A Novel Stochastic Approach for Static Damage Identification of Beam Structures Using Homotopy Analysis Algorithm

Area of Science:

• Structural Engineering
• Mechanical Engineering
• Computational Mechanics

Background:

• Accurate damage identification in beam structures is crucial for structural health monitoring.
• Existing methods often struggle with uncertainties in static measurement data and initial structural models.
• Stochastic parameters and modeling errors introduce significant challenges in damage detection.

Purpose of the Study:

• To develop a robust damage identification approach for beam structures with stochastic parameters.
• To address challenges posed by uncertain static measurement data and modeling errors.
• To provide a reliable method for damage identification even with relatively large uncertainties.

Main Methods:

• Formulation of stochastic damage identification equations based on damage indices.
• Application of a novel homotopy analysis algorithm for solving these equations.
• Integration of static condensation and L1 regularization techniques to handle limited data and ill-posed problems.

Main Results:

• The proposed approach demonstrates good accuracy and efficiency in numerical examples.
• It outperforms the first-order perturbation method, especially with larger measurement and modeling errors.
• Successful damage identification was achieved in static tests on a simply supported concrete beam.

Conclusions:

• The developed method offers a reliable solution for damage identification in beam structures under uncertainty.
• It effectively accounts for both measurement and modeling errors, enhancing diagnostic capabilities.
• The damage probability index provides a quantitative measure for assessing potential structural damage.