基于Levenberg-Marquardt算法的航空发动机模型求解混合算法

为了降低航空发动机非线性模型求解的收敛性要求，将模型非线性方程组的求解问题转化为最小二乘问题，提出了基于Levenberg-Marquardt(L-M)算法的混合算法。为了使L-M算法跳出局部解，混合算法使用动力学方法修正局部解；为了提高计算效率，利用Broyden拟牛顿法加速L-M算法。以涡扇发动机为研究对象，应用混合算法、L-M算法、牛顿法和Broyden拟牛顿法进行稳态和瞬态仿真。结果表明：在稳态工况下，L-M算法和混合算法收敛范围更大，在随机初值条件下能达到90%以上的收敛率，远高于牛顿法和Broyden拟牛顿法不到20%的收敛率，且混合算法计算速度与Broyden拟牛顿法相当。在瞬态工况下，L-M算法和混合算法能够在牛顿法和Broyden拟牛顿法都不收敛的强瞬变工况收敛，且混合算法瞬态计算时间仅为Broyden拟牛顿法的1.13倍。仿真结果表明该算法在航空发动机模型求解上具有良好的适用性。

Hybrid algorithm for aero-engine model solving based on Levenberg-Marquardt algorithm

In order to reduce the convergence requirements for solving the nonlinear model of aeroengine, the problem of solving the model nonlinear equations was transformed into the least square problem. A hybrid algorithm based on Levenberg-Marquardt (L-M) algorithm was proposed. The hybrid algorithm avoided the local solution by modifying the local solution with dynamic method. Meanwhile, Broyden quasi-Newton method was used to accelerate the L-M algorithm. Targeting turbofan engine, the hybrid algorithm, L-M algorithm, Newton method and Broyden quasi-Newton method were used for steady-state and transient simulation. Results showed that: under the steady-state condition, if L-M algorithm and hybrid algorithm had larger convergence range, the convergence rate can reach more than 90% under the random initial value condition, much higher than the convergence rate of Newton method and Broyden quasi-Newton method which was less than 20%, and the calculation speed of hybrid algorithm was similar to that of Broyden quasi-Newton method. Under transient condition, L-M algorithm and hybrid algorithm can converge at strong transient condition where neither Newton method nor Broyden quasi-Newton method converged, and the transient computation time of hybrid algorithm was only 1.13 times that of Broyden quasi-Newton method. Simulation results show that the algorithm has good applicability in solving aero-engine model solving.