Total kernel projection to latent structures (T-KPLS) has been widely used in the fault detection control field

its core idea is to conduct the covariance matrix decomposition of the data matrix

without using the higher-order statistics and other useful information of the data

which will cause an information loss in the feature extraction process

then result in a bad fault recognition performance. Aiming to solve the problem

a statistics pattern analysis (SPA) combing with the T-KPLS based multi-way statistics pattern analysis total kernel projection to latent structures (MSPAT-KPLS) is proposed. First

different order statistics of the data samples are constructed to map the data from the original data space into the statistic sample space

then utilize kernel function to map the statistic sample space into the higher dimensional kernel space

and according to the quality variable

the feature space will be divided into 4 subspaces

namely: process variable related to quality variable space

process variable not related to quality variable space

process variable orthogonal to quality variable space and residual error space; Lastly

aiming at the process variable related to quality variable subspace and the residual error space

different detection models are constructed

which will trace the fault variables when faults are detected. In the end

apply the proposed method on the microbial fermentation process

and the comparison results with the traditional methods show that the proposed method could achieve a better detection.