Parameter-adaptive variational autoencoder for linear/nonlinear blind source separation

Abstract

Blind source separation (BSS) serves as an important technique in the field of structural health monitoring (SHM), particularly for solving modal decomposition tasks. This study proposes a novel approach to both linear and nonlinear BSS problems in the Variational Autoencoder (VAE) framework, where the encoding and decoding processes of VAE are interpreted as procedures for inferring sources from observations and remixing these sources, respectively. In this way, the distribution of latent variables inferred by VAE is equivalent to the distribution of sources. We make improvements to the vanilla VAE to augment its effectiveness for BSS. First, we substitute standard normal distributions with trainable Gaussian processes (GP) as priors for latent variables and implement an exponential function as the activation function for adaptive parameters in the GP kernel functions. While the form of the priors is set as GP, the parameters of their kernel functions are not fixed but automatically converge to suitable values during the model training process. Additionally, a hyperparameter is introduced to balance the terms in the loss function. The proposed method is referred to as parameter-adaptive VAE (PAVAE). Then, upon different assumptions of the variances of sources, the proposed PAVAE is branched into two types: homoscedastic PAVAE (Ho-PAVAE) and heteroscedastic PAVAE (He-PAVAE). Through numerical and laboratory experiments, we demonstrate the effectiveness of the proposed method in solving BSS problems and their potential to underpin future research in SHM.