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.

随着修剪分析中未知数的增加，问题变得更加复杂，传统方法开始失效。传统方法的常见问题可能是病态矩阵、舍入误差和被零除。此外，这些方法可能会找到局部最优值，而不是全局最优值。在这种情况下，建议与遗传算法等智能方法混合使用。本研究选取牛顿-拉夫森法难以求解的飞行情况进行六自由度非线性配平分析。修剪分析分别使用 Newton-Raphson 方法、遗传算法和它们的混合使用进行。尽管初始猜测非常好，但 Newton-Raphson 方法存在收敛问题。遗传算法能够自己解决同样的问题。纵倾分析中的未知数，例如升降舵、方向舵和副翼的偏转角，具有物理限制，而这些限制使常规方法更加复杂，并且在遗传算法中使用这些限制的能力缩小了解空间和减少计算时间。GA 和 Newton-Raphson 方法的混合使用显着提高了 Newton-Raphson 方法的性能并消除了收敛问题。研究表明，传统数值方法（如 Newton-Raphson 方法）难以求解的 6 自由度修整问题可以通过混合使用 GA 和 Newton- 轻松有效地求解。拉夫森法。