## 4 Methodology
### Proposed Model and Synthetic Data Generation  
After the pre-processing, the data are then split into 75% and 25% ratios, namely the training and testing datasets, respectively. The training dataset is then fed into the proposed model named MTS-TGAN. MTS-TGAN consists of two components: adversarial and auto-encoder components. The components of MTS-TGAN are shown in Figure 4, wherein the real sequence and random noise act as inputs to the model and at the end, after the overall training and testing, we obtain the synthetic data as an output. Figure 4 clearly shows training and loss functions; components to which loss functions are applied are indicated by dashed arrows, and the data flow is indicated by solid arrows. The sequence discriminator and generator as well as the recovery and embedding function are the four sub-components that makeup MTS-TGAN. The major finding is that the auto-encoding and adversarial components are trained together so that the proposed model simultaneously learns to encode features, generate sequences and iterate over time. The adversarial network acts in the latent space that the embedding network supplies and a supervised loss synchronize the latent dynamics of both real and synthetic data. Each sub-component is individually described in Figure 5.  
The detailed description of the MTS-TGAN architecture is explained further down the section. The overview of the components in the proposed model is shown in Figure 4; all components are composed of an input layer, six GRU layers [15] with 60 s as a sequence length followed by a dense layer [36]. A detailed explanation of each is given as follows:  
* Adversarial Component: The generator's input is a random multivariate noise sequence defined in the feature space of the dataset, which in this case has six dimensions because there are six signals/features present in the data. The latent space, which in this instance was set to four feature spaces, determines the generator's output. As a result, the generator network's final layer is dense, consisting of four units. When every neuron in a layer receives input from every neuron in the layer below it, the layer is considered to be dense in a neural network. To make sure that the network terminates in the desired dimension, the dense layer was implemented. Since the discriminator operates in the latent space, its input and output must have the same shape as well as that of the embedder functions. A scalar representing the discriminator's output indicates whether it believes the sample it was given to be legitimate or bogus. As a result, the discriminator architecture must have a dense layer with one output unit at its end. An overview of these architectures is presented in Figure 5a,b. * Auto-Encoding Component: The embedding function converts the real data samples into the latent space with 6-dimensional and 4-dimensional latent spaces as input and output, respectively. The embedding function consequently has a dense layer composed of 4 units. The recovery function acts within the latent space, just like the discriminator. Consequently, the embedder's output shape and input shape are the same as a generator. The recovery function, as opposed to the discriminator, generates reconstructions of the samples back to feature space. As a result, the recovery function has a 6-unit dense layer at its conclusion. An overview of these architectures is presented in Figure 5c,d. These dimensions are set to \"None\" to enable the insertion of various values during training and testing that is, simply telling the network that any input parameters are acceptable here when the input is defined by setting these dimensions to \"None\". This is essential, as the model should be able to generate samples in multiples and of any sequence length. The decision to use GRU layers in the proposed model is given to recurrent neural networks (RNNs) [37], which are appropriate for TS data [8; 25; 26] as analyzed from related works in Section 2.