A reduced nonstationary discrete convolution kernel for multimode process monitoring

The multimodal behavior is common in industrial process. Since multimodal data distribution can be regarded as a special kind of nonlinearity, kernel method is empirically effective in constructing the multimode process monitoring model. However, kernel methods suffer its high complexity when a large number of data are collected. In order to improve the fault detection performance in multimodal data and reduce the computational complexity, we propose a reduced nonstationary discrete convolution kernel which is inspired by the structural design of radial basis function (RBF) neural network, as an alternative to the RBF kernel and the nonstationary discrete convolution (NSDC) kernel. By deleting the unnecessary accumulated terms in the NSDC kernel, the computational complexity of the proposed NSDC kernel algorithm is effectively reduced and the speed of fault detection is accelerated on the premise of ensuring the fault detection performance. The effectiveness of the proposed algorithm is demonstrated on a numerical example and multimodal TE process under the standard kernel principal component analysis framework.