PSI - Issue 64

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

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Lim et al./ Structural Integrity Procedia 00 (2019) 000–000

Deflection (mm)

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Fig. 5. Prediction results of LSTM model: (a) Scheme 1; (b) Scheme 2; (c) Scheme 3; (d) Scheme 4. 4.3.4. Scheme 4: Ambient temperature, ܶ ௔ → Span-6 deflection, ܦ ௜ Analogous to scheme 3, this section takes ܶ ௔ as the input variables, while output ܦ ௜ as prediction values. The comparison between measured ܦ ௜ and output prediction ܦ ௜ is shown in Fig. 5(d). Table 1. Hyperparameters of LSTM network Type of hyperparameter Value Input size 1 Number of hidden units 128 Number of hidden layers 1 Batch size full-batch Learning rate Learning drop rate 0.001 0.2 Optimizer adam Epoch 1000 4.4. Evaluation of prediction model With the output results of the LSTM prediction model, root mean squared error (RMSE), mean absolute error (MAE), maximum absolute error (Max-AE) are calculated and presented in Table 2. Linear regression generated the worst prediction compared to LSTM model of scheme 1, therefore, the discussion will focus on the LSTM model in the following. From the perspective of temperature, girder temperature generated better prediction with lower errors in RMSE, MAE, and Max-AE compared to ambient temperature, in both span-1 and span-6. Considering the different spans, span-6 generated lower errors than span-1, attributed to its smaller variation of temperature-induced deflection. In summary, a satisfactory accuracy of predicted deflection is achieved in both span-1 and span-6 using girder temperature. 5. Residual analysis of prediction results Residual analysis has been proven to be a potent methodology for examining the adequacy of the derived regression model in relation to the original dataset, as well as for identifying the necessity of incorporating additional explanatory independent variables into a regression model (Framstad et al., 1985). As observed in Fig. 6, the residual plot of scheme 3 and scheme 4 demonstrate a similar pattern trend, indicating that temperature-induced deflection may possess additional variables or, in other word, may require the inclusion of more explanatory variables in the corresponding model. Fig. 7 shows a histogram of residual values. The mean of the residual values for the four schemes are, in order, 0.0003mm, 0.0613mm, 0.7654mm, and -0.0854mm respectively, which are close to zero. These residual values clearly conform to the normal distribution, which proves the preciseness and stability of LSTM model.