Structural damage detection using low-rank matrix approximation and cointegration analysis

Abstract

This paper proposes a novel approach of time series analysis to identify the potential changes in structural conditions, e.g., degradation owing to accumulated damage. Although the damage-sensitive features (DSFs) of structures depend on the environmental and operational conditions and thus vary over time, they usually have a common trend when the effects of environmental and operational variations (EOVs) are linear or quasi-linear. Therefore, cointegration analysis, which can combine several time series into a stationary residual purged of the common trend, is used to remove the effects of EOVs and assess the structural condition. The main contribution of this study is that a low rank matrix approximation (LRMA) algorithm is introduced to constrain the rank of the stacked DSF matrix, thereby suppressing the random errors inevitable in structural damage detection and both the linear and nonlinear effects induced by EOVs. The nonlinear effects have been observed in the identified natural frequency data of several bridges in service and cannot be easily handled by the general cointegration due to its linear nature. Another advantage of this process is that the missing entities in the DSF series can be automatically imputed, taking full advantage of incomplete data acquired for analysis. The effectiveness of the proposed method is demonstrated by using the benchmark data of the KW51 Railway Bridge in structural condition identification. Results indicate that the changes in the structural condition can be correctly detected despite the existence of random errors and nonlinear effects induced by EOVs. The proposed method can also work when only a small amount of incomplete data is available.