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- 4D commercial trajectory optimization for fuel saving and environmemtal impact reductionPublication . Ahmed, Kawser; Bousson, KouamanaThe main purpose of the thesis is to optimize commercial aircraft 4D trajectories to improve flight efficiency and reduce fuel consumption and environmental impact caused by airliners. The Trajectory Optimization Problem (TOP) technique can be used to accomplish this goal. The formulation of the aircraft TOP involves the mathematical model of the system (i.e., dynamics model, performance model, and emissions model of the aircraft), Performance Index (PI), and boundary and path constraints of the system. Typically, the TOP is solved by a wide range of numerical approaches. They can be classified into three basic classes of numerical methods: indirect methods, direct methods, and dynamic programming. In this thesis, several instances of problems were considered to optimize commercial aircraft trajectories. Firstly, the problem of optimal trajectory generation from predefined 4D waypoint networks was considered. A single source shortest path algorithm (Dijkstra’s algorithm) was applied to generate the optimal aircraft trajectories that minimize aircraft fuel burn and total trip time between the initial and final waypoint in the networks. Dijkstra’s Algorithm (DA) successfully found the path (trajectory) with the lowest cost (i.e., fuel consumption, and total trip time) from the predefined 4D waypoint networks. Next, the problem of generating minimum length optimal trajectory along a set of predefined 4D waypoints was considered. A cubic spline parameterization was used to solve the TOP. The state vector, its time derivative, and control vector are parameterized using Cubic Spline Interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into a Nonlinear Programming (NLP) problem, which is then solved numerically using a well-established NLP solver. The proposed method generated a smooth 4D optimal trajectory with very accurate results. Following, the problem considers generating optimal trajectories between two 4D waypoints. Dynamic Programming (DP) a well-established numerical method was considered to solve this problem. The traditional DP bears some shortcomings that prevent its use in many practical real-time implementations. This thesis proposes a Modified Dynamic Programming (MDP) approach which reduces the computational effort and overcomes the drawbacks of the traditional DP. The proposed MDP approach was successfully implemented to generate optimal trajectories that minimize aircraft fuel consumption and emissions in several case studies, the obtained optimal trajectories are then compared with the corresponding reference commercial flight trajectory for the same route in order to quantify the potential benefit of reduction of aircraft fuel consumption and emissions. The numerical examples demonstrate that the MDP can successfully generate fuel and emissions optimal trajectory with little computational effort, which implies it can also be applied to online trajectory generation. Finally, the problem of predicting the fuel flow rate from actual flight data or manual data was considered. The Radial Basis Function (RBF) neural network was applied to predict the fuel flow rate in the climb, cruise, and descent phases of flight. In the RBF neural network, the true airspeed and flight altitude were taken as the input parameters and the fuel flow rate as the output parameter. The RBF neural network produced a highly accurate fuel flow rate model with a high value of coefficients of determination, together with the low relative approximation errors. Later on, the resulted fuel flow rate model was used to solve a 4D TOP by optimizing aircraft green cost between two 4D waypoints.
- Nonlinear Time-varying Parameter Estimation from Noisy MeasurementsPublication . Coelho, Milca; Bousson, K.; Ahmed, KawserOnline parameter estimation for time-varying systems is a fundamental part of adaptive control, real-time system monitoring and prediction. A well-known framework for dealing with such a task is the Kalman filtering. Meanwhile Kalman filtering may be cumbersome for some time-critical systems and inappropriate for systems whose stochastic characteristics are not Gaussian. To overcome these shortcomings, a parameter estimation algorithm devised from Sutton’s dynamic learning rate techniques and based on a learning window and forgetting factor criterion has been used. In doing so, the proposed algorithm avoids the need for heuristic choices of the initial conditions and noise covariance matrices required by the Kalman filtering. The performance of the proposed method is demonstrated successfully on a lateral-directional flight dynamics parameter estimation process for an unmanned aerial vehicle through computational simulation.
- Optimal Fuel Saving in 4D Waypoint NetworksPublication . Ahmed, Kawser; Coelho, Milca; Bousson, K.The purpose of this work is to develop a trajectory optimization method that generates a fuel optimal trajectory from a predefined 4D waypoint networks, where the arrival time is specified for each waypoint in the network. A single source shortest path algorithm is presented to generate the optimal flight trajectory that minimizes fuel burn. Generating such trajectories enables the airlines to cope with increasing fuel costs and to reduce aviation induced climate change, as emission is directly related to the amount of fuel burn. Two case studies were considered and the simulation results showed that flying a fuel optimal trajectory based on the proposed algorithm leads to a reduction of average fuel consumption on international flights by 2-4% compared with the conventional trip fuel.
- Spline parameterization based nonlinear trajectory optimization along 4D waypointsPublication . Ahmed, Kawser; Bousson, K.; Coelho, MilcaFlight trajectory optimization has become an important factor not only to reduce the operational costs (e.g.,, fuel and time related costs) of the airliners but also to reduce the environmental impact (e.g.,, emissions, contrails and noise etc.) caused by the airliners. So far, these factors have been dealt with in the context of 2D and 3D trajectory optimization, which are no longer efficient. Presently, the 4D trajectory optimization is required in order to cope with the current air traffic management (ATM). This study deals with a cubic spline approximation method for solving 4D trajectory optimization problem (TOP). The state vector, its time derivative and control vector are parameterized using cubic spline interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into nonlinear programming problem (NLP). The proposed method is successfully applied to the generation of a minimum length optimal trajectories along 4D waypoints, where the method generated smooth 4D optimal trajectories with very accurate results.
- Generating Time Optimal Trajectory from Predefined 4D waypoint NetworksPublication . Ahmed, Kawser; Bousson, K.The main purpose of this paper is to develop a trajectory optimization method to generate optimal trajectories that minimize aircraft total trip time between the initial and final waypoint in predefined 4D waypoint networks. In this paper, the 4D waypoint networks only consist of waypoints for climb, cruise and descent approach without the take-off and landing approach phases. The time optimal trajectory is generated for three different lengths of flights (short, medium, and long-haul flight) for two different commercial aircraft and considering zero wind condition. The Results about the presented applications show that by flying a time optimal trajectory, which was found by applying a single source shortest path algorithm (Dijkstra’s algorithm), can lead to the reduction of average travel time by 2.6% with respect to the total trip time.
- 4D Fuel Optimal Trajectory Generation from Waypoint NetworksPublication . Ahmed, Kawser; Bousson, KouamanaThe purpose of this thesis is to develop a trajectory optimization algorithm that finds a fuel optimal trajectory from 4D waypoint networks, where the arrival time is specified for each waypoint in the network. Generating optimal aircraft trajectory that minimizes fuel burn and associated environmental emissions helps the aviation industry cope with increasing fuel costs and reduce aviation induced climate change, as CO2 is directly related to the amount of fuel burned, therefore reduction in fuel burn implies a reduction in CO2 emissions as well. A single source shortest path algorithm is presented to generate the optimal aircraft trajectory that minimizes the total fuel burn between the initial and final waypoint in pre-defined 4D waypoint networks. In this work the 4D waypoint networks only consist of waypoints for climb, cruise and descent phases of the flight without the takeoff and landing approach. The fuel optimal trajectory is generated for three different lengths of flights (short, medium and long haul flight) for two different commercial aircraft considering no wind. The Results about the presented applications show that by flying a fuel optimal trajectory, which was found by implying a single source shortest path algorithm (Dijkstra’s algorithm) can lead to reduction of average fuel burn of international flights by 2.8% of the total trip fuel. By using the same algorithm in 4D waypoints networks it is also possible to generate an optimal trajectory that minimizes the flight time. By flying this trajectory average of 2.6% of total travel time can be saved, depends on the trip length and aircraft types.