S. Gibson FSI Offline Analysis 9 th October FSI Alignment: Offline Analysis Overview ATLAS Group, University of Oxford Stephen Gibson, Danny Hindson, Pawel Bruckman de Renstrom, Paul Coe, Tony Weidberg Reminder of FSI What FSI provides Node reconstruction Analysis approaches: Reverse FEA Eigenmode decomposition

S. Gibson FSI Offline Analysis 9 th October SCT monitored with FSI geodetic grids SemiConductor Tracker monitored using a geodetic grid of 842 length measurements. Forward SCT grid Barrel SCT grid

S. Gibson FSI Offline Analysis 9 th October FSI System Installed on Barrel 3 FSI grid nodes

S. Gibson FSI Offline Analysis 9 th October Barrel FSI grid node: “Scorpion” Pre-alignment jig Installed on barrel

S. Gibson FSI Offline Analysis 9 th October Endcap FSI Grid Node: “Viking”

S. Gibson FSI Offline Analysis 9 th October Endcap FSI Grid Node: “Viking” Now in pre-alignment jig – see hardware tour

S. Gibson FSI Offline Analysis 9 th October Endcap FSI: Pre-alignment jig

S. Gibson FSI Offline Analysis 9 th October What does FSI provide? One FSI scan provides a set of precise length measurements between grid nodes (<1micron). Not absolute but relative measurements – interested in differences between scans. Timescale: Each laser scan will take a few minutes (to generate the raw data). Rate of scans will depend on:  Available processor resources.  Data storage: Interferometer data ~ 1 GB per scan. Length data ~ only 10 kB per scan.  Demand for FSI data (during a fill/ between fills/ shutdowns). Frequent measurements allow short time scale distortions to be followed and corrected. Access to low spatial frequency modes of tracker distortion (sagitta).

S. Gibson FSI Offline Analysis 9 th October Alignment System Calibration scanning head Initial Module Co-ordinates Initial Node Positions X-ray survey FSI scan FSI System Calibration simultaneous

S. Gibson FSI Offline Analysis 9 th October Analysis of FSI data Interferometer data analysis: This data consists of sinusoidal fringes from each grid line interferometer (for both lasers) + gas measurements.  Total ~ 1GB per scan. PC farm will process data in quasi-real-time to determine the set of lengths for each scan. Time to process each scan? Result is 842 lengths kept on record. How to use these 842 lengths?

S. Gibson FSI Offline Analysis 9 th October Analysis of FSI data FSI Grid Lengths Reconstruction Module Co-ordinates Interpolation Node DoF Want to determine parameters of a model. Model to be defined Reconstruction software. Node reconstruction already shown for simple prototype grids. ATLAS grid simulations: see next slide. Interpolation process: Shape parameterisation FEA: barrel and disc eigenmodes Check with ESPI studies Calibration from initial X-ray survey

S. Gibson FSI Offline Analysis 9 th October Reconstruction Software Status Preliminary investigations: A. Fox-Murphy Thesis Final grid designs: Barrel grid error propagations:  Inner barrel grid quadrant  Single barrel grid  End-flange grid  Full Barrel SCT grid Endcap grid error propagations:  Initial simulation: ATL-IS-AP  Improved final design described in ATL-IS-ES Node reconstruction already shown for simple prototype grids. Will extend simulations of ATLAS grids to allow node reconstruction. (PPARC fellowship) Simulated: ATL-IS-ES-0026 In progress: S. Gibson Thesis (to be published) Simulated: S. Gibson Thesis

S. Gibson FSI Offline Analysis 9 th October Precise Grid Measurements Precise three dimensional node reconstruction 1m1m Well within ATLAS 10  m requirement

S. Gibson FSI Offline Analysis 9 th October Endcap Grid Reconstruction Simulation Error in reconstructing the translational DoF of each disc with respect to the first disc.

S. Gibson FSI Offline Analysis 9 th October Endcap grid: reconstruction errors Error in reconstructing the translational DoF of each disc with respect to a reference disc. ‘Pinch’ effect: on redefining the reference disc, the errors change as shown. Smallest errors when ‘held’ at centre (disc 6). Reconstructed endcap shape should be model independent – effect is simply a global coordinate transformation.

S. Gibson FSI Offline Analysis 9 th October Interpolation Process Output from reconstruction doesn’t have to be x,y,z of each FSI node. (Rather fitted DoF defined in model). Must provide node DoF in format compatible with interpolation process. Some possible formats:  FSI node x,y,z (for 3 independent frames A,B,C).  6 DoF of objects that contain nodes, with further internal DoF. (barrel SCT: contains 4 barrels: barrel distortion; endcap: contains 9 discs: disc distortion). Need to incorporate track data. Two approaches so far considered for offline analysis:  Reverse FEA  Eigenmode decomposition (shape parameterisation)

S. Gibson FSI Offline Analysis 9 th October Interpolation process Shape parameterisation  Fit eigenmodes of SCT support structure to FSI grid node positions to determine barrel shape. Reverse FEA  Insert FSI node positions to FEA model and solve directly for module coordinates. ESPI Test process experimentally with independent structural monitoring using: Electronic Speckle Pattern Interferometry.

S. Gibson FSI Offline Analysis 9 th October Reverse FEA 1. Apply realistic force to barrel eg gravity with missing support 3. Run reverse FEA to interpolate positions of other FEA nodes 2. Retain positions of FSI nodes only. Fix the positions of these nodes Interpolated positionsActual positions

S. Gibson FSI Offline Analysis 9 th October Reverse FEA: residuals This assumes elastic properties of barrel are known perfectly If rerun with wrong Young’s modulus, wrong Poissons ratio (10% out), mean difference is still <1 micron

S. Gibson FSI Offline Analysis 9 th October Reconstruction and interpolation process must be checked experimentally. Measure lengths of an FSI grid. Reconstruct nodes and interpolate dummy module positions. Monitor dummy module positions independently with Electronic Speckle Pattern Interferometry. Possible Check with ESPI ESPI FSI grid Distorted barrel

S. Gibson FSI Offline Analysis 9 th October Offline Analysis Method 1 Module Coords X24 (assume scan per hour) Base line Module coords Initial Module Co-ordinates X-ray survey Reverse FEA Adjust hit positions Corrections to module coords Run track alignment 24 hrs FSI corrected data A,B,C FSI Node DoF Tracks Database Interpolate in time? Time adjust modules Time dep. modules X24 Time dep. modules time

S. Gibson FSI Offline Analysis 9 th October Eigenmode Decomposition  SCT shape (or sub components of it) can be expressed as a sum of eigenmodes. (see next slide) Spatial frequency eigenmode FSI Time seconds minutes hours days months Tracks X-ray survey FEA Module metrology Module temperature

S. Gibson FSI Offline Analysis 9 th October Offline Analysis Method 2 Initial Module Co-ordinates X-ray survey Global Fit to for eigenmodes A,B,C FSI Node DoF Tracks Database Interpolate in time? Time dep. modules Time dep. modules time FEA information metrology

S. Gibson FSI Offline Analysis 9 th October Comments/Conclusions Reconstruction software:  Endcap grid fully simulated  Barrel grid partially simulated – rest should be done by end March  Will extend simulations to full reconstruction. Interpolation Some initial thoughts, but much to be decided: Reverse FEA:  Relatively simple.  Modular approach.  Mechnical constraints added after fit for nodes.  Reliability of result? Eigenmode decomposition  Ideal way to proceed.  More difficult to combine all information.  Ease of inclusion of mechanical properties?  We can improve the model with time.