# Machine-Learning-Based Methods for Acoustic Emission Testing: A Review
## 4 Deep-Learning (DL) Methods for AE Testing
### Recurrent Neural Network (RNN) Based Applications  
RNNs are DL models introduced for the processing of sequential data, or data in which the order of the observations is important [87]. These algorithms find application above all in the analysis of time series [88]. The idea behind the RNN is the sharing of parameters or the use of the same parameters along positions, instants of time, or, more generally, steps of the sequence, for two main reasons:  
* Possibility of applying the model, in the test phase, on sequences of different lengths from those seen by the algorithm in the training phase;
* Reduction in the number of parameters and the ability to recognize information in different positions along the sequence. An important role in these networks is played by hidden units. In fact, when the RNN is trained to carry out an activity that requires forecasting the future through the past, typically, the network learns to use the hidden units as a lossy summary of the aspects relevant to the activity of the input sequence up to time t [89]. This summary, in general, is necessarily affected by losses since the hidden layer maps a sequence of arbitrary length into a vector of fixed length [90]. A problem with this type of model is that for sequences that are particularly long over time, the gradients tend to be infinity, to vanish, and for this reason, it is called a vanishing gradient. This means that an RNN thus constructed struggles to code temporally distant dependencies. To counteract the vanishing gradient, cells with a specific structure are used, which contain methods to build a memory that can also be propagated [91]. One of these is the long short-term memory (LSTM), which represents a particular RNN that solves the problem of a vanishing and exploding gradient that compromises the effectiveness of the RNN [92]. The principle behind the LSTM is the memory cell, which maintains the state outside the normal flow of the recurring network. The state, in fact, has a direct connection with itself. Since the activation function for updating the state is, in fact, an identity function, the derivative will be unitary; therefore, the gradient in the back-propagation will not vanish or explode but will remain constant through all the time instants of the unfolded network (Figure 6) [93]. In many applications where the goal is not the prediction of one or more future values starting from the past (known) values, bidirectional recurrent neural networks can be used. This type of algorithm uses two recurring layers in the same network, but without direct connections between them, thus exploiting both the information in the order passed as input to the model and the opposite one, therefore solving a limitation of the classic recurring networks to the detriment of the introduction of parameters [94]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Input** & **Features Extracted** & **Accuracy** \\ \hline [PERSON] et al. [79] & AE from plain bearing systems & Continuous wavelet transform & 82.5\% \\  & AE from an excited & & \\ [PERSON] et al. [80] & aluminum plate using Hsu–Nielsen source & Waveforms & 95.2\% \\ [PERSON] et al. [82] & AE from rail crack monitoring & Synchrosqueezed wavelet transform & 91–97\% \\  & AE from damage in & & \\ [PERSON] et al. [83] & carbon-fiber-reinforced composites & Frequency domains & 99\% \\  & AE from bearing & & \\ [PERSON] et al. [84] & monitoring & Envelope spectrum & 94.8\% \\ [PERSON] et al. [85] & AE from bearing & Acoustic spectral imaging & 94.67\% \\  & monitoring & Temporal and spatial & \\ [PERSON] et al. [86] & AE from rotating machinery & information of the raw data & 99.41\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._The signals deriving from acoustic emission represent an example of a temporal sequence that can be effectively modeled using RNNs. [PERSON] et al. [95] have effectively identified the arrival of a microseismic emission by exploiting the RNN.