冲击载荷下频率响应函数的高斯过程回归方法

Gaussian process regression method for the frequency response function under impact loads

锤击法测试是学术和工业界广泛采用的实验模态分析方法,通常使用谱估计方法计算频率响应函数(FRF),极易受到测量数据长度和质量的影响。近年来,贝叶斯学习技术为系统和控制领域提供了一种新的探索途径。受此启发,应用复高斯过程对FRF的先验信息进行统计描述,发展了冲击载荷下FRF估计的贝叶斯推断方法,不仅得到了FRF的最大后验估计,还给出了FRF估计的方差。利用QR分解技术改善了超参数优化的数值正定性。通过数值算例和振动实验证明了提出方法的有效性和可靠性。

A hammering test is an experimental modal analysis method widely used in academia and industry.The spectral estimation method is usually used to calculate the frequency response function(FRF),which is extremely susceptible to length and quality of the measurement data.In recent years,the Bayesian learning technology has provided a new exploration approach for the system and the control field.Inspired by this,the prior information of the FRF is statistically described by a complex Gaussian process,and a Bayesian inference method is developed for estimating the FRF under impact loads.The maximum posteriori estimation of the FRF is obtained,and the variance of the FRF estimation is also given.Furthermore,the numerical positive definiteness for optimizing the hyper-parameters is improved by applying QR decomposition.Finally,the effectiveness and reliability of the proposed method are verified by numerical examples and vibration experiments.