Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors

Patki, A. S.; Patterson, E. A.

doi:10.1007/s11340-011-9570-4

Cited by 20 publications

(20 citation statements)

References 42 publications

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“…for fingerprint recognition [11] and human face recognition [12] can be appropriately adapted for this purpose. Orthogonal decomposition to reduce the dimensionality of 'raw' data has been recently applied to displacement and strain image decomposition [13][14][15], as well as to finite element model updating [16]. Orthogonal polynomials, such as Zernike, Tchebichef or Krawtchouk are advantageous because they are very effective in data reduction and are also invariant to scale, rotation and translation, thus enabling direct comparison of results regardless of whether the data fields are in the same coordinate system, have the same scale, orientation, or sampling grid.…”

Section: Decomposition Of Displacement and Strain Fieldsmentioning

confidence: 99%

“…Therefore, each deviation d i is multiplied by a respective weighting parameter p i resulting in the following expression (10) For each moment, the weighting parameter is expressed by the ratio of the magnitude of the moment to the sum of all moments: (11) and (12) While this can be done independently for moments from the simulation and experiment, it is more appropriate to use an average value for the moment pair such that the sum of average values of the normalization parameters remains equal to unity, i.e. (13) Hence combining Equations (10) and (12) leads to the following expression for the weighted average deviation (14) The weighted and non-weighted average deviations for the displacements and strain fields in regions 1 and 2 are presented in Table 3, from which general indications about the model quality may be drawn, although the type of error norm applied (weighted or non-weighted) influences significantly the conclusion. Table 3: Weighted and non-weighted average deviation based on equations (10) and (14) respectively, for the moments representing the displacement and strain data fields for the regions shown in Figure 2.…”

Section: Error Norm Comparisonmentioning

confidence: 99%

“…(13) Hence combining Equations (10) and (12) leads to the following expression for the weighted average deviation (14) The weighted and non-weighted average deviations for the displacements and strain fields in regions 1 and 2 are presented in Table 3, from which general indications about the model quality may be drawn, although the type of error norm applied (weighted or non-weighted) influences significantly the conclusion. Table 3: Weighted and non-weighted average deviation based on equations (10) and (14) respectively, for the moments representing the displacement and strain data fields for the regions shown in Figure 2.…”

Section: Error Norm Comparisonmentioning

confidence: 99%

See 2 more Smart Citations

On the validation of solid mechanics models using optical measurements and data decomposition

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Lin

et al. 2015

Simulation Modelling Practice and Theory

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Engineering simulation has a significant role in the process of design and analysis of most engineered products at all scales and is used to provide elegant, lightweight , optimized designs. A major step in achieving high confidence in computational models with good predictive capabilities is model validation. It is normal practice to validate simulation models by comparing their numerical results to experimental data. However, current validation practices tend to focus on identifying hot-spots in the data and checking that the experimental and modeling results have a satisfactory agreement in these critical zones. Often the comparison is restricted to a single or a few points where the maximum stress / strain is predicted by the model. The objective of the present paper is to demonstrate a step-by-step approach for performing model validation by combining fullfield optical measurement methodologies with computational simulation techniques. Two important issues of the validation procedure are discussed, i.e. effective techniques to perform data compression using the principles of orthogonal decomposition, as well as methodologies to quantify the quality of simulations and make decisions about model validity. An I-beam with open holes under three-point bending loading is selected as an exemplar of the methodology. Orthogonal decomposition by Zernike shape descriptors is performed to compress large amounts of numerical and experimental data in selected regions of interest (ROI) by reducing its dimensionality while preserving information; and different comparison techniques including traditional error norms, a linear comparison methodology and a concordance coefficient correlation are used in order to make decisions about the validity of the simulation.

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Section: Decomposition Of Displacement and Strain Fieldsmentioning

confidence: 99%

Section: Error Norm Comparisonmentioning

confidence: 99%

Section: Error Norm Comparisonmentioning

confidence: 99%

See 1 more Smart Citation

On the validation of solid mechanics models using optical measurements and data decomposition

Lampeas

Pasialis

Lin

et al. 2015

Simulation Modelling Practice and Theory

View full text Add to dashboard Cite

show abstract

“…The capabilities of DIC performed for high-speed events offer the potential for more rigorous validation and refinement of computational solid mechanics models, which is essential for high-fidelity simulations, 6 but create the challenge of how to quantitatively compare data-rich displacement and/or strain fields from experimentation and simulation. It has been shown previously that shape or image descriptors can be used to represent strain fields with reduced dimensionality 7 and employed in validation procedures, 8 in static or pseudo-static load cases, and for finite element (FE) updating in both static 9 and vibration 10 loading cases. For the latter cases, the frequency response function of the shape features has been investigated.…”

Section: Introductionmentioning

confidence: 99%

Analysis of displacement fields from a high-speed impact using shape descriptors

Burguete

Lampeas

Mottershead

et al. 2013

The Journal of Strain Analysis for Engineering Design

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A composite bonnet liner subject to a high-velocity (70 m/s), low-energy (\ 300 J) impact by a 50-mm-diameter projectile has been investigated using computational simulation and by experiment. High-speed digital image correlation was employed to generate maps of displacement fields over the 1-m 2 bonnet at 0.2 ms increments for 0.1 s, that is, 500 datasets, and the results have been compared to those predicted by finite element analysis. Image decomposition was utilised to reduce the dimensionality of both datasets by representing them using adaptive geometric moment descriptors; these descriptors were used to perform quantitative comparisons of the datasets and to test the validity of the model based on all the available data. The model was found to be a good representation of the physical experiment during the first half of the impact event but a less good representation in the remainder of the test, probably because damping effects were not adequately incorporated into the simulation. The methodologies for data comparison and evaluation of model validity proposed and demonstrated in this study represent a significant advance in procedures for ensuring model fidelity and for creating model credibility in the simulation of dynamic engineering events.

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“…These descriptors tend to be easier to compute and exhibit better information-preservation than contourbased descriptors and most region-based descriptors, such as Zernike moments; 13 however Fourier descriptors do not achieve any data compression. This combination of advantages and disadvantages led Patki and Patterson 6,14 to propose a new shape descriptor viz. the Fourier-Zernike descriptors in which Zernike moments are evaluated for the Fourier transform of a strain map.…”

Section: Introductionmentioning

confidence: 99%

Damage assessment of fibre reinforced composites using shape descriptors

Patki

Patterson

2012

The Journal of Strain Analysis for Engineering Design

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This study explores the use of a generic shape descriptor for quantitative comparisons between the full-field strain data acquired from virgin and damaged composite panels using digital image correlation. These descriptors are capable of decomposing images with 10 3 to 10 6 pixels into a feature vector with less than a few hundred elements. Strain distributions in four composite specimens with incremental impact damage and a virgin specimen, all subject to a tensile load, were decomposed using the newly developed Fourier-Zernike descriptors. Pearson's correlation coefficient, cosine similarity and Euclidean distance were employed to compare quantitatively the feature vectors evaluated for the strain distributions in the four damaged specimens with the strain distribution in the virgin specimen. The deviation of the Pearson correlation coefficient from unity was found to be an effective damage indicator, which could be evaluated automatically and without the need for subjective assessment of the damage.

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Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors

Cited by 20 publications

References 42 publications

On the validation of solid mechanics models using optical measurements and data decomposition

On the validation of solid mechanics models using optical measurements and data decomposition

Analysis of displacement fields from a high-speed impact using shape descriptors

Damage assessment of fibre reinforced composites using shape descriptors

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