Issue 50

A. Kostina et alii, Frattura ed Integrità Strutturale, 50 (2019) 667-683; DOI: 10.3221/IGF-ESIS.50.57

Tab. 3 summarizes values of the SNR for each considered signal processing technique calculated using the optimal parameters of the filter. It can be seen that Savitzky-Golay and median filters give the best results and the worst result is obtained by simple moving average. However, the developed Kalman-based filtration method gives higher values of the SNR even for the case when the applied model of temperature contrast evolution describes the reference data incorrectly (Fig. 12). Moreover, the analysis conducted in the previous section has shown that proper calibration of the R and Q parameters as well as a hypothesis on the approximate depth of the defect allows one to obtain a very high value of the SNR (near one thousand or more).

SNR

Signal processing technique

Simple moving average

48

Gaussian filter

55

Savitzky-Golay filter

215

Median filter

191

Kalman-based filter 929 Table 3 : Signal to noise ratio obtained for the various filtration techniques applied to the detection of the 8 mm defect located at the depth of 0.6 mm.

C ONCLUSION

I

n this study, a numerical simulation of subsurface defect identification by pulsed thermography is presented. The object under investigation is a steel plate with artificial defects of various sizes located under the ceramic coating. Subsurface defects have been modelled as parts of the specimen filled with air. The simulation has been carried out on the base of the model which takes into account complex heat exchange by convection, conduction and radiation. The verification has shown that the proposed model can capture the main features of the temperature distribution obtained by a pulsed heating of the sample. The developed model has been applied to the investigation of the influence of the heating parameters on the maximum value of the temperature contrast and the peak contrast time. Due to the fact that the temperature contrast is often susceptible to surface noise of various nature the Kalman-based signal processing technique was developed. The results obtained by numerical simulation were used as reference noise-free signals. The proposed method of filtration is based on the analytical solution to the problem of an infinite plate heated by a Dirac pulse. This solution allows us to propose a universal filtration procedure for signals obtained by pulsed thermography which does not require specific information on the heating parameters. The technique gives satisfactory results even if this information is unknown. In addition, the proposed methodology has been compared to the main well-known and widely used techniques of signal reconstruction. The obtained results have shown that:  Specific features of the heat source (the shape, rise and fall times) substantially affect the temperature contrast value and simulation results. This means that heating of the object by heat sources with the same power can give different values of the temperature contrast.  There is a threshold size of the defect with the specific depth for which the temperature contrast is universal. For example, in the considered problem the size is equal to 6 mm for a depth of 0.6 mm.  Defects with smaller thickness attain the peak contrast time earlier. For instance, defects with the size of 2 mm and a thickness of 0.14 mm reach the peak at t =0.9 s, while defects with a size of 2 mm and a thickness of 3.5 mm have the peak at t =1 s.  Decrease in the heating time leads to the substantial decline in the maximum value of the temperature contrast which can make experimental defect detection difficult due to the presence of the noise.  The temperature contrast is non-linearly dependent on the coating thickness while the peak contrast time depends on it almost linearly.

681