| Title |
Full-Waveform Inversion for Material Profile Reconstruction of Prestressed Lifeline Structures |
| Authors |
김민성(Kim, Min Seong);김홍주(Kim, Hongju);강준원(Kang, Jun Won) |
| DOI |
https://doi.org/10.12652/Ksce.2025.45.3.0313 |
| Keywords |
전체파형역해석, 휨파동, 프리스트레스트 라이프라인 구조물, Winkler 기초, 편미분방정식 구속 최적화 Full-waveform inversion, Flexural wave propagation, Prestressed lifeline structures, Winkler foundation, Partial differential equation-constrained optimization |
| Abstract |
This study presents a full-waveform inversion (FWI) framework that utilizes flexural wave measurements to reconstruct the elastic
modulus and soil stiffness profiles of prestressed lifeline structures embedded in the ground. The forward problem of a flexural wave
propagation in the prestressed beam-soil system is formulated as an initial-boundary value problem, incorporating the Euler-Bernoulli
beam equation with a prestressing term and the Winkler foundation model. The dynamic flexural response of a beam supported by an
elastic foundation is numerically computed using the Galerkin finite element method with C1 shape functions and the Newmark-β time
integration scheme. The inverse problem for reconstructing the material properties of the prestressed beam-soil system is formulated
as a partial differential equation-constrained optimization problem, where the objective is to minimize the difference between measured
and computed deflections to determine the optimal values of the beam’s Young’s modulus and soil stiffness. The optimization process
employs a Lagrangian functional, integrating the objective functional and constraints, and derives the state, adjoint, and control
problems from the first-order optimality conditions of the Lagrangian. These problems are iteratively solved in a reduced space of the
control variables to reconstruct the Young’s modulus and the soil stiffness. Numerical examples are presented for two cases: (1)
reconstruction of the beam’s Young’s modulus when the soil stiffness is known, and (2) reconstruction of the soil stiffness when the
beam’s Young’s modulus is known. The effect of regularization during the inversion on the reconstruction accuracy is presented, and
the results show that, in all cases, the reconstruction error remains below 0.06 % of the initial values, confirming the accurate recovery
of the material profiles. The methodology presented in this study can be applied to the condition assessment of various prestressed
lifeline structures, such as water pipelines. |