An Enhanced Statistical Damage Detection Algorithm Using Time Series Analysis

A damage diagnosis approach using time series analysis of vibration signals was recently proposed by the Los Alamos National Laboratory. In this paper, the application of this approach to the damage detection of the benchmark problem designed by the ASCE task group on health monitoring is explored. The damage detection approach is modified to consider the influence of excitation variability and the orders of the ARX prediction model on the originally extracted damagedetection feature. Residual error of a new signal from an unknown structural condition associated with the prediction model is compared with those of signals from the undamaged structure in the damage decision. The applicability of the modified approach is investigated using various acceleration responses generated with different combinations of structural finite element models, excitation conditions and damage patterns in the benchmark study. INTRODUCTION Damage detection and localization is still a daunting problem in structural health monitoring and extreme event damage evaluation [1]. Various methods have been developed in recent years [2], many of which rely on cumbersome finite element modeling processes and/or linear modal properties for damage diagnosis. For practical applications, these methods have been shown to be ineffective because of computationally intensive tuning and significant uncertainties caused by user interaction and modeling errors. Recently, a damage detection approach using time series analysis of vibration signals was proposed by [3,4,5,6]. The structural health monitoring problem is posed in a statistical pattern recognition framework [7], which consists of four-parts: (i) the evaluation of a structure’s operational environment, (ii) the acquisition of structural response measurements, (iii) the 1 Department of Civil and Environmental Engineering, Stanford University, Stanford, CA extraction of features that are sensitive to damage, and (iv) the development of statistical models for feature discrimination. This damage detection approach has shown great promise in the identification of damage in the hull of a high-speed patrol boat as well as in several relatively simple laboratory test specimens. In this paper, a modified damage detection algorithm is proposed that considers the influence of excitation variability and the order of the ARX model. The new algorithm is tested with data from the benchmark problem proposed by the ASCE Task Group on Health Monitoring [8]. ASCE HEALTH MONITORING BENCHMARK PROBLEM In order to coordinate research activities in the area of damage detection, a benchmark problem was proposed by the ASCE Task Group on Health Monitoring [8]. The benchmark structure is a 4-story 2-bay by 2-bay steel frame scale model structure. Two analytical models for used in the numerical simulation of the structure’s response include a 12DOF shear building model and a 120DOF finite element model with more structural details. Structural damage is simulated by removing the stiffness of various elements in the finite element models. Five damage patterns defined in the benchmark study are: (i) removing all braces in the 1st story, (ii) removing all braces in both the 1st and 3rd stories, (iii) removing one brace in the 1st story, (iv) removing one brace in each of 1st and 3rd story, and (v) damage pattern 4 with the floor beam partially unscrewed from the column in the 1st floor. Excitation to the structure is either ambient wind loading at each floor in the ydirection or a shaker force applied on the roof at the center column position. To account for the uncertainty of environmental loads, the loads are modeled as filtered Gaussian white noise. More information on the benchmark problem can be obtained from the web site: http://wusceel.cive.wustl. edu/asce.shm/benchmarks.htm. A MATLAB program was provided by the ASCE Task Group to numerically simulate dynamic responses at the measurement locations on each floor. Different combinations of structural finite element models, excitation conditions and damage patterns results in various dynamic response histories. DAMAGE DETECTION USING TIME SERIES OF VIBRATION SIGNALS The damage diagnosis approach proposed by [3,4,5] is based solely on the statistical analysis of vibration signals from a structure of interest. It is posed in the context of statistical pattern recognition paradigm. In this paper, we explore the application of this approach in the damage detection of the benchmark structure [8]. First, an ensemble of acceleration responses ) t ( x j (j=1, 2, ..., N) at one of the measurement locations (the ac accelerometer measurement shown in Figure 1 of the undamaged structure subject to different excitation samples is generated using the MATLAB program. These signals form ‘the reference database’ [6] and are standardized as follows: ) x ( ) x ( m ) t ( x ) t ( x̂ j j j j σ − = (1) where ) t ( x̂ j is the standardized signal and ) x ( m j and ) x ( j σ are the mean and standard deviation of ) t ( x j , respectively. (For simplicity, ) t ( x j is used to denote ) t ( x̂ j hereafter.) For each time series ) t ( x j in the reference database, an AR (auto-regression) model with p AR terms is constructed as [9]