Numerical and experimental assessment of the modal curvature method for damage detection in plate structures

Use of modal curvatures obtained from modal displacement data for damage detection in isotropic and composite laminated plates is addressed through numerical examples and experimental tests. Numerical simulations are carried out employing COMSOL Multiphysics as finite element solver of the equations governing the Mindlin-Reissner plate model. Damages are introduced as localized non-smooth variations of the bending stiffness of the baseline (healthy) configuration. Experiments are also performed on steel and aluminum plates using scanning laser vibrometry. The obtained results confirm that use of the central difference method to compute modal curvatures greatly amplifies the measurement errors and its application leads to unreliable predictions for damage detection, even after denoising. Therefore, specialized ad hoc numerical techniques must be suitably implemented to enable structural health monitoring via modal curvature changes. In this study, the Savitzky-Golay filter (also referred to as least-square smoothing filter) is considered for the numerical differentiation of noisy data. Numerical and experimental results show that this filter is effective for the reliable computation of modal curvature changes in plate structures due to defects and/or damages

Numerical Differentiation Of Equally Spaced And Not Equally Spaced Experimental Data

Procedures are given for smoothing and differentiating experimental data with both equal and nonequal spacing in the independent variable. Selection of the number of points to be included in the movable strip technique and of the degree of the polynomial is discussed. Equations are given to estimate the error by calculating a confidence interval on each slope. A technique for handling certain types of nonrandom errors is presented. © 1967, American Chemical Society. All rights reserved

Bias in particle tracking acceleration measurement

We investigate sources of error in acceleration statistics from Lagrangian Particle Tracking (LPT) data and demonstrate techniques to eliminate or minimise bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to position uncertainty and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the spatial resolution and sampling rate required to adequately measure statistics of Lagrangian acceleration

Derivative-free online learning of inverse dynamics models

This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the literature typically exploit joint velocities and accelerations, which need to be approximated resorting to numerical differentiation schemes, in this paper a new `derivative-free' framework is proposed that does not require this preprocessing step. An extensive experimental study with real data from the right arm of the iCub robot is presented, comparing different model classes and estimation procedures, showing that the proposed `derivative-free' methods outperform existing methodologies.Comment: 14 pages, 11 figure

Techniques in numerical differentiation of experimentally noisy data

A comparison of different methodologies for spatial differentiation of experimental noisy data is presented. The transient displacement fields resulting from bending wave propagation on aluminum plate were measured with pulse TV-holography. A new method to perform the numerical spatial differentiation and a strategy for dealing with the border problem are presented. The method here presented results for the third order derivative and showed to be superior to the other methods tested. A good agreement between the new method and the Finite Elements Method was achieved

On compression rate of quantum autoencoders: Control design, numerical and experimental realization

Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the compression rate for a given quantum autoencoder and present a learning control approach for training the autoencoder to achieve the maximal compression rate. The upper bound of the compression rate is theoretically proven using eigen-decomposition and matrix differentiation, which is determined by the eigenvalues of the density matrix representation of the input states. Numerical results on 2-qubit and 3-qubit systems are presented to demonstrate how to train the quantum autoencoder to achieve the theoretically maximal compression, and the training performance using different machine learning algorithms is compared. Experimental results of a quantum autoencoder using quantum optical systems are illustrated for compressing two 2-qubit states into two 1-qubit states

A hybrid technique for damage detection on laminated plates

This work presents an experimental/numerical technique for delamination damage detection on thin laminated composite plates. The delamination is identified using a technique based on the curvature differences of the plate modes shapes measured before and after impact damage. The natural frequencies are extracted from Frequency Response Functions. A double pulse TV holography is used for no-contact and accurate measurement of the amplitude mode shapes. The curvature is obtained by applying an improved differentiation /smoothing technique to the experimental data. Finally, the curvatures of each mode are subtracted and the damage is located

Determination of Mode I Fracture Toughness of Cortical Human Bone using the DCB Test

The fracture behaviour of human cortical bone was analysed considering a miniaturized version of theDouble Cantilever Beam (DCB) test. A specific data reduction scheme based on crack equivalentconcept was used to obtain the resistance curves. The definition of the cohesive laws mimicking thefracture process was performed measuring the crack tip opening displacement by digital imagecorrelation during the test. The differentiation of the relation between the strain energy release rate andcrack tip opening displacement allows to define the experimental cohesive law. In order to validate theprocedure, trapezoidal cohesive laws with bilinear softening were adjusted to the experimental ones.The DCB tests were simulated by finite element analysis including cohesive zone modelling with theadjusted laws. The resulting numerical load-displacement and resistance curves were compared withthe numerical ones. Good agreement was obtained which validates the proposed procedure