题目： Total Projection to Latent Structures for Process Monitoring

                  用于过程监控的潜在结构的全投影

1、引入

原因：

standard PLS的缺点：

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.

改进：

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、标准PLS

模型：

an oblique projection decomposition on X space：

a new sample ：

3、T-PLS1:a single output y

模型：

模型求解：

an oblique decomposition on X-space：

新样本：

统计量和控制限：

性质：

        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、b

b.he X-space is partitioned into four subspaces by T-PLS2 in a similar way as shown in T-PLS1

c.统计量和控制限、新样本也和T-PLS1一样

5、the relation between PLS and T-PLS

and together to detect faults related to y,

,, andare used together to detect faults unrelated to y,

6、总结

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