Uncertainty Quantification in Stochastic Subspace Identification Using a Simulation Method with DBSCAN-Based Outlier Detection

There are variance errors in the modal parameters estimated by stochastic subspace identification (SSI), with specified model order and time lag parameter. To quantify the variance of the identified modal parameters, the commonly used computation scheme derives the covariance formula, by exploring the first-order sensitivity of the identified parameters to the perturbations of the measured output-only data. Despite the merits of high accuracy, the computation scheme is not easily implemented in engineering practice since it involves complex and intricate mathematical derivations. Besides, when the time lag parameter in SSI is large, the computation scheme encounters heavy memory burden and low computational efficiency. To address these problems, a simulation method is proposed in the paper for estimating the covariance of the SSI-identified parameters. The proposed method simulates different samples for the output correlation matrices and for each generated sample implements regular procedures of SSI to obtain the modal parameters. With the obtained samples for the modal parameters, the algorithm of Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is adopted for the outlier detection, and then the statistical analysis is implemented to provide the covariance estimates of the identified modal parameters. As shown in two illustrative examples, there is good agreement between the estimation results from the proposed simulation method and the computation scheme, which verifies the accuracy of the proposed method and provides additional support to the formulas in the computation scheme. Furthermore, the proposed simulation method is easier to implement and can achieve improved computational efficiency and significantly reduced memory burden; thus it can serve as a good complement to the computation scheme.