基于局部保持嵌入-K近邻比率密度的半导体蚀刻过程故障诊断策略

A novel fault diagnosis strategy based on neighborhood preserving embedding–K nearest neighbor ratio density in semiconductor etching processes

针对多模态间歇过程存在数据维度高且方差差异较大的特征,提出一种基于局部保持嵌入–K近邻比率密度(NPE–KRD)规则的故障检测方法.首先,利用局部保持嵌入(NPE)方法将原始的高维数据投影到低维空间;其次,在低维空间通过计算样本的密度及其前K近邻密度的均值来建立K近邻比率密度(KRD);最后,根据核密度估计法确定统计量控制限并进行故障诊断.NPE方法既能够在低维空间保持数据局部近邻结构,又能够降低故障检测过程的计算复杂度.通过引入比率密度,NPE–KRD可以降低多模态方差结构差异对故障检测的影响,提高过程故障检测率.通过数值例子和半导体工业过程的仿真实验,并与主元分析、K近邻、局部保持嵌入等方法进行比较,验证了本文方法的有效性.

Aiming at characteristics with high dimensions and large differences in variance of multimodal batch process,a fault detection method based on neighborhood preserving embedding–K nearest neighbor ratio density(NPE–KRD)rule is proposed.Firstly,the raw high dimensional data are projected into a low dimensional space using neighborhood preserving embedding(NPE).Secondly,K nearest neighbor ratio density(KRD)is established by calculating the density of the sample and the mean of its K nearest neighbor in the low dimensional space.Finally,the control limit of statistics is determined by kernel density estimation method and fault diagnosis is carried out.NPE can not only maintain the local neighbor structure of data in the low dimensional space,but also reduce the computational complexity of the fault detection process.By introducing ratio density,NPE–KRD can reduce the influence of multimode variance structure difference on fault detection and improve the fault detection rate of processes.Compared with principal component analysis,K nearest neighbor and neighborhood preserving embedding,the effectiveness of the proposed method is verified in a numerical cases and semiconductor industrial processes.