Comparison of the Newton–Raphson Method and genetic algorithm solutions for nonlinear aircraft trim analysis

Abstract

As the number of unknowns in trim analysis increases, the problem becomes more complicated, and traditional methods begin to fail. Common problems with conventional methods may be an ill-conditioned matrix, rounding errors, and division by zero. Furthermore, these methods are likely to find the local optimum, not the global optimum. In such cases, hybrid use with intelligent methods such as genetic algorithms is recommended. In this study, a flight situation that the Newton–Raphson method has for difficulty in solving is selected for a six-degree-of-freedom nonlinear trim analysis. Trim analysis was performed using the Newton–Raphson method, genetic algorithm, and by their hybrid use, respectively. The Newton–Raphson method had convergence problems despite very good initial guesses. The genetic algorithm was able to solve the same problem by itself. The unknowns in trim analysis, such as deflection angles of an elevator, a rudder, and an aileron, have physical limits, whereas the constraints make conventional methods more complicated, and the ability to use these limits in the genetic algorithm narrows the solution space and reduces the computation time. The hybrid use of the GA and Newton–Raphson method significantly increased the performance of the Newton–Raphson method and eliminated the convergence problem. It has been shown that a 6-degree-of-freedom trim problem, which traditional numerical methods such as the Newton–Raphson method have for difficulty in solving, can be solved easily and effectively with the hybrid use of the GA and the Newton–Raphson method. The strength of the proposed hybrid method to solve a highly nonlinear trim problem was demonstrated.

Stick-free Flight Stability Problem Revisited: A Modeling and Simulation Approach

“…Combining appropriate control surface deflections and aircraft states to allow the aircraft to carry out the specified flight task can be a definition of trimming an aircraft [32]. The aircraft trim problem has been solved using an optimization approach for years and is still discussed with various optimization methods as well as under different flight circumstances [33][34][35][36][37]. However, the stick-free level flight trim algorithm has been never discussed, and no open public study exists.…”