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.

多模态行为在工业过程中很常见。由于多模态数据分布可以看作是一种特殊的非线性，核方法在构建多模态过程监测模型方面是经验上有效的。然而，当收集大量数据时，内核方法会受到其高度复杂性的影响。为了提高多模态数据中的故障检测性能并降低计算复杂度，我们提出了一种减少的非平稳离散卷积核，其灵感来自径向基函数（RBF）神经网络的结构设计，作为 RBF 核的替代方案。非平稳离散卷积（NSDC）内核。通过删除 NSDC 内核中不必要的累加项，在保证故障检测性能的前提下，有效降低了所提出的NSDC核算法的计算复杂度，加快了故障检测速度。在标准核主成分分析框架下，通过数值示例和多模态 TE 过程证明了所提算法的有效性。