Decomposition-based calibration/validation metrics for use with full-field measurement situations

Abstract

Calibration and validation metrics that involve decomposition of simulation and test data have been developed for potential use in the quantification of margin and uncertainty. The uniqueness of these validation metrics allows for nearly fullfield, simulation and test data over a wide range of spatial realizations (three-dimensional responses over multiple input conditions) and temporal (time or frequency) information, as needed. Currently, no other calibration/validation metrics have been developed that span multiple spatial realizations and temporal information simultaneously. A demonstration example utilizing two datasets explains how the calibration/validation metrics are formed and how they can be used to quantify the margin between the simulation and the test data as well as how it can quantify the uncertainty. The primary advantage of a proposed principal component analysis validation metric is that it preserves the engineering units of the original data so that the quantifications of margin and uncertainty can be made in engineering unit. A second advantage of the principal component analysis validation metric is that it can be used over a wide range of temporal information. The potential case of using sets of data with mismatched degree of freedom information is also explored. The general approach of using decomposition methods as the basis for calibration/validation metrics is extended to image decomposition methods. All decomposition methods successfully quantify margin and uncertainty in this general calibration/validation metric approach.

Comparing full-field data from structural components with complicated geometries

“…The result of the modal assurance criterion is a value between 0 and 1 indicating the quality of agreement. This normalization makes it difficult to define an acceptance criterion as the criterion output cannot be related to the measurement uncertainty of the experiment [ 5 ]. Others have explored using singular value decomposition to compare mode shapes.…”

“…Others have explored using singular value decomposition to compare mode shapes. These approaches reduce the dimensionality of the data by projecting it onto an orthogonal set of kernels resulting in a feature vector with the same units as the originally measured or simulated data-field [ 5 ]. This feature vector is therefore more readily related to the measurement uncertainty of the experiment.…”

The use of charge-coupled device cameras for characterizing the mean deflected shape of an aerospace panel during broadband excitation

“…The frequency response of each of these 20 descriptors was then computed to produce the so-called shape descriptor frequency response function (SD-FRF), and the first 11 mode shapes were constructed from the 20 shape descriptors. Subsequently, Allemang et al 25,26 explored the use of principal component analysis (PCA), based on singular value decomposition (SVD), to perform similar transformations on their data. They concluded that the results obtained from SVD-PCA and orthogonal decomposition techniques were comparable, but the former was more straightforward to implement.…”

“…The use of decomposition methods to reduce the dimensionality of the resultant data and enable more straightforward comparisons has also been established. 13,[25][26][27] While, recently, Berke et al 28 have shown the correlation between modal shapes for simple rectangular plates and the kernels of the Chebyshev polynomials used in orthogonal decomposition. Hence, orthogonal decomposition based on Chebyshev polynomials was chosen for use in this study to reduce the dimensionality of the out-of-plane displacement fields measured using stereoscopic DIC.…”

Advances in Validation of Computational Mechanics Models

“…An example for the use of decomposition methods as an essential part of full-field validation process is described by engineers of the aerospace field. 3 They conclude that the decomposition methods successfully quantify margin and uncertainty in their approach to validation metrics.…”