Cross Modal Strain Energy Method for Damage Detection Using Limited Modal Data

Abstract

This paper extends the recently developed cross modal strain energy (CMSE) method for damage localization and severity estimation, using limited modal data, with iterative process. For investigating the performance and verifying the effectiveness of the present CMSE method, the numerical study of this article chooses a damaged beam that was investigated in a published article. The numerical result indicates that the CMSE method is capable of detecting the damage locations and estimating their severities properly, even when only few spatially incomplete, noisy modes are utilized.

An iterative total least squares‐based estimation method for structural damage identification of 3D frame structures

“…Since N q is usually greater than N d , the structural damage identification is transformed into a problem of solving the over‐determined CMSE equations. Typically, α can be estimated with the LS method (abbreviated as LS‐CMSE method in this paper): …”

“…It is unavoidable that the estimated modal parameters always contain errors, which are not only due to the measurement noise but also due to the uncertainties in the modal parameter identification process; therefore, the error distribution in modal parameters has a lot of uncertainties. In order to study the error propagation from the measured mode shapes to the estimate of the damage severity, the errors in modal parameters (or simply termed as modal noise ) are simply simulated by adding a series of uncorrelated random numbers on the theoretically calculated modal parameters in numerical studies . The basic goal is to understand how sensitive the modal noise to the damage identification results.…”

“…Compared with similar methods, this method has many advantages, for example, it does not require the analytical and measured modes to be consistent in scale or to be normalized in any specific way. At first, the CMSE method was only used to estimate the structural damage severity, then it was extended to simultaneously localize and estimate the damage even with spatial‐incomplete modal parameters …”

“…Very small errors in modal parameters may lead to large errors in the damage identification results. Originally, the least square (LS) estimation method was employed to solve the CMSE equations, which can give reasonable damage identification results for some simple structures (e.g., beams) . However, when it comes to complex structures (e.g., 3D frame structures), the estimated solutions are usually poor or unusable.…”

“…At first, the CMSE method was only used to estimate the structural damage severity, then it was extended to simultaneously localize and estimate the damage even with spatial-incomplete modal parameters. [24][25][26] Similar to other such approaches, the ill-conditioning problem is unavoidable in the CMSE equations. Very small errors in modal parameters may lead to large errors in the damage identification results.…”