Active Thermography Based on Tensor Rank Decomposition

Peter W Spaeth; Peter L Takunju; Joseph N Zalameda

NASA NTRS · 20220003591

Active Thermography Based on Tensor Rank Decomposition

Peter W Spaeth·Peter L Takunju·Joseph N Zalameda

Abstract

Principal Component Thermography applies Singular Value Decomposition (SVD) to post-process data that are derived from active thermographic inspections. SVD provides useful compression of the data and allows for better understanding of substructure and indications of potential damage. In the standard approach, SVD is applied to a certain reshaping of a three-dimensional data stack into a two-dimensional array. This work applies the CANDECOMP-PARAFAC (CP) tensor rank decomposition directly to the three-dimensional data to avoid the initial reshaping step in order to begin to develop an inspection method that can more accurately detect defects in non-homogeneous and anisotropic materials. Tests against simulated data that compare the CP decomposition method with traditional Principal Component Thermography based on SVD are described. Finally, the method of Proper Generalized Decomposition (PGD) is used to derive the CP decomposition, and its performance against other algorithms is also discussed.

Explore related subjects

Thermography Singular Value Decom CANDECOMP-PARAFAC Decomposition Alternating Least Squares Proper Generalized Decomposition Tensor Approximation

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Peter W Spaeth, Peter L Takunju, Joseph N Zalameda. Active Thermography Based on Tensor Rank Decomposition. https://ntrs.nasa.gov/citations/20220003591

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

NASA NTRS2012

Thermal Imaging with Novel Infrared Focal Plane Arrays and Quantitative Analysis of Thermal Imagery

We have developed a single long-wavelength infrared (LWIR) quantum well infrared photodetector (QWIP) camera for thermography. This camera has been used to measure the temperature profile of patients. A pixel coregistered simultaneously reading mid-wavelength infrared (MWIR)/LWIR dual-band QWIP camera was developed to improve the accuracy of temperature measurements especially with objects with unknown emissivity. Even the dualband measurement can provide inaccurate results due to the fact that emissivity is a function of wavelength. Thus we have been developing a four-band QWIP camera for accurate temperature measurement of remote object.

Thermography↗

NASA NTRSDate not supplied

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

NASA NTRSDate not supplied

Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. The quadrupole method has been shown as a viable technique for rapidedly simulating the thermal repsonse of layered systems. Often, the effort has focused on a one-dimentional models, in particular for improved analysis of thermal data. For composites, the in-plane heat diffusion often significantly impacts the thermal response of defects of interest, therefore three-dimensional simulations are desirable. This paper discusses the extension of the quadrupole methodology to perform simulations of thermographic responses in three-dimensional configuration. This enables the more realistic simulations of the thermal response of delaminiations in composites. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are known obtained from other sources.

Thermography↗