A method for vibration-based structural interrogation and health monitoring based on signal cross-correlation

Vibration-based structural interrogation and health monitoring is a field which is concerned with the estimation of the current state of a structure or a component from its vibration response with regards to its ability to perform its intended function appropriately. One way to approach this problem is through damage features extracted from the measured structural vibration response. This paper suggests to use a new concept for the purposes of vibration-based health monitoring. The correlation between two signals, an input and an output, measured on the structure is used to develop a damage indicator. The paper investigates the applicability of the signal cross-correlation and a nonlinear alternative, the average mutual information between the two signals, for the purposes of structural health monitoring and damage assessment. The suggested methodology is applied and demonstrated for delamination detection in a composite beam

A method for vibration-based structural interrogation and health monitoring based on signal cross-correlation

Vibration-based structural interrogation and health monitoring is a field which is concerned with the estimation of the current state of a structure or a component from its vibration response with regards to its ability to perform its intended function appropriately. One way to approach this problem is through damage features extracted from the measured structural vibration response. This paper suggests to use a new concept for the purposes of vibration-based health monitoring. The correlation between two signals, an input and an output, measured on the structure is used to develop a damage indicator. The paper investigates the applicability of the signal cross-correlation and a nonlinear alternative, the average mutual information between the two signals, for the purposes of structural health monitoring and damage assessment. The suggested methodology is applied and demonstrated for delamination detection in a composite beam

Modern Modal Testing: A Cautionary Tale

Over the past 50 years, great advances have been achieved in both analytical modal analysis (i.e. finite element models and analysis) and experimental modal analysis (i.e. modal testing) in aerospace and other fields. With the advent of more powerful computers, higher performance instrumentation and data acquisition systems, and powerful linear modal extraction tools, analysts and test engineers have a breadth and depth of technical resources only dreamed of by our predecessors. However, some observed recent trends indicate that hard lessons learned are being forgotten or ignored, and possibly fundamental concepts are not being understood. These trends have the potential of leading to the degradation of the quality of and confidence in both analytical and test results. These trends are a making of our own doing, and directly related to having ever more powerful computers, programmatic budgetary pressures to limit analysis and testing, and technical capital loss due to the retirement of the senior component of a bimodal workforce. This paper endeavors to highlight some of the most important lessons learned, common pitfalls to hopefully avoid, and potential steps that may be taken to help reverse this trend

Representativity error for temperature and humidity using the Met Office high-resolution model

The observation-error covariance matrix used in data assimilation contains contributions from instrument errors, representativity errors and errors introduced by the approximated observation operator. Forward model errors arise when the observation operator does not correctly model the observations or when observations can resolve spatial scales that the model cannot. Previous work to estimate the observation-error covariance matrix for particular observing instruments has shown that it contains signifcant correlations. In particular, correlations for humidity data are more significant than those for temperature. However it is not known what proportion of these correlations can be attributed to the representativity errors. In this article we apply an existing method for calculating representativity error, previously applied to an idealised system, to NWP data. We calculate horizontal errors of representativity for temperature and humidity using data from the Met Office high-resolution UK variable resolution model. Our results show that errors of representativity are correlated and more significant for specific humidity than temperature. We also find that representativity error varies with height. This suggests that the assimilation scheme may be improved if these errors are explicitly included in a data assimilation scheme. This article is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland

Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement (ADFP) and its effects on permeability

Resin transfer moulding is one of several processes available for manufacturing fibre-reinforced composites from dry fibre reinforcement. Recently, dry reinforcements made with Automated Dry Fibre Placement have been introduced into the aerospace industry. Typically, the permeability of the reinforcement is assumed to be constant throughout the dry preform geometry whereas in reality it possesses inevitable uncertainty due to variability in geometry. This uncertainty propagates to the uncertainty of the mould filling and the fill time, one of the important variables in resin injection. It makes characterisation of the permeability and its variability an important task for design of the resin transfer moulding process. In this study, variability of the geometry of a reinforcement manufactured using Automated Dry Fibre Placement is studied. Permeability of the manufactured preforms is measured experimentally and compared to stochastic simulations based on an analytical model and a stochastic geometry model. The simulations showed that difference between the actual geometry and the designed geometry can result in 50% reduction of the permeability. The stochastic geometry model predicts results within 20% of the experimental values

Behavior of granite-epoxy composite beams subjected to mechanical vibrations

The capacity to damp mechanical vibrations is one of the most important properties of granite-epoxy composites, even superior to the cast iron one. For this reason, these materials have been adopted for manufacturing of tool machine foundations and precision instruments. This work presents a study concerning the behavior of particulate composite beams, based on granite powder and epoxy, subjected to mechanical vibrations. Composite samples were prepared with different combinations of processing variables, like the weight fraction of epoxy in the mixture and size distributions of granite particles. The damping behavior of the material was investigated adopting the logarithmic decrement method. Samples, in the form of prismatic beams, were excited in the middle point and the output signal was measured in a point located at the extremity. The obtained results showed that composite samples, with weight fractions of about 80% of granite and 20% of epoxy, presented damping properties approximately three times greater than gray cast iron

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Defining the roughness sublayer and its turbulent statistics

The roughness sublayer in a turbulent openchannel flow over a very rough wall is investigated experimentally both within the canopy and above using particle image velocimetry by gaining complete optical access with new methodologies without disturbing the flow. This enabled reliable estimates of the double-averaged mean and turbulence profiles to be obtained by minimizing and quantifying the usual errors introduced by limited temporal and spatial sampling. It is shown, for example, that poor spatial sampling can lead to erroneous vertical profiles in the roughness sublayer. Then, in order to better define and determine the roughness sublayer height, a methodology based on the measured spatial dispersion is proposed which takes into account temporal sampling errors. The results reveal values well below the usual more ad hoc estimates for all statistics. Finally, the doubleaveraged mean and turbulence statistics in the roughness sublayer are discussed

Sensitivity of Chaos Measures in Detecting Stress in the Focusing Control Mechanism of the Short-Sighted Eye

yesWhen fixating on a stationary object, the power of the eye’s lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ( 0.64±0.330.64±0.33 vs. 0.39±0.20 D/s0.39±0.20 D/s ) and a lower embedding dimension than the LOMs ( 3.28±0.463.28±0.46 vs. 3.67±0.493.67±0.49 ). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi