Subspace-based Damage Detection Research Articles

Statistical Subspace-Based Damage Detection and Jerk Energy Acceleration for Robust Structural Health Monitoring

This paper introduces a multistep damage identification process that is both straightforward and useful for identifying damage in buildings with regular plan geometries. The algorithm proposed in this study combines the utilization of a multi-damage sensitivity feature and MATLAB programming, providing a comprehensive approach for the structural health monitoring (SHM) of different structures through vibration analysis. The system utilizes accelerometers attached to the structure to capture data, which is then subjected to a classical statistical subspace-based damage detection test. This test focuses on monitoring changes in the data by analyzing modal parameters and statistically comparing them to the structure’s baseline behavior. By detecting deviations from the expected behavior, the algorithm identifies potential damage in the structure. Additionally, the algorithm includes a step to localize damage at the story level, relying on the jerk energy of acceleration. To demonstrate its effectiveness, the algorithm was applied to a steel shear frame model in laboratory tests. The model utilized in this study comprised a total height of 900 mm and incorporated three lumped masses. The investigation encompassed a range of scenarios involving both single and multiple damages, and the algorithm proposed in this research demonstrated the successful detection of the induced damages. The results indicate that the proposed system is an effective solution for monitoring building structure condition and detecting damage.

Noise effects analysis on subspace-based damage detection with neural networks

Structural health monitoring (SHM) is nowadays a significant and topical issue in the civil engineering field, whose first-level task is the damage detection job. Recent advances in artificial intelligence (AI) combined with non-destructive assessments based on output-only vibration signals represent the frontier of SHM. The present research study has handled an AI-based multi-class damage classification task on a numerical benchmark beam problem with three different procedures. The main purpose was to investigate the noise effects of the analyzed damage detection procedures simulating real-world accelerometer sensors. The first damage identification method leverages simple statistical features of vibration signals, whereas the second method additionally considers a subspace-based damage indicator. The third method relies on a dataset composed of a specific set of damage indicators. Two deep learning (DL) techniques have been adopted to compare and verify the results, i.e. a multi-layer perceptron (MLP) and a one-dimensional convolutional network (1D-CNN). Three groups of different reasonable signal-to-noise ratio (SNR) levels were set up to simulate micro electro-mechanical system (MEMS) accelerometer sensors in real-world conditions to evaluate noise effects. In a nutshell, the results demonstrated that the DL models based on stochastic subspace identification (SSI) methods have good noise immunity performance for damage detection purposes.

Sensor placement with optimal damage detectability for statistical damage detection

Damage diagnosis based on global structural vibrations critically depends on the sensor layout, in particular when a small number of sensors is used for large structures under unknown excitation. This paper proposes a sensor placement strategy that yields an optimized sensor layout with maximum damage detectability in selected structural components. The optimization criterion is based on the Fisher information, which quantifies the information that the damage-sensitive feature carries on the design parameters of structural components, such as material constants or cross-sectional values. It is evaluated using a finite element model, and considers the statistical uncertainties of the damage-sensitive feature. The methodology is shown for the stochastic subspace-based damage detection method, but can be applied to any damage-sensitive feature whose distribution can be approximated as Gaussian. It is suitable to find the optimal layout for a fixed number of sensors and to choose an appropriate number of sensors. Since the Fisher information is defined component-wise, the sensor layout can be tuned to become more sensitive to damage in local structural components, such as damage hotspots, non-inspectable components, or components that are critical for the safety and serviceability of the structure. For proof of concept, the sensor layout on a laboratory beam is optimized based on numerical simulations, and it is showcased that the optimal sensor layout leads to the highest damage detectability for experimental data.

Statistical subspace-based damage detection with estimated reference

The statistical subspace-based damage detection technique has shown promising theoretical and practical results for vibration-based structural health monitoring. It evaluates a subspace-based residual function with efficient hypothesis testing tools, and has the ability of detecting small changes in chosen system parameters. In the residual function, a Hankel matrix of output covariances estimated from test data is confronted to its left null space associated to a reference model. The hypothesis test takes into account the covariance of the residual for decision making. Ideally, the reference model is assumed to be perfectly known without any uncertainty, which is not a realistic assumption. In practice, the left null space is usually estimated from a reference data set to avoid model errors in the residual computation. Then, the associated uncertainties may be non-negligible, in particular when the available reference data is of limited length. In this paper, it is investigated how the statistical distribution of the residual is affected when the reference null space is estimated. The asymptotic residual distribution is derived, where its refined covariance term considers also the uncertainty related to the reference null space estimate. The associated damage detection test closes a theoretical gap for real-world applications and leads to increased robustness of the method in practice. The importance of including the estimation uncertainty of the reference null space is shown in a numerical study and on experimental data of a progressively damaged steel frame.

Damage Detection of Transmission Tower Based on Stochastic Subspace and Statistic Model

During the long service period of the transmission tower, the severe environment, material aging and fatigue effects result in the damage accumulation and resistance fading of the transmission tower, which even lead to the structural failure. In this paper, a stochastic subspace-based damage detection algorithm combined with statistical model is proposed for the damage identification of transmission tower structures through processing and analysing its vibration signals. Based on the structural modal parameters identified from the structural vibration response, the nominal modal parameters are defined. Considering that the Hankel matrixes constructed by the system observability matrix and the system output covariance matrix have the same kernel space, the damage index sensitive to the modal parameters is constructed. In the manuscript, firstly, the damage index establishment method and process of the algorithm are presented; and then the vibration data of transmission tower structure simulation under different damage conditions are obtained through numerical simulations; finally, above data are analysed to obtain the damage identification results of transmission tower. The results show that the method proposed in this work can effectively identify the local damage of transmission tower structure.

A reliability-based approach to determine the minimum detectable damage for statistical damage detection

This paper derives a formula to determine the minimum detectable damage based on ambient vibration data. It is a key element to analyze which damage scenarios can be detected before a monitoring system is installed. For the analysis, vibration data from the reference structure as well as a finite element model are required. Minimum detectability is defined by adopting a code-based reliability concept that considers the probability of detection and the probability of false alarms. The results demonstrate that the minimum detectable damage depends on three elements: the uncertainty of the damage-sensitive feature (which decreases with increasing measurement duration), its sensitivity towards model-based design parameters, and the reliability requirements regarding the damage diagnosis results. The theory is developed for the stochastic subspace-based damage detection method but can be applied to any damage-sensitive feature provided its sensitivities and statistical properties can be characterized. For proof of concept, the minimum detectable change in stiffness and mass of a pin-supported beam are analyzed in a numerical and experimental study, respectively. The predictions with the developed approach appear to be accurate and robust to noise effects for both simulated and real data.

Statistical methods for damage detection applied to civil structures

Damage detection consists of monitoring the deviations of a current system from its reference state, characterized by some nominal property repeatable for every healthy state. Preferably, the damage detection is performed directly on vibration data, hereby avoiding modal identification of the structure. The practical aspect of using only the output measurements cause difficulties because of variations in ambient excitation due to variability in the environmental conditions, like sea, wind, and temperature. In this paper, a new Mahalanobis distance-based damage detection method is studied and compared to the well-known subspace-based damage detection algorithm in the context of two large case studies. Both methods are implemented in the modal analysis and structural health monitoring software ARTeMIS, in which the joint features of the methods are concluded in a control chart in an attempt to enhance the resolution of the damage detection. The damage indicators from both methods are evaluated based on the ambient vibration signals from numerical simulations on a novel offshore support structure and an experimental campaign with a full scale bridge. The results reveal that the performance of the two damage detection methods is similar, hereby implying merit of the new Mahalanobis distance-based approach, as it is less computational complex. The fusion of the damage indicators in the control chart provides the most accurate view on the progressively damaged systems.

A New Composite Bridge: Feasibility Validation and Vibration Monitoring

The first part of this article presents the feasibility study of a new structure for a 10-m-span bridge deck, taking into account the possibilities offered by new and high-strength materials and the advantages of a traditional environmental-friendly material. This 10-m-span element is formed by wooden beams braced at the ends, on supports atop a thin slab (7 cm thick) made of pre-cast ultra-high performance fiber-reinforced concrete, and fiber-reinforced polymer at the bottom of the wooden beams. The issue of connecting the ultra-high performance fiber-reinforced concrete to the wooden beams of high but possibly mismatching performance is addressed. An adhesive connection has been considered, following an increasing trend for composite structures where materials savings and optimal performance are searched in every component. The second part of this article presents the vibration-based damage monitoring. Small localized damages are hardly detected by global monitoring methods. The effectiveness of vibration-based detection depends on the accuracy of the modal parameter estimates and is limited by the low sensitivity of the modal parameters to a local stiffness reduction. A local reduction of stiffness related to frequency changes less than 1% was successfully detected on the bridge mockup after loading up to the serviceability limit state (SLS). Such a small decrease in the stiffness was not detected by the monitoring of the static load-deflection measurements but was confirmed by nonlinear local strain measurements. Statistical subspace-based damage detection successfully detected the change of the modal parameters of the investigated structure. Further analysis with a finite element model was conducted for assessing the consistency of the expected location and extent of the damaged elements.

Subspace-based damage detection under changes in the ambient excitation statistics

In the last ten years, monitoring the integrity of the civil infrastructure has been an active research topic, including in connected areas as automatic control. It is common practice to perform damage detection by detecting changes in the modal parameters between a reference state and the current (possibly damaged) state from measured vibration data. Subspace methods enjoy some popularity in structural engineering, where large model orders have to be considered. In the context of detecting changes in the structural properties and the modal parameters linked to them, a subspace-based fault detection residual has been recently proposed and applied successfully, where the estimation of the modal parameters in the possibly damaged state is avoided. However, most works assume that the unmeasured ambient excitation properties during measurements of the structure in the reference and possibly damaged condition stay constant, which is hardly satisfied by any application. This paper addresses the problem of robustness of such fault detection methods. It is explained why current algorithms from literature fail when the excitation covariance changes and how they can be modified. Then, an efficient and fast subspace-based damage detection test is derived that is robust to changes in the excitation covariance but also to numerical instabilities that can arise easily in the computations. Three numerical applications show the efficiency of the new approach to better detect and separate different levels of damage even using a relatively low sample length.

Structural damage assessment using output-only measurement: Localization and quantification

In this article, a systematic way of structural damage assessment algorithm, including identification of damage location and damage quantification, is proposed using output-only measurement. First, the null-space-based and subspace-based damage detection methods are used to confirm the damage severity of a structure. Then, the stochastic subspace identification technique is adopted to identify the time-varying system natural frequencies from the global response measurement. Finally, the novelty index, defined as the Euclidean norm of the time–frequency Hilbert amplitude spectrum of measurement between the intact and the damaged structures, is applied to locate the damage. To quantify the damage, the complete system realization is obtained from the identified modal properties through stochastic subspace identification method. From which, the inter-story stiffness reduction ratio can be identified using the normalized stiffness matrix. For case of limited measurement, the multi-setup operational modal analysis is applied to construct the complete system matrix. Verification of the proposed damage assessment algorithm using response data from a series of shaking table test of a six-story steel structure with the cut in column member to simulate the damage is demonstrated.

Null subspace-based damage detection of structures using vibration measurements

A damage detection method of mechanical system based on subspace identification concepts and statistical process techniques is presented. The aim is to propose a method that is sensitive to small-sized structural damages and suitable for on-line monitoring. Measured time-responses of structures subjected to artificial or environmental vibrations are assembled to form the Hankel matrix, which is further factorised by performing singular-value decomposition to obtain characteristic subspaces. It may be demonstrated that the structural responses are mainly located in the active subspace defined by the first principal components, which is orthonormal to the null subspace defined by the remaining principal components. If no structural damage occurs, the orthonormality relation between the subspaces remains valid with small residues when consecutive data sets are compared, and these residues may be evaluated by the proposed damage indicators. The method is validated using an experimental mock-up of an airplane subjected to different levels of damages simulated. It is also applied in environmental vibration testing of a street lighting device to monitor structural fatigue evolution.

ON-LINE MODAL MONITORING OF AIRCRAFT STRUCTURES UNDER UNKNOWN EXCITATION

In this paper, we present the application of recently proposed subspace-based damage detection and isolation algorithms in on-line structural monitoring of an airplane structure under unknown excitation. The first step of the approach is a subspace-based modal analysis of the safe structure, using output-only measurements. The monitoring step consists in the computation of a χ2-variable, which reflects possible deviations of newly collected output-only data w.r.t. the reference (safe) modal behaviour. No re-identification of the possibly damaged structure is required. An on-line version of the detection algorithm is proposed. Monitoring certain critical modes can also be achieved through sensitivity tests. Experimental results for the proposed monitoring algorithms are reported, in the case of the Paris MS760 airplane, on which mass as well as stiffness changes are introduced. Moreover, the results of the output-only subspace-based modal analysis are compared with the modal appropriation method.