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Kernel principal component analysis (KPCA) has been widely applied to nonlinear process monitoring. Conventionally, a single Gaussian kernel function with the width parameter determined empirically is selected to build a single KPCA model. Obviously, it is very blind to determine only a single Gaussian kernel function only by experience, especially when the fault information is unavailable. If a poor Gaussian kernel function is selected unfortunately, the detection performance may be degraded greatly. Furthermore, a single kernel function usually cannot be most effective for all faults, i.e., different faults may need different width parameters to maximize their respective monitoring performance. To address these issues, we try to improve the KPCA-based process monitoring method by incorporating the ensemble learning approach with Bayesian inference strategy. As a result, the monitoring performance is not only more robust to the width parameter selection but also significantly enhanced. This is validated by two case studies, a simple nonlinear process and the Tennessee Eastman benchmark process.

Recently, deep generative models have become increasingly popular in unsupervised anomaly detection. However, deep generative models aim at recovering the data distribution rather than detecting anomalies. Moreover, deep generative models have the risk of overfitting training samples, which has disastrous effects on anomaly detection performance. To solve the above two problems, we propose a self-adversarial variational autoencoder (adVAE) with a Gaussian anomaly prior assumption. We assume that both the anomalous and the normal prior distribution are Gaussian and have overlaps in the latent space. Therefore, a Gaussian transformer net T is trained to synthesize anomalous but near-normal latent variables. Keeping the original training objective of a variational autoencoder, a generator G tries to distinguish between the normal latent variables encoded by E and the anomalous latent variables synthesized by T, and the encoder E is trained to discriminate whether the output of G is real. These new objectives we added not only give both G and E the ability to discriminate, but also become an additional regularization mechanism to prevent overfitting. Compared with other competitive methods, the proposed model achieves significant improvements in extensive experiments. The employed datasets and our model are available in a Github repository.

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