Inverse mathematical modeling and reliability parameter estimation in structural engineering systems under environmental variations
Keywords:
Inverse modeling, minimax optimization, structural reliability, parameter estimation, environmental uncertainty, saddle-point theory.Abstract
In this paper, a methodology is developed for structural parameter identification and reliability analysis subject to environmental uncertainty in the form of an inverse mathematical modeling framework. In particular, the developed framework represents parameter estimation as a regularized minimax optimization problem where the unknown structural parameters are obtained from minimizing the maximum admissible error in model predictions caused by environmental disturbances that are bounded and have no probability distributions. The proposed minimax formulation offers an estimation method for uncertain parameters that does not need any probability information about environmental factors. The identified parameters are then used in a limit-state reliability model in order to estimate failure probability and reliability of the structure. In this way, a worst-case reliability index is defined as the minimum value of the reliability index obtained over all possible environmental uncertainty sets. Under appropriate compactness, continuity, and convexity-concavity conditions, existence and optimality conditions for the minimax estimator are obtained based on the saddle-point theory. In addition, an algorithm of alternating minimization-maximization is developed for numerical computation of the minimax optimization problem. The efficacy of the proposed framework is illustrated by a typical example of structural engineering problems with different environmental conditions. Numerical results show that the minimax formulation can give a more stable parameter estimation compared to the conventional least squares estimation.
Downloads
Downloads
Published
Issue
Section
License
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
