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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respectively. The periodic cycles induced by temperature effects are preserved, while the high frequency components caused by live loads, such as vehicles and winds are eliminated. Afterward, 1-hour averaging is used to reduce the amount of data samples of temperature and temperature-induced deflection. Consequently, the amount of data samples is reduced from 7776000 originally to 2160. 4. Deep learning regression model 4.1. Preparation of training and testing data The preprocessed data from section 3.2. are divided into a training set and a testing set. The first 80% of the data are classified as the training set and the remaining 20% are classified as the testing set. Due to the restriction of the activation function in LSTM network, the input data need to be normalized into the range of [0,1]. The following is the normalization formula, where {� � ,� � ,…,� � } are the normalized data from the time step 1 to time step � ; � � is the original value of data at time step ; � ��� is the minimum value in X dataset; � ��� is the maximum value in X dataset. � � = � � −� ��� � ��� −� ��� � (6) 4.2. Building of LSTM network architecture In this paper, the modeling of LSTM network is carried out using Deep Learning Toolbox provided by MathWorks, and the deep learning process is conducted in the Matlab environment. The architecture of the LSTM network is mainly composed of four parts: input layer, hidden layer, fully connected layer and output layer. The hyperparameters of LSTM network are listed in Table 1. 4.3. Prediction model of deflection 4.3.1. Scheme 1: Span-1 girder temperature, � � → Span-1 deflection, � � In this section, � � is used as the input variable, while � � is the output prediction value. The training set of � � and � � is fed into the LSTM network for model training. The prediction values of � � are generated by inputting the testing set of � � into the trained LSTM network. Notably, the input variable � � is normalized before the training process, therefore, the output prediction of � � should go through inverse normalization to obtain the real value of � � . The following is the inverse normalization formula, where {� � ,� � ,…,� � } from the normalized prediction values output from LSTM network; � � is the prediction value through inverse normalization; � ��� is the minimum value in Y dataset; � ��� is the maximum value in Y dataset. Afterward, the comparison between measured � � and output prediction � � is conducted as shown in Fig. 5(a). � � =(� ��� −� ��� )� � +� ��� (7) 4.3.2. Scheme 2: Span-6 girder temperature, � � → Span-6 deflection, � � Analogous to scheme 1, this section replaces � � with � � as the input variable, while � � is the output prediction value. The comparison between measured � � and output prediction � � is shown in Fig. 5(b). 4.3.3. Scheme 3: Ambient temperature, � � → Span-1 deflection, � � To analyze the effect of ambient temperature on the deflection of bridge, this section takes � � as the input variable, while � � is the output prediction value. The comparison between measured � � and output prediction � � is shown in Fig. 5(c).