Structural damage detection based on virtual element boundary measurement

A novel demodulation method with a reference signal for operational modal analysis and baseline-free damage detection of a beam under random excitation

Long-gauge fiber Bragg grating strain sensors have been widely employed because of their broader measuring range and higher sensitivity. However, current structural damage detection methods using macro-strain modal parameters are based on structural frequency response function or stationary power spectrum density, which are not applicable to non-stationary responses. To overcome this limitation, an improved method is proposed in this paper for structural damage detection based on structural macro-strain responses under unknown multi-point non-stationary excitations. First, a new concept of macro-strain energy spectrum transmissibility (MEST) is proposed using structural non-stationary macro-strain responses, and it is derived that MEST at a certain system pole equals the ratio of macro-strain mode shape. Then, the singular value decomposition technique is adopted for the MEST matrix to identify structural natural frequencies and macro-strain mode shapes. Finally, two damage detection indicators are constructed based on the identified normalized macro-strain mode shape (NMMS). The first indicator is the difference in structural NMMS before and after structural damage. The second one is based on the curvatures of structural NMMS, which can be used for structures without intact baseline. Numerical verifications are conducted to identify beam-type structural damage under multi-point non-stationary excitations or vehicle loads. Five damage scenarios with different measurement noise levels are investigated, and damage detection results validate the effectiveness of the proposed method.

Experimental study of laser Doppler vibrometer and ambient vibration for vibration-based damage detection

In the present work, to describe the behavior of the shell, the classical theory based on the Kirchhoff-Love hypotheses is used. An approach is proposed which allows us to approximate model equations, taking account of any external loads. Virtual elements and expansion in Fourier's series are applied to determine the stress state of isotropic and orthotropic rotational shells under local loading conditions. Calculation results for shells subjected to different types of local mechanical loads are presented. Comparison of the stress state obtained using virtual elements and that calculated by the finite elements method is carried out. Calculations indicate that the application of the concept of a virtual shell element and the decomposition of loading in Fourier's series make it possible to reduce the dimensionality of the problem by 1.In addition, the high accuracy of approximation of external loads and the characteristics of the stress state of isotropic and orthotropic rotational shells is provided.

Nondestructive evaluation (NDE) for detection and quantification of damage in composite materials is fundamental in the assessment of the overall structural integrity of modern aerospace systems. Conventional NDE systems have been extensively used to detect the location and size of damages by propagating ultrasonic waves normal to the surface. However they usually require physical contact with the structure and are time consuming and labor intensive. An automated, contactless laser ultrasonic imaging system for barely visible impact damage (BVID) detection in advanced composite structures has been developed to overcome these limitations. Lamb waves are generated by a Q-switched Nd:YAG laser, raster scanned by a set of galvano-mirrors over the damaged area. The out-of-plane vibrations are measured through a laser Doppler Vibrometer (LDV) that is stationary at a point on the corner of the grid. The ultrasonic wave field of the scanned area is reconstructed in polar coordinates and analyzed for high resolution characterization of impact damage in the composite honeycomb panel. Two methodologies are used for ultrasonic wave-field analysis: scattered wave field analysis (SWA) and standing wave energy analysis (SWEA) in the frequency domain. The SWA is employed for processing the wave field and estimate spatially dependent wavenumber values, related to discontinuities in the structural domain. The SWEA algorithm extracts standing waves trapped within damaged areas and, by studying the spectrum of the standing wave field, returns high fidelity damage imaging. While the SWA can be used to locate the impact damage in the honeycomb panel, the SWEA produces damage images in good agreement with X-ray computed tomographic (X-ray CT) scans. The results obtained prove that the laser-based nondestructive system is an effective alternative to overcome limitations of conventional NDI technologies.

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.

Two-stage structural damage detection using fuzzy neural networks and data fusion techniques

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.

• Weak formulation of configurational forces (CFs) in the VEM is derived. • Automated mesh refinement based on CFs improves VEM approximations. • Accurate crack tip loading analyses are demonstrated. • Internal moments in virtual elements must not be disregarded in fracture analyses. • Efficient and accurate crack growth simulations with non-convex crack tip elements. The Virtual Element Method (VEM) constitutes a generalization of the Finite Element Method, allowing for spatial discretizations with arbitrary, even non-convex polygonal elements. This offers significant advantages, particularly for problems involving moving discontinuities, local stress concentrations, or multiple phases with distinctly different dimensions. The theory of configurational forces (CF) represents a very flexible basis to quantify driving forces for virtual defect displacements within a thermodynamical framework, and at the same time provides an indicator for the local mesh quality in numerical calculations. In combination, the VEM and the CF theory thus constitute an effective basis for numerical simulations of crack growth within the context of a classical approach with strong discontinuities and sharp crack tips. Challenges to cope with are attributable to the lacking knowledge of shape functions within virtual elements, the numerical integration on arbitrary polygonal elements, and the requirement of an automated generation of polygonal meshes. The weak form of the energy-momentum balance is derived from a variational approach, uniquely separating nodal CFs acting at free surfaces from those driving the defect. Furthermore, internal degrees of freedom, which are inherent to higher-order virtual elements, have to be interpreted within the context of CFs. Unphysical, so-called spurious, CFs are exploited for an improved mesh design at crack tips, eventually generating accurate results of crack tip loading and crack path simulation.

For a high speed mobile communication system, Doppler shift affects its performance seriously. In the future, broad band communication based on orthogonal frequency division multiplexing which depends on the orthogonality among sub-carriers will become popular. The absence of the orthogonality due to being destroyed by Doppler shift, leads to the failure of signal demodulation. So Doppler shift must be estimated and compensated for, which is the main purpose of previous work. On the other hand, many applications have shown that Doppler shift can be utilized to acquire the direction and speed or improve the quality of a signal. In this paper, we propose a method of not only estimating and compensating for Doppler shift, but also generating multiple non-frequency shifted signals, which can be regarded as the output of a virtual antenna array. As to the method, uniform phase sampling is the key algorithm. At first, the relation between uniform time sampling and uniform phase sampling is discussed in detail. This relation shows that the equivalence between uniform phase sampling and uniform time sampling is the necessary and sufficient condition for a non Doppler shifted signal. Next, the algorithm of Doppler shift compensation and virtualized antenna array is proposed, in which 1) original Doppler shifted signal is processed with interpolation, 2) new signals are generated by uniform phase sampling and buffered, 3) buffered new signals are read out by uniform time sampling. The theory of this process and the performance improvement for a high speed mobile communications system is mathematically analyzed, and the hardware architecture model of this algorithm is also given. The diversity gain could be obtained when an antenna array is used. In order to verify that this virtualized antenna array has the same benefit, the ability to suppress the interference and the bit error rate is analyzed with numerical simulation. The number of virtual elements and the virtual element distance are two variables related to the direction pattern of virtual antenna array. The effects of these two variables are given by the simulation, showing that the more virtual elements, the narrower beam are obtained. But more virtual elements result in more complicated hardware source. In addition, the communications scenarios of two communications radiators at different sites are simulated to verify whether this algorithm can suppress interference signal. The frequency spectrum of beamformed virtual antenna array signal shows that the interference signal can be suppressed effectively. These characteristics cannot be provided by pure Doppler frequency shift compensation. Thus these results show that high speed mobile communication systems on aircrafts or high speed trains would obtain better performances when a received Doppler shift signal is processed by this method to construct a virtual antenna array.

This study is focused on exploring the feasibility of an all-optic surface scanning method in determining the size and position of a submerged, laser generated, optoacoustic (OA) source. The optoacoustic effect in this case was generated when the absorption of a short electromagnetic pulse in matter caused a dielectric breakdown, a plasma emission flash and a subsequent acoustic wave. In the experiment, a laser pulse with λ = 1064 nm and 12 ns pulse length was aimed at a volume of deionized water. When the laser beam was focused by a f = 16 mm lens, a single dielectric breakdown spot occurred. When a f = 40 mm was used several breakdowns in a row were induced. The breakdowns were photographed using a double shutter camera. The acoustic wave generated by the dielectric breakdowns were detected at a point on the water surface using a laser Doppler vibrometer (LDV). First, the LDV signal was used to calculate the speed of sound with an accuracy of 10 m/s. Secondly, the location and length of the dielectric breakdown was calculated with an accuracy of 1 mm. The calculated position matched the breakdown location recorded by a camera. The results show that it is possible to use LDV surface measurements from a single spot to determine both the position and length of the OA source as well as the speed of sound in the medium. Furthermore, the LDV measurements also show a secondary peak that originates from the OA source. To unravel the origin and properties of this interesting feature, further investigations are necessary

An innovative methodology based on the use of fiber Bragg gratings as strain sensors and strain field pattern recognition is proposed for damage detection in composite materials structures. The strain field pattern recognition technique is based on principal component analysis. Damage indices ( T2 and Q) and detection thresholds are presented. New techniques for unfolding and scaling tridimensional matrices arrays obtained from structures working under variable load conditions are presented.

Detection of structural damage is an inverse problem in structural engineering. There are three main questions in the damage detection: existence, location and extent of the damage. In concept, the natural frequency and mode shapes of any structure must satisfy an eigenvalue problem. But, if a potential damage exists in a structure, an error resulting from the substitution of the refined analytical finite element model and measured modal data into the structural eigenvalue equation will occur, which is called the residual modal forces, and can be used as an indicator of potential damage in a structure. In this study, a useful damage detection method is proposed and compared with other two methods. Two degree-of-freedom system and Cantilever beam are used to demonstrate the approach. And the results of three introduced method are compared.

The detection of structural damages, either on-line or almost on-line, based on vibration data measured from sensors, is essential for the structural health monitoring system. The problem is quite challenging, in particular when the external excitations are not completely measured and when the structural system is complex. In practical applications, external excitations (inputs), such as seismic excitations, wind loads, traffic loads, etc., may not be measured or may not be measurable, and the structure may not always be shear-beam type which can be easily represented as spring-mass system. In this paper, a newly proposed damage detection method, referred to as the adaptive quadratic sum-squares error with unknown inputs (AQSSE-UI), is used for the detection of structural damages of a plane steel truss with finite element model. In this approach, external excitations and some structural responses may not be measured. Analytical recursive solution for the proposed AQSSE-UI method will be presented. The accuracy and effectiveness of the proposed approach will be demonstrated by numerical simulations where the structure is excited by different external loads. The simulation results indicate that the proposed approach is a viable damage detection technique capable of: (i) identifying structural parameters, (ii) tracking the changes of parameters leading to the detection of structural damages, and (iii) identifying the unknown external excitations.

Damage detection for beam-like structures using the normalized curvature of a uniform load surface