Theoretical Study on Multi-Parameter Inversion Non-Uniqueness Based on Elastic Displacements of Concrete Gravity Dams

HUANG Yaoying; YIN Xiaohui; LI Chunguang

doi:10.21656/1000-0887.400164

Volume 41 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(2): 171-181

HUANG Yaoying, YIN Xiaohui, LI Chunguang. Theoretical Study on Multi-Parameter Inversion Non-Uniqueness Based on Elastic Displacements of Concrete Gravity Dams[J]. Applied Mathematics and Mechanics, 2020, 41(2): 171-181. doi: 10.21656/1000-0887.400164

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Theoretical Study on Multi-Parameter Inversion Non-Uniqueness Based on Elastic Displacements of Concrete Gravity Dams

doi: 10.21656/1000-0887.400164

¹College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang, Hubei 443002, P.R.China;²State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, P.R.China

Funds: The National Natural Science Foundation of China(51779130)

Received Date: 2019-05-09
Rev Recd Date: 2019-05-31
Publish Date: 2020-02-01

Abstract

Abstract

Inversion analysis is an important part of the closed-loop system of on-site monitoring, inversion analysis, engineering practice test, forward analysis and prediction, and the back analysis problem in engineering practice mainly involves the parameter back analysis. Aimed at the uniqueness of multi-parameter inversion analysis on concrete gravity dams, the objective functions were established based on the theoretical solution of gravity dam displacements on homogeneous foundation under water pressure, and a convex programming problem was constructed with the objective function and the non-empty convex set. Then the positive definiteness of the Hessian matrix of the objective function was analyzed to verify the strict convexity of the objective function, thereby to identify whether the constructed convex programming problem has a unique global minimum. The analysis on different combinations of elastic constants of dams and rock foundations shows that, when the l₁ norm of the difference between the theoretical value and the measured value is used as the objective function, the Hessian matrix of the objective function cannot be guaranteed to be a positive definite matrix, that is, the multi-parameter elastic displacement inversion analysis of concrete gravity dams does not have a unique global minimum point.
- multi-parameter inversion,
- inversion based on displacement,
- convex programming problem,
- Hessian matrix,
- uniqueness

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References

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