The aim of this article is to propose novel damage indices for damage localization and quantification based on time series modeling. In order to extract damage-sensitive features from time series models, it is essential to choose adequate and robust orders in such a way that the models are able to extract uncorrelated residuals. On this basis, a new iterative order determination method is proposed to select robust orders of time series models under residual analysis by Ljung–Box Q-test. The damage-sensitive features are the parameters and residuals of an AutoRegressive (AR) model obtained from current feature extraction approaches. In this study, the AR model is identified as the most compatible time series model with measured vibration time-domain responses using Box–Jenkins methodology and Leybourne–McCabe hypothesis test. The proposed damage indices are the parametric assurance criterion and the residual reliability criterion that exploit the parameters and residuals of AR models, respectively. The main idea behind locating a damage is to define threshold limits for both damage indices using the features of undamaged conditions based on an unsupervised learning way. The major contributions of this article are to propose an iterative order determination method for time series models and two novel damage indices for locating and quantifying damage. The accuracy and performance of the proposed methods are experimentally demonstrated on a three-story laboratory frame and a model-scale steel structure. Results show that the proposed iterative approach leads to uncorrelated residuals, and the proposed parametric assurance criterion and the residual reliability criterion methods are promising and efficient tools in damage detection problems under varying operational and environmental conditions.

Feature extraction by time-series analysis and decision making through distance-based methods are powerful and efficient statistical pattern recognition techniques for data-driven structural health monitoring. The motivation of this article is to propose an innovative residual-based feature extraction approach based on AutoRegressive modeling and a novel statistical distance method named as Partition-based Kullback–Leibler Divergence for damage detection and localization by using randomly high-dimensional damage-sensitive features under environmental and operational variability. The key novel element of the proposed feature extraction approach is to establish a two-stage offline and online learning algorithms for extracting the residuals of AutoRegressive model as the main damage-sensitive features. This technique brings the great benefit of reducing the computational time and storage space for feature extraction in long-term monitoring conditions. The major contribution of Partition-based Kullback–Leibler Divergence method is to exploit a partitioning strategy for dividing random features into individual partitions and utilize numerical information of partitioning in distance calculation rather than directly applying random samples. Dealing with the major challenging issue of using the high-dimensional features in decision making and applicability to both correlated and uncorrelated random datasets are the main advantages of Partition-based Kullback–Leibler Divergence method. The accuracy and reliability of the proposed approaches are experimentally validated by two well-known benchmark structures. The stationarity and linearity of measured vibration responses for using in AutoRegressive modeling are evaluated by two hypothesis tests. Comparative studies are also conducted to demonstrate the superiority of the proposed methods over some exciting state-of-the-art techniques. Results show that the methods presented here succeed in detecting and locating damage and make time-saving and efficient tools for feature extraction and damage diagnosis.

Ambient excitations applied to structures may lead to non-stationary vibration responses. In such circumstances, it may be difficult or improper to extract meaningful and significant damage features through methods that mainly rely on the stationarity of data. This article proposes a new hybrid algorithm for feature extraction as a combination of a new adaptive signal decomposition method called improved complete ensemble empirical mode decomposition with adaptive noise and autoregressive moving average model. The major contribution of this algorithm is to address the important issue of feature extraction under ambient vibration and non-stationary signals. The improved complete ensemble empirical mode decomposition with adaptive noise method is an improvement on the well-known ensemble empirical mode decomposition technique by removing redundant intrinsic mode functions. In addition, a novel automatic approach is presented to select the most relevant intrinsic mode functions to damage based on the intrinsic mode function energy level. Fitting an autoregressive moving average model to each selected intrinsic mode function, the model residuals are extracted as the damage-sensitive features. The main limitation is that such features are high-dimensional multivariate time series data, which may make a difficult and time-consuming decision-making process for damage localization. Multivariate distance correlation methods are introduced to cope with this drawback and locate structural damage using the multivariate residual sets of the normal and damaged conditions. The accuracy and robustness of the proposed methods are validated by a numerical shear-building model and an experimental benchmark structure. The effects of sampling frequency and time duration are evaluated as well. Results demonstrate the effectiveness and capability of the proposed methods to extract sufficient and reliable features, identify damage location, and quantify damage severity under ambient excitations and non-stationary signals.

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Data-driven damage localization is an important step of vibration-based structural health monitoring. Statistical pattern recognition based on the prominent steps of feature extraction and statistical decision-making provides an effective and efficient framework for structural health monitoring. However, these steps may become time-consuming or complex when there are large volumes of vibration measurements acquired by dense sensor networks. To deal with this issue, this study proposes fast unsupervised learning methods for feature extraction through autoregressive modeling and damage localization through a new distance measure called Kullback–Leibler divergence with empirical probability measure. The feature extraction approach consists of an iterative algorithm for order selection and parameter estimation aiming to extract residuals in the training phase and another iterative process aiming to extract residuals only in the monitoring phase. The key feature of the proposed approach is the use of correlated residual samples of the autoregressive model as a new time series at each iteration, rather than handling the measured vibration response of the structure. This is shown to highly reduce the computational burden of order selection and feature extraction; moreover, it effectively provides low-order autoregressive models with uncorrelated residuals. The Kullback–Leibler divergence with empirical probability measure method exploits a segmentation technique to subdivide random data into independent sets and provides a distance metric based on the theory of empirical probability measure with no need to explicitly compute the actual probability distributions at the training and monitoring stages. Numerical and experimental benchmarks are then used to assess accuracy and performance of the proposed methods and compare them with some state-of-the-art approaches. Results show that the proposed approaches are successful in feature extraction and damage localization, with a reduced computational burden.

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