Transcript Institute of Construction Informatics, Prof. Dr.-Ing

Technische
Universität
Dresden
Faculty of Civil Engineering
Institute of Construction Informatics , Prof. Dr.-Ing. Scherer
Management Information Systems
Part 5: Monitoring and System Identification
Prof. Dr.-Ing. Raimar J. Scherer
Institute of Construction Informatics
Dresden, 17.12.2012
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Goal
With monitoring we observe the actual behaviour of the system.
The goal is to find out if the function of the system is
•as planned
•sufficient
•optimal
We compare the actual behaviour with planned behaviour,
so we receive the deviations.
What we want to know is why the system behaves in another way
as planned, calculated and finally designed.
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden

Monitorable Quantities
In a pipe system, we can monitor
(1) Water input
(2) Water consumption
(3) Water throughput
(4) Pressure

at input node
at output node
at pipe start/end
at each node
All these quantities are time-dependent
Example of water flow record (it is a simulated one, not a real record).
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observed water flow [m³]
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daily hours
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Monitoring requirements and methods
Need:
stationary system for a certain time window
Goal:
approximate time-dependent, recorded quantities
by step-wise constant functions
Methods:
- Signal Analysis
- Statistics, stochastic Methods
- Data Mining: classification, subsumption, separation
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Monitoring data processing
Solution, pragmatic and straightforward:
•
•
•
•
Zero line correction
Trend estimate (by moving average or other low pass filtering)
Moving average Standard Deviation (STD)
Selection of time windows with nearly constant trend
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AND
observed water flow [m³]
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small STD !
true trend
Moving avg. filtered (0.5h)
+-STD(data-trend)
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Recommended
window length of
moving average
= 3-5 cycles
of the fluctuations
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daily hours
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Monitoring data processing
Select time windows with nearly
constant trend AND small STD!
4 selected windows, however,
only window 2 is recommended
to be used, due to the strong
STD in the other windows.
Problem:
The selected time windows of all
measurement points throuout the
system have to coincide
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observed data
Moving avg. filtered (0.5h)
-STD(data-trend)
+STD(data-trend)
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daily hours
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Consequences due to Approximations (1)
Values
correct
A
Values
B
C
D
Measuring Point
correct
new
Approximation D=0
A
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B
C
D
Measuring Point
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Consequences due to Approximations (2)
Values
A
B
C
D
B
C
D
Measuring Point
Values
A
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Measuring Point
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Consequences due to Approximations (3)
St’Venant principle:
In elastic systems approximations are following St’Venant principle:
Changing in 1 point, propagates in the neighbourhood points in a
decreasing exponential function in the mean.
Data Mining:
The mean values of different sets of measurements leading to the best
trained neural network
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Deviations
We can compare recorded quantities (actual) with planned quantities (to be)
and calculate their deviation
DQ = Qto be – Qactual
Dp = pto be – pactual
With this deviation quantities we can construct an descriptor and classify the system in
classes, using data mining methods, i.e. to find out classes like
-
good performance
-
sufficient performance
-
under performance
-
bad performance
or classes like
-
no improvement necessary
-
improvement recommended
-
improvement urgent
The same can be done considering only subsystems. This is a first step.
As the second step, we want to know what has to be improved. This needs methods
called system identification.
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Identification
Problems:

Each system parameter can take values which are different from its
assumed value, hence each parameter is an unknown quantity.
Usually we are not able to measure so much quantities, hence we are
faced with an over determined math. system

Often we can not measure the system parameter directly. We can only
measure a deduced quantity.
System parameters are:
roughness k:
water input Qin:
water consumption:
water loss:
no
yes
yes (at all points?)
no

the system can be non-linear

the system can be non-stationary

the system can be stochastic
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measurable
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Quantification
One possible load case:
given
Pressure at
input
Pressure at
output
water put
through
water input
water
consumption
water loss
energy loss
(roughness)
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calculated monitored identify
bar
bar
bar
m³/sec
m³/sec
m³/sec
m³/sec
m³/sec
m³/sec
bar
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Identification
Solution: (pragmatic)
(1) assume a deterministic system
(2) consider only time windows with approximate stationary system
behaviour, i.e. constant trend, small STD
(3) consider only windows with approximately linear system behaviour

Now the system can be mathematically formulated as a linear matrix
equation, which can be solved (inverted) if the matrix is regular.
But we are still faced with the problem, that the math. system is overdetermined, because we have less measured quantities than unknown
system parameters. This means, there exist many system states which
are explaining (fitting to) the measured quantities
(4) We have to find strategies to reduce the number of unknowns, i.e. to find
those system parameters
- which have most probably not or little changed
- which have most probably considerably changed
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Dependencies
We can establish a system influence function
- for each system parameter
- for each measurable quantity
A system influence function
(1) is a deviation of a system state according to its planned behaviour, if
only one parameter change.
(2) shows dependencies (relationships, "association rules") between one
system parameter and all other parameters.
One can identify
(3) the strongest relationship(s) in an ordered form.
(4) certain patterns of deviation between the real system influence
function and the system influence function of the planned ('to be')
system. (Information Mining methods of pattern recognition, pattern
matching)
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for roughness
All parameters are
unchanged, except of
Qin
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1
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2
2
Qout2
3
3
Qout3
(1)
Change of
roughness for
pipe2
(2)
Change of
roughness of
several pipes
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Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for roughness
All parameters are
unchanged, except of
(1)
Change of
roughness for
pipe2
(2)
Change of
roughness of
several pipes
p
(1)
(2)
(1) ≡ (2)
Q
Qin
1
1
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2
2
Qout2
3
3
Qout3
4
4
Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for roughness
(2)
Dp
DQ
(1)
All parameters are
unchanged, except of
(1) ≡ (2) ; DQ = 0
(1)
Change of
roughness for
pipe2
(2)
Change of
roughness of
several pipes
p
(1)
(2)
(1) ≡ (2)
Q
Qin
1
1
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2
2
Qout2
3
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Qout3
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Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for water loss
All parameters are
unchanged, except of
(1)
water loss in
pipe 2 and/or
node 3
Remark:
A continuous water
loss can not be
monitored but only
the loss accumulated
up to the next
measurement point
water loss
Qin
1
1
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2
2
Qout2
3
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Qout3
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Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for water loss
All parameters are
unchanged, except of
(1)
p
water loss in
pipe 2 and/or
node 3
Remark:
A continuous water
loss can not be
monitored but only
the loss accumulated
up to the next
measurement point
(1)
(1)
Q
planned
water loss
Qin
1
1
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2
2
Qout2
3
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Qout3
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Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System influence function for water loss
Dp
All parameters are
unchanged, except of
(1)
DQ
(1)
(1)
p
water loss in
pipe 2 and/or
node 3
Remark:
A continuous water
loss can not be
monitored but only
the loss accumulated
up to the next
measurement point
(1)
(1)
Q
planned
water loss
Qin
1
1
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2
2
Qout2
3
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Qout3
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Qout4
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Qout5
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Identificators
We need identificators.
Identificators are
(1)
recorded values
(2)
derivatives, e.g. changes of curves
(3)
trend in curves
(4)
any combination of (1) – (3)
In the curves of the system influence function we have already learned
some identificators, namely:
(1)
DQ is total water loss
(2)
change of DQ is local water loss
location is anywhere between the two measurement points
(3)
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dDpk d (Dp  DpQ )

dl
dl
is the pressure loss due to increased roughness; location see (2)
MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Identification Strategies
(1) Identify water loss in DQ function
(2) Then identify change of roughness in Dp function
Remark: Because Q and p are interdependent, but not Q
and k. Therfore the expected DpQ due to water loss has to
be extracted form from Dp to receive Dproughness
(3) investigate as much as possible different system states, to
receive mean values and to reduce mal identifications
(4a) either an optimization problem is mathematically formulated.
- A practical overkill OR
(4b) data mining methods are applied in order to find the most
probable changed system quantities
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Identification Strategies
(5) Reduce the number of system parameters as much as possible by
neglecting all those, which change not very much, i.e. assume for
them D=0
(6) repeat this for different system states for identifying the best fitting
(right) set of D=0. Different system states have show the same
(7) improve this procedure by using the subsystem method, i.e.:
divide the system in subsystems by cutting the branches from the
main system. Repeat the above identification procedure for each
subsystem as well as the remaining main system
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
System Identification Strategies
(8) repeat the sub system method several times by using
different partitions (see methods in data mining for choosing
training and test sets)
(9) Densify the sensor system by adding new sensors and
repeat the recording
(10) Move sensors from less important parts of system, where no
or little changes are identified to parts where changes are
stronger in order to densify the sensor system there. Use the
preliminary identified parameters for the less important part
of the system or cut those parts if they can be approximated
as subsystems
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Monitored System
We can not (up-to-day) monitor all water output nodes.
Therefore we reduce by cutting the total system to the monitored system.
At each cutting point we need Q and P - recording or an assumption of
Q and P consumption.
This monitored system for the as planned behaviour is named basic
sensor system.
For each basic sensor system several measurements could be carried
out (not modelled here) resulting in several system states.
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Sensor System
Each sensor system have to be partionable into two subsystems:
a basic sensor system and an investigating Sensor system.
1)
Basic sensor system
PQ
PQ
PQ
PQ
PQ
PQ
Sensor system
The total monitored system / subsystem have to be chosen. The
related input and output nodes (incl the cutted nodes) have to be
determined, where sensors have to be allocated in order to obtain
a fully deteminable (computable) system.
This is a system investigating case equivalent to a load case.
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Sensor System
2. Investigating sensor system
PQ
PQ
Q
Q
P
PQ
PQ
PQ
Q
P
PQ
In addition to the basic sensor system we can allocate additional sensors,
which allow us to investigate the system.
For each monitored value, we can evaluate one system parameter.
If we would do so, we would assume, that the total actual (delta)
behaviour of the system we observe with this one sensor can be explained
with one altered system parameter.
This would be mathematically correct but in reality wrong, because one
model assumption of a 1:1 relationship is wrong (
System-Strategy).
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Evaluation process
- Store all data from each monitoring campaigns.
- Retrieve selected data from monitoring campaigns
and instantiate a basic sensor system and a complementary
investigating sensor system.
- Release a set of system parameters to be the unknown
parameters of the system and adjust them to the monitored
system state.
- Repeat this for a different set of system parameters.
- Repeat this for different parts of basic / investigating
sensor systems.
- Repeat this for several monitoring campaigns.
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Monitoring
Start
System
designing
Sensor system
planning
System recoding
Consequences
System
evaluating
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Dimension for Evaluation
Sensor System
constrains
Monitoring n Cases
System design
values
Req. values
1 . MC : P1Q
System Investigation
2 . MC
1.1 S I : Selected (sub) system
Retrieve design values
Retrieve monit. Values
3 . MC
1.2
4.
1.3
deduced
Updated System
Data Dimension for Evaluation
Evaluation
Keval
1.11 EV :{ΔP,ΔQ}
{Qloss , Kact}
{Qloss, Kact}
1.12 EV
1.13 EV
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Sensor System Planning
Sensors are always limited, because of
- procurement
- installation
- maintenance
- signal processing
- costs
Planning of a Sensor system should include always update
campaigns of the sensor system, i.e. densifying of the system at
hot areas. This includes movement of sensors
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Resume
System identification needs information management of
-
many sensor system states
-
many influence function studies ( = system simulations)
These system states and influence functions have to be
classified, clustered and analysed in different combinations
(clusters) in order to find out the most liable parameter set
and the related values best explaining the monitored data.
Therefore system states and influence function data are to be
stored and managed by a data base system.
Influence functions can be seen as a particular system state
and hence have the same data structure
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Management for Design
1) System design values (= plain system data model)
Topology, length, pipe parameters, etc.
2) Required values
max pressure in pipe
min pressure at output
3) System load parameters
Water consumption, pressure at the input
4) System behaviour value ( = reaction values)
pressure at output
pressure at node, in pipe.
water input
water put through
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Management for Monitoring
5) Monitoring of system states
 water input
 pressure at node
 water consumption
 water put through
 pressure at output
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Management for System State
6) Investigated System Case
- Retrieve of selected system the design parameters (1)
- Retrieve of selected system the monitored values
which are to be used as load parameters (3)
- Calculate expected (as planned) system behaviour values (4)
- Store system behaviour values (4)
- Retrieve of complementary monitored (actual) values
- Calculate ΔQ, Δp values.
- Report in graphical form Q , p , ΔQ , Δp diagrams.
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Management for Evaluation
7) System identification (Evaluation Case)
•Release a set of system parameters (K , Qloss)
(determined from the strategy).
•Calculate the released system parameters.
•Store the calculated system parameters.
Repeat step 6
Repeat step 5-6
Repeat step 4-6
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MIS
Institute of Construction Informatics, Prof. Dr.-Ing. Scherer
Technische
Universität
Dresden
Data Management for Decision
8) Decision
- Retrieve recalculated system parameters
- Use statistics and data mining method + eye-methods
(including graphical representation).
to determine the most probable actual new system
parameters.
- Store the new system parameters as the actual version
of the supply system.
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Institute of Construction Informatics, Prof. Dr.-Ing. Scherer