Abstract:

The reasonable selection of quasi-stable points is a key procedure for stability analysis of deformation monitoring networks. In the case of a large number or even more than half of the deformation points, the existing methods have insufficient robustness in selecting quasi-stable points, leading to unreasonable selection results. To improve the correctness of selecting quasi-stable points, a high breakdown point strategy that integrates the robust S-transform model with the K-means clustering algorithm is proposed. First, the residuals of control points are estimated, using the robust S-transform model, from random subsets of homologous points drawn from two-epoch deformation monitoring networks. Then, based on the residuals of points, the K-means clustering method is used to divide the points into quasi-stable, micro-deformation and macro-deformation classes, and the feasibility of the robust S-transform model is assessed via the centroid separation between quasi-stable and macro-deformation clusters. If the robust S-transform model is valid, the points exhibiting minimal residuals are identified as quasi-stable, and the candidate quasi-stable points are selected from the quasi-stable points with high frequency. Finally, the reliable point transformation residuals are acquired by the robust S-transform model from the candidate quasi-stable points, which are used to reasonably determine the quasi-stable points via the K-means clustering algorithm. Through the simulation experiments and a case analysis, the comparisons were made with the traditional similarity transformation model, the iterative weighted similarity transformation model, the similarity transformation model combined with RANSAC algorithm, and the squared M_split similarity transformation model. The results show that when deformation exists in the network, the proposed method has the highest correctness in identifying the deformation points, and the estimated displacement of control points closely matches the actual situation. In the case where the number of the deformation points exceeds the number of the stable points, the proposed method can still maintain its robustness, which means it has a high breakdown point.

Key words: deformation monitoring network, robust S-transform, K-means clustering, stability analysis, quasi-stable point