Himmelblan defines the term " Fault" as a departure from an acceptable range of an observed variable or a calculated parameter associated with a process. And with the development of new sensors and data gathering techniques, large amounts of process data are available in modern industrial processes. Thus, t data-driven techniques have been widely adopted. Given that fault data sets generated by different deterministic faults have been gathered, The objective of fault diagnosis is to classify the online out-of-control observations into predefined fault classes. Fault diagnosis is a multi-classification problem. Fault data belong to smaller subspace instead of all high dimension space. Subspace analysis methods are particularly effective at analyzing fault data. The linear discriminant analysis (LDA) can be used for both dimension reduction and the improvement of the data separation ability. LDA methods outperform PCA-based diagnosis methods.rnHowever, LDA has three limitations including linearity, Gaussian assumption and singularity problems. Marti'nez proposed that even though LDA can overcome these limitations, the diagnosis method still fails to find the optimal feature subspace for classification in some cases. Shen proposed a modified LDA method based on the genetic algorithm to minimize the training classification error under the assumption that fault data is linear separable and there is an optimal discriminant vector in original space. Nevertheless, the modified LDA model is not effective in cases that fault data is linear separable but with no optimal discriminant vector. In consideration of these models, the kernel scatter-difference ( KSD) and kernel clustering based on the discriminate analysis ( KCDA) will be integrated to implicitly map fault data into a high-dimensional kernel feature space to discriminate significantly different fault classes. Meanwhile, integrated algorithm called KSCDA also overcomes the singularity of KCDA.rnIn the first section, this paper reviewed literature on different fault diagnosis models, including linear discriminant analysis ( LDA) , kernel-based linear discriminant analysis ( KLDA) , clustering based discriminate analysis ( CDA) , kernel clustering based discriminate analysis (KCDA) and kernel scatter-difference (KSD). Chen's CDA algorithm can not only help model the structure of multiple clusters, but also satisfy a LDA-like criterion that every pair of clusters falls into different classes and the within-cluster scatting problem is minimized. The literature review also leads to the finding that the center of the cluster for each class should be located in the transformed space and adopt the mean of their corresponding clusters.rnIn the second section, we first generate 12 different fault classes based on the abovementioned assumptions. Second, we choose the LOO-CV method as the appropriate cross-validation strategy. Third, we calculate the discriminant value C to discriminate three fault classes in interval forms. In the third and forth section, the improved KCDA by using KSD called KSCDA was validated by simulating 12 kinds of different fault classes and comparing with KSLDA. The result shows the effectiveness of KSCDA to promote the recognizing rate of fault models from 62.5% to 100% and this method is better than KSLDA. In the fifth section, we further demonstrate that KSCDA is effective by analyzing steel plate faults data set from UCI.rnIn summary, the kernel method can overcome major limitations of LDA. In particular, KSCDA has the best performance. HoweveT, future research may want to focus on examining issues associated with the overlapping among different classes.%针对一类虽然满足线性判别分析算法(LDA)的三种假设,但仍然导致LDA失效的特殊故障模式,提出运用基于高斯核函数和核化离散差判别分析的一种核化聚类判别分析方法( KSCDA),通过模拟12种不同样本,证明KSCDA能有效解决该问题,故障识别率最大提升从62.5％到100％.且KSCDA优于KSLDA.该问题的解决对实践有一定指导意义.
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