摘要
非线性有源自回归(Nonlinear Auto Regressive eXogenous,NARX)模型在辨识过程中要求以随机激励作为输入信号,由于转子系统无法产生该信号,因此传统辨识方法不适用于此类系统。针对该问题,提出一种频域模型结构及对应的扫频辨识方法。首先,通过快速傅里叶变换(Fast Fourier Transform,FFT)得到系统扫频过程中全部时域响应的频谱,提取关键频率成分对应的频域数据,并组建频域模型结构下的候选模型项库。其次,引入基于预测残差平方和的正交向前回归算法(the Orthogonal Forward Regression algorithm,based on the Predictive Residual Sum of Squares,PRESS-based OFR)完成模型项选取。最后,通过简单转子系统数学模型得到的仿真数据及转子实验台得到的真实数据验证所提出建模方法的有效性和适用性,同时,也通过上述两种数据探讨了扫频过程中引入不同的频率成分信息对预测精度的影响。结果表明,采用频域数据得到的模型结构和对应的系数能准确预测系统时域响应。在仿真数据上,模型预测的归一化均方误差(Normalized Mean Square Error,NMSE)不超过0.3%,而实验数据的NMSE进一步降低至0.2%。此外,通过对比不同模型结构,包含二倍频对应数据的模型(模型二)在预测系统二倍频处对应的幅值时的精度比仅使用基频数据建立的模型(模型一)更准确,NMSE在转速为339.3 rad/s工况下提升了95.58%;因此,丰富的频域数据信息有利于得到更准确的模型,提出的方法为谐波激励系统的辨识提供了新思路。
The identification of rotor systems via traditional Nonlinear Auto Regressive eXogenous(NARX)models was not feasible due to the absence of random excitation signals.A novel frequency domain model structure and an accompanying frequency sweep identification method were proposed to address this limitation.The system′s time-domain response spectrum during the frequency sweep was captured using Fast Fourier Transform(FFT).Key frequency components′data were extracted to construct a candidate model term library within the frequency domain model framework.The Orthogonal Forward Regression algorithm,based on the Predictive Residual Sum of Squares(PRESS-based OFR),was employed for model term selection.The proposed modeling method′s effectiveness and applicability were validated using simulation data from a simple rotor system′s mathematical model and actual data from a rotor test rig.The influence of different frequency component information introduced during the frequency sweep on prediction accuracy was also explored.The models derived from frequency domain data were found to accurately predict the system′s time-domain response.The Normalized Mean Square Error(NMSE)of the model predictions was less than 0.3%for simulation data and further reduced to 0.2%for experimental data.Additionally,the model incorporating data for the second harmonic(Model 2)demonstrated higher accuracy in predicting the amplitude at the system′s second harmonic compared to the model using only fundamental frequency data(Model 1),with a 95.58%increase in NMSE at a rotational speed of 339.3 rad/s.The inclusion of rich frequency domain data information in the model term library is advantageous for achieving greater model accuracy,offering a new perspective for the identification of systems subjected to harmonic excitation.
作者
李玉奇
龙天亮
温传美
LI Yuqi;LONG Tianliang;WEN Chuanmei(School of Mechanical Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China;School of Electronic Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China)
出处
《现代制造工程》
北大核心
2025年第12期11-18,157,共9页
Modern Manufacturing Engineering
基金
国家自然科学基金资助项目(52305098)
广西自然科学基金资助项目(2024GXNSFBA010286,2022GXNSFBA035488)
广西科技计划资助项目(桂科AD23026064)。
关键词
频域信息
NARX模型
系统辨识
转子系统
谐波激励
frequency domain information
NARX model
system identification
rotor system
harmonic excitation
