1. A method for manufacturing an otorhinological delivery device, comprising
preparing a core comprising at least one pharmaceutically active agent and an elastomer composition selected from the group consisting of poly(dimethylsiloxane), a siloxane-based elastomer comprising 3,3,3-trifluoropropyl groups attached to the Si-atoms of the siloxane units, a siloxane-based elastomer comprising poly(alkylene oxide) groups and mixtures thereof;
encasing said core with a membrane, said membrane being made of the same or a different elastomer composition than said core, said elastomer composition of said membrane being selected from said group, thereby forming an implantable device,
shaping said implantable device into a shape suitable for implantation into the ear or nose of a human or animal,
wherein the pharmaceutically active agent is selected from the group comprising dexamethasone, betamethasone, beclomethasone, budesonide and mixtures thereof.
2. The method of claim 1, wherein said elastomer composition comprises a siloxane-based elastomer comprising 3,3,3-trifluoropropyl groups attached to the Si-atoms of the siloxane units and wherein in said siloxane-based elastomer 1 to 49.5% of the substituents attached to the Si-atoms of the siloxane units are 3,3,3-trifluoropropyl groups.
3. The method of claim 1, wherein said elastomer composition comprises a siloxane-based elastomer comprising poly(alkylene oxide) groups and wherein said poly(alkylene oxide) groups are present as alkoxy-terminated grafts or blocks linked to the polysiloxane units by silicon-carbon bonds or as a mixture of these forms.
4. The method of claim 3, wherein said poly(alkylene oxide) groups are poly(ethylene oxide) groups.
5. The method of claim 1, wherein said membrane and said core are made of the same elastomer composition.
6. The method of claim 1, wherein said membrane and said core are made of different elastomer compositions.
7. The method of claim 1, wherein said device is an otological delivery device and wherein the elastomer composition comprises poly(dimethylsiloxane) and a siloxane-based elastomer comprising poly(ethylene oxide) groups.
8. A method of treatment of an otological disorder, comprising placing in the ear of a patient in need of said treatment an otorhinological delivery device prepared according to claim 1, wherein said otological disorder is selected from the group consisting of otitis, acute infections, cochlear and vestibular disorders, vertigo, Meniere’s disease, sudden deafness, sensoneurinal hearing loss, tinnitus, motion sickness, endolymphatic hydrops, endolymphatic hypertension, perilymphatic hypertension, perilymphatic hydrops, perilymphatic fistula, intracochlear fistula and ruptures in various membrane structures within the ear.
9. A method of treatment of a nasal disorder, comprising placing in the nose of a patient in need of said treatment an otorhinological delivery device prepared according to claim 1, wherein said nasal disorder is selected from the group consisting of nasal inflammatory disorders, allergic reactions, asthma and fungal infections.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A fault detector for operating process of an electric arc furnace, comprising:
a host computer;
a temperature signal acquisition equipment including an imaging device, a color sensor, two transceiver integrated circuits and a serial communication circuit, the imaging device comprises an objective lens and an eyepiece, the transceiver integrated circuit comprises a microcontroller and a RF transceiver, and one RF transceiver of the two transceiver integrated circuits works as transmitter, and the other works as an acceptor, the input terminal of the color sensor is connected to the imaging device, wherein the objective lens of the imaging device aims a measured target, a photosensitive sensor is fixed in the eyepiece at one end so that the measured target radiation light can be projected to the photosensitive parts of the color sensor by the imaging device, the color sensor is connected to the microcontroller such that when collecting the signal, the microcontroller controls the RF transmitter circuit to transmit wireless RF signals, the RF receiver circuit controls the serial communication circuit to send data to the host computer under the coordination of the microcontroller after receiving signals;
a current signal acquisition equipment including an AC transformer and a Programmable Logic Controller (PLC), the output terminal of the AC transformer is connected to an input terminal of the PLC, and the output terminal of the PLC transformer is connected to the host computer, wherein the AC transformer is respectively connected with the three electrodes of the electric arc furnace in series, large current signals which go through the electrodes is transformed into standard signals of 0 to 5 V, and then, the standard signals are transmitted to an analog input terminal of the PLC, after analogue-to-digital conversion by the PLC, the digital signals are transmitted to the host computer through a serial port of PLC; and
wherein in the first group transceiver integrated circuit, the output terminal of the color sensor is connected to the input terminal of the microcontroller, and the output terminal of the microcontroller is connected to the input terminal of the RF transmitter, the output terminal of the RF transmitter is connected to the input terminal of the RF receiver in the second group transceiver integrated circuit by a wireless network, the output terminal of the RF receiver is connected to the input terminal of the microcontroller in the second group of transceiver integrated circuit, the output terminal of the microcontroller is connected to an input terminal of the serial communication circuit, and an output terminal of the serial communication circuit is connected to the host computer and wherein two identical transceiver integrated circuits are used to transmit and receive wireless signals and to play a different role in the control of the microcontroller, a configuration software of the host computer has the function of real-time display, history enquiry, data storage and alarm processing.
2. A multimode fault monitoring and diagnosis method using the fault detector as claimed in claim 1, comprising the following steps of:
Step 1: acquiring and standardizing data, wherein M operating modes are supposed in the operating process of the electric arc furnace, three-phase current IA, IB and IC in the M operating modes and temperature in the electric arc furnace are acquired when the electric arc furnace operates steadily in different modes, then, the initial dataset {dot over (X)}m=x1,mT, x2,mT, . . . , xl,mT . . . , xNmTT(Nm\xd7J) (m=1, 2, . . . , M) is obtained, where the subscript m is the mth operating mode, Nm is the number of the sample data in the mth operating mode, and J is the number of the variables which is defined as 4 in the present invention, the initial dataset is standardized by the methods of calculating the average and standard deviation, and then, the standard dataset Xm=(Nm\xd7J) (m=1, 2, . . . , M) in the normal operation state can be obtained;
Step 2: decomposing the data and establishing a preliminary monitoring model for the operating process of the electric arc furnace, wherein the M datasets are obtained in Step 1 by standardized, building the preliminary monitoring model for the operating process of the electric arc furnace, that calculate the global main factor matrix Pg under the M different operating modes of the monitoring model to decompose the datasets, wherein the datasets is obtained in the M different operating modes of the electric arc furnace, then close common subsets in these M operating modes and special subsets of every operating mode are obtained; and
Step 3: monitoring and diagnosing the fault of the electric arc furnace work process, wherein the preliminary monitoring model of the electric arc furnace is used to calculate the T2 statistics and the SPE statistics, the score matrices TAS and TBS of special parts of two modes datasets and the residual error matrices EAS and EBS of the special parts can be obtained by combining Principal Component Analysis (PCA) algorithm,
{
T
A
S
=
X
A
S
\u2062
P
A
S
=
X
A
\u2061
(
I
–
P
g
\u2062
P
g
T
)
\u2062
P
A
S
X
^
A
S
=
T
A
S
\u2061
(
P
A
S
)
T
E
A
S
=
X
A
S
–
X
^
A
S
(
26
)
{
T
B
S
=
X
B
S
\u2062
P
B
S
=
X
B
\u2061
(
I
–
P
g
\u2062
P
g
T
)
\u2062
P
B
S
X
^
B
S
=
T
B
S
\u2061
(
P
B
S
)
T
E
B
S
=
X
B
S
–
X
^
B
S
(
27
)
where {circumflex over (X)}AS and {circumflex over (X)}BS are respectively the estimated matrixes of XAS and XBS, PAS (J\xd7RAS) and PBS(J\xd7RBS) are respectively the PCA loading matrixes of two special subsets, RAS and RBS are respectively the number of principle components for each subset, and EAS and EBS are respectively the residual errors of the special subsets and also the residual errors of the final model,
where in the operating process of the electric arc furnace, the scores of the new observation values in the special subsets are tA,newS=(PAS)Txnew and tB,newS=(PBS)Txnew, where PAS is the loading matrix of the special subset for mode A of the electric arc furnace, PBS is the loading matrix of the special subset for mode B of the electric arc furnace, and Xnew is the new observation data in the operating process of the electric arc furnace; the T2 statistics for the special parts of mode A and mode B are calculated as follows:
TS,A2=(tA,newS)T(\u039bAS)\u22121tA,newS\u2003\u2003(32)
TS,B2=(tB,newS)T(\u039bBS)\u22121tB,newS\u2003\u2003(33)
and \u039bAS and \u039bBS respectively represent the diagonal matrix which consists of the eigenvalues of the special subsets,
to calculate the final residual errors eA,newS and eB,newS, {circumflex over (x)}A,newS and {circumflex over (x)}B,newS are supposed to be the estimated values for mode A and mode B, and then, {circumflex over (x)}A,newS, {circumflex over (x)}B,newS and xnewS are submitted into equations (26) and (27) to obtain:
eA,newS=xnewS\u2212{circumflex over (x)}A,newS=(I\u2212Pg,PASPg,PAST)xnew\u2003\u2003(34)
eB,newS=xnewS\u2212{circumflex over (x)}B,newS=(I\u2212Pg,PBSPg,PBST)xnew\u2003\u2003(35)
the SPE statistics SPEA,newS and SPEB,newS for mode A and mode B are obtained with the residual errors:
SPEA,newS=(eA,newS)TeA,newS\u2003\u2003(36)
SPEB,newS=(eB,newS)TeB,newS\u2003\u2003(37)
the T2 statistics and the SPE statistics are used for the fault monitoring, comparing the control charts plotted respectively in mode A and mode B, the current operating mode of the electric arc furnace can be determined, and online fault detection can be performed in the corresponding operating mode, when the T2 statistics and the SPE statistics of the corresponding operating mode go beyond the control limits, some fault may occur, otherwise, the whole operating process is normal.
3. The method as claimed in claim 2, wherein the preliminary monitoring model for the operating process of the electric arc furnace in Step 2 is formed by the following steps of:
1) calculating the global main factor matrix Pg for the operating process of the electric arc furnace, in the operating process of the electric arc furnace, main factors for the subset of the dataset are defined as pm (m=1, 2, . . . , M), where the subscript m represents the number of different operating modes; the relation between the main factor pm of the dataset for each operating mode and the dataset is:
p
m
=
\u2211
n
=
1
N
m
\u2062
a
n
,
m
\u2062
x
n
,
m
=
X
m
T
\u2062
\u03b1
m
(
7
)
\u03b1m=a1,m, a2,m, . . . , an,mT is the coefficient of the linear combination, where the letter n represents the number of rows of \u03b1m, pm can be represented as the linear combination of the Nm vectors of Xm; the global main factor pg is used to describe main factors of the subset for each operating mode; the method to obtain pg is as follows:
pg is made to approximate to the subset main factor pm,j for each operating mode, (pgTXmT\u03b1m)2 is maximized, and the maximum of the polynomial R2=(pgTXmT\u03b1m)2+(pgTX2T\u03b12)2+ . . . +(pgTXMT\u03b1m)2 and the inequality
\u025b
\u2264
(
p
g
T
\u2062
X
1
T
\u2062
\u03b1
1
)
2
(
p
g
T
\u2062
X
2
T
\u2062
\u03b1
2
)
2
=
(
p
g
T
\u2062
X
2
T
\u2062
\u03b1
2
)
2
(
p
g
T
\u2062
X
3
T
\u2062
\u03b1
3
)
2
\u2264
1
\u025b
are calculated, where \u03b5 is a constraint parameter and satisfies the condition of 0.8\u2266\u03b5<1; to make pg approximate to pm,j, solve the following equation:
max
\u2062
R
2
=
max
(
\u2211
m
=
1
M
\u2062
(
p
g
T
\u2062
X
m
T
\u2062
\u03b1
m
)
2
)
(
8
)
satisfy constraints at the same time as follows:
s
.
t
.
{
\u025b
\u2061
(
p
g
T
\u2062
X
m
–
1
T
\u2062
\u03b1
m
–
1
)
2
–
(
p
g
T
\u2062
X
m
T
\u2062
\u03b1
m
)
2
\u2264
0
\u025b
\u2061
(
p
g
T
\u2062
X
m
T
\u2062
\u03b1
m
)
2
–
(
p
g
T
\u2062
X
m
–
1
T
\u2062
\u03b1
m
–
1
)
2
\u2264
0
p
g
T
\u2062
p
g
=
1
\u03b1
m
T
\u2062
\u03b1
m
=
1
(
9
)
mode A and mode B respectively represent the operating modes of the electric arc furnace generated by the voltage A and voltage B, M is 2; an objective function is defined, and the maximum of the objective function is calculated as follows:
F
\u2061
(
p
g
,
\u03b1
,
\u03bb
)
=
(
p
g
T
\u2062
X
A
T
\u2062
\u03b1
A
)
2
+
(
p
g
T
\u2062
X
B
T
\u2062
\u03b1
B
)
2
–
\u03bb
g
\u2061
(
p
g
T
\u2062
p
g
–
1
)
–
\u03bb
A
\u2061
(
\u03b1
A
T
\u2062
\u03b1
A
–
1
)
–
\u03bb
B
\u2061
(
\u03b1
B
T
\u2062
\u03b1
B
–
1
)
–
\u03bb
1
\u2061
(
\u025b
\u2061
(
p
g
T
\u2062
X
A
T
\u2062
\u03b1
A
)
2
–
(
p
g
T
\u2062
X
B
T
\u2062
\u03b1
B
)
2
)
–
\u03bb
2
\u2061
(
\u025b
\u2061
(
p
g
T
\u2062
X
B
T
\u2062
\u03b1
B
)
2
–
(
p
g
T
\u2062
X
A
T
\u2062
\u03b1
A
)
2
)
(
10
)
where: \u03bbg, \u03bbA, \u03bbB, \u03bb1 and \u03bb2 are constants; pg, \u03b1A and \u03b1B in above equation are solved by a partial derivative to obtain the following equations respectively:
(1\u2212\u03bb1\u03b5+\u03bb2)XATXApg+(1\u2212\u03bb2\u03b5+\u03bb1)XBTXBpg=\u03bbgpg\u2003\u2003(11)
\u03b1
A
=
(
1
–
\u03bb
1
\u2062
\u025b
+
\u03bb
2
)
\u03bb
A
\u2062
X
A
\u2062
p
g
=
1
p
g
T
\u2061
(
X
A
T
\u2062
X
A
)
\u2062
p
g
\u2062
X
A
\u2062
p
g
(
12
)
\u03b1
B
=
(
1
–
\u03bb
2
\u2062
\u025b
+
\u03bb
1
)
\u03bb
B
\u2062
X
B
\u2062
p
g
=
1
p
g
T
\u2061
(
X
B
T
\u2062
X
B
)
\u2062
p
g
\u2062
X
B
\u2062
p
g
(
13
)
\u03bbA and \u03bbB can be calculated from equations (11), (12) and (13):
\u03bbA=(1\u2212\u03bb1\u03b5+\u03bb2)pgT(XATXA)pg\u2003\u2003(14)
\u03bbB=(1\u2212\u03bb2\u03b5+\u03bb1)pgT(XBTXB)pg\u2003\u2003(15)
based on the inequality
\u025b
\u2264
(
p
g
T
\u2062
X
1
T
\u2062
\u03b1
1
)
2
(
p
g
T
\u2062
X
2
T
\u2062
\u03b1
2
)
2
=
(
p
g
T
\u2062
X
2
T
\u2062
\u03b1
2
)
2
(
p
g
T
\u2062
X
3
T
\u2062
\u03b1
3
)
2
\u2264
1
\u025b
,
pg should satisfy the following equations:
\u2003
{
\u03bb
1
\u2061
(
\u025b
\u2061
(
p
g
T
\u2062
X
A
T
\u2062
\u03b1
A
)
2
–
(
p
g
T
\u2062
X
B
T
\u2062
\u03b1
B
)
2
)
=
0
,
\u2062
(
16
)
\u03bb
2
\u2061
(
\u025b
\u2061
(
p
g
T
\u2062
X
B
T
\u2062
\u03b1
B
)
2
–
(
p
g
T
\u2062
X
A
T
\u2062
\u03b1
A
)
2
)
=
0
,
\u2062
(
17
)
\u03bb
1
,
\u03bb
2
\u2265
0.
the results of equations (12) and (3) are submitted into equations (16) and (17) to obtain the result as follows:
\u2003
{
\u03bb
1
\u2061
(
\u025b
\u2062
\u2062
p
g
T
\u2061
(
X
A
T
\u2062
X
A
)
\u2062
p
g
–
p
g
T
\u2061
(
X
B
T
\u2062
X
B
)
\u2062
p
g
)
=
0
,
\u2062
(
18
)
\u03bb
2
\u2061
(
\u025b
\u2062
\u2062
p
g
T
\u2061
(
X
B
T
\u2062
X
B
)
\u2062
p
g
–
p
g
T
\u2061
(
X
A
T
\u2062
X
A
)
\u2062
p
g
)
=
0
,
\u2062
(
19
)
\u03bb
1
,
\u03bb
2
\u2265
0.
in above equation, in order to calculate pg, the values of \u03bb1 and \u03bb2 are analyzed as follows:
(1) if \u03bb1\u22600 and \u03bb2\u22600, the equations (18) and (19) are contradictory; therefore, the equation has no solution in this case;
(2) if \u03bb1=0 and \u03bb2=0, the equations (18) and (19) are constantly equal to 0, equations (18) and (19) lose constraints; and equation (11) can be rewritten as follows:
XATXApg+XBTXBpg=\u03bbgpg\u2003\u2003(20)
from equation (20), calculating pg changes to calculating the eigenvector of (XATXA+XBTXB), and using the calculation method can obtain the maximum of polynomial (pgTXAT\u03b1A)2+(pgTXBT\u03b1B)2, however, equations (18) and (19) lose constraints, so pg may not approximate to the main factor of the subset for both mode A and mode B; therefore, the solution pg cannot meet requirements,
(3) if \u03bb1=0 and \u03bb2\u22600, equations (18) and (19) are calculated to obtain:
\u03b5pgT(XBTXB)pg\u2212pgT(XATXA)pg=0\u2003\u2003(21)
where the parameter \u03b5 should meet the condition of 0.8\u2266\u03b5<1; the equation (21) has only one unknown vector pg; equation (21) which has only one unknown vector pg is calculated to obtain the solution as pg, which is defined as pg1,
(4) If \u03bb1\u22600 and \u03bb2=0, the same method is used, and the following equation is obtained:
\u03b5pgT(XATXA)pg\u2212pgT(XBTXB)pg=0\u2003\u2003(22)
the analysis method similar to the method in step (3) is used to obtain the solution of another pg which is defined as pg2,
pg1 and pg2 can be the solutions of pg which meet the conditions; pg1 and pg2 are combined together to constitute a matrix Pg=pg1, pg2 of the R row, where the sum of the rows of pg1 and pg2 is R; then, the global main factor matrix Pg(J\xd7R) for the operating process of the electric arc furnace is obtained as the solution which meets the assuming conditions; and
2) decomposing the datasets for the two operating modes of the electric arc furnace, the global main factor matrix Pg(J\xd7R) for the operating process of the electric arc furnace is obtained by the modeling above; the column vectors of Pg should meet the linear conditions pg=XAT\u03b11 and pg=XBT\u03b12, where \u03b11 and \u03b12 are the linear combination coefficients, pgTpg=1, \u03b11T\u03b11=1, and \u03b12T\u03b12=1; then, the equations above can be translated into \u03b11=XApg and \u03b12=XBpg; R linear combination coefficients \u03b11 and \u03b12 are made respectively to constitute the score matrices TAC and TBC of the two special subsets, and the following equation can be obtained:
TAC=XAPg,TBC=XBPg\u2003\u2003(23)
by the following calculation, the dataset XA for mode A of the electric arc furnace can be decomposed into the common dataset XAC containing common information and the special dataset XAS,
{
X
A
=
X
A
C
+
X
A
S
X
A
C
=
T
A
C
\u2062
P
g
T
=
X
A
\u2062
P
g
\u2062
P
g
T
X
A
S
=
X
A
–
X
A
C
=
X
A
T
\u2061
(
I
–
P
g
\u2062
P
g
T
)
(
24
)
the dataset XB for mode B of the electric arc furnace can be decomposed into the common dataset XBC and special dataset XBS in the same method,
{
X
B
=
X
B
C
+
X
B
S
X
B
C
=
T
B
C
\u2062
P
g
T
=
X
B
\u2062
P
g
\u2062
P
g
T
X
B
S
=
X
B
–
X
B
C
=
X
B
T
\u2061
(
I
–
P
g
\u2062
P
g
T
)
(
25
)
after the decomposition above is completed, the preliminary monitoring model for the operating process of the electric arc furnace is established.
4. The method as claimed in claim 2, wherein calculating the Hotelling T2 statistics and the SPE statistics are as follows:
by the following calculation, the dataset XA for mode A of the electric arc furnace can be decomposed into the common dataset XAC containing common information and the special dataset XAS,
{
X
A
=
X
A
C
+
X
A
S
X
A
C
=
T
A
C
\u2062
P
g
T
=
X
A
\u2062
P
g
\u2062
P
g
T
X
A
S
=
X
A
–
X
A
C
=
X
A
T
\u2061
(
I
–
P
g
\u2062
P
g
T
)
(
24
)
The dataset XB for mode B of the electric arc furnace can be decomposed into the common dataset XBC and the special dataset XBS,
{
X
B
=
X
B
C
+
X
B
S
X
B
C
=
T
B
C
\u2062
P
g
T
=
X
B
\u2062
P
g
\u2062
P
g
T
X
B
S
=
X
B
–
X
B
C
=
X
B
T
\u2061
(
I
–
P
g
\u2062
P
g
T
)
(
25
)
the score matrices TAS and TBS for special parts of the two-mode datasets and the residual error matrices EAS and EBS for the special parts can be obtained by combining with the Principal Component Analysis (PCA) algorithm,
{
T
A
S
=
X
A
S
\u2062
P
A
S
=
X
A
\u2061
(
I
–
P
g
\u2062
P
g
T
)
\u2062
P
A
S
X
^
A
S
=
T
A
S
\u2061
(
P
A
S
)
T
E
A
S
=
X
A
S
–
X
^
A
S
(
26
)
{
T
B
S
=
X
B
S
\u2062
P
B
S
=
X
B
\u2061
(
I
–
P
g
\u2062
P
g
T
)
\u2062
P
B
S
X
^
B
S
=
T
B
S
\u2061
(
P
B
S
)
T
E
B
S
=
X
B
S
–
X
^
B
S
(
27
)
where: {circumflex over (X)}AS and {circumflex over (X)}BS are respectively the estimated matrixes of XAS and XBS, PAS(J\xd7RAS) and PBS(J\xd7RBS) are respectively the loading matrixes of two special subsets by the PCA algorithm, RAS and RBS are respectively the number of principle components for each subset, and EAS and EBS are respectively the residual errors of the special subsets as well as the final model,
the datasets for mode A and mode B are decomposed into common datasets and special datasets, XAC and XAS are obtained from equation (24), and XBC and XBS are obtained from equation (25); and then, the diagonal matrix which consists of eigenvalues of the four matrix,
the eigenvalue of XAC is supposed to be \u03c6, so the characteristic polynomial of XAC is |\u03c6\xb7E\u2212XAC|, where E is the unit matrix; the characteristic polynomial is made to be equal to zero, |\u03c6\xb7E\u2212XAC|=0, so the characteristic equation G(\u03c6)=0 whose variable \u03c6 is obtained after being sorted; the eigenvalues of XAC can be obtained after solving the characteristic equation; the eigenvalues of XAC are used as diagonal elements to obtain the diagonal matrix \u039bAC, diagonal matrixes \u039bAC, \u039bBC, and \u039bBS which consist of the eigenvalues of another three matrixes XAS, XBC and XBS can be obtained in the same method,
fault detection analysis in the common datasets and the special datasets for mode A and mode B are performed respectively, the Hotelling T2 statistics and the SPE statistics are used for fault detection, and faults can be detected by plotting the control chart; xnew(J\xd71) is the new observation data of the electric arc furnace operating process, by projecting xnew to the global main factor Pg, the common datasets score vector of the new sample data for two modes tnewC=PgTxnew can be obtained, At the same time, the T2 statistics TC,A2 and TC,B2 of common parts of mode A and mode B can be obtained by the following equations (30) and (31), the T2 statistics of the common parts of the two modes are calculated as follows:
TC,A2=(tnewC)T(\u039bAC)\u22121tnewC\u2003\u2003(30)
TC,B2=(tnewC)T(\u039bBC)\u22121tnewC\u2003\u2003(31)
the scores of the special subsets of the electric arc furnace operating process, tA,newS=(PAS)Txnew and tB,newS=(PBS)Txnew, are calculated in the similar method, meanwhile equations (32) and (33) below are used to calculate the T2 statistics of the special subsets of mode A and mode B
TS,A2=(tA,newS)T(\u039bAS)\u22121tA,newS\u2003\u2003(32)
TS,B2=(tB,newS)T(\u039bBS)\u22121tB,newS\u2003\u2003(33)
\u039bAS and \u039bBS respectively represent the diagonal matrixes which consist of the eigenvalues of the special subsets,
calculating the final residual errors eA,newS and eB,newS, {circumflex over (x)}A,newS and {circumflex over (x)}B,newS are supposed to be the estimated values of xnewS in mode A and mode B, and {circumflex over (x)}A,newS, {circumflex over (x)}B,newS and xnewS are submitted into equations (26) and (27) to obtain following equations:
eA,newS=xnewS\u2212{circumflex over (x)}A,newS=(I\u2212Pg,PASPg,PAST)xnew\u2003\u2003(34)
eB,newS=xnewS\u2212{circumflex over (x)}B,newS=(I\u2212Pg,PBSPg,PBST)xnew\u2003\u2003(35),
the SPE statistics SPEA,newS and SPEB,newS for mode A and mode B are calculated by the residual errors:
SPEA,newS=(eA,newS)TeA,newS\u2003\u2003(36)
SPEB,newS=(eB,newS)TeB,newS\u2003\u2003(37).