关键词: 固结, 最小二乘问题, Gauss-Newton法, Levenberg-Marquardt法, 传感器布置

Abstract: The study applies the least squares technique in conjunction with a series of spatiotemporally varying pore water pressure measurements to identify the geotechnical parameters of consolidation models. Firstly, a least squares function for pore water pressure, incorporating both temporal and spatial coordinates, is developed. Subsequently, a new Jacobian matrix is constructed to accommodate any number of temporal and spatial measurements. Using Taylor series expansion, the iterative equations for the Gauss-Newton, Levenberg, Marquardt, and Nielsen methods are derived. The proposed methods are validated using two numerical examples. In Case 1, the consolidation coefficient of Terzaghi’s model is identified. Comparative analysis reveals that all four methods converge to the correct solution, although the Marquardt method converges more slowly. In Case 2, the coordinates of a point source in a two-dimensional fluid-saturated medium are identified using a poroelastic consolidation model. The Gauss-Newton method fails to accurately locate the point source, whereas the Nielsen method accelerates convergence but introduces multiple damping coefficient intervals and convergence values. The Marquardt method is more effective for point source identification. Additionally, the study highlights the importance of sensor placement and initial iteration coordinates for accurate point source identification. Both cases show that the proposed methods possess some noise resistance.

Key words: consolidation, least square problem, Gauss-Newton method, Levenberg-Marquardt method, sensor layout