Flight path optimization using nonlinear programming

Patent metadata

Field	Value
Publication number	US-9564056-B1
Application number	US-201514844892-A
Country	US
Kind code	B1
Filing date	Sep 3, 2015
Priority date	Sep 3, 2015
Publication date	Feb 7, 2017
Grant date	Feb 7, 2017

Abstract

A method, medium, and system to receive a mathematical model representation of performance characteristics for an aircraft and an engine combination; perform a projection based model order reduction on the mathematical model representation; eliminate, based on the projected model, fast dynamics components of the mathematical model representation; determine a reduced order model, as a differential algebraic equation, wherein algebraic equations replace the fast dynamics; set a flight path angle and a throttle level angle as a control to minimize fuel consumption for the modeled aircraft and engine combination; discretize equations of motion for the modeled aircraft and engine combination and formulate optimization equations as a nonlinear programming problem; and determine an optimal open loop control that minimizes fuel consumption for the modeled aircraft and engine combination to climb to a prescribed cruise altitude and airspeed.

First claim

What is claimed is:

1. A method of optimizing an operational flight path for a particular aircraft using nonlinear programming, the method comprising:
receiving a mathematical model representation of performance characteristics for a particular aircraft and an engine combination, the mathematical model being applicable to at least one prescribed operating scenario and a representation of performance characteristics for the particular aircraft and engine combination including at least one of engine degradation characteristics, fuel burn as a function of flight variables, a flight dynamics model, and combinations thereof;
performing a projection based model order reduction on the mathematical model representation for the particular aircraft and an engine combination;
eliminating, based on the projected model, fast dynamics components of the mathematical model representation;
determining a reduced order model, as a differential algebraic equation, wherein algebraic equations replace the fast dynamics;
setting a flight path angle and a throttle lever angle as a control to minimize fuel consumption for the modeled aircraft and engine combination;
defining a climb terminal cost as a function of cruise altitude and an airspeed;
discretizing equations of motion for the modeled aircraft and engine combination and formulating optimization equations as a nonlinear programming problem;
determining an optimal open loop control that minimizes fuel consumption for the modeled aircraft and engine combination to climb to a prescribed cruise altitude and airspeed corresponding to the at least one prescribed operating scenario;
generating a flight path based on the determined optimal open loop control; and
navigating, based on the generated flight path, the particular aircraft and an engine combination in one of the prescribed operating scenarios.

2. The method of claim 1 , further comprising verifying the mathematical model representation of the performance characteristics for the aircraft and engine combination.

3. The method of claim 1 , wherein the fast dynamics components of the mathematical model representation are eliminated by setting a pitch moment and vertical forces for the modeled aircraft and engine combination to equilibrium values.

4. The method of claim 1 , further comprising determining a flight trajectory from the determined optimal open loop control and equations of motion for the modeled aircraft and engine.

5. The method of claim 1 , wherein a climb speed (and thrust) for the modeled aircraft and engine combination to climb to the prescribed cruise altitude and airspeed is variable.

6. The method of claim 1 , wherein the mathematical model representation of performance characteristics for the aircraft and engine combination comprises at least one of engine degradation characteristics, fuel burn as a function of flight variables, a flight dynamics model, and combinations thereof.

7. A non-transitory medium storing processor-executable program instructions, the medium comprising program instructions executable by a computer to:
receive a mathematical model representation of performance characteristics for a particular aircraft and an engine combination, the mathematical model being applicable to at least one prescribed operating scenario and a representation of performance characteristics for the particular aircraft and engine combination including at least one of engine degradation characteristics, fuel burn as a function of flight variables, a flight dynamics model, and combinations thereof;
perform a projection based model order reduction on the mathematical model representation;
eliminate, based on the projected model, fast dynamics components of the mathematical model representation;
determine a reduced order model, as a differential algebraic equation, wherein algebraic equations replace the fast dynamics;
set a flight path angle and a throttle lever angle as a control to minimize fuel consumption for the modeled aircraft and engine combination;
define a climb terminal cost as a function of cruise altitude and an airspeed;
discretize equations of motion for the modeled aircraft and engine combination and formulate optimization equations as a nonlinear programming problem;
determine an optimal open loop control that minimizes fuel consumption for the modeled aircraft and engine combination to climb to a prescribed cruise altitude and airspeed corresponding to the at least one prescribed operating scenario;
generate a flight path based on the determined optimal open loop control; and
navigate, based on the generated flight path, the particular aircraft and an engine combination in one of the prescribed operating scenarios.

8. The medium of claim 7 , further comprising program instructions executable by a computer to verify the mathematical model representation of the performance characteristics for the aircraft and engine combination.

9. The medium of claim 7 , wherein the fast dynamics components of the mathematical model representation are eliminated by setting a pitch moment and vertical forces for the modeled aircraft and engine combination to equilibrium values.

10. The medium of claim 7 , further comprising program instructions executable by a computer to determine a flight trajectory from the determined optimal open loop control and equations of motion for the modeled aircraft and engine.

11. The medium of claim 7 , wherein a climb speed (and thrust) for the modeled aircraft and engine combination to climb to the prescribed cruise altitude and airspeed is variable.

12. The medium of claim 7 , wherein the mathematical model representation of performance characteristics for the aircraft and engine combination comprises at least one of engine degradation characteristics, fuel burn as a function of flight variables, a flight dynamics model, and combinations thereof.

13. A system comprising:
a computing device comprising:
a memory storing processor-executable program instructions; and
a processor to execute the processor-executable program instructions to cause the computing device to:

receive a mathematical model representation of performance characteristics for a particular aircraft and an engine combination, the mathematical model being applicable to at least one prescribed operating scenario and a representation of performance characteristics for the particular aircraft and engine combination including at least one of engine degradation characteristics, fuel burn as a function of flight variables, a flight dynamics model, and combinations thereof;
perform a projection based model order reduction on the mathematical model representation;
eliminate, based on the projected model, fast dynamics components of the mathematical model representation;
determine a reduced order model, as a differential algebraic equation, wherein algebraic equations replace the fast dynamics;
set a flight path angle and a throttle level angle as a control to minimize fuel consumption for the modeled aircraft and engine combination;
define a climb terminal cost as a function of cruise altitude and an airspeed;
discretize equations of motion for the modeled aircraft and engine combination and formulate optimization equations as a nonlinear programming problem; and
determine an optimal open loop control that minimizes fuel consumption for the modeled aircraft and engine combination to climb to a prescribed cruise altitude and airspeed corresponding to the at least one prescribed operating scenario;
generate a flight path based on the determined optimal open loop control; and
navigate, based on the generated flight path, the particular aircraf

Assignees

• Gen Electric

Inventors

• Ghaemi Reza
• Westervelt Eric Richard
• Darnell Mark

Classifications

• G06F17/13

  Differential equations (using digital differential analysers G06F7/64) · CPC title

• G06F30/15

  Vehicle, aircraft or watercraft design · CPC title

• G06F30/20

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G01C21/20

  Instruments for performing navigational calculations (G01C21/24, G01C21/26 take precedence) · CPC title

• G05B13/04

  involving the use of models or simulators · CPC title