基于近似似然的频响函数不确定性模型修正

Uncertainty Model Updating of Frequency Response Function Based on Approximate Likelihood Function

贝叶斯模型修正框架下,以频响函数作为目标,提出了一种使用近似似然函数的不确定性模型修正方法。相比于模态参数,频响函数包含了结构更加充分的信息,用于结构动力学模型修正时有诸多优点,但现有的不确定性模型修正方法并不能很好地实现将频响函数作为目标进行修正。针对此问题,介绍了频响函数和贝叶斯框架下的不确定性模型修正理论,基于近似贝叶斯计算提出了一种近似似然函数,可适用于频响函数作为目标进行不确定性修正。将提出的似然函数应用到三自由度数值和H型非对称梁的有限元模型修正算例中,并结合DREAM算法对不确定性参数进行识别。研究结果表明:修正后参数的上、下限与目标值相差无几,修正后模型的频响函数与目标值几乎重合,在一定噪声水平下仍具有较好的修正效果,验证了所提方法的有效性。

An uncertainty model updating method,which is targeted at frequency response function and using an approximate likelihood function,is proposed under the Bayesian framework.Compared with modal parameters,the frequency response function contains more structural information which offers advantages in finite element model updating of structural dynamics.However,the current uncertainty model updating methods rarely work well with a target of the frequency response function.In light of this problem,the uncertainty model updating theory under the Bayesian framework is introduced.An approximate likelihood function suitable based on the approximate Bayesian computational method is presented for the uncertainty model updating with e tfrequency response function.The proposed uncertainty model updating method is verified on a vibration system with three-degree-of-freedom and an unsymmetrical H-shaped beam.The DREAM algorithm is introduced to identify the parameters.The results show that the upper and lower bounds of updated parameters as well as the frequency response function of the updated model vary little from the desired values.The uncertainties are well updated under noise,which verifies the effectiveness of the proposed method.