Efficient Structural Damage Detection with Minimal Input Data: Leveraging Fewer Sensors and Addressing Model Uncertainties

Transfer-learning guided Bayesian model updating for damage identification considering modeling uncertainty

The representation of structural dynamics in the absence of physics-based models, is often accomplished through the identification of parametric models, such as the autoregressive with exogenous inputs, e.g. ARX models. When the structure is amenable to environmental variations, parameter-varying extensions of the original ARX model can be implemented, allowing for tracking of the operational variability. Yet, the latter occurs in sufficiently longer time-scales (days, weeks, months), as compared to system dynamics. For inferring a “global”, long time-scale varying ARX model, data from a full operational cycle has to typically become available. In addition, when the sensor network comprises multiple nodes, the identification of long time-scale varying, vector ARX models grow in complexity. We address these issues by proposing a distributed framework for structural identification, damage detection and localization. Its main features are: (i) the individual estimation of local, single-input-single-output ARX models at every operational point; (ii) the long time-scale representation of each individual ARX coefficient via a Gaussian process regression, which captures dependency on varying Environmental and Operational Conditions (EOCs); (iii) the establishment of a distributed residual generation algorithm for damage detection, which produces time-series of well-defined stationary statistics, with detected discrepancies used for damage diagnosis; and, (iv) exploitation of ARX-inferred mode shape curvatures, obtained via ARX-inferred global state-space models, of the healthy and damaged states, for damage localization. The method is assessed via application on two numerical case studies of different complexity, with the results confirming its efficacy for diagnostics under varying EOCs.

In this paper, an improvement of the elliptical triangulation method for damage detection using Lamb waves is presented. The damage is the main cause of structural failure and often occurs on structures. In order to avoid sudden failure, a special attention was given in the past decades to the damage detection in structures. In order to obtain efficient damage detection techniques, the structural health monitoring has been the main research topic of many scientists worldwide. The elliptical triangulation method, proposed in this paper, is a non-destructive method based on measurement of Lamb waves. This method, through the calculation of the time of flight of the signals and the actuator-sensor positioning, allows to identify position and dimension of the damage. The application of the method to the metallic structures and to the composite material structures is presented in this paper. The complexity connected with the uncertainty of the waves’ propagation speed due to the anisotropy of the composite materials has been explored through an iterative approach. The initialization of the wave propagation speed at first tentative iteration is the key issue for the convergence of the method. Seven different conditions were used to validate the method on both metallic and composite structures combining two damage shapes, two damage dimensions (effective damaged area), and three different positions. Upon evaluating the effectiveness, the method has been applied at two composite panels in order to detect by test the post-impact damages. Tests results have been compared with the numerical ones. The feasibility of the elliptical triangulation method to detect the damage (evaluating the damage position and area) has been proved using the ultrasonic C-Scan.

Vibration-based damage detection methods have inherent uncertainties due to the perturbation of measurement noise, modeling errors, and environmental changes, such as variations in temperature. However, other measured local information, including the static strain and deflection measured by the structural health monitoring system, have not been taken full advantage of. The integration of such global and local information has the potential to lead to more accurate structural damage detection. This paper proposes a method for integrating the global and local information for structural damage detection based on Bayesian theory. First, the Bayesian probability model associated with natural frequencies, displacement mode shapes, and strain modes is developed. In this model, the local strain information is also used as an input. Second, to reduce the model's computational cost in complex structures, the strain energy damage index is employed to determine the potential damage ranges. Finally, the exact damage elements are detected by a proposed sequence elimination method. Numerical simulations on a 14-bay planar rigid structure and the experiment on a 20-bay rigid truss are carried out to demonstrate the effectiveness of the proposed method while considering model uncertainty and measurement noise. The results show that the proposed damage detection method can increase the model's identification accuracy and decrease its misjudgment rate, compared with the method that only uses global information.

The accuracy of vibration-based structural damage identification is affected by uncertainties in vibration measurements and finite element modeling. Moreover, a sufficient number of sensor measurements are not practical in large-scale structures. In this regard, the frequency domain [frequencies and mode shapes (FMS)] and time domain [acceleration cross-correlation function (ACCF)] indexes are put into a parallel convolutional neural network (P-CNN, a new convolutional neural network architecture with dual-channel) to locate and quantify structural damage. First, this approach is verified by a numerical model of a simply-supported beam, and the performance is evaluated by comparing it with methods using FMS and ACCF indexes input to the conventional 2D-CNN, respectively. The comparative results demonstrate that the proposed method can identify the damage with the lowest error, and the errors are less than 5%. In addition, three sparse measurement conditions are adopted to investigate the effect of the number of measuring points on damage identification. It is found that under the influence of uncertainties, even if only four sensors are used, this approach can identify damage accurately. Second, an engineering example of a continuous rigid frame bridge is adopted to validate the feasibility of the proposed method. The results show that when the number of sensors accounts for 65% and 47% of test sensors, respectively, it performs well in locating and quantifying structural damage. Therefore, this method can not only reduce the number of sensors and eliminate uncertainties effects, but also improve the performance of the 2D-CNN through information fusion and complementarity, which is also beneficial to minimize the cost of sensor layout in actual structures.

The accuracy of structural damage identification is affected by the uncertainties in the vibration measurements and the finite element modeling. This paper proposes a novel approach based on sparse deep belief network (DBN) for structural damage identification with uncertain and limited data. Vibration characteristics, that is, natural frequencies and mode shapes, are extracted as the input to the network, while the output are the damage locations and severities of the structure. DBN is chosen to train the generated data sets and identify structural damages. Restricted Boltzmann Machines (RBMs) are used as building blocks to composite a DBN. To further enhance the capacity of the RBMs, an arctan-based sparse constraint is utilized to enable the hidden units to become sparse. This is achieved by adding an arctan norm constraint on the whole of the hidden units' activation probabilities. Numerical and experimental studies are conducted to verify the accuracy and performance of the proposed method. Undetermined damage identification is conducted, in which the quantity of input modal data is less than that of the system parameters to be identified. The identification results show that the proposed sparse DBN based on arctan can identify the damage effectively, and its accuracy is better than those obtained by other methods, even when the modeling uncertainty and the measurement noise exist and only limited data is available.

Motivated by a smart structures philosophy of self-health monitoring in structural systems, a damage detection system for beam structures using subspace rotation techniques is presented. In doing so, the subspace rotation is extended from displacement-based data to strain-based data. Methods for accommodating the additional degrees of freedom of beam elements are presented. Using simulated data, the ability to locate and quantify single and multiple damage events is investigated. It has been found that the higher-order vibration modes are required to locate damage events in beams because the frequency response of beams is much less sensitive to a damage event than that of truss structures. It has also been found that condensation methods cannot be used to remove rotational degrees of freedom in the beam because of the coupled nature of the rotational degrees of freedom to the translational degrees of freedom.

A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports.

This paper proposes a novel approach for improving the identifiability of structural damage by using higher order responses and singular spectrum analysis (SSA)-based phase space topology (PST) technique. SSA is employed to decompose the structural dynamic acceleration response into several low-dimensional components. Then, the change of PST (CPST) reconstructed from the decomposed component with higher order responses of structures under intact and damaged states is utilized to identify the structural condition changes. Numerical studies on a planar truss structure are conducted to investigate the accuracy and reliability of the proposed approach. The dynamic acceleration responses of the truss structure corresponding to intact and several damage scenarios are utilized for signal decomposition by using SSA and damage detection with CPST. The effects of white noise, pink noise, and modeling uncertainties on the accuracy of damage detection are investigated. The proposed method is also validated through experimental studies on a Tee-section prestressed concrete beam model. Vibration acceleration responses under hammer impact loads are measured under intact and damaged states, which are used for the damage detection with the proposed approach. Damage patterns identified by using the proposed approach under different loading levels agree well with the observed crack distributions. Both numerical and experimental results demonstrate that using the higher order response components decomposed by SSA and the proposed method is sensitive to damage and reliable for structural damage detection.

This paper presents a numerical investigation of the Mode Shape Area Difference (MSAD) methodology for structural damage detection in steel frame systems. The MSAD approach quantifies the variation between undamaged and damaged mode shapes by computing the area difference of their displacement curves and spatial derivatives. Three damage indexes – MDAD, MRAD, and MCAD– are formulated based on modal displacement, rotation, and curvature, respectively. The methodology is applied to an industrial steel portal frame modeled using Bernoulli beam elements, with damage simulated as localized reductions in flexural stiffness. A total of 154 damage scenarios are evaluated, encompassing various locations and severity levels. The results show that the MCAD index is the most effective in detecting and localizing damage, demonstrating robustness even for low stiffness reductions (sr = 1%). However, a loss of sensitivity with respect to damage severity is observed in some scenarios near modal nodes or structural supports. These findings suggest that MSAD, especially in its curvature-based form, is a promising non-model-dependent strategy for condition assessment in frame structures. Future developments are discussed.

A new methodology is presented in this work to detect, localize, and relatively quantify damage in structures based on the changes in the second spatial derivative (curvature) of the power spectral density (PSD) of the angular velocity during vibration. The proposed method is based on the output motion only and does not require information about the input forces/motions. The PSD of the angular velocity signal at different locations on structural beams was used to identify the frequencies where the beams show large angular velocity. The curvature of the PSD of the angular velocity at these peak frequencies was then calculated. A damage index is presented that measures the differences between the PSD curvature of the angular velocity of a damaged structure and an artificial healthy baseline structure. The efficacy of the proposed method in detecting and localizing single and multiple damages was numerically demonstrated on structural beams with the presence of white noise. The method was very effective in detecting and localizing small damage on beams with narrow slots even when 10% white noise was added to the measured data. The method also successfully detected and localized a narrow slot in laboratory testing of a cantilever beam.

Thin structures have been applied widely in different areas of engineering. They are prone to elastic vibration when submit to external dynamic excitations or interference, which will not only lower system stability, but also threaten the people's lives. Thus, it is significant to research this topic in depth. Generally, many acceleration sensors are put on the cover of the structure to measure the vibrations. Also, strain sensors have been recently used for measuring vibration. However, strain is difficult to measure in thin structures and there are also limitations when applying multi-spot distributed measurement method. Based on the theory that the vibration of practical structure can be decoupled into multiple vibration modes, a new concept of curvature modal sensors with optical fiber is proposed to measure vibration modes.

In this paper, a new application of resonant acoustic spectroscopy (RAS) is examined for constructing asphalt concrete mastercurves from seismic testing. The frequency-dependent material properties can be characterized from multiple modes of vibration through the use of RAS. Beam-shaped asphalt specimens are tested at multiple temperatures to determine the resonance frequencies of the specimens. The resonance frequencies are estimated by applying a small load impulse and measuring the resulting acceleration through the specimens. Using RAS, the material properties of the specimens are determined numerically using the measured resonance frequencies. The results presented show that the frequency-dependent dynamic modulus of the asphalt concrete specimens can be characterized using several modes of vibration at each testing temperature.

The paper focuses on damage detection of civil engineering structures and especially on concrete bridges. A method for structural health monitoring based on vibrational measurements is presented and discussed. Experimentally identified modal parameters (eigenfrequencies, mode shapes and modal masses) of bridge structures are used to calculate the inverse stiffness matrix, the so-called flexibility matrix. By monitoring of the stiffness matrix, damage can easily be detected, quantified and localized by tracking changes of its individual elements. However, based on dynamic field measurements, the acquisition of the flexibility matrix instead of the stiffness matrix is often the only choice and hence more relevant for practice. But the flexibility-based quantification and localisation of damage are often possible but more difficult, as it depends on the type of support and the location of the damage. These issues are discussed and synthetized, that is an originality of this paper and is believed useful for engineers in the damage detection of different bridge structures. First the theoretical background is briefly repeated prior to the illustration of the differences between stiffness and flexibility matrix on analytical and numerical examples. Then the flexibility-based detection is demonstrated on two true bridges with real-time measurement data and the results are promising.

Deep transfer learning-based damage detection of composite structures by fusing monitoring data with physical mechanism