冲击振动测试因其方便、低成本，且单次冲击能同时激发多阶模态等特点，被广泛应用于模态分析中。为实现冲击测试中模态参数识别的高效求解和不确定性分析，提出一种快速贝叶斯快速傅里叶变换模态参数识别方法。该研究从频域结构振动方程入手，构建似然函数，基于拉普拉斯逼近算法以高斯概率分布形式近似求解模态参数的后验概率分布。首先，求得各模态参数的梯度并利用坐标下降法最小化负对数似然函数 (negative log likelihood function，NLLF)，此时得到的模态参数值即为后验均值。然后，基于矩阵代数手段，求得NLLF在后验均值处的二阶导数矩阵，其逆矩阵给出模态参数的后验协方差矩阵。最后，通过数值模拟和试验室测试数据验证该算法的准确性和高效性，以及相对于基于环境激振测试和自由振动测试的优越性。
Abstract
The impact vibration test is widely used in modal analysis, because of its convenience, low cost, and efficiency in identifying multiple modes with a single impact.To achieve efficient and accurate estimation and uncertainty quantification of modal parameters in the impact test, a fast Bayesian fast Fourier transform method was proposed.The likelihood function was first developed based on the equation of motion and the complex normal assumption of measurement error, and the Laplace approximation was then adopted to obtain the posterior distribution of modal parameters, i.e., fitting the posterior distribution with a Gaussian distribution, whose mean was computed by minimizing the negative log likelihood function (NLLF) while the covariance matrix was obtained by taking the inverse of the Hessian matrix of NLLF at the posterior mean.A coordinate descent algorithm was proposed to minimize the NLLF taking advantage of the analytical gradient of NLLF.The Hessian matrix was obtained via the calculus of complex matrix, allowing an efficient implementation.Finally, the performance of the proposed method was validated through synthetic and laboratory data.A comparison with the methods based on free and ambient vibration tests was also provided, respectively.
关键词
冲击振动测试 /
贝叶斯方法 /
试验模态分析 /
模态识别 /
不确定性量化
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Key words
impact vibration test /
Bayesian method /
experimental modal analysis /
modal identification /
uncertainty quantification
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