Transient multivariable sensor evaluation
A method and system for performing transient multivariable sensor evaluation. The method and system includes a computer system for identifying a model form, providing training measurement data, generating a basis vector, monitoring system data from sensor, loading the system data in a non-transient memory, performing an estimation to provide desired data and comparing the system data to the desired data and outputting an alarm for a defective sensor.
1. A method of performing transient multivariable sensor evaluation in a system, comprising the steps of,
identifying a model form corresponding to the system;
providing training measurement data;
generating a basis vector;
receiving, from a plurality of sensors, system data;
loading the system data;
performing an estimation to provide desired data; and
identifying a defective sensor and system data associated therewith within the plurality of sensors by comparing the system data to the desired data and outputting an alarm for the defective sensor; and
generating an estimator to replace the identified defective sensor system data with a value based upon the plurality of sensor's system data excluding the identified defective sensor system data.
2. The method as defined in claim 1 wherein the model form comprises an auto-regressive moving average (ARMA) form.
3. The method as defined in claim 2 wherein the ARMA form comprises,
ΕδZ k =0, where
E
=
[
I
A
1
A
2
…
A
n
-
C
0
-
C
1
…
-
C
n
]
and
δ
Z
k
=
[
δ
y
k
δ
y
k
-
1
⋮
δ
y
k
-
n
δ
u
k
δ
u
k
-
1
⋮
δ
u
k
-
n
]
.
4. The method as defined in claim 3 wherein the ARMA form for causality operation comprises,
[
A
-
C
]
[
δ
Y
δ
U
]
=
0
where
A
=
[
I
A
1
A
2
…
A
n
]
C
=
[
C
0
C
1
…
C
n
]
and
δ
Y
=
[
δ
y
k
δ
y
k
-
1
⋮
δ
y
k
-
n
]
δ
U
=
[
δ
u
k
δ
u
k
-
1
⋮
δ
u
k
-
n
]
.
5. The method as defined in claim 4 wherein the ARMA form for input controllable operation comprises
[δY 1 δY 2 . . . δY K−n ] T [C L −1 A] T =[δU 1 δU 2 . . . δU K−n] T
6. The method as defined in claim 4 wherein the ARMA form for output observable operation comprises,
[δY 1 δY 2 . . . δY K ]=A L −1 C[δU 1 δU 2 . . . δU K−n ]
[δU 1 δU 2 . . . δU K−n ] T [A L −1 C] T =[δY 1 δY 2 . . . δY K−n ] T
7. The method as defined in claim 4 wherein the ARMA form is re-cast into a reduced form based on the following two mathematical properties of stable physical systems,
h ij [n]= 0, n< 0 and
Σ n=−∞ ∞ |h ij [n]|=Σ n=o ∞ |h ij [n]|<∞,
where h represents a physical component and
h[n]=x[n]=Σ n=∞ ∞ h[k]x[n−k]
and in a discrete time domain becomes,
(
y
1
[
n
]
⋮
y
l
[
n
]
)
=
(
h
11
[
n
]
…
h
1
m
[
n
]
⋮
⋱
⋮
h
l
1
[
n
]
…
h
l
m
[
n
]
)
*
(
x
1
[
n
]
⋮
x
m
[
n
]
)
(
h
11
[
0
]
…
h
11
[
K
]
…
h
1
m
[
0
]
…
h
1
m
[
K
]
-
1
…
0
⋮
h
l
1
[
0
]
…
h
l
1
[
K
]
…
h
l
m
[
0
]
…
h
l
m
[
K
]
0
…
-
1
)
·
(
x
1
[
n
]
⋮
x
1
[
n
-
K
]
⋮
x
m
[
n
]
⋮
x
m
[
n
-
K
]
y
1
[
n
]
⋮
y
l
[
n
]
)
=
0.
8. The method as defined in claim 7 wherein the step of generating the basis vectors comprises specifying normal sensor measurement accuracy, initializing number of time lags to zero, generating a training matrix from measurements of the system data by applying
A=(X 1 . . . X r )
computing a singular value decomposition of the training data matrix by applying,
X n εnull(C); and
testing whether σ points are less than the normal sensor measurement accuracy, and if is less than, then form the matrix of the basis vectors, and if not less than the normal sensor measurement accuracy, increment by K and return to composing the training data matrix step and then recycling until the σ points are less than the normal sensor measurement accuracy.
9. A system for performing transient multivariable sensor evaluation, comprising:
a plurality of sensors;
a computer system in communication with the plurality of sensors; the computer system having a non-transient memory with a computer software program and a mathematical representation of the system and basis vectors stored therein for executing instructions to;
receive system data from the plurality of sensors;
perform an estimation to provide desired data; and
compare the system data to the desired data;
identify defective sensors and outputting an alarm for defective sensors;
generate an estimator to replace the identified defective sensor system data with a value based upon the plurality of sensor's system data excluding the identified defective sensor system data.
10. The system of claim 9 , wherein the computer system includes instructions to execute the steps of identifying a model form.
11. The system of claim 9 , wherein the system comprises a heat exchanger.
12. The system as defined in claim 10 wherein the model form comprises an auto-regressive moving average (ARMA) form.