, destination, m0=m0, payload=payload)
    opt.setup(nodes=nodes, max_iter=max_iter)
    df = opt.trajectory(objective="fuel")
    return opt, df


def along_track_distance_km(df):
    if "distance" in df.columns:
        return df.distance / 1000
    segment_m = (df.x.diff().fillna(0) ** 2 + df.y.diff().fillna(0) ** 2) ** 0.5
    return segment_m.cumsum() / 1000


def summarize(label, opt, df):
    dry_payload_mass = opt.oew + (opt.payload or 0.0)
    return {
        "case": label,
        "success": opt.success,
        "status": opt.stats["return_status"],
        "initial_mass_kg": df.mass.iloc[0],
        "final_mass_kg": df.mass.iloc[-1],
        "fuel_burn_kg": df.mass.iloc[0] - df.mass.iloc[-1],
        "estimated_fuel_onboard_kg": df.mass.iloc[0] - dry_payload_mass,
        "flight_time_min": df.ts.iloc[-1] / 60,
        "max_altitude_ft": df.altitude.max(),
    }

Cruise Example

cruise_fixed, cruise_fixed_df = run_case(top.Cruise)
cruise_payload, cruise_payload_df = run_case(top.Cruise, payload=payload)

pd.DataFrame(
    [
        summarize("cruise: fixed m0", cruise_fixed, cruise_fixed_df),
        summarize("cruise: payload optimized", cruise_payload, cruise_payload_df),
    ]
)

/home/junzi/arc/code/1-public/opentop/opentop/cruise.py:38: UserWarning: payload is provided; m0 is used only as the initial mass guess and does not fix the initial mass.
  super().__init__(

	case	success	status	initial_mass_kg	final_mass_kg	fuel_burn_kg	estimated_fuel_onboard_kg	flight_time_min	max_altitude_ft
0	cruise: fixed m0	True	Solve_Succeeded	66299.999900	61587.854094	4712.145806	23699.999900	104.725498	35087.0
1	cruise: payload optimized	True	Solve_Succeeded	56600.404982	52599.999902	4000.405080	4000.404982	104.603878	39991.0

The payload case has a bounded initial mass decision variable. The bounds are visible after init_conditions() or after solving.

{
    "minimum_mass_kg": cruise_payload.mass_min,
    "initial_mass_lower_bound_kg": cruise_payload.mass_init_lb,
    "initial_mass_upper_bound_kg": cruise_payload.mass_init_ub,
    "m0_initial_guess_kg": cruise_payload.mass_init,
    "optimized_initial_mass_kg": cruise_payload_df.mass.iloc[0],
}

{'minimum_mass_kg': 52600.0,
 'initial_mass_lower_bound_kg': 52600.0,
 'initial_mass_upper_bound_kg': 76810.0,
 'm0_initial_guess_kg': 66300.0,
 'optimized_initial_mass_kg': np.float64(56600.404982006374)}

fig, axes = plt.subplots(2, 1, figsize=(9, 6), sharex=True)

for label, df in {
    "fixed m0": cruise_fixed_df,
    "payload optimized": cruise_payload_df,
}.items():
    distance_km = along_track_distance_km(df)
    axes[0].plot(distance_km, df.altitude, label=label)
    axes[1].plot(distance_km, df.mass, label=label)

axes[0].set_ylabel("Altitude [ft]")
axes[1].set_ylabel("Mass [kg]")
axes[1].set_xlabel("Distance [km]")
axes[0].legend()
axes[1].legend()
fig.tight_layout()

CompleteFlight Example

The same payload= behavior is available for CompleteFlight.

full_fixed, full_fixed_df = run_case(top.CompleteFlight)
full_payload, full_payload_df = run_case(top.CompleteFlight, payload=payload)

pd.DataFrame(
    [
        summarize("complete flight: fixed m0", full_fixed, full_fixed_df),
        summarize("complete flight: payload optimized", full_payload, full_payload_df),
    ]
)

/home/junzi/arc/code/1-public/opentop/opentop/full.py:37: UserWarning: payload is provided; m0 is used only as the initial mass guess and does not fix the initial mass.
  super().__init__(

	case	success	status	initial_mass_kg	final_mass_kg	fuel_burn_kg	estimated_fuel_onboard_kg	flight_time_min	max_altitude_ft
0	complete flight: fixed m0	True	Solve_Succeeded	66299.999905	61004.928140	5295.071765	23699.999905	118.405395	36055.0
1	complete flight: payload optimized	True	Solve_Succeeded	57270.367327	52599.999901	4670.367427	4670.367327	118.438900	40384.0

fig, axes = plt.subplots(2, 1, figsize=(9, 6), sharex=True)

for label, df in {
    "fixed m0": full_fixed_df,
    "payload optimized": full_payload_df,
}.items():
    distance_km = along_track_distance_km(df)
    axes[0].plot(distance_km, df.altitude, label=label)
    axes[1].plot(distance_km, df.mass, label=label)

axes[0].set_ylabel("Altitude [ft]")
axes[1].set_ylabel("Mass [kg]")
axes[1].set_xlabel("Distance [km]")
axes[0].legend()
axes[1].legend()
fig.tight_layout()