Data processing: measuring – calibrating – or testing – Measurement system – Statistical measurement
Reexamination Certificate
2001-06-12
2003-12-09
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system
Statistical measurement
C702S181000, C702S194000, C706S022000
Reexamination Certificate
active
06662140
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates generally to systems for processing measured signal values, and more specifically to systems for estimating parameter values relating to a set of measured signal values based on fuzzy logic techniques.
BACKGROUND OF THE INVENTION
Systems for processing a number of measured signal values and determining a corresponding set of parameter values are known and commonly used in physical system modeling applications. Such applications are generally useful for aligning model parameters with test data resulting from the measured signal values.
An example of one known physical system modeling application
10
is illustrated in FIG.
1
and includes a physical system
12
having a number of physical processes associated therewith. A number, K, of physical process sensors
14
1
-
14
K
are suitably disposed relative to system
12
, wherein K may be any positive integer. Sensors
14
1
-
14
K
are generally operable to sense operating conditions associated with physical system
12
, and produce resulting operating condition signals (c
i
, i=1, . . . , K) on corresponding signal paths
16
1
-
16
K
. Application
10
further includes a performance analysis system
18
receiving the operating condition signals on signal paths
16
1
-
16
K
and determining predicted performance parameters therefrom. System
18
includes a pre-processing unit
20
having a first set of inputs electrically connected to the various physical process sensors
14
1
-
14
K
via signal paths
16
1
-
16
K
, a second number, L, of inputs electrically connected to a corresponding number, L, of outputs of a model-based parameter predictor block
30
via signal paths
36
1
-
36
L
, and a number, L, of outputs electrically connected to an equation solver
22
via a corresponding number, L, of signal paths
24
1
-
24
L
, wherein L may be any positive integer. Generally, K>L, and the pre-processor unit
20
is operable to combine one or more of the operating condition signals c
i
, i=1, . . . , K) to form a number, L, of corresponding operating parameter signals p
j
, j=1, . . . , L. The model-based parameter predictor block
36
is operable to produce L model parameter values mp
j
, j=1, . . . , L, wherein the model parameter values mp
j
, j=1, . . . , L correspond to the computed model values of the operating parameter signals p
j
, j=1, . . . , L. The pre-processor unit
20
is, in turn, operable to compute a number, L, of parameter delta values &dgr;p
j
(j=1, . . . , L), wherein &dgr;p
j
=p
j
−mp
j
, j=1, . . . , L, and to produce the parameter delta values &dgr;p
j
on corresponding signal paths
24
1
-
24
L
.
System
18
further includes an equation solver block
22
having a first set of inputs receiving the parameter delta values &dgr;p
j
(j=1, . . . , L) on signal paths
24
1
-
24
L
, a second set of inputs receiving a number of unknown variables &dgr;x
i
and corresponding weighting factors W
ji
from the model-based parameter predictor block
30
via a number, N, of signal paths, wherein N may be any positive integer, and a set of outputs producing a number, J, of estimated values of the unknown variables &dgr;x
i
, i=1, . . . , J.
The unknown variables &dgr;x
i
, i=1, . . . , J represent functional distortions of the various components of physical system
12
. For example, where performance analysis system
18
represents an engine performance modeling application, the functional distortions &dgr;x
i
may correspond to compressor efficiency, turbine efficiency, flow capacity, pressure ratio, pressure drop, and the like, relating to one or more corresponding components of physical system
12
. The weighting factors W
ji
correspond to the equation constants in the system of equations forming the particular model contained within the model-based parameter predictor block
30
, wherein block
30
may include any number of models. In general, the equation solver
22
is thus operable to solve a system of equations of the form:
W
ji
&dgr;x
i
=&dgr;p
j, i=
1, . . . , J and j=1, . . . , L (1),
where,
W
ji
=[∂p
j
/∂x
i
], j=1, . . . , L and i=1, . . . , J and define the various weighting factors linking the model parameter values mp
i
, i=1, . . . , L to the functional distortions &dgr;x
i
, i=1, . . . , J.
The equation solver
22
is electrically connected to a set of inputs of a post processor unit
26
via signal paths
28
1
-
28
J
, and a set of inputs/outputs of post processor unit
26
are electrically connected to a corresponding set of inputs/outputs of the model-based parameter predictor
30
via a number, M, of signal paths
32
1
-
32
M
. In general, blocks
12
,
20
,
22
,
26
and
30
form a closed-loop equation solving system using an iterative approach to compute a solution to the system of equations defined thereby. In this regard, the post-processor unit
26
is operable to receive from the model-based parameter predictor block
30
the estimated &dgr;x
i
values from the previous iteration, to receive from the equation solver block
22
the estimated &dgr;x
i
values from the present iteration, and compute an error vector &egr;
k
=&dgr;x
k
−&dgr;x
k−1
, wherein k=iteration number. The post-processor block
26
is operable to halt the iterative equation solving process when &egr;
k
is within a desired range, and to accordingly notify the model-based parameter predictor
30
via one of the signal paths
32
1
-
32
M
.
The model-based parameter predictor
30
is electrically connected to a model storage and/or display unit
38
via a number, R, of signal paths
40
1
-
40
R
, wherein R may be any positive integer. Unit
38
may include a display and/or printer for viewing the results of the model, and may further include a data storage unit for recording the model results.
In the ideal case, the equation solver
22
can determine the correct or true solution associated with the unknown variables &dgr;x
i
by solving any “J” of the “L” equations (assuming L>J) represented by equation (1) above. An example of such an ideal case is illustrated in
FIG. 2
with L=5 and J=2. In this ideal case, the pre-processor unit
20
is operable to produce five parameter delta values (&dgr;p
j
, j=1, . . . , 5), based on five corresponding measured operating conditions of physical system
12
, and the model produced by the model-based parameter predictor
30
has two unknowns X and Y (e.g., &dgr;x
1
and &dgr;x
2
). X and Y represent ratios and are therefore dimensionless. The true solution of the resulting system of equations
15
1
-
15
5
is defined by the intersection of equations
15
1
-
15
5
, and is indicated on the plot of
FIG. 2
by the point TS. The equation solver
22
, in this example, can determine TS by solving a system of any two of the five equations
15
1
-
15
5
for the corresponding variables X and Y defining TS.
Due to limitations associated with known signal measurement instrumentation and with the physical application
10
in general, the ideal case illustrated in
FIG. 2
typically does not occur. For example, measurement inaccuracies as well as model non-linearities each contribute to offsets in the measured operating condition signals on signal paths
16
1
-
16
K
, resulting in deviations in the system of equations from the true solution TS. A real-world representation of the example illustrated in
FIG. 2
(e.g., L=5, J=2) is shown in
FIG. 3
as a set of five system equations
17
1
-
17
5
having two unknowns X and Y. Due to instrumentation measurement inaccuracies as well as model non-linearities, equations
17
1
-
17
5
do not intersect at the true solution TS, but are instead offset therefrom by varying amounts as illustrated in FIG.
3
.
In systems
10
of the type illustrated in
FIG. 1
, known Newton-type iterative techniques are typically used in the equation solver block
22
to solve the syste
Barlow John
Barnes & Thornburg
Cherry Stephen J.
Rolls-Royce Canada Limited
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