Issue 50

A. Kostina et alii, Frattura ed Integrità Strutturale, 50 (2019) 667-683; DOI: 10.3221/IGF-ESIS.50.57 678 Fig. 12 presents results of filtration of the reference signal obtained for the defect with the minimal size of 2 mm (a purple curve in Fig. 7 (a)) using values of R =7 and Q =0.003. In this case, we have a much smaller value of the optimal SNR which is equal to 241. The reason for this decline is that the used analytical model for the temperature evaluation (10) does not take into account the size of the defect and depends only on the depth. To achieve more accurate results of filtration it is necessary to employ more precise analytical models for evolution of the temperature contrast. The analytical model (12) contains the depth of the defect as one of the governing parameter defining the behavior of the temperature contrast evolution. However, in real applications of pulsed thermography for defect detection this value is often unknown. Fig. 13 displays the effect of the false depth on the reconstructed signal. The reference signal corresponds to the numerical results of the temperature contrast obtained for 2 mm subsurface defect located at the depth of 2 mm. Fig. 13 (a) shows results of the reconstruction attained with the use of the precise depth of the defect and values of R =9, Q =0.03. It can be seen that the reconstructed signal repeats the shape of the reference signal with high accuracy). Fig. 13 (b) provides results obtained for the false depth of the defect L which was equal to 0.6 mm. Calibration of the R parameter allows us to reconstruct the shape of the signal close to the original. The applied value of R was equal to 6, the value of Q was the same. Thus, in case when the applied value of the depth is far from the proper, the inaccuracy of the model can be compensated by the measurement noise covariance. (a) (b) Figure 11 : Application of the Kalman-based filtration technique to the detection of the 8 mm defect located at the depth of 0.6 mm (1 – reconstructed signal, 2 – reference signal, 3 – initial signal with noise): (a) SNR = 929 (b) SNR = 1150. Figure 12 : Application of the Kalman-based filtration technique to the detection of the 2 mm defect located at the depth of 0.6 mm (1 – reconstructed signal, 2 – reference signal, 3 – initial signal with noise). Comparison with other signal processing techniques The proposed filtration technique is formulated in the time domain. Hence, a comparative study will be carried out with the use of the four most widely applied time-domain signal processing techniques: simple moving average, Gaussian,