PSI - Issue 37

Alexey Tatarinov et al. / Procedia Structural Integrity 37 (2022) 453–461 Alexey Tatarinov et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Step 1: For a control specimen, which is a test case for the decision rule model, steps 1-4 in the section 2.3.1 “Creation of decision r ules” were repeated. Step 2: The values set of Th W and W was divided into a certain number of intervals. In each interval of ThW and W, each i -th statistical criterion of the control specimen # [ ] was compared with the corresponding i -th decision rule [ ] within the accuracy range ±∆ : { # [ ] − ∆≤ [ ] ≤ # [ ] + ∆} = { _ [ ] = 1 _ [ ] = 0 where: ∆= 0,5 ∙ 2 ∙ ( ( [ ]) − ( [ ])) ; 1 – the selection threshold of the actual frequency interval; 2 – the relative error of value # [ ] ; _ – the number of intersections in the interval. Fig.4.c) illustrates the use of the decision rule for one criterion. Step 3: At each interval, the number of intersections of the set of statistical criteria with the corresponding decision rules was computed as = ∑ _ [ ] . The interval, where the number of the intersections is maximal, gives the final estimate of the both factors of interest for the control specimen, Th W and W.

Fig.5. Illustration of finding the area of a probable solution using the superposition of two decision rules.

3. Results and discussion 3.1. Ultrasonic spatiotemporal profiles.

Ultrasonic spatiotemporal waveform profiles at 50 and 100 kHz were obtained in three series of specimens W1, W2 and W3 with gradual variation of Th W in each series. Examples of the profiles a shown in Fig.6. The profiles presented complex waveform patterns, where the Rayleigh surface wave dominated, but other waves presented as well, including the head P-wave, waves in layers, and waves reflected from the bottom and edges of the specimen. Changes in ultrasonic profiles were revealed depending on the both factors, Th W and W, and manifested in notable shifts of ultrasonic propagation packets in the time domain due to the changes of phase and group velocities of ultrasonic waves. In the current study, the profiles composing two-factor (Th W and W) grid at 50 and 100 kHz, were processed by the model based on the formal statistical criteria only (Criteria #1-#13). However, it doesn’t exclude the opportunity of using other criteria derived from the physical features of ultrasound propagation in the time domain.