Transformation of measurement uncertainties into low-dimensional feature vector space

Advances in technology allow the acquisition of data with high spatial and temporal resolution. These datasets are usually accompanied by estimates of the measurement uncertainty, which may be spatially or temporally varying and should be taken into consideration when making decisions based on the data. At the same time, various transformations are commonly implemented to reduce the dimensionality of the datasets for postprocessing or to extract significant features. However, the corresponding uncertainty is not usually represented in the low-dimensional or feature vector space. A method is proposed that maps the measurement uncertainty into the equivalent low-dimensional space with the aid of approximate Bayesian computation, resulting in a distribution that can be used to make statistical inferences. The method involves no assumptions about the probability distribution of the measurement error and is independent of the feature extraction process as demonstrated in three examples. In the first two examples, Chebyshev polynomials were used to analyse structural displacements and soil moisture measurements; while in the third, principal component analysis was used to decompose the global ocean temperature data. The uses of the method range from supporting decision-making in model validation or confirmation, model updating or calibration and tracking changes in condition, such as the characterization of the El Niño Southern Oscillation

Robust Empirical Predictions of Residual Performance of Damaged Composites with Quantified Uncertainties

Robust predictions with estimated uncertainties were made for the residual strength of impact-damaged composite laminates based on simple non-destructive measurements of the size of the damage from ultrasound C-scans. Experimental data was acquired for two sets of composite coupons, one with a crossply and the other with a quasi-isotropic layup. The laminates were subject to drop-weight impacts, non-destructively evaluated using ultrasound and then loaded to failure in bending. An empirical model of the residual strength of each laminate layup, as a function of the ultrasound measurements, was generated by fitting a Bayesian linear regression model to the normalised measured data. Bayesian linear regression was demonstrated to provide conservative estimates when only minimal data is available. Unlike classical regression, this technique provides a robust treatment of outliers, which avoids underestimation of residual strength. The Leave-One-Out-Cross-Validation (LOOCV) metric was used to assess the performance of models allowing for the quantitative comparison of the predictive power of regression models as well as being consistent in the presence of outliers in the data. The LOOCV metric indicated that predictions of residual strength are up to 25% more accurate when based on damage area than when using measurements of the damage width or length. The proposed approach provides a robust methodology for performing damage assessments in safety critical composite components based on reliable predictions with quantified uncertainties

An experimental study on the manufacture and characterization of in-plane fibre-waviness defects in composites

A new method has been developed for creating localized in-plane fibre waviness in composite coupons and used to create a large batch of specimens. This method could be used by manufacturers to experimentally explore the effect of fibre waviness on composite structures both directly and indirectly to develop and validate computational models. The specimens were assessed using ultrasound, digital image correlation and a novel inspection technique capable of measuring residual strain fields. To explore how the defect affects the performance of composite structures, the specimens were then loaded to failure. Predictions of remnant strength were made using a simple ultrasound damage metric and a new residual strain-based damage metric. The predictions made using residual strain measurements were found to be substantially more effective at characterizing ultimate strength than ultrasound measurements. This suggests that residual strains have a significant effect on the failure of laminates containing fibre waviness and that these strains could be incorporated into computational models to improve their ability to simulate the defect

Dynamic Response of a Thermally Stressed Platewith Reinforced Edges

Conditions in hypersonic flight generate non-uniform temperature distributions that affect the performance and longevity of aircraft components. Historically, a limited amount of experimental work has been performed on the mechanical behaviour of reinforced aircraft structures subjected to very high temperatures. In this work on Hastelloy-X plates, non-contact techniques were used to measure the full-field temperature and deflection of a 1 mm thick plate with reinforced edges. The geometry was designed to emulate an aircraft’s skin with the reinforced edges performing the function of stringers and ribs. High temperatures were achieved using quartz lamps arranged in various configurations with controllable power output. Digital image correlation (DIC) was used to measure surface displacements and a micro-bolometer mapped the temperature distribution across the plate. Deflection results for the reinforced plate showed it to behave as a dynamic system that buckles out-of-plane when heated before relaxing to a steady state. It is demonstrated that the out-of-plane displacement field experienced by the plate is influenced both by the in-plane temperature gradient and the energy supplied

Identification of defects in composite laminates by comparison of mode shapes from electronic speckle pattern interferometry

A novel technique for identifying defects in carbon fibre reinforced plates has been developed. Firstly, modal analysis by impact excitation was performed to obtain the first five resonant frequencies for three defect-free and three defective specimens with in-plane fibre waviness. Then amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) was used to obtain the mode shapes at these frequencies. The contours of the nodal regions visible in the mode shapes were extracted using a specially-developed algorithm employing density-based spatial clustering of applications with noise (DBSCAN). Fourier descriptors, that are invariant to rotations, translations, and scaling, were used to decompose the contours to reduce data dimensionality and make comparisons. The differences in contours between the two sets of specimens showed that the 4th and 5th mode shapes can be used for identifying the presence of the waviness defects. This technique for nodal region comparison was found to greatly simplify the comparison of fringe patterns for the purpose of damage assessment and could potentially be used as part of validation procedures

Comparing full-field data from structural components with complicated geometries

A new decomposition algorithm based on QR factorization is introduced for processing and comparing irregularly shaped stress and deformation datasets found in structural analysis. The algorithm improves the comparison of two-dimensional data fields from the surface of components where data is missing from the field of view due to obstructed measurement systems or component geometry that results in areas where no data is present. The technique enables the comparison of these irregularly shaped datasets without the need for interpolation or warping of the data necessary in some other decomposition techniques, for example, Chebyshev or Zernike decomposition. This ensures comparisons are only made between the available data in each dataset and thus similarity metrics are not biased by missing data. The decomposition and comparison technique has been applied during an impact experiment, a modal analysis, and a fatigue study, with the stress and displacement data obtained from finite-element analysis, digital image correlation and thermoelastic stress analysis. The results demonstrate that the technique can be used to process data from a range of sources and suggests the technique has the potential for use in a wide variety of applications