Chapter8 Noise Sensitivity Evaluation of Autoregressive Features Extracted from Structure Vibration Ruigen Yao and Shamim N. Pakzad Abstract In the past few decades many types of structural damage indices based on structural health monitoring signals have been proposed, requiring performance evaluation and comparison studies on these indices in a quantitative manner. One tool to help accomplish this objective is analytical sensitivity analysis, which has been successfully used to evaluate the influences of system operational parameters on observable characteristics in many fields of study. In this chapter, the sensitivity expressions of two damage features, namely the Mahalanobis distance of autoregressive coefficients and Cosh distance of autoregressive spectra, will be derived with respect to the measurement noise level. The effectiveness of the proposed methods is illustrated in a numerical case study on a 10 DOF system, where their results are compared with those from direct simulation and theoretical calculation. Keywords Sensitivity analysis • Structural vibration monitoring • Autoregressive modeling • Autoregressive spectrum estimation • Yule-Walker method 8.1 Introduction Damage detection is a very crucial part in the regular assessment and maintenance routine for civil infrastructure. Traditionally this task is carried out by human inspection, and thereby is expensive, time consuming, and the accuracy relies on individual expertise. Recently, the advancements in sensing and computational technology have made it feasible for a sensor network to be installed on a civil structure, and data collected from the sensors will then be processed to produce information pertaining to the structural condition. To date many research studies in the literature [1–4] devoted to this topic can be found, forming a promising branch of study often referred to as data-driven structural health monitoring (SHM). Ideally, the new system will cost less than traditional method because of the lowering prices of sensing systems, and produce more accurate and reliable decisions that are free of human judgment bias or expertise. Moreover, SHM has the capability to reveal problems undetectable via ‘naked-eye’ inspection such as internal fracture and delamination. Vibration responses (e.g. acceleration, strain) are among the most commonly measured signals for structural monitoring purposes. One category of widely employed vibration-based damage indices consists of modal properties extracted using system identification/modal realization approaches [5–7]. Recently, many alternative damage features [8–10] based on structural output are proposed to address the computational efficiency (especially for time domain extraction algorithms) issues concerning modal properties estimators [1]. Time series analysis [11] for single channel acceleration measurements is one of the notable techniques attempted in a number of research articles [12–15], where algorithms such as scalar autoregressive (AR), autoregressive/autoregressive with exogenous input (AR-ARX), autoregressive with moving average (ARMA) modeling have been applied and functions of estimated model parameters used as damage features. These features are reported to be less complicated to compute and more sensitive to local damage in their respective applications. While it is important to propose and test new features to improve the state-of-the -art of structural damage detection, examination of the effect of environmental and operational factors on established features in an analytically rigorous manner is also crucial for optimal feature selection for different practices. Previously, research has been conducted on evaluating the R. Yao ( ) • S.N. Pakzad Department of Civil and Environmental Engineering, Lehigh University, Bethlehem, PA18015, USA e-mail: ruy209@Lehigh.edu; pakzad@Lehigh.edu H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__8, © The Society for Experimental Mechanics, Inc. 2014 79
RkJQdWJsaXNoZXIy MTMzNzEzMQ==