Page 79 - IJAMD-2-2

International Journal of AI for
Materials and Design Prediction of AM defect based on DL

contrastive divergence. Pre-training and fine-tuning resilient backpropagation (grprop), adjusting the learning
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are implemented while training a DBN. The following rate associated with the sag or the slr.
is specific information regarding the methodology and The calculation of ACC, FPR, and FNR (Equations I, II,
related algorithms. 21,22 The network energy is expressed as and III) in this paper is based on the confusion matrix and
E(v,h).
the components in the matrix. The confusion matrix (CM)
Let p(v) be the probability of a visible vector, and it is is given as follows:
described as follows:  FP TN
1 CM =    
p v − ( , )E vh (VII)  FN TP  (XII)
( ) = ∑ e
Z h
where Z = ∑ exp( −E ( ))vh is the partition function. 5. Results and discussion
,
To train an RBM, weights are updated as follows: 5.1. Results of the Elman neural network and the
Jordan neural network
ij (
wt + ) = () +⋅1 wt η ∂ logp v(( )) (VIII) Both the Elman neural network and the Jordan neural
ij
w
∂
ij
network are RNNs. An Elman neural network can be
4.3. Regular DNNs thought of as a model that is constantly unfolding as a
sequence of predictors. A Jordan neural network uses
In the DNN learning, 23,24 each training tuple can be a context layer to process sequential data. The dataset
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handled in two steps: Propagating inputs forward and (Table 1) used in this paper is experimental data that can
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backpropagating the error. For an input vector V = (V1, be regarded as a sequential dataset over time.
V2,…, V ), each hidden layer transforms its inputs from
p
the layer to the next layer by applying an affine transform Tables 2 and 3 show part of the results of the Elman
and a nonlinear mapping as follows: neural network and the Jordan neural network after min-
max normalization and z-score standardization on the
z = V (IX) dataset, respectively. It was shown that both the Elman and
(1)
j ∑
l ()
l ()
l () ( −1
y = N j=1 l () w z i l ) +θ j ( l = 2 ,, … 3 L , ) (X) Jordan neural networks did not work well in establishing
DL models on a small dataset (with unbalanced data) and
ij
predicting the LOF of the LPBF. Most of the ACC values
z j l () = f y( j l () ) (XI) were low, and most of the FPR values, as well as most of
the FNR values, were high or somewhat high. The reason
is the small dataset and the unbalanced data in the dataset.
l ()
where L is the number of layers; N , θ , and w are
l ()
l ()
j
ij
the number of nodes in the l layer, the bias of the node j in The structures of context layers show the number of nodes
th
in the context layers. For instance, c(8) indicates that eight
the l layer, and the weight of the connection from node i
th
in the previous layer to node j of the l layer, respectively; nodes are in the context layer.
th
and f is the activation function (nonlinear). 5.2. Results of the DNN with weights initialized by
In this paper, the Elman neural network, the Jordan the DBN
neural networks, the DNN with weights initialized by Tables 4 and 5 list part of the results of the DNN with weights
the DBN, and regular DNN based on various algorithms initialized by the DBN after min-max normalization and
were employed to establish DL models and implement z-score standardization are employed, respectively. It was
the prediction of the LOF of LPBF because all of the DL shown that DNN-DBN did not work well in establishing
methods achieved good ACC, FNR, and FPR when large DL models on a small dataset (with unbalanced data) and
and quality databases such as “spambase” (https://archive. predicting the LOF of LPBF. There are the input layer,
ics.uci.edu/ml/datasets/Spambase) were employed in the the output layer, and two or three hidden layers in this
author’s past research work. technique. The performance (according to the ACC, FPR,
Four algorithms, “rprop+”, “rprop−”, “sag,” and “slr,” and FNR) of the established DL models was not good due
were used in this paper. “rprop+” and “rprop−“ refer to to the small dataset and the unbalanced data in the dataset.
the resilient back-propagation with and without weight The structures of hidden layers indicate the number of
backtracking, respectively. “sag” and “slr” induce the usage nodes in the hidden layers. For instance, c(8, 6, 4) indicates
of the modified globally convergent algorithm globally that there are three hidden layers, and the number of nodes
Volume 2 Issue 2 (2025) 73 doi: 10.36922/IJAMD025060005