Abstract: A co-working equations solving method based on neural network was proposed for turbo-shaft engine modeling. The back propagation (BP) neural network，for equations solving，was trained by the off-line data gathered from the model based on Newton - Raphson (N-R) method. The inputs of the network were the residuals of the co-working equations before N-R iteration start. The outputs of the network were the adjustment of the equation guess value after N-R iteration convergence. The varying zoom factor firefly algorithm was adopt to optimize the neural network parameters，and the adjustment of the equation guess value prediction accuracy was enhanced. The training data were gathered from the nominal engine model in certain area of the envelope，and the simulation state of the helicopter was flying forward. The parameters of the network train by the varying zoom factor firefly – BP method was applied to solve the co-working equation of the component level model of turbo shaft engine. The tests were carried out during the helicopter climbing at the envelope of training data gathering area，during the helicopter flying forward at the envelope far from the training data gathering area. The deviations of the model output to that of the model based on N-R method were calculated and compared with the single iteration per time step method，the max model output deviations of the proposed method are about 1/34 to 1/4 to that of the single iteration per time step method，and the time consuming of the model based on the proposed method is about 2/5 to that of the single iteration per time step method. The simulation results show the validation of the proposed method.

Key words: Turbo-shaft engine；Mathematical model；Co-working equation；BP Neural network；Firefly algorithm

摘要： 提出了基于神经网络的涡轴发动机共同工作方程求解方法。在基于牛顿-拉夫逊迭代法求解共同工作方程的模型上采集离线训练数据，以共同工作方程迭代求解前的残差为输入，迭代收敛后的共同工作方程猜值修正量为输出，训练BP神经网络，对共同工作方程进行求解。采用变缩放因子的萤火虫算法优化神经网络参数，提高了猜值修正量的预测精度。在飞行包线的某一区域内，采集额定发动机在直升机前飞过程的数据进行神经网络离线训练，并将网络参数代入部件级模型对共同工作方程进行求解，在训练数据采集区域附近的爬升状态、远离训练数据采集区域的前飞状态下进行测试，计算模型输出与牛顿-拉夫逊迭代算法模型输出的偏差，与一次通过算法相比，本文提出方法模型输出最大偏差约为一次通过算法的1/34到1/4，模型运行耗时约为一次通过算法的2/5，验证了算法的有效性。

关键词: 涡轴发动机；数学模型；共同工作方程；BP神经网络；萤火虫算法