不确定转子系统动力学降阶模型构建与模型散度参数辨识

Construction method of dynamical reduced order model of uncertain rotor systems and identification of model dispersion parameters

在航空、航天、船舶等领域的实际工程转子系统中,广泛存在高维复杂的非线性系统。在航空发动机转子系统、燃气轮机转子系统等重点研究领域,通常还难以对高维复杂非线性系统进行直接的数据处理和分析统计。针对不确定性转子系统的模型维度较高等问题,提出了一种模型不确定性动力学降阶计算模型构建和模型散度参数辨识方法。首先,根据确定性动力学模型和静态矩阵降阶方法,完善了确定性动力学降阶模型;然后,基于随机矩阵理论和非参数动力学建模方法,提出了不确定性动力学降阶模型;最后,利用系统确定性模型的一阶临界转速、振型和实验数据,对不确定性动力学模型的散度参数进行了辨识;为了验证散度参数辨识方法的有效性,笔者又在转子实验平台上进行了实验验证。研究结果表明:实验结果与降阶之后振动响应均值的差异性较小,且与不确定性动力学模型相差不超过10%,表明所采用的理论模型在描述转子系统行为方面具备了较高的准确性和可靠性,该模型可以为深入研究模型不确定性转子系统提供参考。

High dimensional and complex nonlinear systems widely exist in practical engineering rotor systems such as aviation,aerospace and shipbuilding.In the key research fields such as aviation engine rotor systems and gas turbine rotor systems,these high-dimensional complex systems are often difficult to directly process data and analyze statistics.A method of construction of dynamical reduced order model of uncertain rotor systems and identification of model dispersion parameters was proposed to address the problem of high model dimensions in uncertain rotor systems.Firstly,based on the deterministic dynamic model and the static matrix reduction method,the deterministic dynamic reduction model was further improved.Then,based on random matrix theory and non-parametric dynamic modeling methods,an uncertain dynamic reduction model was proposed.Finally,the divergent parameters of the uncertain dynamic model were identified using the first-order critical speed,vibration mode,and experimental data of the system deterministic model.The identification results of divergence parameters were experimentally verified on a rotor experimental platform.The research results indicate that the difference between the experimental results and the mean vibration response after reducing the order is small,and the difference between the experimental results and the uncertain dynamic model is not more than 10%,indicating that the theoretical model used has high accuracy and reliability in describing the behavior of the rotor system.This model can provide a reference for further research on the uncertain rotor system of the model.