Transcript MONALISA Compact Straightness Monitor Simulation and

MONALISA
Compact Straightness Monitor
Simulation and Calibration
Week 7 Report
By Patrick Gloster
1
Where We Stood
Last Week
• Bowtie problem in 2D
• Launch heads no longer a point source
• Further additions – allowed them to protrude
slightly from the plate (so all of the launch heads
aren’t necessarily at x=0)
2
Switching which of the launch heads
measures which distance
1m
(0,b2)
L2
2cm
10 cm
(x2,y2)
L4
(a4,b4)
(a3,b3)
L3
2mm
(0,0)
L1
(x1,y1)
3
Now the outer launch heads measure the cross distances
1m
(0,b2)
L2
2cm
10 cm
(x2,y2)
L4
(a4,b4)
L3
(a3,b3)
2mm
L1
(x1,y1)
4
Sparsity pattern
• With lsqnonlin you can hand it the sparsity
structure of the jacobian to speed it up
• This is particularly useful for programs which
perform many repetitions (some of mine do this!)
• My program now examines the jacobian from the
first use of lsqnonlin, derives the sparsity pattern
and hands it to the function for all subsequent
lsqnonlin evaluations
5
Problems
• I tried changing the error on our initial
estimates – this was a test which should
have produced no change in the results
• Instead I found that the results seem to jump
around depending on the accuracy of the
initial values
• This should not happen!
6
Changing error on initial estimates
7
More problems
• Although the standard deviations of the results of
now very good, looking at the mean reveals some
another concern
• The mean difference is greater than the standard
deviation – this mean is the average difference
between the true and calculated values, and should
be extremely close to zero
• Finding a mean greater than the standard deviation
seems to indicate the results are clustered about
the wrong points
8
Possible cause
• It is likely that these high means are due to a low
level of accuracy in determining the positions of
the launch heads on the stationary plate
• This was tested by running a program without any
uncertainty on their positions; this resulted in
means that were approximately zero
• We therefore need to find the locations of the
launch heads more accurately
9
Finding optimum parameters
• The rest of my week has been spent varying
the amount that we move plate 2 to
determine which range of movement will
give us the most accurate results
• Initially I just looked at each case with 5
different known seeds, and compared the
effects of the changes on each different
seeded run
10
More samples
• However, looking at the same 5 seeds each
time is not particularly useful
• New technique – run the minimization 50
times for each setting (this is where the
sparsity pattern is useful) and examine
results
11
Results
A lot of
graphs
like this
12
General trends
• The larger the range of angle, plate movement and
plate size, the better the results
• The jump to a much worse accuracy as we
continue to increase these parameters comes from
the minimization being halted by TolX, rather than
TolFun
• It is difficult to say a specific optimum value for
each parameter, since different values give
optimum accuracy for different variables
13