題目： Total Projection to Latent Structures for Process Monitoring
? ? ? ? ? ? ? ? ? 用于過程監(jiān)控的潛在結(jié)構(gòu)的全投影
1、引入
原因：
standard PLS的缺點(diǎn)：
a.PLS uses many components, which makes the predictor model difficult to interpret.
b.These PLS components still include variations orthogonal to Y which have no contribution for predicting Y.
c.the X-residuals from the PLS model are not necessarily small in covariances.There are many cases in which the X-residuals contain larger variability of X than the PLS scores because PLS does not decompose the X-variations in descending order. This makes the use of Q statistic on X-residuals inappropriate.
改進(jìn)：
a.the orthogonal signal correction (OSC) :remove systematic information in X not correlated to Y before a PLS model was built.
b.the orthogonal projections to latent structures (O-PLS):a preprocessing or filtering method to remove systematic orthogonal variation to Y froma given data set X
But:
the above methods are regression methods, which are not designed for process monitoring.
So:
the total projection to latent structures (T-PLS)
注：T-PLS has the same result on the decomposition of T as the O-PLS algorithm. However, T-PLS further decomposes the X-residual E, which is useful for process monitoring.
2放妈、標(biāo)準(zhǔn)PLS
模型：
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
an oblique projection decomposition on X space：
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ?
a new sample 
：
3北救、T-PLS1:a single output y
模型：
模型求解：
an oblique decomposition on X-space：
新樣本：
統(tǒng)計(jì)量和控制限：
性質(zhì)：
? ? ? ? a.
? ? ? ? b.
4、T-PLS2:multiple outputs Y
模型：
求解算法：
注：
a.The properties of TPLS1 also hold for T-PLS2,a芜抒、b
b.he X-space is partitioned into four subspaces by T-PLS2 in a similar way as shown in T-PLS1
c.統(tǒng)計(jì)量和控制限珍策、新樣本也和T-PLS1一樣
5、the relation between PLS and T-PLS
and
together to detect faults related to y,
,
, and
are used together to detect faults unrelated to y,
6宅倒、總結(jié)
For faults related to quality variables Y, T-PLS based methods can give lower false alarm rate and missing alarm rate than PLS-based methods in most simulated cases
