Quantized Pressure Data Modeling
Simulation and Modeling
Professor: Ernesto Guitierrez-Miravete
Chuck Clothier
197-66-2240
December 14th, 1999
Introduction:
The purpose of this project is to study the effects due to variance on a real world
controller interface. In its simplest form serves as the link between the actual transducer
which is measuring a particular environmental parameter of interest and the solid state
controller which is using the measured data for control system functions. For the sake of
discussion, a pressure transducer is being studied, therefore, a certain environmental
pressure is being measured, and represented by the transducer as a voltage. This voltage
is then wired to the controller interface. The simulation of interest begins at the pressure
signal’s voltage input into the controller. The interface itself is broken down into major
components which perform specific tasks: an input multi-plexer (low level mux) which
reads and queues the voltage until the controller is ready to convert the signal, a amplifier
which magnifies the voltage in order to retain the highest resolution of the signal as it is
being converted, a high level mux which queues all of the outputs of all of the low level
mux, and finally the analog to digital converter (A/D). Every element of this interface
will delay the voltage being processed for a variable amount of time, and subject the
voltage to a variable amount of error. Since most commercial controllers are built from
off-the-shelf interface components it is possible that the combination of components may
introduce too much error into voltage being measured. Modeling the interface may also
provide foresight in methods to counter-act the interface error in software.
Report Summary:
Modeling this system was more difficult than expected due to each component having its
own element of variance. It was found that the timing of the simulation was more time
consuming than finding the individual error distributions. However, once the simulation
was running reasonably, it was possible to iterate the various interface gain and offset
distributions to find a solution. It was found that pressure voltage supported by the
interface modeled in this study can only support a pressure voltage from 0 to1.5 volts
(1500 millivolts).
Design Requirements:
The controller interface must be sized so that the input transducer voltage does not
exceed 10 volts in any of the multi-plexers:
Low Mux Max Voltage: 0 to 10 Volts
High Mux Max Voltage: 0 to 10 Volts
Therefore the input voltage can not be too large (> 10 Volts ) after adding all of the premux error component voltages. These design requirements were used to validate the
simulation model. Because there were many points of variance in the simulation, it was
vital to gain as much data from the real world system as possible. I referred to two
technical company's private (Hamilton Standard) manuals in order to find the nominal
values of any source of error.
Problem Formulation:
Having found the hardware constraints after the initial interface study, it was possible to
form the problem statement as follows: Determine the standard pressure transducer
sizing that can be accommodated by the pre-selected electronic controller interface. All
data shall be transmitted with full resolution. No interface limits shall be exceeded.
Objectives:
Model the general interface and all elements of error variance. Verify proper operation
of simulation, and validate using the hardware requirements. Proper error input modeling
requires holding all variances to a constant nominal value while varying the desired error
distribution. It will be necessary to achieve to find adequate error distribution (interface
gains and offsets), via iteration.
Error Variance studies:
Because there were many points of variance in the simulation, it was vital to gain as
much data from the real world system as possible. I referred to two technical company's
private (Hamilton Standard) manuals in order to find the nominal values of any source of
all interface errors. In order to meet stringent Federal Aviation Administration (FAA)
guidelines for Electrical Aircraft controllers, Hamilton Standard ensures that all interface
components manufactured are within 6 sigma of the nominal design tolerances. Because
the exact design nominal values are company private, I used values that would
approximate a real world interface.
Pre-mux input model:
The Pre-mux region consists of the pressure cable wiring from the transducer to the
electronic interface pins, the pins themselves, and the copper tracing on the motherboard
from the pins to the input of the low level mux. All of the above pieces of hardware are
subject to small degrees variable error. The cable wiring and the controller interface are
subject to a small degree of error due to thermal fluxes. The copper trace is not as
susceptible to changes in temperature due the environmental controls inside the controller
box (i.e. heaters and fans are used to control the temperature and moisture). To model
these errors, first it assumed that all of the various errors in this portion of the interface
could be linearly stacked. Next, referring the Inset #1 of Figure #1 of the Appendix, it
can be seen that the linear relationship between pressure and voltage will shift along the
voltage axis by an offset value, and will change slope according to a gain value. In
essence adding a linear error to a linear parameter can be represented by the shift in the
line defined by P1 - P2 to P3 – P4.
The nominal values are approximated from the
Interface design documentation, and the error offset and error gain are modeled as
“Normal” distributions whose means are the nominal value and the standard deviation is
small relative to the mean. This error is mostly temperature dependent, and any errors
would be small and slow acting. Actual values of the standard deviations were found
after the entire interface was defined. Holding all post mux variance fixed, the standard
deviations were iterated until the final pressure voltage was less than the target of 8.5
volts at all times. Final values of the mean and standard deviations for the input offset
and gain are seen in the configuration file, Table 4 in the appendix.
Low Mux input voltage =[ (Input Pressure Voltage)*(pre-mux error gain) ]+ (pre-mux
error offset)
Low Mux Interface Model:
The low level mux was treated in a similar manner as the pre-mux interface. The low
mux interface consists of the AC/DC converter and a voltage amplifier, which both are
highly accurate and slow varying. It was assumed The mux itself was modeled as a time
delay only, because the linear error components were modeled individually as low mux
offset and low mux gain. The main area of concern here was that the low mux gain is
very large compared to the other gains in the system. This gain is an actual interface
AC/DC amplifier that has a high degree of accuracy. Therefore, the low mux gain was
modeled as a normal distribution with a dominant mean (dominant compared to the
relative error of the interface), and a rather small standard deviation of 0.1 volt/volt. At
the beginning of the project distribution was assumed to be exponential with mean equal
to the nominal amplifier gain. The voltage amplification was sporadic as a result, and the
distribution was replaced by a normal distribution.
High Mux input voltage =[ (Low Mux Pressure Voltage)*(Low-mux error gain) ]+ (Low
mux error offset)
High mux Interface model:
The High mux is followed by the Analog/Digital (A/D) converter, which will add a
varying error each and every pass through the converter. All interfaces up to this point
have relatively constant error applied to each voltage passing through the interface. The
High Mux error gain was initially modeled as an exponential distribution. During the
Validation phase it was found that the gain error varied by too much each pass, and as a
result it was replaced with a normal distribution with a relatively large standard deviation.
Therefore during each pass through this High mux A/D converter the error would be
different, but within the guarantee limits of the hardware manufacturer. The offset error
was treated in a similar fashion.
Pressure Output voltage =[ (High Mux Pressure Voltage)*(High mux error gain) ]+
(High mux error offset)
Validation Iteration to match design requirements:
As mentioned in each of the above interface models, it was critical to study the effects of
all of the variances. To facilitate the iteration process, two models were constructed, one
was the production version with all variances in tact, the other a similar model but with
all standard deviations kept at very tight tolerances (Single variance model). As the total
interface was studied, one error element at a time was allowed to have an error variance.
Then by running 10-hour trial runs, a realistic value of the error standard deviation was
determined. Eventually it was found that with the A/D errors in the High Mux interface
modeled as exponential distributions, no solution could be found. Starting over with
Normal distributions proved to be an acceptable substitute. After speaking with some of
the hardware interface designers at Hamilton Standard, it was found that the A/D error is
indeed best suited as a normal distribution. After correcting the A/D errors, the AC/DC
voltage amplifier in the Low level mux interface was changed to a normal distribution for
similar reasons. Finally, after being satisfied with all of the error model distributions, it
was time to vary the actual input pressure voltage in search of the maximum allowable
pressure input voltage into the controller interface. It was found that the maximum
pressure voltage allowed into the interface was 1.5 Volts DC.
Lessons Learned from Project:
The major mistake that was made during the course of this project was in picking an
acceptable arrival rate for the pressure voltage. Originally the arrival rate was once every
2 seconds (the real controller uses a millisecond time scale, but Promodel was run using
seconds instead) But it would take six times as long for the entity to travel through the
entire interface. Because variables were used to represent the voltages in the model, if
two or more entities were travelling through the interface, then the output pressure (which
was a function of the variable “pressure_voltage” would climb as high as 54 volts! This
was because at any particular time slice in the model there might be one or more entities
that are inside separate error gain locations. Each time this happened the
pressure_voltage variable would be subject to multiple gains at the same time ( i.e.
pressure_voltage = ( (pressure_voltage*low mux Gain)*(high mux Gain))*(input mux
gain) ). In the real interface only one voltage is allowed to travel through at a time. The
controller software itself dictates the passage of the voltage through the interface. After
decreasing the voltage arrival rate to one every 10 seconds (milliseconds on the real
interface), it was possible to validate the model using iteration techniques. Trying to
troubleshoot this problem took several days with many iterations of the procedure logic
within Promodel.
Figure 1 Hardware Interface
Layout:
Pressure
(Voltage)
Inset #1:
Pre-mux
Region
P4
Low Mux
Interface
Low Mux
Gain
P3
y
x
Low Mux
Gain
Low Mux
Offset
Pressure Input
(Volts)
P2
P1
Input 2
Pressure
(PSIA)
Input 3
Input 4
Input 5
Low Level
Input Mux
High Mux
Interface
Input 1
Input 2
Input 3
Input 4
Input 5
Low Level
Input Mux
#2
High Level
Interface Mux
Input 1
Inset #2:
Input 2
P6
Pressure
(Voltage)
Input 3
High Mux
Gain
Input 4
P5
y
x
Input 5
High Mux
Offset
Low Level
Input Mux
#3
After Low P4
Level Mux
P3
Pressure
(PSIA)
Figure 2: Steps in a Simulation Study
Problem formulation
Setting of objectives
and overall project
plan
Model
Conceptualization
Data
Collection
Model
translation
No
Verified?
Yes
No
No
Validated?
Yes
Experimental
design
Production runs
And Analysis
No
Yes
More
runs?
Yes
Documentaion
And Reporting
Implementation
Table 1:
-------------------------------------------------------------------------------------------------------------------
Model 10-hour Run Results
-------------------------------------------------------------------------------General Report
Output from C:\ProMod4\models\Final\Final\Interface2.MOD [Digital Control Interface
Simulation]
Date: Dec/17/1999
Time: 04:39:52 PM
-------------------------------------------------------------------------------Scenario
: Normal Run
Replication
: Average
Period
: Final Report (0 sec to 10 hr Elapsed: 10 hr)
Simulation Time : 10 hr
-------------------------------------------------------------------------------LOCATIONS
Location
Scheduled
Current
Name
Hours
Contents % Util
---------------- --------- -----Hi Level Mux
10
0
14.86 (Average)
Hi Level Mux
0
0
0.00 (Std. Dev.)
Lo Level Mux
10
0
14.95 (Average)
Lo Level Mux
0
0
0.14 (Std. Dev.)
Input Gain error
10
0
10.08 (Average)
Input Gain error
0
0
0.07 (Std. Dev.)
Input Oset error
10
0
9.85 (Average)
Input Oset error
0
0
0.00 (Std. Dev.)
Lomux gain
10
0
1.00 (Average)
Lomux gain
0
0
0.00 (Std. Dev.)
Lomux offset
10
0
1.00 (Average)
Lomux offset
0
0
0.00 (Std. Dev.)
Himux gain
10
0
1.00 (Average)
Himux gain
0
0
0.01 (Std. Dev.)
Himux offset
10
0
1.00 (Average)
Himux offset
0
0
0.00 (Std. Dev.)
RAM
10
0
0.99 (Average)
RAM
0
0
0.00 (Std. Dev.)
Input que
10
1
0.00 (Average)
Input que
0
0
0.00 (Std. Dev.)
Total
Average
Seconds
Average
Maximum
Capacity
Entries
Per Entry
Contents
Contents
--------
-------
---------
-----------
--------
1
3600
1.485601
0.14856
1
0
0
0.000045
4.51763e-06
0
1
3600
1.495067
0.149507
1
0
0
0.013934
0.00139339
0
1
3600
1.007903
0.10079
1
0
0
0.006627
0.000662716
0
1
3600
0.984744
0.0984744
1
0
0
0.000118
1.17851e-05
0
1
3600
0.099982
0.00999819
1
0
0
0.000183
1.82669e-05
0
1
3600
0.099922
0.00999222
1
0
0
0.000346
3.45697e-05
0
1
3600
0.100340
0.010034
1
0
0
0.000568
5.6765e-05
0
1
3600
0.099843
0.00998431
1
0
0
0.000257
2.57308e-05
0
1
3600
0.099407
0.00994069
1
0
0
0.000438
4.38013e-05
0
999999
3601
0.010017
0.00100194
1
0
0
0.000236
2.35702e-05
0
LOCATION STATES BY PERCENTAGE (Multiple Capacity)
-------
Location
Name
--------Input que
Input que
Scheduled
Hours
--------10
0
%
Empty
----99.90
0.00
%
Partially
Occupied
--------0.10
0.00
%
Full
---0.00
0.00
|
|
|
|
|
|
%
Down
---0.00
0.00
(Average)
(Std. Dev.)
LOCATION STATES BY PERCENTAGE (Single Capacity/Tanks)
Location
Name
---------------Hi Level Mux
Hi Level Mux
Lo Level Mux
Lo Level Mux
Input Gain error
Input Gain error
Input Oset error
Input Oset error
Lomux gain
Lomux gain
Lomux offset
Lomux offset
Himux gain
Himux gain
Himux offset
Himux offset
RAM
RAM
Scheduled
Hours
--------10
0
10
0
10
0
10
0
10
0
10
0
10
0
10
0
10
0
%
Operation
--------14.86
0.00
14.95
0.14
10.08
0.07
9.85
0.00
1.00
0.00
1.00
0.00
1.00
0.01
1.00
0.00
1.00
0.01
%
Setup
----0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
NODE ENTRIES FOR Net1
Node
Name
---N2
N2
N3
N3
N4
N4
N5
N5
N6
N6
N7
N7
N8
N8
N9
N9
N10
N10
N1
N1
Total
Entries
------0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Blocked
Entries
------0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
FAILED ARRIVALS
Entity
Name
-------------Pressure Input
Pressure Input
ENTITY ACTIVITY
Location
Name
--------Input que
Input que
Total
Failed
-----0
0
(Average)
(Std. Dev.)
%
Idle
----85.14
0.00
85.05
0.14
89.92
0.07
90.15
0.00
99.00
0.00
99.00
0.00
99.00
0.01
99.00
0.00
99.00
0.01
%
Waiting
------0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
%
Blocked
------0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
%
Down
---0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
(Average)
(Std. Dev.)
Entity
Name
-------------Pressure Input
(Average)
Pressure Input
(Std. Dev.)
Total
Exits
----3600
Current
Quantity
In System
--------1
Average
Seconds
In
System
-------5.482829
Average
Seconds
In Move
Logic
-------0.000000
Average
Seconds
Wait For
Res, etc.
--------0.000000
Average
Seconds
In
Operation
--------5.482829
Average
Seconds
Blocked
-------0.000000
0
0
0.006943
0.000000
0.000000
0.006943
0.000000
ENTITY STATES BY PERCENTAGE
Entity
Name
-------------Pressure Input
Pressure Input
%
In Move
Logic
------0.00
0.00
%
Wait For
Res, etc.
--------0.00
0.00
%
In Operation
-----------100.00
0.00
%
Blocked
------0.00
0.00
(Average)
(Std. Dev.)
VARIABLES
Variable
Name
---------------himuxoffsetvolts
(Average)
himuxoffsetvolts
(Std. Dev.)
himuxgainvolts
(Average)
himuxgainvolts
(Std. Dev.)
himuxvolts
(Average)
himuxvolts
(Std. Dev.)
lomuxoffsetvolts
(Average)
lomuxoffsetvolts
(Std. Dev.)
lomuxgainvolts
(Average)
lomuxgainvolts
(Std. Dev.)
lomuxvolts
(Average)
lomuxvolts
(Std. Dev.)
in offsetvolts
(Average)
in offsetvolts
(Std. Dev.)
in gainvolts
(Average)
in gainvolts
(Std. Dev.)
Pressure voltage
(Average)
Pressure voltage
(Std. Dev.)
Input pressure
(Average)
Input pressure
(Std. Dev.)
Ouput pressure
(Average)
Total
Changes
------3600
Average
Seconds
Per Change
---------9.998454
Minimum
Value
---------0
Maximum
Value
----------0.0465208
Current
Value
----------0.0297316
Average
Value
----------0.0279197
0
0.000611
0
0.000836189
0.00196059
2.71285e-05
3600
9.998419
0
1.3943
1.03551
1.0206
0
0.000593
0
0.0204291
0.0609246
0.000181345
3600
9.998394
-0.666288
10.8117
5.33593
4.79395
0
0.000581
0.443979
0.536734
5.9527
0.000707733
3600
9.998246
0
0.0461816
0.0269444
0.0280268
0
0.000426
0
0.00155605
0.0028268
7.29339e-05
3600
9.998203
0
2.5233
2.52051
2.51972
0
0.000428
0
0.000196439
0.000290147
7.18552e-05
3600
9.998190
-0.255645
4.17164
2.05843
1.85032
0
0.000438
0.168487
0.209624
2.29431
0.000697936
3600
9.997836
-0.0831365
0.333311
0.169246
0.120406
0
0.000157
0.00742956
0.00974088
0.116824
0.00250873
3600
9.997378
0
1.13996
1.09124
1.09997
0
0.000192
0
0.00964944
0.0152744
8.82023e-05
28800
1.249811
-0.765322
12.1236
1
1.91608
0
0.000077
0.533521
0.507584
0
0.000776544
3601
9.997223
-0.200874
3.34011
2.01077
1.50088
0
0.000000
0.121698
0.061381
0.0198809
0.00366749
3600
9.998489
-0.765322
5.87004
5.03054
12.1236**
Ouput pressure
(Std. Dev.)in mux
0.446491 (Average)
in mux
(Std. Dev.)
** This
0
0.000613
14400
0.533521
2.499622
0.507584
0
6.6709
1
0.00414398
0
0
0.000153
0
0
0
0.00138063
max output pressure value was encountered during simulation transient period.
********************************************************************************
*
*
*
Formatted Listing of Model:
*
*
C:\ProMod4\models\Final\Final\Interface2.MOD
*
*
*
********************************************************************************
Time Units:
Distance Units:
Seconds
Feet
********************************************************************************
*
Locations
*
********************************************************************************
Name
---------------Hi_Level_Mux
Lo_Level_Mux
Input_Gain_error
Input_Oset_error
Lomux_gain
Lomux_offset
Himux_gain
Himux_offset
RAM
Input_que
Cap
-------1
1
1
1
1
1
1
1
1
INFINITE
Units
----1
1
1
1
1
1
1
1
1
1
Stats
----------Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Rules
Cost
-------------- -----------Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, FIFO,
********************************************************************************
*
Entities
*
********************************************************************************
Name
Speed (fpm) Stats
Cost
-------------- ------------ ----------- -----------Pressure_Input 0.01
Time Series
********************************************************************************
*
Path Networks
*
********************************************************************************
Name
Type
T/S
From
-------- ----------- ---------------- -------Net1
Non-Passing Speed & Distance N1
N2
N3
N4
N5
N6
N7
N8
N9
To
-------N2
N3
N4
N5
N6
N7
N8
N9
N10
BI
---Bi
Bi
Bi
Bi
Bi
Bi
Bi
Bi
Bi
Dist/Time
---------15.63
13.37
14.86
11.35
9.75
12.57
11.17
9.73
7.28
Speed Factor
-----------1
1
1
1
1
1
1
1
1
********************************************************************************
*
Interfaces
*
********************************************************************************
Net
Node
---------- ---------Net1
N2
N3
N4
N5
N6
N7
N8
N9
N1
Location
---------------Input_Oset_error
Lo_Level_Mux
Lomux_gain
Lomux_offset
Hi_Level_Mux
Himux_gain
Himux_offset
RAM
Input_Gain_error
********************************************************************************
*
Processing
*
********************************************************************************
Process
Routing
Entity
Location
Operation
Rule
Move Logic
-------------- ---------------- ------------------ ---------------- -----------Pressure_Input Input_que
wait u(0.01,0.01)
Blk
in_mux=0
Input_Gain_error IF in_mux = 0, 1
Pressure_Input Input_Gain_error Wait u(1,1)
1
Output
Destination
---- -------------- ---------------
Pressure_Input
pressure_voltage = input_pressure
in_gainvolts = n(1.1,0.01)
Pressure_voltage=Pressure_voltage*in_gainvolts
in_mux=1
1
Pressure_Input
Input_Oset_error FIRST 1
Pressure_Input Input_Oset_error Wait U(1,1)
in_offsetvolts = n(0.12,0.06)
Pressure_voltage = Pressure_voltage +
pressure_voltage*in_offsetvolts
in_mux=1
FIRST 1
Pressure_Input Lo_Level_Mux
1
Pressure_Input Lo_Level_Mux
Wait U(1.5,1.5)
lomuxvolts = pressure_voltage
1
FIRST 1
Pressure_Input Lomux_gain
Pressure_Input Lomux_gain
Wait U(.1,.1)
lomuxgainvolts = n(2.52,0.001)
Pressure_voltage = Pressure_voltage*lomuxgainvolts
1
FIRST 1
Pressure_Input Lomux_offset
Pressure_Input Lomux_offset
Wait U(0.1,0.1)
lomuxoffsetvolts = n(0.028,0.005)
pressure_voltage = pressure_voltage +
pressure_voltage*lomuxoffsetvolts
1
FIRST 1
Pressure_Input Hi_Level_Mux
Pressure_Input Hi_Level_Mux
Wait U(1.5,1.5)
himuxvolts = Pressure_voltage
1
Pressure_Input Himux_gain
FIRST 1
Pressure_Input Himux_gain
Wait U(0.1, 0.1)
himuxgainvolts = n(1.02,0.1)
pressure_voltage = pressure_voltage*himuxgainvolts
1
FIRST 1
Pressure_Input Himux_offset
Himux_offset
Wait U(0.1,0.1)
himuxoffsetvolts = n(0.028,0.005)
pressure_voltage = pressure_voltage +
pressure_voltage*himuxoffsetvolts
1
FIRST 1
Pressure_Input RAM
Pressure_Input RAM
Wait U(0.1,0.1)
Ouput_pressure = pressure_voltage
Pressure_voltage = 1.0
in_mux = 0
1
Pressure_Input EXIT
FIRST 1
********************************************************************************
*
Arrivals
*
********************************************************************************
Entity
Location Qty each
First Time Occurrences Frequency Logic
-------------- --------- ---------- ---------- ----------- ---------- -----------Pressure_Input Input_que 1
0
INF
10
Input_pressure =
n(1.5,0.5)
********************************************************************************
*
Attributes
*
********************************************************************************
ID
Type
Classification
---------- ------------ -------------#
#This is the Voltage Level of the Pressure Input
Volts
Real
Entity
********************************************************************************
*
Variables (global)
*
********************************************************************************
ID
---------------himuxoffsetvolts
himuxgainvolts
himuxvolts
lomuxoffsetvolts
lomuxgainvolts
lomuxvolts
in_offsetvolts
in_gainvolts
Pressure_voltage
Input_pressure
Ouput_pressure
in_mux
Type
-----------Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
Real
Integer
Initial value
------------0
0
0
0
0
0
0
0
0
0
0
0
Stats
----------Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series
Time Series