6.1 Prediction Performance of the Network Trained for 21 mm Dataset Initial training for 21 mm thickness data sets was made through for goal being set to zero and the epoch level 100. 

Clear examination on the training flow intimates that for logsig transfer function, steady declination in curve to reach the goal was targeted from initial state. Figure 21 and 22 point up the theory of network performance. But when the same network was trained for higher epoch levels and for 21 mm data sets, finer results were attained for tansig transfer functions. Deep and steady flow of graph can be envisaged through figure 24. For this particular data sets stabilized training outcomes was obtained at 700000 epochs approximately. Upon further training of the network, considerable change performance could not be seen and hence the network was ended at these early epoch levels for 21 mm thickness of the valve body.. 

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## 7. Testing And Validation

The theory of artificial intelligence utters an inevitable fact that the data used for testing and validation should not be included in training circumstances. As a first step the network has to be triggered for training the data sets by comparing experimental results and predicted outcomes. The next step in evaluation is, to test the Back-Propagation network performance with the other test samples that were never applied to network before [5]. Hence the network models developed by ANN were subjected to testing with 40 newer data sets collected for this purpose and their results are to be predicted. The weights obtained through training process were supplied as initial weights for validation purpose. Even though the desired goal set to zero was not reached, the network model developed yielded better results. Upon the effective completion of validation, the initial weights were reverted with weights observed through training of the network model developed for testing purpose also. In order to check the robustness of the BackPropagation network controller 11 input data sets were fed into the trained network. A detailed analysis on the tested data as per the theory of ANN [3,6,8] the obtained results are well within the predictable ranges. After training the network successfully,it has been tested by using the known test data. Statistical methods were used to compare the results produced by the network. Errors occurring at the learning and testing stages are called the root-mean squared (RMS), absolute fraction of variance 
(R2), and mean error percentage values. These are defined in many literatures [6,17,18] and are as follows, respectively: 

![0_image_1.png](0_image_1.png)

The prediction errors were achieved on calculations using the equations 1, 2, 3 to account the performance of the ANN network developed for blending design domains. There is no definite rule as how the training and prediction errors correlate [17, 18]. The RMS error for the training data is reduced as the training continues though the improvement of some iteration becomes very small and sometimes RMS error may begin to increase. 

## 8. Conclusion

In this study, finite-element modeling (FEM) and artificial neural networks (ANN) analysis were combined to establish relationship between material design and product design domains. As a result of this study, it was possible to