## 3 Results
### Prediction by BPNN-GA Model  
To evaluate and compare the optimization performances of the BPNN-GA model and the integrated BBD-BPNN-GA model. Initially, the BPNN-GA architecture was employed to predict the performance of PSA. In this model, the inputs parameters included adsorption time, feed flow rate, and pressure equalization time, while the outputs included hydrogen purity and productivity. Figure 2 presents a flowchart illustrating the procedure of the BPNN-GA model, where the BPNN component is highlighted by the black frame on the right. The procedure can be divided into three main parts. First, the structure of the BPNN is established based on predefined inputs and outputs, and the initial weights and bias values of the neural network are initialized. Second, a GA is introduced to optimize these parameters, resulting in optimal initial weights and bias values for the BPNN. Finally, training and prediction are conducted using an existing database with the optimized BPNN-GA model. The operational procedure of the BPNN-GA primarily consists of population initialization, fitness function calculation, and genetic operator execution. The objective of using the BPNN-GA approach is to improve the accuracy and performance of the model by optimizing the initial weights and bias values. A total of 130 datasets were utilized for training the neural network. These datasets were partitioned into three segments randomly: 80% for the training set, 10% for the validation set, and 10% for the test set. The training set serves as the primary data for  
Figure 7: The influences of independent optimization parameters on hydrogen purity (**a**) and productivity (**b**). (Dots: the performance of the response variable at different levels; contours: the interaction effects between two factors). model learning and optimization. The validation set is employed to prematurely terminate training if the performance of network fails to improve or plateaus over several epochs. Meanwhile, the test set is dedicated to evaluating the network's generalization performance, independently of the training process. The test error is utilized as a metric for assessing the performance of the BPNN-GA. Due to convergence issues arising from using raw experimental data as input, data preprocessing is conducted. This involves normalizing the data using the min-max normalization technique, which scales the data to the range [1; 2; 3]. This normalization step enhances the efficiency of neural network training. At the conclusion of each algorithm, the outputs are denormalized back to their original data format to obtain the desired results [37]. Figure 8 illustrates the fluctuation of mean square error (MSE) for the training and validation set over various epochs. Initially, the MSE declines rapidly, but as the number of epochs increases, the rate of decline slows down. The MSE reaches its minimum validation value of 0.0035 at epoch 5, prompting the termination of the training process. In Figure 9, the actual values from Aspen and the predicted values generated by BPNN-GA model are compared. The R-value, also known as the correlation coefficient, is utilized to quantify the correlation. An R-value closer to 1 indicates a higher accuracy of the BPNN-GA predictions. Figure 10 displays the R-values for the training, validation, test, and overall sets, comparing the predicted outputs of the BPNN-GA model with the actual outputs from the Aspen model. The results indicate that, despite some errors, the BPNN-GA model can be effectively utilized for predicting and optimizing the PSA process. Figure 8: The MSE performance of BPNN–GA model (green circle: best validation performance). Figure 10: The correlation coefficient (R) between the predicted outputs of the BPNN–GA and actual outputs of the Aspen model on the training, validation, test, and overall sets. Figure 9: The comparison between predictive and actual values of purity (**a**) and productivity (**b**) of BPNN–GA model.