November 2022 Volume 4

FORGING RESEARCH

1b) using a different non-linear function which is referred to as an activation function and generate the predicted outcomes. This process is known as forward propagation.

process outcomes. An additional challenge is that the training data must span a sufficiently wide range that includes both optimal and out-of-spec process conditions. For example, if defects are to be predicted, the training data must also include enough data points which are known to generate this condition. Generating a sufficient number of training data points can be problematic for forging in that equipment and material may not be readily available for this purpose. However, in the case of forging, one solution is to use finite element (FE) simulation to create a virtual data training set. Once a Design Of Experiments (DOE) model has been defined, dozens or hundreds of models are created and run without the need for further user intervention. This approach was used in the present project and was facilitated by the availability of design of experiments (DOE) functionality in the DEFORM® v12 system (Figure 3) which enabled the team to generate sufficient training data in a matter of hours using a 2Dmodel.

a) b) Figure 1: Schematic diagram showing a) an ANN architecture with a single layer and b) a hidden node showing inputs, weights, summation, nonlinear transformation function, and outputs. For the open die setup used in Phase 1, the input parameters that were selected were based on thermomechanical parameters that were considered to affect the outcome of the bust station. A second criterion in selecting the conditions was that it was desired to explore the ANN performance over a wide range of possible process combinations. The ANN outputs selected were billet diameter at selected heights and press tonnage. The ANN inputs and outputs used in the study are listed in Table 1. The final ANN (Figure 2) consisted of six input nodes, two hidden layers (32 and 8 nodes respectively), and three output nodes. Table 1: ANN Inputs and ouputs used in the open die forging set-up. Input parameter Output Parameter Die temperature Peak tonnage Die friction Final billet diameter Billet temperature Final billet height Initial billet diameter Initial billet height Percent reduction target

Figure 3: Photograph showing a screenshot of the DOE simulation environment in DEFORM® v12. An ANN is trained using supervised learning, which means that there is label data where one data point consists of six inputs and three matching outputs. Training is iteratively performed where examples are processed through the ANN individually and weights are adjusted to improve the ANN’s predictive performance. During this process, system error is also calculated, and information is back-propagated to further adjust the weights and improve ANN performance. After training is complete, the weights can also be examined to determine which input data is most critical to the prediction as well as which input data can potentially be omitted. DEFORM was used to simulate 4,176 different bust combinations, yielding 4,176 data points. Using the well-known MATLAB® program as the platform to run the software, half of the input data were used to train the ANN while the second half was reserved for testing. The stochastic optimizing algorithm known as Adam was used to find the weights of the ANN, which was trained for 1,000 epochs. An epoch refers to an individual cycle where the training data is run through the ANN. The order of input presentation to

Figure 2: ANN Architecture with six inputs, 32x8 hidden nodes, and three outputs. After deciding which inputs and outputs were to be used in an ANN model, the network was trained. One of the key tasks associated with ANN development is generating enough training data points and the number of points needed is typically on the order of hundreds or thousands. The problem with using an insufficient amount of training data is that this results in excessive variability where the ANN is not able to accurately predict the

FIA MAGAZINE | NOVEMBER 2022 79