PSI - Issue 52

Wu Zonghui et al. / Procedia Structural Integrity 52 (2024) 203–213 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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adopted different loss functions with UED are shown in Table 6.

Table 5. Result of ANNs with large-size samples. Loss function P f β

Mean value of β

MSE

4.70 × 10 -6 4.75 × 10 -6 4.75 × 10 -6

4.431 4.428 4.428

MSAPE MAPE

4.429

Table 6. Reliability index of ANNs with small-size sample set. Loss function P f β MSE 5.85 × 10 -6 4.383 MSAPE 5.50 × 10 -6 4.397 MAPE 5.10 × 10 -6 4.413 Different degrees of deviation appeared in calculation results when questionable data was added to the training set. The consequence of reliability indexes computed by ANNs with 300 samples is shown in Fig.11.

Fig. 11. Reliability index of ANNs with wrong samples.

3.2.1. Engineering error simulation In the incorrect samples stated previously, the value of the output becomes its opposite number, which is one of the most serious situations but rare in real engineering. In practical engineering, a small deviation occurs frequently while a large deviation is a small probability event. So three kinds of questionable data are considered in this section: tiny vibrations( ± δ 1 ) caused by the surrounding environment, small deviations caused by equipment error( ± δ 2 ), and large deviations( ± Δ ) caused by accidental events. The values of these three errors are δ 1 =5Mpa, $ ± δ 2 =10Mpa and Δ =300Mpa. Five normal statuses are under consideration: 1. Errors caused by external factors (all samples add or minus δ 1 stochastically); 2. Positive equipment error (all samples add δ 2 ); 3. Negative equipment error (all samples minus δ 2 ); 4. Surrounding error and positive equipment error; 5. Surrounding error and negative equipment error. And their results are shown in Fig.12. Two small probability events are considered: 1. Surrounding error + positive equipment error + a large shock ( ± Δ ) in partial samples; 2. Surrounding error + negative equipment error + a large shock ( ± Δ ) in partial samples. The result of event 1 is shown in Fig.13 and event 2 is shown in Fig.14.