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A new method named quality-relevant kernel neighborhood preserving embedding (QKNPE) has been proposed. Quality variables have been considered for the first time in kernel neighborhood preserving embedding (KNPE) method for monitoring multimodal process. In summary, the whole algorithm is a two-step process: first, to improve manifold structure and to deal with multimodal nonlinearity problem, the neighborhood preserving embedding technique is introduced; and second to monitoring the complete production process, the product quality variables are added in the objective function. Compared with the conventional monitoring method, the proposed method has the following advantages: (1) the hidden manifold which related to the character of industrial process has been embedded to a low dimensional space and the identifying information of the different mode of the monitored system has been extracted; (2) the product quality as an important factor has been considered for the first time in manifold method. In the experiment section, we applied this method to electrofused magnesia furnace (EFMF) process, which is a representative case study. The experimental results show the effectiveness of the proposed method

Fault Detection for Multimodal Process Using Quality-Relevant Kernel Neighborhood Preserving Embedding