# A Novel Parallel Auto-Encoder Framework for Multi-Scale Data in Civil Structural Health Monitoring
## 4 Performance Evaluation  
The above both baseline datasets and noise datasets are utilised to evaluate the performances of the proposed approach against the state-of-the-art model, for example, \"Sparse Auto-encoder Framework (SAF)\" [34]. For each of the model training, the pre-processed dataset is randomly split into training, validation and testing subsets according to the percentages 70%, 15% and 15% respectively. Finally, the Mean Squared Error (MSE) value and Regression value (R-value) are used to evaluate the quality of damage predictions of the proposed parallel model with the state-of-the-art models on the testing datasets. In particular, the MSE measures the distance between the estimated output of testing datasets from the proposed model and the labelled output. R-value represents the coefficient of correlation,which is used to measure the correlation between estimated output and labelled output. For our case, the higher R-value the more accurate of the proposed model. The details of proposed model architecture and evaluated performances are presented as follows. In our experiment, the proposed parallel auto-encoder framework utilizes one hidden layer for each parallel block in dimensionality reduction component, with 9 hidden neurons in the 1 st block for frequency data while 13 hidden neurons for the rest of 7 blocks for mode shape data. Since we implement sparse auto-encoders in this component, the number of hidden neurons are chosen carefully to allow the model to have more capacity for learning. To demonstrate the effectiveness of utilising many relationship learning layers, five hidden layers of having 90, 85, 80, 75 and 70 neurons respectively are defined in the relationship learning component. By using the decreasing number of hidden units in the hidden layers, the input vector is gradually compressed and regressed to the target vector. To perform a fair comparison with SAF, a simple proposed parallel model Para-AF-0 with the same number of hidden layers and neurons (90-80-70) as SAF in relationship learning component is also evaluated in this study. The performances of using the SAF and the proposed approach are compared by investigating the MSE values and R-values on the testing datasets. Both baseline datasets and noise datasets with measurement noise and uncertainty effect are used. The performance evaluation results are shown as below. As shown in Table 1, for the baseline dataset, MSE values obtained from SAF, Para-AF-0 and Para-AF are \(2.9\times 10^{-5}\), \(1.8\times 10^{-5}\) and \(1.3\times 10^{-5}\), respectively. Para-AF-0 has marginally improved the performance over SAF with a smaller MSE value for baseline dataset. Meanwhile, for noisy datasets, we can observe a 3% increment in R-value of Para-AF-0 versus SAF. They indicate that the proposed parallel dimensionality reduction has achieved the expected effectiveness by extracting features in parallel from multi-scale datasets. In addition, a significant increment (around 8%) in R-value is observed in Para-AF-0 against Para-AF, which shows the effectiveness of applying more relationship learning layers. For both datasets, the performances of these three methods show the same trend. Therefore, the proposed parallel method not only improves the effectiveness but also improves the noise robustness for damage detection/identification. Since dealing with the noise dataset is much more challenging in the real-world, only this case will be further presented in the following comparisons. To further evaluate the quality of damage identification in terms of both magnitudes and locations, the prediction of a single damage case and a multiple damage case randomly selected from the testing datasets are shown in Figures 5 and 6 respectively. Firstly, for the single damage case, SAF can predict the true location of the single damage but fail to identify the true magnitude of the damage.