Sparse Wasserstein stationary subspace analysis for fault detection and diagnosis of nonstationary industrial processes

Fault detection and diagnosis of nonstationary processes are crucial for ensuring the safety of industrial production systems. However, the nonstationarity of process data poses multifaceted challenges to them. First, conventional stationary fault detection methods encounter difficulties in discerning evolving trends within nonstationary data. Secondly, the majority of current nonstationary fault detection methods directly extract features from all variables, rendering them susceptible to redundant interference. Moreover, nonstationary trends possess the capacity to conceal and modify the correlations among variables. Coupled with the smearing effect of faults, it is challenging to achieve accurate fault diagnosis. To address these challenges, this paper proposes sparse Wasserstein stationary subspace analysis (SWSSA). Specifically, a ${\ell }_{2,p}$-norm constraint is introduced to endow the stationary subspace model with excellent sparse representation capability. Furthermore, recognizing that fault variables within the sparse stationary subspace influence only a limited subset of stationary sources, this paper proposes a novel contribution analysis method based on local dynamic preserving projection (LDPP), termed LDPPBC, which can effectively mitigate the smearing effect on nonstationary fault diagnosis. LDPPBC establishes a LDPP matrix by extracting the latent positional information of fault variables within the stationary subspace. This allows LDPPBC to selectively analyze the contributions of variables within the latent fault subspace to achieve precise fault diagnosis while avoiding the interference of variable contributions from the fault-free subspace. Finally, the superiority of the proposed method is thoroughly validated through a numerical simulation, a continuous stirred tank reactor, and a real industrial roaster.