Damage Identification In Plates Research Articles

Response Surface Model of the Reduced Flexibility Matrix for Bayesian Damage Identification.

The present work is concerned with the use of a Response Surface Model of the reduced flexibility matrix for structural damage identification. A Response Surface Model (RSM) is fitted with the aim at providing a polynomial relationship between nodal cohesion parameters, used to describe the damage field within the structure, and elements of the reduced flexibility matrix. A design of experiment built on combinations of a relatively small number of nodal cohesion parameters is used to fit the RSM. The damage identification problem is formulated within the Bayesian framework and the Delayed Rejection Adaptive Metropolis method is used to sample the posterior probability density function of the uncertain cohesion parameters. Numerical simulations addressing damage identification in plates were carried out in order to assess the proposed approach, which succeeded in the identification of the different damage profiles considered. Besides, the use of a RSM, instead of a FEM of the structure, resulted in reductions of up almost 78% in the required computational cost.

Guided waves-based damage identification in plates through an inverse Bayesian process

The use of guided waves to identify damage has become a popular method due to its robustness and fast execution, as well as the advantage of being able to inspect large areas and detect minor structural defects. When a travelling wave on a plate interacts with a defect, it generates a scattered field that will depend on the defects geometry. By analysing the scattered field, one can thus characterize the type and size of the plate damage. A Bayesian framework based on a guided waves interaction model for damage identification of infinite plate for the first time is presented here. A semi-analytical approach based on the lowest order plate theories is adopted to obtain the scattering features for damage geometries with circular symmetry, resulting in an efficient inversion procedure. Subsequently, ultrasound experiments are performed on a large aluminium plate with a circular indentation to generate wave reflection and transmission coefficients. With the aid of signal processing techniques, the effectiveness and efficiency of the proposed approach are verified. A full finite element model is used to test the damage identification scheme. Finally, the scattering coefficients are reconstructed, reliably matching the experimental results. The framework supports digital twin technology of structural health monitoring.

Guided Waves-Based Damage Identification in Plates Through an Inverse Bayesian Process

Guided Waves-Based Damage Identification in Plates Through an Inverse Bayesian Process

Damage identification in plates under uncertain boundary conditions

Nondestructive damage identification is a central task in industrial applications in, for example, aeronautical, civil and naval engineering. The identification approaches based on (physical) models rely on the accuracy of the model predictions, and typically suffer from effects caused by ubiquitous modeling errors and uncertainties. The identification problems are typically unstable inverse problems but may also be (apparently) stable when considering low dimensional parametrizations for the defects. The present paper considers the identification of defects in plates under uncertain boundary conditions. To partially compensate for the boundary uncertainties, we adopt the Bayesian framework for inverse problems and use approximate marginalization over the model uncertainties: the process of marginalization propagates the model uncertainties to the uncertainties in the estimated parameters. We employ a low dimensional parametrization for the defects, which would, in principle, allow for least squares or the more general maximum likelihood estimation approaches. We will show, however, that under uncertain boundary conditions, maximum likelihood estimates can yield unfeasible estimates while the approximate marginalization over uncertainties provides feasible ones.

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

Mode shapes have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature mode shapes (CMSs) to identify damage in plates; the method is applicable to mode shapes associated with low and high elastic modes on dense and coarse measurement grids and robust against measurement noise. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a mode shape of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamaged one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a mode shape of an undamaged plate can be well approximated using a polynomial of a properly determined order that fits a mode shape of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. Fitting and convergence indices are introduced to quantify the level of approximation of a mode shape from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A weight function is applied to the proposed CDIs to alleviate adverse effects of measurement noise on the CDIs and manifest existence of damage in the CDIs. A mode shape of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified. The experimental damage identification results were numerically verified by applying the proposed method to the mode shape associated with the same mode as that of the measured one from a finite element model of the damaged plate.

Frequency domain damage detection of plate and shell structures by finite element model updating

Plate- and shell-like elements are the main constituent of many engineering structures such as ships and airplanes. This paper develops a frequency domain model updating method using power spectral density function and seeks its viability in damage identification of plates and shells. The derivation of the sensitivity equation is exact and measured natural frequencies of few lower modes are used to overcome the drawbacks of incomplete measurement. The method is numerically examined in several damage cases. The robustness of method against measurement and mass modelling error is numerically assessed using Monte-Carlo analysis and numerically simulated error contaminated data. The method proves to be robust against both kind of errors and performs well, both in cases of plate and shell elements.

Non-model-based damage identification of plates using measured mode shapes

Mode shapes (MSs) have been extensively used to detect structural damage. This paper presents a new non-model-based damage identification method that uses measured MSs to identify damage in plates. A MS damage index (MSDI) is proposed to identify damage near regions with consistently high values of MSDIs associated with MSs of different modes. A MS of a pseudo-undamaged plate can be constructed for damage identification using a polynomial of a properly determined order that fits the corresponding MS of a damaged plate, if the associated undamaged plate is geometrically smooth and made of materials that have no stiffness and mass discontinuities. It is shown that comparing a MS of a damaged plate with that of a pseudo-undamaged plate is better for damage identification than with that of an undamaged plate. Effectiveness and robustness of the proposed method for identifying damage of different positions and areas are numerically investigated using different MSs; effects of crucial factors that determine effectiveness of the proposed method are also numerically investigated. Damage in the form of a machined thickness reduction area was introduced to an aluminum plate; it was successfully identified by the proposed method using measured MSs of the damaged plate.

Damage characterization in plates using singularity of scale mode shapes

Damage is a prevailing physical phenomenon in in-service structures; accumulation of damage can cause catastrophic structural failure. For damage identification in plates, the concept of scale mode shape with fractal singularity is formulated based on 2D Gabor wavelet transform incorporating fractal dimension analysis of measured mode shapes. With this concept, a scale fractal complexity spectrum is created to reveal mode shape singularities by eliminating noise and interference. The singularity manifests the abnormality of the mode shape, clearly indicating damage. This study develops a philosophy of fusing wavelets and fractals to detect singularities of physical fields in noisy conditions.

Damage identification in plates based on the ratio of modal strain energy change and sensitivity analysis

A two-step method based on modal strain energy is presented for damage identification in thin plates. In the first step, damage is localized with the modal strain energy change ratio approach. A method is proposed to weaken the ‘Vicinity Effect’, thus reduces the false alarms in the localization of damage. In the second step, the damage extents of the suspected damaged elements are obtained iteratively with modal strain energy change sensitivity-based finite element model updating approach. Model reduction is introduced to eliminate the measurement of rotation degrees-of-freedom in the mode shapes. Two numerical examples are studied to demonstrate the effectiveness and robustness of the proposed method. Both single damage and multiple damage cases are studied and good identification results are obtained. The effect of measurement noise on the identification results is investigated.

A two-step approach for damage Identification in plates

This paper presents a two-step approach based on modal strain energy and response sensitivity analysis to identify the local damages in isotropic plates with moderate thickness. The first step focuses on detection of damage location. The local damage is simulated by a reduction in the elemental Young’s modulus of the plate. It is determined from the modal strain energy change ratio approach. A method to weaken the “vicinity effect” is proposed to reduce the false alarms in the localization of damage. In the second step, an approach based on response sensitivity-based finite element model updating is used to further identify the locations and extents of the local damages in time domain. The identified results are obtained iteratively with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single and multiple damages can be identified successfully and the effect of measurement noise on the identification results is investigated. Good identified results can be obtained from the short time histories of a few number of measurement points.

Damage identification in plates using vibratory power estimated from measured accelerations

Vibratory power is defined as the rate of energy transmitted through a cross section of unit width in a vibrating structure. It is known that the vibratory power is a function of the source and travel path. Therefore the spatial distribution of the vibratory power may contain information on the state of a structure. Vibratory power can be estimated experimentally by measuring accelerations. By combining numerical predictions with experimental measurements the location and severity of damage can be identified. This method has been successfully applied to prismatic beam problems. In the present work, the idea is extended to identifying damage in thin plate problems. To identify damage in thin plates by the proposed vibratory power method, the two-dimensional damage index and damage index ratio are newly introduced. The plate is assumed to be of uniform thickness and damaged in the form of a crack simulated as a straight cut of finite length. The vibratory power of the plate is estimated from frequency response functions to random excitations. First, the proposed method is applied numerically and then verified experimentally. Both numerical and experimental results show the present method can identify not only the location of damage but also its direction. The location and direction can be identified by investigating the damage index, the damage index ratio, and local principal axes of the index peak in the vicinity of the damage. The spatial distribution of the damage index, newly introduced in beam problems, can be considered as a scalar field in plate problems. In the neighborhood of the damage, the damage index has the shape of a semi-ellipsoid or a semi-ovoid, and it is found that the major principal axis corresponds to the direction of the crack. It enables us to identify the damage direction correctly without ambiguity.

Structural damage identification in plates via nonlinear structural intensity maps

A nonlinear structural intensity concept is presented as an approach for the identification of defects displaying nonlinear vibration behavior. The nonlinear structural dynamic response exhibited by a riveted joint with loosened fasteners connecting a stiffener with a flat panel is investigated. The excitation, generating elastic waves with dominant bending components, triggers the nonlinear contact between the plate and the stiffener inducing a dynamic response rich with nonlinear harmonics. Experimental structural intensity maps are evaluated at the super-harmonic frequencies. This technique provides an experimental approach for the characterization and two dimensional visualization of nonlinear types of defects.

Structural damage identification in plates using spectral strain energy analysis

In this paper, a vibration response parameter known as spectral strain energy (SSE) is proposed for structural damage identification in plate-like structures in the context of a non-model-based damage identification approach. The SSE presented in this study is derived from moment–curvature response in which all the modal parameters (namely natural frequency, mode shapes and modal damping) are taken into account. First, displacement response power spectral density obtained from a plate element is used to determine moment power spectral density (MSD) and curvature power spectral density (CSD). A statistical parameter known as mean-square value (MSV) of the response spectral density is then obtained and used to derive SSE based on the assumption that the excitation force is a stationary, ergodic random noise. Consequently, various damage indices are computed and employed for damage detection and localization in simply supported plate and beam elements. The level of sensitivity to damage and performance of the SSE method is illustrated using extensive numerical simulation studies and by comparing the results with those obtained from the modal strain energy (MSE) method. Moreover, the performance and robustness of the SSE method is verified using the experimental modal data obtained from a full-scale bridge structure.