PSI - Issue 37

Deniss Mironovs et al. / Procedia Structural Integrity 37 (2022) 410–416 Deniss Mironovs/ Structural Integrity Procedia 00 (2019) 000 – 000

413

4

Young’s modulus E, GPa

137.82 0.33357 2.9597 1549.7

7.1796

137.82 0.33357 2.9597

Poisson’s ratio υ

0.3

Shear modulus G, GPa

6.9269

Density ρ, kg/m 3

The result is formed into a matrix Y with 5 rows, corresponding to the number of calculated modes. Each row has the frequency value as the first element and a mode shape vector for elements 2 to 203. Potentially this matrix can be populated with measured data of environmental and operational factors, but the further data processing stays identical. In order to simulate numerous cases of modal analysis measurements under stable environmental and operating conditions, a Gaussian noise of ± 0.2 % was added to reference state modal parameters matrix Y , thus creating 5000 unique samples. Damaged state is modelled as delamination with a degree of 5% of beam area. There are four damaged states, with the same degree of delamination positioned at diffe rent locations along the beam’s length. The total amount of generated samples is 5004. For anomaly detection algorithm 3000 training samples are chosen out of total amount of samples, all being representative of healthy state. The mean matrix Μ( ) is calculated between these training samples. Each training samples multivariate probability ( ) is then calculated, where the mean matrix has the maximum probability. The distribution of ( ) is naturally Gaussian. Next, cross-validation CV samples are formed – another 1000 healthy states and two damaged states, 1002 samples combined. Multivariate probability ( ) is calculated for 1002 cross-validation samples. Scholars show that one can set the threshold between states at a ±3 limit, i.e. standard deviation with a factor of 3, which gives 99.7 % confidence in true results. Alternatively, for higher precision, ( ) is compared to a state label vector, where 0 denotes healthy and 1 – damaged states. This labeling allows to automatically establish a threshold between healthy and damaged state, using F1 score calculation. When the probability model is created and a healthy state threshold is established, a test sample set is formed out of remaining 1000 healthy states and 2 damaged states, thus ensuring independent data for objective algorithm validation. Probability ( ) is calculated and compared to the threshold. For ( ) < the sample is considered to be damaged and vice versa.

a

b

Fig. 1. a) Composite beam, reference state; b) healthy state 4 th mode, 3rd bending shape.

4. Results and discussion The presented algorithm has been able to correctly identify both damaged states from test sample set for modes 1, 2 and 4, which are all bending modes. For modes 3 and 5, which are torsional modes, the mode shape vector is formed