PSI - Issue 64

Marco Pirrò et al. / Procedia Structural Integrity 64 (2024) 661–668 Author name / Structural Integrity Procedia 00 (2019) 000–000

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lowpass filter (cut-off frequency of 16.5 Hz and a 0.05 dB peak-to-peak ripple in the passband) and (b) down sampled to 41.3 Hz (i.e., decimated 20 times). 4.2. Training of the network From the 5 min accelerations dataset, time series of 1 min duration are randomly extracted, each of them with 2478 samples (i.e., 41.3 ´ 60 = 2478). The collection of 4 ´ 2478 matrices of the accelerations from the period after the retrofitting (i.e., from 28/09/2019 to 15/01/2020) are used to train the autoencoder, for a total of 155 matrices. To determine the parameters of the network, the 75% of selected matrices (i.e. 116 matrices) are used for proper training procedure and the remaining 25% for validation purposes (i.e., 39 matrices). The training procedure permits to implement the network with the parameters briefly resumed in Table 1. It is worth noticing that: (a) the training time series are re-scaled between [ − 10, 10] to avoid numerical problem for the convergence of the ADAM optimization method; (b) the computational time required during training procedure was about 42 min, using a PC with a 16 GB RAM and a 2.7 GHz Intel Core i5 dual-core processor.

Table 1. Parameters adopted in the AE training.

Parameter

Value

Encoder activation function Decoder activation function

sigmoid

linear

Maximum number of training iterations (epochs)

100

No. nodes in hidden layer

25% of the signal length

4.3. Testing of the network

Once the AE was trained, the accelerations collected before and during retrofitting are fed into the AE model for data reconstruction purposes. The indicator adopted to quantify the goodness of reconstruction of the input time series is the Mean Absolute Error (MAE) between the input and the output sequences (Eq. 3). It is expected that the network might not reconstruct well the accelerations collected before the retrofitting since the structural behavior is different from the one accounted during training (i.e., after the retrofitting). By assuming that MAE values follow a normal distribution and most of values are within 99% of the curve, the 99 th percentile of the MAE values computed during the training is selected as the threshold for the outlier occurrence. Figure 5 shows typical reconstructed sequences before (a), during (b) and after (c) the retrofitting, highlighting the inability of the trained network to reconstruct time series associated to conditions that are different from the training ones. (a) 25/11/2018 08:00 (b) 13/07/2019 12:00 (c) 25/12/2019 00:00

Fig. 5. Channel 3, comparison between original and reconstructed sequence: (a) before; (b) during and (c) after retrofitting (validation set).