题目：A comparison and evaluation of key performance indicator-based multivariate statistics process monitoring approaches
注：KPIs consider a broader range of variables including operation cost, maintenance cost, and production rate
基于关键绩效指标的多元统计过程监控方法的比较与评价
1、前言
研究对象：
the key performance indicator (KPI)-based multivariate statistical process monitoring and fault diagnosis (PM-FD) methods：
1).direct；2).linear regression-based(LS、PCR)；3).PLS-based(PLS、T-PLS、C-PLS).（classify them according to their computational characteristics）
研究内容：
review three methods、interconnections、geometric properties 、computational costs 、a new evaluation index calledexpected detection delay for PM-FD of KPIs
2、review three methods
1).direct:
建模：
a singular value decomposition (SVD) on the cross-covariance matrix between y and
统计量：
控制限：
故障判断：
2).linear regression-based(LS、PCR):
>>>LS：
建模：
解：a QR decomposition on LS
统计量：
控制限：
故障判断：
>>>PCR：
建模：
PCA is first performed on Y
解：a QR decomposition on
统计量:
控制限：同direct methods
故障诊断：
3).PLS-based(PLS、T-PLS、C-PLS):
Original PLS-based method：
T-PLS-based method：
C-PLS-based method：
3、Comparison
3.1 Interconnections ：
direct：
LS:
PCR:
a.LS derives the based on the LS regression matrix
, while PCR finds
indirectly from the principal space of y (
) obtained by a PCA decomposition on Y.
b.LS-based method involves more statistical characteristics than PCR.
c.the training dataand
that are uneven in length, LS can still work with part of
and
estimating
, and all Y estimating
, but PCR cannot
d.The PCA decomposition in PCR makes it strongly against the overfitting, a common problem usually occurs in LS.
PLS:
T-PLS: the same as LS
C-PLS: fairly resembles the property in LS
3.2 Summary of projectors
the direct solution, LS and C-PLS related approaches use orthogonal projections, while the others use oblique ones.
3.3 Information about KPI-related subspaces
3.4 Summary of the computational complexity and parameter
PCR中
4、A new performance evaluation index
原始方法：
FAR---A false alarm occurs when an alarm is announced under normal operating condition.
FDR---Fault detection alarm represents an effective alarm issued while there exists a fault
缺点：
FDR can only reflect the detectable probability of the PM-FD indexfor the fault with fixed parameters, but cannot tell whether the fault could beinstanta neously detected or not.
In addition, when the fault is successfully detected, the timetaken to detect the fault is also important.
新方法：the expecteddetection delay(EDD)
1)-FDR(k):
in a time varying faulty scenario, the FDR is also time-varying and should be modified depending on the time instant k
2)-DD:
a.DD = the possible time interval between the occurrenceof the fault and the successful detection of it
b.J denote DD, J may take the value j, where j = 0, 1, 2, .. . ∞
c.The probability that J takes the value j is based on the fact thatand can be shown as
d.the fault is constant. In this case, ∀k, FDR(k) = FDR,
3)-EDD the expectation of DD
a.
注：
if FDR →1, that leads to EDD →0
if FDR →0, EDD approaches infinity
if EDD crosses the threshold, it cannot identify this fault
b.an integrated EDD corresponding to all faulty episodes
注： is the number of faults,
represents the detection delay given by ith type of fault, and
is the probability when the ith fault occurs, which must be specified beforehand based on theprocess knowledge.
4)-评估
对于受 KPI 影响的故障提供较小的 EDD，基于 PLS 的方法显示出较小的 EDD，其中 T-PLS 和 C-PLS 尤为首选(PLS,LS, the direct ,EDD由小到大)
对于对 KPI 没有影响的故障提供较大的 EDD，基于线性回归的方法具有最好的性能，因为在大多数故障情况下，不能检测到故障，提供了最少的错误检测。基于 PLS 的方法在任何情况下显示出最小的 EDD，这表明这种方法具有最高的虚警概率。在 PLS 系列中，T-PLS 和C-PLS 的 EDD 小于 PLS，这意味着它们遭受的误报警风险较高。(当发生 KPI 无关故障时，基于PLS 的方法是不合适的，但基于线性回归的方法更可靠)
