Flight Path Optimization via Nonlinear Programming
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Solution Overview
Problem
Existing flight management systems (FMS) rely on outdated assumptions and constant constraints, such as constant aircraft speed during climb, which do not accurately represent real-world conditions, limiting their ability to generate optimized flight paths that minimize fuel consumption and adhere to realistic operational constraints.
Innovation Solution
The use of nonlinear programming techniques to model actual aircraft and engine performance characteristics, eliminating arbitrary constraints and optimizing flight paths by minimizing fuel consumption while satisfying altitude-speed, altitude-distance, and speed-distance constraints, using a system that determines optimal control trajectories for climb, cruise, and descent phases.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If constant speed assumption is used during climb phase, then calculation complexity is reduced and legacy systems can operate, but fuel consumption optimization is compromised and real-world constraints are not satisfied
Solution Approach 1:
The patent transitions from static constant speed assumptions to dynamic speed profiles that adapt to real-world constraints. The system uses nonlinear programming to determine optimal speed as a function of altitude, distance, and time, allowing the aircraft to vary speed throughout the climb phase rather than maintaining a fixed constant value, thereby achieving both optimization and realism.
Solution Approach 2:
The invention changes the fundamental parameters from constant values to variable functions. Instead of assuming constant speed, the system optimizes speed as a varying parameter along the flight path. This allows the aircraft to operate at different speeds at different altitudes and positions, achieving fuel savings while satisfying operational constraints that were previously ignored.
2Device complexity
If lookup tables with constant values are used, then system simplicity is maintained, but accuracy of flight path optimization is reduced
Solution Approach 1:
The patent replaces the mechanical lookup table approach with a computational optimization system. Instead of relying on pre-computed constant values from tables, the system uses nonlinear programming algorithms to calculate optimal flight paths in real-time based on actual aircraft performance data and constraints, significantly improving accuracy while maintaining computational feasibility through modern processing capabilities.
Solution Approach 2:
The system performs preliminary formulation of the optimization problem by defining the cost function and constraints before execution. By pre-defining the mathematical model, objective function, and constraint equations, the system prepares the optimization framework in advance, allowing accurate real-time calculations without requiring complex runtime decision-making, thus balancing accuracy with computational efficiency.
3Adaptability or versatility
If arbitrary constraints are imposed on flight paths, then legacy system compatibility is maintained, but operational efficiency and fuel savings are limited
Solution Approach 1:
The patent removes static arbitrary constraints and replaces them with dynamic constraint formulations that reflect real operational requirements. Instead of imposing fixed speed limits or rigid flight path restrictions, the system uses inequality constraints in the nonlinear programming formulation that allow flexibility within safe and efficient operating envelopes, enabling the aircraft to adapt its flight path continuously for optimal performance.
Solution Approach 2:
The invention changes constraint parameters from fixed arbitrary values to variable bounds based on actual aircraft performance and operational requirements. The system formulates constraints as mathematical inequalities that define feasible regions in the state space, allowing the optimizer to find solutions that satisfy safety and operational requirements while maximizing fuel efficiency, rather than being forced into suboptimal constant-speed trajectories.
Data Source
AI summary
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.