# Material Degradation Inverse Identification for Cantilever Beams Using Experimental Frequency Response Function

## TL;DR

This paper introduces a new method to detect material degradation in cantilever beams using frequency response data and Bayesian inference.

## Contribution

A novel stochastic framework with adaptive constraints for identifying material degradation in structures is proposed.

## Key findings

- The KL expansion reduces dimensionality in material degradation modeling.
- The two-phase constraint strategy improves physical plausibility and algorithmic stability.
- Experimental validation shows accurate localization of degradation in steel beams.

## Abstract

This paper presents a stochastic framework for the inverse identification of structural material degradation (SMD) in cantilever beams. The method combines the Karhunen–Loéve (KL) expansion for the efficient parameterisation of spatially varying material decay with experimental Frequency Response Function (FRF) data within a Bayesian inference scheme. This approach employs a low-dimensional spectral parameterisation via the KL expansion, which mitigates the curse of dimensionality inherent in element-wise model updating, and provides a full-field probabilistic description of SMD. A two-phase constraint strategy was developed to address the fundamental tension between physical plausibility and algorithmic stability of the inverse identification algorithm: (1) physical regularisation during identification stabilises the ill-posed inverse problem, and (2) post-convergence selective regularisation eliminates physically impossible stiffness enhancements (exceeding 1.1 × baseline) that arise from measurement and modelling uncertainties. This phased approach prevents the algorithm distortion that occurs when constraints are applied too stringently during iteration, while ensuring final results respect fundamental physical principles. The framework is experimentally validated on a steel cantilever beam with a symmetric open-edge cut. Laser vibrometry measurements under swept-sine excitation demonstrate successful localisation and quantification of SMD, with the 95% credible interval accurately capturing the damaged region after physical constraint application. The adaptive constraint strategy resolves the delicate balance between mathematical stability and physical plausibility in inverse identification.