4D commercial trajectory optimization for fuel saving and environmemtal impact reduction

The 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.O principal objetivo desta tese é otimizar as trajetórias em 4D de aeronaves comerciais, de forma a melhorar a eficiência de voo e reduzir o consumo de combustível e o impacto ambiental causado pelos aviões. A técnica de otimização de trajetória pode ser utilizada para atingir este objetivo. A formulação do problema de otimização de trajetória de uma aeronave envolve o modelo matemático do sistema (isto é, modelo de dinâmica, modelo de desempenho, e modelo de emissões de aeronaves), a função objetiva e os limites e restrições do sistema. Normalmente, o problema de otimização de trajetória é solucionado por uma ampla variedade de abordagens numéricas, que podem ser classificadas em três classes básicas de métodos numéricos: métodos indiretos, métodos diretos e programação dinâmica. Nesta tese, foram consideradas várias instâncias de problemas para otimizar trajetórias de aeronaves comerciais. Em primeiro lugar, foi considerado um problema de geração de trajetória ótima em 4D a partir de redes de waypoints predefinidas. Para tal, foi aplicado um algoritmo de single source shortest path (neste caso, algoritmo de Dijkstra), de forma a gerar trajetórias ótimas que minimizem o consumo de combustível da aeronave e o seu tempo total de viagem. O algoritmo de Dijkstra encontrou com sucesso a trajetória com menor custo, isto é, a trajetória de menor consumo de combustível e menor tempo total de viagem, a partir da rede predefinida de waypoints. Em seguida, foi considerado o problema de gerar uma trajetória ótima em 4D de comprimento mínimo ao longo de um conjunto de waypoints predefinidos. Para tal, foi utilizada uma parametrização da spline cúbica. O vetor de estado, a sua derivada e o vetor de controlo são parametrizados utilizando a interpolação cúbica da spline. Consequentemente, a função objetivo e as restrições são expressas como funções do valor de estado e controlo nos nós temporais. Esta representação transforma o problema de otimização de trajetória em um problema de programação não-linear, que por sua vez, é resolvido numericamente por um solucionador já bem estabelecido de programação não-linear. O método proposto gerou uma trajetória ótima em 4D com resultados precisos. Posteriormente, considerou-se o problema de geração de trajetórias ótimas em 4D entre dois waypoints. Para solucionar este problema foi utilizado a programação dinâmica que é um método numérico já bem estabelecido. A programação dinâmica apresenta algumas deficiências que impedem o seu uso em muitas aplicações práticas de tempo-real. Por isso, esta tese propõe uma abordagem de programação dinâmica modificada que reduz o esforço computacional e supera as desvantagens do Programação Dinâmica tradicional. A abordagem programação dinâmica modificada proposta, foi implementada com sucesso em vários casos de estudo, em que foram geradas trajetórias ótimas que minimizam o consumo de combustível da aeronave e as suas emissões. Estas trajetórias são, posteriormente, comparadas com a trajetória de voo comercial de referência, para quantificar a potencial redução do consumo de combustível da aeronave e das suas emissões. Os exemplos numéricos demonstram que a programação dinâmica modificada pode gerar com sucesso e com pouco esforço computacional trajetórias ótimas para o combustível e as emissões, o que sugere que este método pode ser aplicado em situações online, isto é, geração de trajetórias online. Por fim, foi considerado o problema de previsão da taxa temporal de consumo de combustível (FF) a partir de dados de voo reais. A rede neural da função de base radial (RBF) foi aplicada para prever a essa mesma taxa temporal nas fases de voo: subida, cruzeiro e descida. Na aplicação da rede neural RBF, a velocidade real e a altitude de voo foram consideradas como parâmetros de entrada e a FF foi considerada como parâmetro de saída. A rede neural RBF foi capaz de produzir um modelo adequado para estimar corretamente essa taxa temporal, com um elevado valor de coeficientes de determinação, juntamente com baixos valores nos erros relativos de aproximação. Posteriormente, este modelo de FF foi utilizado para resolver o problema de otimização de trajetórias em 4D, em que o custo total entre dois waypoints foi otimizado

Air Vehicle Optimal Trajectories for Radar Exposure Minimization

This study addresses the problem of analyzing the single vehicle path planning problem for radar exposure minimization. The calculus of Variations and optimal control are applied to formulate the cost function and numerical algorithms are used to solve for the optimal paths. Cost sensitivity to path length is analyzed for flight against one radar; a second radar is then included in the formulation and the optimal path for flight between the radars is found for cases of equal and unequal radar power. The costs of the optimal path, direct path, and Voronoi diagram-generated paths are compared. Results indicate low sensitivity of the cost to suboptimal paths for flight versus one radar; against two radars, approaching the Voronoi curves optimally from the endpoints may be feasible for on-line use

Hybrid Solution of Stochastic Optimal Control Problems using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms

Two numerical methods, Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithm, were combined to form a hybrid algorithm for solving nonlinear optimal control and optimal path planning problems with uncertain parameters. The algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a mission planning problem sponsored by USSTRATCOM. The mission planning scenario was constructed to find the path that minimizes the probability of being killed by lethal threats whose locations are uncertain to statistically quantify the effects those uncertainties have on the flight path solution, and to use the statistical properties to estimate the probability that the vehicle will be killed during mission execution. The results demonstrated that the method is able to effectively characterize how the optimal solution changes with uncertainty and that the results can be presented in a form that can be used by mission planners and aircrews to assess risks associated with a mission profile

An interactive fuzzy physical programming for solving multiobjective skip entry problem

The multi-criteria trajectory planning for Space Manoeuvre Vehicle (SMV) is recognised as a challenging problem. Because of the nonlinearity and uncertainty in the dynamic model and even the objectives, it is hard for decision makers to balance all of the preference indices without violating strict path and box constraints. In this paper, to provide the designer an effective method and solve the trajectory hopping problem, an Interactive Fuzzy Physical Programming (IFPP) algorithm is introduced. A new multi-objective SMV optimal control problem is formulated and parameterized using an adaptive technique. By using the density function, the oscillations of the trajectory can be captured effectively. In addition, an interactive decision-making strategy is applied to modify the current designer’s preferences during optimization process. Two realistic decision-making scenarios are conducted by using the proposed algorithm; Simulation results indicated that without driving objective functions out of the tolerable region, the proposed approach can have better performance in terms of the satisfactory degree compared with other approaches like traditional weighted-sum method, Goal Programming (GP) and fuzzy goal programming (FGP). Also, the results can satisfy the current preferences given by the decision makers. Therefore, The method is potentially feasible for solving multi-criteria SMV trajectory planning problems

Analysis of optimization strategies for solving space manoeuvre vehicle trajectory optimization problem

In this paper, two types of optimization strategies are applied to solve the Space Manoeuvre Vehicle (SMV) trajectory optimization problem. The SMV dynamic model is constructed and discretized applying direct multiple shooting method. To solve the resulting Nonlinear Programming (NLP) problem, gradient-based and derivative free optimization techniques are used to calculate the optimal time history with respect to the states and controls. Simulation results indicate that the proposed strategies are effective and can provide feasible solutions for solving the constrained SMV trajectory design problem