PSI - Issue 64

Lim Boon Xuan et al. / Procedia Structural Integrity 64 (2024) 791–798 Lim et al./ Structural Integrity Procedia 00 (2019) 000–000

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uneven amplitudes (Huang et al., 1998). The decomposed signals into different IMFs defer to two properties: firstly, an IMF exhibits only one extremum between consecutive zero crossings, ensuring that the difference in the number of local minima and maxima does not exceed one; secondly, an IMF possesses a mean value of zero. The first IMF comprises the highest frequency component in original signal, with frequencies decreasing in the subsequently IMFs. The signal �(�) decomposed into different level of frequency IMFs � � (�) and a residual �(�) as showed below: �(�)=∑ � � (�)+�(�) � (1) 2.2. Long Short-Term Memory Network (LSTM) LSTM is a type of recurrent neural network (RNN) that addresses the issue of vanishing gradients in conventional RNNs, making it more effective in capturing long-term dependencies in sequential data (Gunarto et al., 2023). This is specifically achieved through the short-term and long-term memory possessed by LSTM, as shown in Fig. 1(a), whereas conventional RNNs possess only short-term memory. Fig.1(b) demonstrates a single cell unit of the LSTM network at time step � . � � denotes the input data at time step � ; � � denotes the prediction output at time step � ; ℎ � denotes the hidden state output at time step � ; � � denotes the cell state output at time step � ; � � ,� � , � � and � � denote forget gate, cell candidate, input gate and output gate respectively; �,� and � denote the learnable input weight, recurrent weight and bias respectively; ��� and ���ℎ denote the logistic sigmoid and hyperbolic tangent activation functions respectively. The two outputs of LSTM cell, ℎ � and � � can be represented as: ℎ � =���(� � � � +� � ℎ ��� +� � )⊙���ℎ (� � ) (2) � � =���(� � � � +� � ℎ ��� +� � )⊙� ��� +���(� � � � +� � ℎ ��� +� � )⊙���ℎ(� � � � +� � ℎ ��� +� � ) (3) ���(�) = (1 + � �� ) �� (4) ���ℎ(�)= � � −� �� � � +� �� � (5)

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Fig. 1. (a) Simple flow concept of LSTM network; (b) Structure of a single cell in the LSTM network.

Fig.2. Elevation of the bridge.