飞机颤振模态参数辨识的期望最大化

The Application of Expectation Maxmization Algorithm in Aircraft Flutter Model Parameter Identification

文章采用一种适用于噪声环境的期望最大化算法,准确地辨识飞机的颤振模态参数。在建立随机状态空间模型的基础上,该算法以迭代的形式计算似然函数的最大值,它包括两步:期望和最大化。无需计算对数似然函数的二阶偏导及其近似式,可提高似然函数收敛于平稳点的可能性。算前采用新息方差准则估计出系统的阶数,以减少计算复杂度。最后利用试飞试验数据辨识飞机的系统参数,验证了其方法的有效性。

The traditional least- squares identification method gives biased parameter estimates when the observed input -output data are corrupted by noises. A general EM algorithm is adopted for aircraft flutter model parameter identification under the noisy environment. The EM algorithm is an iterative algorithm based on the stochastic state space model. It is used to compute the maximum value for the likelihood function that consists of two steps ： namely the E - and M - steps. No calculation of the second order derivatives or approximated values is needed. This algorithm can increase the likelihood function converging to a stationary point. Before applying the algorithm,the innovation variance criterion is used to estimate the system＇s order in order to decrease the complexity. Finally the efficiency of this method is illustrated with a simulation example.