A principled multiresolution approach for signal decomposition

Iason Iakovidis,Elizabeth J Cross,Keith Worden

doi:10.1088/1742-6596/1106/1/012001

Iason Iakovidis, Elizabeth J Cross + Show 1 more

Open Access

https://doi.org/10.1088/1742-6596/1106/1/012001

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Abstract

One of the common issues with the Structural Health Monitoring (SHM) of civil infrastructure, is that signals measured from structures are nonstationary. The nonstationarity is the result of uncontrolled variations in the environmental and operational variations (EOVs) in the structure, which result from the fact that monitoring can only be carried out in situ. Unfortunately, the EOVs prove to be a problem for damage detection, as they can mask the onset of damage, itself a nonstationary process. The aim of the current paper is to demonstrate a principled, but simple, decomposition method, which can separate signals into stationary and nonstationary components; the stationary component can then be used as a feature for SHM. The method is based on a wavelet/multiresolution analysis of the signal of interest, followed by a sequence of wavelet level-by-level tests for stationary using the ADF (Augmented Dickey-Fuller) test statistic. The decomposition is illustrated using data from the famous SHM campaign on the Z24 Bridge. The paper should be of interest, not just to engineers, but to econometricians, or anyone concerned with nonstationary signal processing.

Highlights

In the context of Structural Health Monitoring (SHM), signals obtained by continuous monitoring exhibit variability, both in the shorter and longer terms, which can be associated with the impact of Environmental and Operational Variations (EOVs)
An important conclusion from the SHM literature is that the impact of environmental and operational variations (EOVs) on SHM signals can occur on widely disparate time scales; their quantification and elimination is not a straightforward matter
Of particular interest here is the concept of Multiresolution Analysis (MRA) [3], which has been employed in SHM in order to decompose a given SHM signal into band-limited frequency components and evaluate the damage sensitivity of each one [4]

Summary

Introduction

In the context of Structural Health Monitoring (SHM), signals obtained by continuous monitoring exhibit variability, both in the shorter and longer terms, which can be associated with the impact of Environmental and Operational Variations (EOVs). A byproduct of the analysis was to show that there existed a critical frequency fc for given sample parameters, such that any signal components containing only frequencies below fc would be judged nonstationary by the ADF test This result is used here to motivate the definition of a simple, but principled, decomposition method for signals, which can resolve them into their stationary and nonstationary components. In order to establish the noise component in the signal, one computes the ACF for any levels in the stationary component (stationarity is required in the definition of the ACF) and moves into the noise component any levels which are delta-correlated This completes the description of how the new decomposition is defined. The procedure will be illustrated on a case study

Case Study

Conclusions