A semi-supervised temporal modeling strategy integrating VAE and Wasserstein GAN under sparse sampling constraints

Abstract

Time series network models are widely applied in process industries for soft sensing, fault monitoring, and real-time optimization, serving as a powerful tool to enhance the safety and efficiency of industrial production. Typically, time series networks require labeled data for supervised learning. However, labeled data often exhibits sparse sampling characteristics in industrial settings, which limits the model's performance. To address this issue, a semi-supervised modeling strategy based on Variational Autoencoder (VAE) and Wasserstein Generative Adversarial Network (WGAN) is proposed in this paper. The strategy consists of three steps. First, for the labeled samples, process data and labeled data are used as input to train a supervised VAE model (SVAE). Upon completion of the training, the posterior distribution of the latent variable z_S is obtained. Second, in all samples, only process data is used to train an unsupervised VAE model (UVAE) to extract the latent variable z_U, and the WGAN discriminator is introduced to distinguish between "fake data" (z_U) and "real data" (z_S). Through adversarial learning between the UVAE and WGAN discriminator, the posterior distribution of z_U is forced to approximate z_S. Finally, the encoder of UVAE and the decoder of SVAE are combined to form a Semi-Supervised Variational Autoencoder model (SS-VAE), which extracts the latent variable z_SS and the reconstructed labeled data from the decoder as inputs for the time series network. Long Short-Term Memory (LSTM) and Temporal Convolutional Network (TCN) are selected as two basic time series models, and their performance, both with and without the proposed semi-supervised approach, is compared to assess the effectiveness and robustness of the strategy. The improvements observed in two industrial case studies validate the efficiency of the proposed approach.