PSI - Issue 44

Valentina Giglioni et al. / Procedia Structural Integrity 44 (2023) 1948–1955 Valentina Giglioni et al./ Structural Integrity Procedia 00 (2022) 000–000

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damage conditions with a limited number of false prediction errors and computational burden, thereby proving to be promising for a rapid assessment of bridges’ post-earthquake scenarios.

2. Multi-Layer Perceptron Autoencoder The Multi-Layer Perceptron autoencoder is a feedforward neural network with fully-connected layers, composed of an encoder and a decoder part. The former is used to compress a 1D input into a latent representation characterizing the bottleneck layer, while the latter is aimed at reconstructing the original input back from its encoded form. The system can be described by the following equations: (1) (2) where ℎ ! is the i-th node at the hidden layer, " and " represent the j-th value of the input and output vector, respectively, and denote the weight matrices of the encoder and the decoder, while and are the biases terms. The activation functions handling the flow of information through the different hidden layers of the encoder and the decoder are indicated with and , respectively. The aim of the training process is to estimate the weights and biases parameters with backpropagation algorithms so that the reconstruction loss between the original and the reconstructed input is minimized: (3) 3. The proposed autoencoder-based damage detection technique The proposed unsupervised ML approach for automatically identifying the occurrence of damage during post earthquake conditions is described in Fig. 1. The methodology only requires raw acceleration data continuously acquired by the Structural Health Monitoring (SHM) system installed on the bridge. Acceleration time-histories collected by the -th sensor, with = 1… , are firstly pre-processed through a standardization, to have zero mean and standard deviation equal to 1, and a normalization yielding values between -1 and 1. This allows to improve the numerical stability of the model and speed up the training process. Then, a user-defined length window is fixed to split the original dataset into multiple acceleration sequences, utilized as input to the MLP autoencoder. The learning process of the -th implemented network aims at reproducing acceleration sequences collected during sound conditions. To evaluate the differences between the original and the reconstructed model output, a specific index, called Original-to-Reconstructed-Signal Ratio (ORSR) and introduced hereafter, is computed to characterize each sequence: 1 ( ) i ij j h f W x b = + 2 ( ' ) j ij i y g W h b = + W ' W 1 b 2 b f g ( , ) 0 L = x y

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Same length sequences of unknown scenarios are afterwards fed into the autoencoder to test and validate the reconstruction capability. Referring to the baseline population of the extracted features, this methodology proposes to (i) fix a first threshold # ( ) to assign short sequence labels based on a level of significance of 5% and to (ii)