13th international workshop on accelerator alignment ...13th international workshop on accelerator...

1 BROOKHAVEN SCIENCE ASSOCIATES

13th International Workshop on Accelerator Alignment October 13-17, 2014, IHEP, Beijing, China

Smoothing Based on Best-fit Transformation

C. Yu



Outline

• Introduction

• Principle

• Application in SSRF

• Application in NSLS-II

• More Consideration

• Conclusion



What’s Smoothing

• a technique to achieve accurate relative

alignment of components

• a main concern of accelerator alignment

The reason for smoothing:

• limitation of survey control network

• slow floor movement

• tight relative alignment tolerance

• loose global alignment tolerance

Introduction

Smoothing techniques

• cubic spline functions (DESY)

• First Principle Component analysis (APS)

• Based on best fit transformation



What’s best fit transformation

• Mathematically, take out the overall

translation or rotation between reference and

as-built coordinate systems

Smoothing Requirement

• Reference value of fiducials

• As-built value of fiducials

• Check the as-built location WRT reference

and can be realized by best fit transformation

Best Fit Transformation

Benefits

• Easy to understand

• Readily available in software

• Handily available with regard to reference

and as-built data

• And more

From Spatial Analyzer User Manual

3 translation, 3 rotation and 1 scale parameters



How to use it for one set of girders or

magnet groups?

• Obtain reference data

• Obtain as-built data

• Perform best-fit transformation

• Compare the residuals of fiducials

• Decide if the beam orbit is smooth according

certain criteria.

What has been done by best-fit

transformation is taking out of the rotations

and translations of as-built values with

respect to global coordinate system and

showing the deviations relatively.

Repeat many times to check the whole

ring

Smoothing Based on Best Fit Transformation-Basics

Layout of C08G2 and C08G4 girder fiducials and best-

fit deviations of NSLS-II Storage ring

Comparison of C08G2 and C08G4 girder

fiducials before and after best-fit transformation.



• In practice, 3 adjacent girders are used

• Overlap between cells is important. The number of best fit transformation equals to the number of

girders.

• It’s important to have accurate as-built survey data

• In order to describe the deviations clearly and make them easy to understand, local frames for each

girder should be established.

• The fiducials should be sorted in each group according to their location with respect to beam

• When a girder is determined to be adjusted, its upstream and downstream girders will be used to

transform the as-built survey data to reference data

• The method is not limited to circular accelerator.

Smoothing Based on Best Fit Transformation-More



Application in SSRF (1)

• SSRF storage ring 432m

• Initial alignment 2007

• Re-alignment in 2012

• The best-fit transformation

based smoothing technique

was initialized.

• Sextupoles and quadrupoles

centers were used during best-

fit transformation process.

• Girders were rotated based on

the roll angle

• Multiple iterations (Realized by

MP of Spatial Analyzer) to

minimize the residuals



Application in SSRF (2)

Computed adjusted amount in horizontal direction Computed adjusted amount in vertical direction

The good

• Circumference error >10 mm ignored.

• Most of the adjustment below 300 micron

• First attempt to apply this innovative idea,

alignment result was excellent

The bad

• 7 beam lines of phase 1 had to be re-

adjusted



Application in NSLS-II (1)

• Storage ring ~791.5m

• Girder alignment for ~1 year

• No final survey before

commissioning

• Epoch 7 survey during shutdown

in May 2014 shows deviations of

components.

• Smoothing based on best fit

transformation of girder fiducials

were used.




Steps:

•Perform comprehensive survey for girder of

interested and its upstream and downstream ones.

•Compute the measured relative location of 3 girders.

•Perform a best-fitting between the measured and

reference coordinates to see if there are large

deviations. As a rule of thumb, the fitting RMS in both

X and Y direction should be below 0.05.

•If the fitting result is larger than 0.05, the downstream

fiducials of upstream girder and upsteam fiducials of

downstream girder will be used to establish girder

adjustment control network. The nominal coordinates

of those 4 fiducials will be used to best-fit and

transform the measured point group. The measured

point group will be used as survey control network and

the reference coordinates will be used as alignment

goal.

“DX Goal” and “DY Goal” shows the goal of

adjustment.




The fiducial deviations after best-fit transformation among all 3 adjacent girders.

Fiducial best-fit result

•Each fiducial will be shown 3 times

•RMS deviation in X and Y direction is 0.034

mm and 0.021 mm respectively

Work has been done

•22 girders which had been checked

•8 girders had been adjusted

•The maximum adjustment amount is below

300 micron.




The girder center deviations before and after smoothing.

Global deviation

•All girder centers WRT epoch 7 survey

•Still not a smooth curve, but relative girder

alignment is well within tolerance.

Nomenclature

•“O” means original survey

•“C” means it has been checked

•“A” means it has been aligned.

Lessons learned

•Girders should be checked in a consecutive manner



Discussions

• The best-fit transformation based smoothing technique is easy to understand and use

• Its application is successful for the partial alignment of NSLS-II project.

• It also yielded excellent alignment quality when it was applied in SSRF for a whole

machine re-adjustment during 2012 shutdown.

• The best-fit transformation based smoothing technique can tackle beamline alignment

constraints by avoid moving girders around straight section unless it’s absolutely

necessary.

• By surveying and adjusting the storage ring cell by cell, good storage ring alignment can

be maintained. This is important for a new machine as no major shutdown will be

necessary at the early stage of running due to large floor settlement.



Summary

• Best-fit transformation is a basic technique for accelerator alignment in the current time,

but smoothing seems a little bit fancy as it usually associates with different language,

such as Fourier function, cubic spline or Principal Curve Analysis etc. But the application

of best-fit transformation makes smoothing a lot easier and any surveyor can do it.

• It’s not only a great tool for partial and whole alignment of an accelerator at the beginning

of running a machine, but also a possible solution for long term maintenance of storage

ring when more constraints present.

• With dedicated script, the whole smoothing process can be fully automated and high

efficiency is expected.



Acknowledgment

The author would like to thank all the staff who involved in the

NSLS-II and SSRF alignment activities.



Thanks for your attention!

13th international workshop on accelerator alignment ...13th international workshop on accelerator...

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