Multiblock PLS-based localized process diagnosis(基于多模块PLS 局部化过程诊断)

论文题目：Multiblock PLS-based localized processdiagnosis

            基于多模块的PLS 局部化过程诊断

一种新的PLS方法：Multiblock Partial Least Squares---MBPLS

1、引入：

First:

PCA：maximize the covariance of predictor variables

PLS：maximize the covariance between predictorand response variables

PLS approximate both predictor and response blocks and to model the relationship between them；use toestimate quality variables and monitor process operating performance.

But:

if have many process variables from several processing units in a complex process, the process monitoring and diagnosis problem becomes complicated and the results obtained by the PLS method are hard to interpret and get a proper decision.

Thus:

Hierarchical or multiblock approaches--- divide the total variable block into several meaningful sub-blocks    MBPLS

2、模型：

MBPLS模型：

deflates the residuals based on super scores.

            Modeling：

              Prediction:

3、MBPLS 故障检测

统计量和统计量、控制限

total、block两种情况：

N: # of training samples,

K: # of principal components,

S: sample variance of,

: sample mean of ,

: sample variance of ,

:sample mean of.

4、故障诊断之贡献分析

A contribution plot represents the contribution of each process variable or each variable group to the monitoring statistic.

4.1 block and variable contributions to the Q statistic

the bth block to the total Q statistic:

the ith variable to the block Q statistic:

4.2. Variable contribution to each score

PCA：

the ith element ofthe kth loading vector

PLS:

4.3. block and variable contribution to the  statistic

(一)  the block to the total statistic:

    PCA-the variable contribution:

    PLS-the variable contribution:

                                               is not an exact value ；the exact value of t is

    variable contribution to in the regular or multiblock PCA:

   the exact variable contribution to in PLS:

                                                                                                                   

the total statistic:

 the block contribution to the total statistic:

Ab is the bth column block corresponding to xb

(二)  variable contribution to the block statistic

the kth score in the bth block：

the block statistic ：

the variable contribution to the block statistic:

Bb(:,i) is the ith column of Bb and xb(i) is the ith variable in the bth variable block

(三) responsible for current abnormal condition

the upper control limit (UCL) of each variable (or block) contribution C：

                                              

                             其中，m(C) and s(C) is the mean and sample standard deviation of C

if the relative contribution of a variable，select it as the variable (or block) responsible for current abnormal condition

[注]：本文所涉及图表均出自原论文，仅用作学术笔记，不作商用。