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

456

4

2.3. Proposed mathematical approach to data processing. The proposed mathematical approach for the assessment of the thickness and quality of the surface layer of “weak” concrete is based on the principles of pattern recognition. The evaluation study consisted of two parts: 1) creation of a set of decision rules using the data of a training set of specimens and 2) validation of the decision rules by substitution the data of control specimens into the model and comparison of predicted and experimental data. 2.3.1. Creation of decision rules Step 1: For a specimen with a priori known Th W , sets of profiling signals were collected at frequencies of 50 and 100 kHz. At one profiling step, two discrete signals s ( t ) were obtained. Step 2: Each of the discrete signals s(t) (t ∈ [t_min;t_max]) was converted by the discrete Fourier transform [10] into the spectral signal ( ) , ∈ [ _ ; _ ] describing the magnitude spectrum: ( ) = √( ( )) 2 + ( ( )) 2 where: ( ) = ∑ ( ) ∙ ( 2 ∙ ∙ − _ ) _ = _ and ( ) = ∑ ( ) ∙ ( 2 ∙ ∙ − _ ) _ = _ . In further processing, the considered interval ω satisfied the following conditions: ( ) ≥ 1 ∙ { ( )} and ≤ 0,5 ∙ ( _ − _ ) Step 3 : In the selected interval ω, the values of three functions were calculated: _ ( ) = { ( )} ; ( ) = { ( )} and _ ( ) = { ( )} Step 4: Statistical tests were performed in the selected interval ω. Criterion #1: the number of values that fulfil the condition: ( ) ≥ ( _ ( )), ( #1) ; Criterion #2: the ratio between the maximal values of the functions _ ( ) and _ ( ) : #2 = ( _ ( )) ( _ ( )) Criterion #3: the ratio of the maximum derivative value for the function _ ( ) to the maximal value for the function _ ( ) : #3 = | _ ( )| ( _ ( )) where: _ ( ) = _ ( ) − _ ( − 1) . Criterion #4: the ratio of the maximum derivative of function _ ( ) to the maximal value for the function _ ( ) : #4 = | _ ( )| ( _ ( )) where: _ ( ) = _ ( ) − _ ( − 1) . Criterion #5: the ratio of the maximum derivative of function _ ( ) to the maximal value for the function _ ( ) : #5 = | _ ( )| ( _ ( )) where: _ ( ) = _ ( ) − _ ( − 1) . Criteria #6, #7 and #8: approximation of function _ ( ) by quadric polynomial ( ) = ∙ 2 + ∙ + , where polynomial coefficients can be found using the method of least squares: