Measurement uncertainty can affect the accuracy of estimating parameters of vibrating systems. This article is concerned with the development of a method for estimating parameters from the free vibration response of a nonlinear system in which the response signal is contaminated with Gaussian white noise. The backbone curve and envelope of the response are first estimated from the free vibration signal. An algorithm based on the Bayesian approach is then used to identify the stiffness and damping parameters of a nonlinear system excited at a single resonant frequency. A numerical example is provided to illustrate the proposed method, which is then applied to the experimental data from a nonlinear vibration absorber system that was excited at its first resonant frequency. The proposed approach provides the distribution and confidence intervals of the parameter estimates, which is an improvement on methods that provide a single number for each estimate. As the signal-to-noise ratio decreases, the variances of the posterior distributions increase as do the confidence intervals, reflecting greater uncertainty in the parameter estimates. The approach is effective provided that the signal-to-noise ratio is greater than about 10.

中文翻译：

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利用受高斯白噪声干扰的自由响应来识别非线性系统的刚度和阻尼

测量不确定度会影响振动系统参数估计的准确性。本文涉及一种从非线性系统的自由振动响应中估计参数的方法的开发，该系统的响应信号受到高斯白噪声的污染。首先根据自由振动信号估算响应的主干曲线和包络线。然后使用基于贝叶斯方法的算法来识别以单个共振频率激发的非线性系统的刚度和阻尼参数。提供了一个数值示例来说明所提出的方法，然后将其应用于来自非线性减振器系统的实验数据，该系统在其第一共振频率下被激发。所提出的方法提供了参数估计的分布和置信区间，这是对为每个估计提供单个数字的方法的改进。随着信噪比的降低，后验分布的方差和置信区间也随之增加，这反映了参数估计中的更大不确定性。如果信噪比大于约10，则该方法有效。