An effective strategy for online safety assessment is the guarantee and fundamental to ensuring the safe and stable operation of industrial systems. However, in increasingly dynamic and complex industrial systems, operational condition transitions and production state changes may cause the probability density function (PDF) to exhibit notable irregularities or even severe collapse. This renders the conventional methods for process safety index calculation no longer applicable, let alone conducting online safety assessments based on the process safety index. To solve the problem, a modified process safety index calculation method based on the Gaussian mixture variational autoencoder (GMVAE) is proposed in this article. This method, through the nonlinear capability of GMVAE, transforms the irregular PDFs into Gaussian-distributed PDFs in the latent space, and then denotes the probability within the safety region determined by the PDFs as the process safety index. Afterward, the process safety index calculated in the latent space is mapped back to the original feature space for safety assessment in real-world scenarios. Finally, the experimental case is designed on the actual industrial process to verify and validate the effectiveness and superiority of the proposed method.

