1 MONALISA Compact Straightness Monitor Simulation and Calibration Week 7 Report By Patrick Gloster

2 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)

3 Switching which of the launch heads measures which distance (x2,y2) (0,b 2 ) L4 (x1,y1)(0,0)L1 L2 L3 10 cm 1 m (a 3,b 3 ) (a 4,b4) 2cm 2mm

4 Now the outer launch heads measure the cross distances L2 (x2,y2) (0,b 2 ) L4 (x1,y1) L1 L3 10 cm 1 m (a 3,b 3 ) (a 4,b4) 2cm 2mm

5 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

6 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!

7 Changing error on initial estimates

8 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

9 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

10 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 Finding optimum parameters

11 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

12 Results A lot of graphs like this

13 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