Damage detection in structural systems by improved sensitivity of modal strain energy and Tikhonov regularization method

In this article, new methods for detecting damage in structural systems are presented. These methods are categorized as damage localization and damage quantification, respectively. Hence, direct changes of modal strain energy are applied to identify locations of damage. Moreover, some restraints such as incomplete measured modes and simple assumptions in structural modeling may cause failure in the results of damage localization. Therefore, a correlation-based method is utilized to obviate these limitations and precisely detect damage sites. Subsequently, an improved sensitivity of modal strain energy is generated to determine damage severities. To achieve appropriate results in damage quantification, Tikhonov regularization approach is utilized instead of classical methods such as applying penalty function and current inverse problem techniques. Applicability and effectiveness of proposed methods are numerically verified using two practical examples consisting of a planner truss and a portal frame, respectively. Eventually, numerical results indicate that the proposed damage localization approach provides an influential algorithm for precisely identifying damage sites. Furthermore, obtained damage severities show that utilizing the sensitivity of modal strain energy and also solving the damage equation by Tikhonov regularization makes it possible to accurately determine damage extents in the case of incomplete modal data

Damage localization in shear buildings by direct updating of physical properties

The objective of this article is to present a new method for identifying the damage location in a multi-story shear building by direct model updating method. In this regard, structural perturbation matrices should be determined that are directly defined as the discrepancy between mass and stiffness matrices of undamaged and damaged structures. As a result of expanding the dynamic orthogonality conditions, mass and stiffness perturbation matrices are formulated by the initial information of undamaged structures as well as the structure’s modal parameters before and after the occurrence of damages. These matrices cannot easily detect the damage site. Therefore, a more explicit determination of damage location is performed dividing the amount of change in these matrices’ diagonals by the physical properties of undamaged structure. This modification facilitates the damage localization process and yields precise and preferable results in comparison with applying classical methods such as natural frequencies, mode shapes and structural properties changes. Subsequently, the applicability and effectiveness of the proposed damage detection method are verified numerically and experimentally. For numerical verification of the proposed methods, a six-story shear building is utilized as a discrete system. Then, the experimental verification of proposed methods is conducted detecting the location of damages in a simple laboratory frame. It can be deduced that the proposed damage localization method can reliably detect and also localize the structural damage

Improving feature extraction via time series modeling for structural health monitoring based on unsupervised learning methods

Feature extraction by time series modeling based on statistical pattern recognition is a powerful approach to Structural Health Monitoring (SHM). Determination of an adequate order and identi cation of an appropriate model play prominent roles in extracting sensitive features to damage from time series representations. Early damage detection under statistical decision-making via high-dimensional features is another signi cant issue. The main objectives of this study were to improve a residual-based feature extraction method by time series modeling and to propose a multivariate data visualization approach to early damage detection. A simple graphical tool based on Box-Jenkins methodology was adopted to identify the most compatible time series model with vibration time-domain measurements. Furthermore, k-means and Gaussian Mixture Model (GMM) clustering techniques were utilized to examine the performance of the residuals of the identi ed model in damage detection. A numerical concrete beam and an experimental benchmark model were applied to verifying the improved and proposed methods along with comparative analyses. Results showed that the approaches were successful and superior to a state-of-the-art order determination technique in obtaining a sufficient order, generating uncorrelated residuals, extracting sensitive features to damage, and accurately detecting early damage by high-dimensional data

A Multi-stage Machine Learning Methodology for Health Monitoring of Largely Unobserved Structures Under Varying Environmental Conditions

Structural Health Monitoring (SHM) via data-driven techniques can be based upon vibrations acquired by sensor networks. However, technical and economic reasons may prevent the deployment of pervasive sensor networks over civil structures, thus limiting their reliability in terms of damage detection. Moreover, the effects of environmental (and operational) variability may lead to false alarms. To address these challenges, a multi-stage machine learning (ML) method is here proposed by exploiting autoregressive (AR) spectra as damage-sensitive features. The proposed method is framed as follows: (i) computing the distances between different sets of the AR spectra via the log-spectral distance (LSD), providing also the training and test datasets; (ii) removing the potential environmental variability by an auto-associative artificial neural network (AANN), to set normalized training and test datasets; (iii) running a statistical analysis via the Mahalanobis-squared distance (MSD) for early damage detection. The effectiveness of the proposed approach is assessed in the case of limited vibration data for the laboratory truss structure known as the Wooden Bridge. Comparative studies show that the AR spectrum is a reliable feature, sensitive to damage even in the presence of a limited number of sensors in the network; additionally, the multi-stage ML methodology succeeds in early detecting damage under environmental variability

System architecture for the Canadian interim mobile satellite system

The system architecture for the Canadian Interim Mobile Satellite Service (IMSS) which is planned for commencement of commercial service in late 1989 is reviewed. The results of an associated field trial program which was carried out to determine the limits of coverage and the preliminary performance characteristics of the system are discussed

Damage Detection in Largely Unobserved Structures under Varying Environmental Conditions: An AutoRegressive Spectrum and Multi-Level Machine Learning Methodology

Vibration-based damage detection in civil structures using data-driven methods requires sufficient vibration responses acquired with a sensor network. Due to technical and economic reasons, it is not always possible to deploy a large number of sensors. This limitation may lead to partial information being handled for damage detection purposes, under environmental variability. To address this challenge, this article proposes an innovative multi-level machine learning method by employing the autoregressive spectrum as the main damage-sensitive feature. The proposed method consists of three levels: (i) distance calculation by the log-spectral distance, to increase damage detectability and generate distance-based training and test samples; (ii) feature normalization by an improved factor analysis, to remove environmental variations; and (iii) decision-making for damage localization by means of the Jensen-Shannon divergence. The major contributions of this research are represented by the development of the aforementioned multi-level machine learning method, and by the proposal of the new factor analysis for feature normalization. Limited vibration datasets relevant to a truss structure and consisting of acceleration time histories induced by shaker excitation in a passive system, have been used to validate the proposed method and to compare it with alternate, state-of-the-art strategies

Improving the Power Quality in Tehran Metro Line-Two Using the Ant Colony Algorithm

This research aims to survey the improvement of power quality in Tehran metro line 2 using the ant colony algorithm and to investigate all the factors affecting the achievement of this goal. In order to put Tehran on the road of sustainable development, finding a solution for dealing with air pollution is essential. The use of public transportation, especially metro, is one of the ways to achieve this goal. Since the highest share of pollutants in Tehran belongs to cars and mobile sources, relative statistical indicators are estimated through assuming the effect of metro lines development and subsequently reduction of traffic on power quality index

Fast unsupervised learning methods for structural health monitoring with large vibration data from dense sensor networks

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

Damage localization under ambient excitations and non-stationary vibration signals by a new hybrid algorithm for feature extraction and multivariate distance correlation methods

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

An unsupervised learning approach by novel damage indices in structural health monitoring for damage localization and quantification

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