Deformation analysis by a rigorous similarity transformation

Abstract

Abstract In this contribution, deformation analysis is rigorously performed by a non-linear 3-D similarity transformation. In contrast to traditional methods based on linear least-squares (LS), here we solve a non-linear problem without any linearization. To achieve this, an extended weighted total least-squares (WTLS) approach is implemented to deformation analysis problem. Although some researchers have been trying to solve deformation analysis using TLS approaches, these attempts require modification since they used to apply unstructured TLS techniques such as Generalized TLS (GTLS) to similarity transformation which requires structured TLS (STLS) techniques while the WTLS approach preserves the structure of the functional model when based on the perfect description of the variance-covariance matrix. Also Akaike Information Criterion (AIC) confirms that the WTLS method provides the most accurate results among the linear LS, GTLS and WTLS approaches in a landslide area which is located in Turkey as a case study for deformation analysis.