題目：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
基于關(guān)鍵績效指標(biāo)的多元統(tǒng)計(jì)過程監(jiān)控方法的比較與評價
1拢军、前言
研究對象：
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句旱、C-PLS).（classify them according to their computational characteristics）
研究內(nèi)容：
review three methods、interconnections薇组、geometric properties 、computational costs 序目、a new evaluation index calledexpected detection delay for PM-FD of KPIs
2薪前、review three methods
1).direct:
建模：
a singular value decomposition (SVD) on the cross-covariance matrix between y and ?
統(tǒng)計(jì)量：
控制限：
故障判斷：
2).linear regression-based(LS、PCR):
>>>LS：
建模：
解：a QR decomposition on LS
統(tǒng)計(jì)量：
控制限：
故障判斷：
>>>PCR：?
建模：
PCA is first performed on Y
解：a QR decomposition on
統(tǒng)計(jì)量:
控制限：同direct methods
故障診斷：
3).PLS-based(PLS览效、T-PLS却舀、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
缺點(diǎn)：
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)-評估
? ? 對于受 KPI 影響的故障提供較小的 EDD但校，基于 PLS 的方法顯示出較小的 EDD篱昔，其中 T-PLS 和 C-PLS 尤為首選(PLS,LS,?the direct ,EDD由小到大)
? ? 對于對 KPI 沒有影響的故障提供較大的 EDD，基于線性回歸的方法具有最好的性能始腾，因?yàn)樵诖蠖鄶?shù)故障情況下州刽，不能檢測到故障，提供了最少的錯誤檢測浪箭∷胍危基于 PLS 的方法在任何情況下顯示出最小的 EDD，這表明這種方法具有最高的虛警概率奶栖。在 PLS 系列中匹表，T-PLS 和C-PLS 的 EDD 小于 PLS，這意味著它們遭受的誤報(bào)警風(fēng)險較高宣鄙。(當(dāng)發(fā)生 KPI 無關(guān)故障時袍镀，基于PLS 的方法是不合適的，但基于線性回歸的方法更可靠)
