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

457

5

( ∑ 4 ∑ 3 ∑ 2 ∑ 3 ∑ 2 ∑ ∑ 2 ∑ − ) −1 ∙ (

∑ 2 ∙ _ ( ) ∑ ∙ _ ( ) ∑ _ ( ) )

( ) =

#6 = ; #7 = ; #8 = . Criterion #9: the ratio between the maximal values of functions _ ( ) and _ ( ) : #9 = ( _ ( )) ( _ ( )) Criteria #10 - #13: the integral criteria defined as the ratios of the areas bounding functions _ ( ) , _ ( ) and ( ) . The criteria were calculated as follows: #10 = ; #11 = ; #12 = − ; #13 = − where: = { _ 1 ( )} ∙ ∑ _ ( ) _ = _ = { _ 1 ( )} ∙ ∑ _ ( ) _ = _ = { _ 1 ( )} ∙ ∑ _ ( ) _ = _ Step 5: Based on the data obtained on the training set of specimens for each statistical criterion, a data set was formed (Fig.4a) and further interpolated using a bilinear interpolation scheme [11]. As a result, the decision rules were created for each statistical criterion (Fig.4b). 2.3.2. Use of decision rules Assessment the thickness Th W of the “weak” concrete laye r and the degree of concrete degradation W (modeled by decrease of the cement-sand ratio) using decision rules consisted of the following steps.

a)

b)

c)

Fig.4. a) Topology of initial data, b) decision rule for selected criterion c) use of decision rule for recognition case.