PSI - Issue 8

D’A ccardi Ester/ Structural Integrity Procedia 00 (2017) 000 – 000

3

E. D’Accardi et al. / Procedia Structural Integrity 8 (2018) 354–367

356

( ) 0 t ( ) ( ) T C T t T t sound sound def def    ( ) 0 t T

(2)

where T is the temperature signal, t is the variable time, while the subscripts def and sound refer to the defect and sound area, respectively; the time t 0 is the time at which the cooling starts. In this work, a quantitative data analysis has been performed by referring to the normalized contrast C n of tested parameters, such as the phase, the principal components, the slope and the correlation coefficient:

def n C P P  

sound

(3)



where P is the chosen parameter and σ is the standard deviation. All the relations have been normalized respect to σ to consider the noise influence and to compare the used algorithms.

2.2. Pulsed Phase thermography (PPT)

Pulsed phase thermography (PPT), Ibarra-Castanedo C. (2005), Maldague X. et all (1996), is a technique that transforms data in time domain into the frequency domain using Fast Fourier Transform (FFT). This algorithm combines the techniques of lock-in thermography and pulsed thermography, analyzing through the phase and amplitude parameters, the specimen cooling transition. The extraction of various frequencies, to each of them corresponds a phase and amplitude maps, is done by using the FFT of the thermal signal for each pixel. This transformation is performed as:

 

N-1 k 0 

nk/N)) ((-i2 

F = t

T(k t) exp 

= Re + Im

(4)

n

n

n

where Re and Im are respectively the real part and imaginary part of the transformed and the subscript n is the increasing frequency. The maps are finally obtained using the following relation:

( Re tan Im 1 phase n n 

)

n  

) Re Im ( 2 2 amplitude

A

n n  

(5)

n

In general, N thermograms generate N/2+1 phase maps, associated with frequencies ranging from 0 to N/2* Δf , with Δf = 1/t oss ( t oss = observation time of heat phenomenon).

2.3. Principal component thermography (PCT)

As well as PPT, the Principal Component Thermography (PCT), Rajic N. (2002), Parvataneni R. (2009), transforms the raw thermography data using orthogonal base functions-the principal component. The Principal Component