Self-supervised spectral learning with an application to condition monitoring of tunnel ventilation systems under sparse data conditions

This paper presents a self-supervised spectral learning framework for condition monitoring of industrial equipment under sparse data conditions. Our approach integrates a spectral regularization term—derived from a cosine divergence between the empirical and modeled spectral energy distributions—into a variational Expectation-Maximization (EM) algorithm. By extracting intrinsic supervisory signals directly from the data, the proposed method reconstructs latent input patterns and recovers clean system dynamics without relying on external labels or explicit event detection. The framework is formally developed using a data-adaptive basis via Singular Spectrum Analysis (SSA) to generate a tailored spectral representation, which is then incorporated into the variational inference process. We validate our methodology through extensive experiments on both synthetic datasets and real-world tunnel ventilation data, where our method consistently outperforms conventional techniques such as Fourier-based filtering, wavelet denoising, classical SSA, and standard variational EM in terms of reconstruction accuracy and the physical plausibility of the recovered signal. • Spectral losses used in self-supervised learning to extract latent features. • Divergence defined by comparing SSA energy of model output and observed data. • Only method to recover physical relation in tunnel ventilation amid non-stoch noise.