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Deformation analysis by an improved similarity transformation

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 (LLS), here we solve a non-linear problem without any linearization. To achieve this goal, a new weighted total least-squares (WTLS) approach with general dispersion matrix 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. As a secondary scope, here it is analytically proved that LLS is not identical to nonlinear estimations such as the WTLS methods and rigorous nonlinear least-square (RNLS) as opposed to what in some contributions has been claimed. The third attainment of this contribution is proposing another algorithm for rigorous similarity transformation with arbitrary rotational angles. It is based on the RNLS method which can obtain the correct update of misclosure. Moreover, compared to transformation methods that deal with arbitrary rotational angles, we do not need to impose any orthogonality constraints here. Two case studies numerically confirm that the WTLS and RNLS methods provide the most accurate results among the LLS, GTLS, RNLS and WTLS approaches in two landslide areas.

Ketersediaan
230551.136Perpustakaan BIG (Eksternal Harddisk)Tersedia
Informasi Detail
Judul Seri
Applied Computing and Geoscience - Open Access
No. Panggil
551.136
Penerbit
Amsterdam : Elsevier.,
Deskripsi Fisik
9 hlm PDF, 705 KB
Bahasa
Inggris
ISBN/ISSN
2590-1974
Klasifikasi
551.136
Tipe Isi
text
Tipe Media
-
Tipe Pembawa
-
Edisi
Vol.25, February 2025
Subjek
Deformation analysis
Weighted total least-squares method
Nonlinear similarity transformation
Structured total Least-
Squares problem
Info Detail Spesifik
-
Pernyataan Tanggungjawab
Versi lain/terkait

Tidak tersedia versi lain

Lampiran Berkas
  • Deformation analysis by an improved similarity transformation
    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 (LLS), here we solve a non-linear problem without any linearization. To achieve this goal, a new weighted total least-squares (WTLS) approach with general dispersion matrix 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. As a secondary scope, here it is analytically proved that LLS is not identical to nonlinear estimations such as the WTLS methods and rigorous nonlinear least-square (RNLS) as opposed to what in some contributions has been claimed. The third attainment of this contribution is proposing another algorithm for rigorous similarity transformation with arbitrary rotational angles. It is based on the RNLS method which can obtain the correct update of misclosure. Moreover, compared to transformation methods that deal with arbitrary rotational angles, we do not need to impose any orthogonality constraints here. Two case studies numerically confirm that the WTLS and RNLS methods provide the most accurate results among the LLS, GTLS, RNLS and WTLS approaches in two landslide areas.
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