Statistical pattern recognition for Structural Health Monitoring using time series modeling: Theory and experimental verifications

Abstract

Statistical pattern recognition methodologies have gained considerable attention for Structural Health Monitoring (SHM) applications to detect changes in a structure (e.g. damage). For most of such applications, outlier analysis of the damage sensitive features obtained from the SHM data is used to detect the changes in the structure. There are a number of different approaches used by different research groups and it is widely accepted that success of a certain methodology may depend on the structure and/or structural change to be identified. Therefore, it is very important that promising methodologies are verified by using different test structures and damage cases. The main objective of this study is to investigate statistical pattern recognition methods in the context of SHM using different laboratory structures. Time series modeling, i.e. auto-regressive models, is used in conjunction with Mahalanobis distance-based outlier detection algorithms to identify different types of structural changes on different test structures. Similar approaches were reported in the literature but here the methodology is modified by using random decrement functions to eliminate the effects of the exogenous input. Then a number of tests are conducted by using two different test structures in laboratory conditions in order to evaluate the results in a comparable fashion. The first test specimen is a simply supported steel beam where the second structure is a highly redundant steel grid structure. Various damage conditions are simulated by using these structures. The ambient vibration data is analyzed by using the methodology described and results are presented. Finally, the advantages and drawbacks of the methodology are discussed in the light of experimental results.

Introduction

Structural Health Monitoring (SHM) is the research area focusing on condition assessment of various types of structures. Having the earliest SHM applications in aerospace engineering, mechanical and civil applications have gained momentum in the last few decades. Although SHM is inarguably a broader research area, most of SHM applications have been focusing on damage detection. Traditionally, structural system identification techniques have been commonly used by relating the damage to the change in the vibration characteristics of the structure. Example studies for such applications can be found in the literature review by Doebling et al. [1] and the references therein.

However, there are a number of challenges to be overcome before routine applications of SHM. For example, environmental and operational effects may induce significant changes on the dynamic characteristics of the structure and these effects can mask the changes caused by structural deterioration [2], [3]. Furthermore, a successful application of system identification-based SHM methodology might require good quality data with a relatively dense sensor resolution, a detailed and calibrated finite element model (FEM) and monitoring of environmental effects. A review of the health monitoring of civil infrastructure was published by Chang et al. [4], where the authors discussed a number of different global and local monitoring techniques. Another review report was published by Sohn et al. [5], where the authors discussed different aspects of SHM in detail, such as feature extraction and statistical analysis.

Due to the many uncertainties in most of the real-life applications, applications of statistical pattern recognition in SHM have recently gained an increased attention. Most of the studies focusing on statistical pattern recognition applications on SHM use a combination of time series modeling with a statistical novelty detection methodology (e.g. outlier detection). One of the main advantages of such methodologies is that it requires only the data from the undamaged structure in the training phase (i.e. unsupervised learning) as opposed to supervised learning where data from both undamaged and damaged conditions is required to train the model. The premise of the statistical pattern recognition approach is that as the model is trained for the baseline model, new data coming from the damaged structure will likely be classified as outliers in the data.

Most of these statistical models are used to identify the novelty in the data by analyzing the feature vectors, which include the damage sensitive features. For example, Sohn et al. [6] used a statistical process control technique for damage detection. Coefficients of auto-regressive (AR) models were used as damage-sensitive features and they were analyzed by using X-bar control charts. Different levels of damage in a concrete column were identified by using the methodology. Worden et al. [7] and Sohn et al. [8] used Mahalanobis distance-based outlier detection for identifying structural changes in numerical models and in different structures. Worden et al. [7] used transmissibility function as damage-sensitive features, whereas Sohn et al. [8] used the coefficients of the AR models. Manson et al. [9] also used similar methodologies to analyze data coming from different test specimens including aerospace structures.

In another study, Omenzetter and Brownjohn [10] used auto-regressive integrated moving average (ARIMA) models to analyze the static strain data coming from a bridge during its construction and when the bridge was in service. The authors were able to detect different structural changes by using the methodology. They also mentioned the limitations of the methodology, for example, it is unable to detect the nature, severity, and location of the structural change. Nair et al. [11] used an auto-regressive moving average (ARMA) model and used the first three AR components as the damage-sensitive feature. The mean values of the damage-sensitive features were tested using a hypothesis test involving the t-test. Furthermore, the authors introduced two damage localization indices using the AR coefficients. They tested the methodology using numerical and experimental results of the ASCE benchmark structure [12]. It was shown that the methodology was able to detect and locate even different types of damage cases for numerical case. However, it was concluded by the authors that more investigations were needed for experimental data.

Another methodology was proposed by Zhang [13], where the author used a combination of AR and auto-regressive models with exogenous output (ARX models) for damage detection and localization. The standard deviation of the residuals of the ARX model was used as damage-sensitive feature. Although the methodology was verified by using a numerical model, the author indicated that further studies should be conducted to make the methodology applicable in practice. In a recent study, Carden and Brownjohn [14] used ARMA models and a statistical pattern classifier, which uses the sum of the squares of the residuals of the ARMA model. The authors stated that the algorithm was generally successful in identifying the damage and separating different damage cases from each other. However, the authors noted that the vibration data was coming from forced excitations tests and the methodology may not be applicable for structures with only ambient dynamic excitation.

As summarized in sections above, there are a number of different approaches utilizing time series modeling in conjunction with an outlier detection or novelty measurement methodology to identify structural change. It is observed, however, that most of these methodologies need more investigation by means of experiments. Therefore, this study employs experimental data coming from different test structures and damage cases to examine a statistical pattern recognition approach for SHM. The methodology uses auto-regressive models in conjunction with a Mahalanobis distance-based outlier detection algorithm. In the proposed methodology, random decrement (RD) functions are used to obtain free vibration response from the ambient vibration data. The methodology is investigated by using experimental data from the two different test structures for a number of different structural configurations. Various damage conditions are simulated and the advantages and drawbacks of the methodology are discussed in the light of the experimental results.