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针对非线性拟合法建立航空发动机状态变量模型过程中的初值问题,提出了一种能够避免该问题的线性拟合法,即在离散域情况下,利用已知的状态序列来构建系统矩阵与模型响应之间呈线性关系的目标函数,从而使非线性最小二乘问题转化为线性最小二乘问题.应用该方法建立某型涡扇发动机的小偏差状态变量模型,并与非线性拟合法进行了对比研究,结果表明该方法不仅避免了初值问题,而且具有较高的建模精度,从而验证了该方法的有效性.
Aiming at the initial value problem of aero-engine state variables model by non-linear fitting method, a linear fitting method that can avoid this problem is proposed. That is to say, in the case of discrete domain, the known state sequence is used to construct the system matrix and model Response to the linear relationship between the objective function, so that the nonlinear least squares problem into a linear least squares problem.Application of this method to establish a small turbofan engine small deviation state variable model, and with the non-linear fitting method The results show that this method not only avoids the initial value problem but also has higher modeling accuracy, which verifies the effectiveness of this method.