We develop an efficient Bayesian model class selection method for vector autoregressive (VAR) model order selection, so that uncertainties of system identification can be rigorously quantified, and structural dynamic properties can be well captured. The general theory of Bayesian model class selection is first derived in terms of a VAR model to construct the evidence of a model class that is used as the criterion for model order selection. We then approximate the extremely high dimensional integral involved in calculating the evidence based on the Laplace asymptotic approximation. The fast calculation is thus feasible using only the most probable values of VAR parameters. Numerical problems are solved for practical applications. The propagation of uncertainties from VAR parameters to modal parameters is also discussed. A laboratory shear building and a full-scale old factory building are used to demonstrate the good performance of the proposed method in model class selection, system identification, and uncertainty quantification.

中文翻译：

---

用于系统识别的向量自回归模型的高效贝叶斯模型类选择

我们为向量自回归 (VAR) 模型阶数选择开发了一种有效的贝叶斯模型类选择方法，从而可以严格量化系统识别的不确定性，并可以很好地捕获结构动力学特性。贝叶斯模型类选择的一般理论首先根据 VAR 模型推导出来，以构建用作模型顺序选择标准的模型类的证据。然后，我们基于拉普拉斯渐近近似来近似计算证据所涉及的极高维积分。因此，仅使用最可能的 VAR 参数值进行快速计算是可行的。针对实际应用解决了数值问题。还讨论了不确定性从 VAR 参数到模态参数的传播。