An Improved Finite Element Model Updating Method Based on the Singular Values of Frequency Response Functions

Aiming at the problems that Markov chain Monte Carlo algorithm is not easy to converge, has high rejection rate, and is easy to be disturbed by the noise when the parameter dimension is high, an improved model updating method combining the singular values of frequency response functions and the beetle antennae search algorithm is proposed. Firstly, the Latin hypercube sampling is used to extract the training samples. The Hankel matrix is reconstructed using the calculated frequency response functions and is decomposed by singular value decomposition. The effective singular values are retained to represent the frequency response functions. Secondly, according to the training samples and the corresponding singular values, the support vector machine surrogate model is fitted and its accuracy is tested. Then, the posterior probability distribution of parameters is estimated by introducing the beetle antennae search algorithm on the basis of standard Metropolis–Hastings algorithm to improve the performance of Markov chains and the ergodicity of samples. The results of examples show that the Markov chains have better overall performance and the acceptance rate of candidate samples is increased after updating. Even if the Gaussian white noise is introduced into the test frequency response functions under the single and multiple working damage conditions, satisfactory updating results can also be obtained.