Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present...Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.展开更多
二次调节流量耦联系统为非线性系统,在Volterra级数描述该系统的基础上,通过SISO多项式类非线性系统的GFRF递推算式获得二次调节流量耦联系统的广义频率响应函数GFRF(generalized frequency response function).基于系统的GFRF,在频域...二次调节流量耦联系统为非线性系统,在Volterra级数描述该系统的基础上,通过SISO多项式类非线性系统的GFRF递推算式获得二次调节流量耦联系统的广义频率响应函数GFRF(generalized frequency response function).基于系统的GFRF,在频域内应用非线性控制理论为系统设计了镇定控制器和非线性H∞控制器,不仅使系统稳定,而且能达到无超调、无稳态误差.此外,在白噪声条件下证明该控制器比线性控制器抗干扰性强.展开更多
介绍了故障诊断技术的基本概念,重点阐述了非线性系统Volterra级数模型的原理及其在故障检测中的应用,并基于这一方法设计了飞机刹车系统惯性传感器故障检测设备。在这一应用系统中,被测系统的故障特征是广义频率响应函数GFRF(Generaliz...介绍了故障诊断技术的基本概念,重点阐述了非线性系统Volterra级数模型的原理及其在故障检测中的应用,并基于这一方法设计了飞机刹车系统惯性传感器故障检测设备。在这一应用系统中,被测系统的故障特征是广义频率响应函数GFRF(Generalized Frequency Response Functions)谱特征。简要介绍了故障诊断的方法,在工程应用实现中设计了相关的硬件电路,实验结果说明了此诊断方法是有效可行的。展开更多
为实现水轮机转轮状态及时有效地识别,运用基于模型的状态识别方法建立水轮机转轮模型,从而提取转轮不同状态下的特征,达到状态识别的目的。鉴于水轮机转轮模型的输入量非常复杂且不易测得的特点,假定水轮机转轮受到的不均匀力作为一个...为实现水轮机转轮状态及时有效地识别,运用基于模型的状态识别方法建立水轮机转轮模型,从而提取转轮不同状态下的特征,达到状态识别的目的。鉴于水轮机转轮模型的输入量非常复杂且不易测得的特点,假定水轮机转轮受到的不均匀力作为一个随机输入,利用水导轴承摆度作为输出,提出了基于Volterra模型盲辨识的水轮机转轮状态识别方法。利用在线监测系统中已有的水导轴承摆度数据作为输出,辨识出水轮机转轮Volterra时域模型。结合多维傅里叶变化,建立转轮的广义频率响应模型(generalized frequency response function,GFRF)。通过模型频域上的变化,分析转轮状态的变化。仿真实验和实例研究表明,Volterra模型盲辨识方法能够很好地反映原系统的频域特性,实现了水电机组转轮频域特征的良好提取,进而可采用该方法对水轮机转轮进行状态识别。展开更多
基金supported by the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10902068,51121063 and 10702039)+1 种基金the Shanghai Pujiang Program (10PJ1406000)the Opening Project of State Key Laboratory of Mechanical System and Vibration (MSV201103)
文摘Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
文摘二次调节流量耦联系统为非线性系统,在Volterra级数描述该系统的基础上,通过SISO多项式类非线性系统的GFRF递推算式获得二次调节流量耦联系统的广义频率响应函数GFRF(generalized frequency response function).基于系统的GFRF,在频域内应用非线性控制理论为系统设计了镇定控制器和非线性H∞控制器,不仅使系统稳定,而且能达到无超调、无稳态误差.此外,在白噪声条件下证明该控制器比线性控制器抗干扰性强.
文摘介绍了故障诊断技术的基本概念,重点阐述了非线性系统Volterra级数模型的原理及其在故障检测中的应用,并基于这一方法设计了飞机刹车系统惯性传感器故障检测设备。在这一应用系统中,被测系统的故障特征是广义频率响应函数GFRF(Generalized Frequency Response Functions)谱特征。简要介绍了故障诊断的方法,在工程应用实现中设计了相关的硬件电路,实验结果说明了此诊断方法是有效可行的。
文摘为实现水轮机转轮状态及时有效地识别,运用基于模型的状态识别方法建立水轮机转轮模型,从而提取转轮不同状态下的特征,达到状态识别的目的。鉴于水轮机转轮模型的输入量非常复杂且不易测得的特点,假定水轮机转轮受到的不均匀力作为一个随机输入,利用水导轴承摆度作为输出,提出了基于Volterra模型盲辨识的水轮机转轮状态识别方法。利用在线监测系统中已有的水导轴承摆度数据作为输出,辨识出水轮机转轮Volterra时域模型。结合多维傅里叶变化,建立转轮的广义频率响应模型(generalized frequency response function,GFRF)。通过模型频域上的变化,分析转轮状态的变化。仿真实验和实例研究表明,Volterra模型盲辨识方法能够很好地反映原系统的频域特性,实现了水电机组转轮频域特征的良好提取,进而可采用该方法对水轮机转轮进行状态识别。
