Atomizer/studies/M1_Mirror/m1_mirror_cost_reduction

M1 Mirror Cost Reduction Optimization

TPE single-objective optimization targeting mass reduction while maintaining optical performance.

Created: 2025-12-17 Protocol: TPE (Tree-structured Parzen Estimator) with Weighted Sum Status: Ready to Run Baseline: Best design from V11-V15 campaign (Trial #725, WS=121.72)

---

1. Engineering Problem

1.1 Objective

Reduce the mass of the M1 telescope primary mirror while maintaining acceptable wavefront error (WFE) performance across operational elevation angles and manufacturing orientation.

1.2 Physical System

• Component: M1 Primary Mirror Assembly with whiffle-tree support
• Material: Zerodur Class 2 glass ceramic (E=91 GPa, density=2.53 g/cm³, CTE~0)
• Baseline Mass: 91.02 kg
• Loading: Self-weight gravity at multiple elevation angles
• Boundary Conditions: 18-point whiffle-tree axial support, 3-point lateral support
• Analysis Type: Linear static (Nastran SOL 101) with 4 subcases (20, 40, 60, 90 deg)

1.3 Optical Workflow

Reference: 20 deg (interferometer baseline)

Operational Tracking:
  - 40 deg - 20 deg = tracking deformation at 40 deg
  - 60 deg - 20 deg = tracking deformation at 60 deg

Manufacturing:
  - 90 deg - 20 deg = polishing correction needed

1.4 Cost Reduction Strategy

This study explores geometry parameters that affect mass:

• blank_backface_angle: Increases blank taper, reducing material volume
• inner_circular_rib_dia: Controls rib structure extent
• whiffle_*: Support geometry (indirect mass effect via blank shape)

---

2. Mathematical Formulation

2.1 Objectives

Objective	Goal	Weight	Formula	Target	Units
Operational 40-20	minimize	5.0	\text{RMS}_{filt}(Z_{40} - Z_{20})	4.0	nm
Operational 60-20	minimize	5.0	\text{RMS}_{filt}(Z_{60} - Z_{20})	10.0	nm
Manufacturing 90-20	minimize	2.0	\text{RMS}_{J1-J3}(Z_{90} - Z_{20})	20.0	nm
Mass	minimize	1.0	M1_Blank part mass	-	kg

Where:

• Z_\theta = Zernike coefficients at elevation angle \theta
• \text{RMS}_{filt} = RMS with J1-J4 (piston, tip, tilt, defocus) removed
• \text{RMS}_{J1-J3} = RMS with only J1-J3 (piston, tip, tilt) removed

2.2 Weighted Sum Objective

f(\mathbf{x}) = 5 \cdot O_{40-20} + 5 \cdot O_{60-20} + 2 \cdot O_{mfg} + 1 \cdot M_{kg}

This formulation:

• Prioritizes optical performance (5+5=10 weight on tracking)
• Includes manufacturing workload (2 weight)
• Adds mass as secondary objective (1 weight)

2.3 Design Variables

Parameter	Symbol	Bounds	Baseline	Units	Enabled	Description
whiffle_min	w_{min}	[30.0, 72.0]	58.63	mm	Yes	Whiffle tree minimum extent
whiffle_outer_to_vertical	w_{ov}	[60.0, 80.0]	77.96	deg	Yes	Whiffle outer to vertical angle
whiffle_triangle_closeness	w_{tc}	[65.0, 80.0]	67.33	mm	Yes	Whiffle triangle spacing
blank_backface_angle	\beta	[4.5, 5.0]	4.50	deg	Yes	Mirror blank backface taper
inner_circular_rib_dia	d_{rib}	[480.0, 620.0]	537.86	mm	Yes	Inner rib diameter
lateral_inner_angle	\alpha_i	[25.0, 30.0]	27.70	deg	No	(Fixed)
lateral_outer_angle	\alpha_o	[11.0, 17.0]	13.03	deg	No	(Fixed)
lateral_outer_pivot	p_o	[9.0, 12.0]	11.24	mm	No	(Fixed)
lateral_inner_pivot	p_i	[5.0, 12.0]	8.16	mm	No	(Fixed)
lateral_middle_pivot	p_m	[15.0, 27.0]	22.88	mm	No	(Fixed)
lateral_closeness	c_l	[9.5, 12.5]	9.84	mm	No	(Fixed)

Active Design Space: \mathbf{x} \in \mathbb{R}^{5} (5 enabled parameters)

---

3. Optimization Algorithm

3.1 TPE Configuration

Parameter	Value	Description
Algorithm	TPE	Tree-structured Parzen Estimator
n_trials	150	Total FEA simulations
n_startup_trials	15	Random exploration before TPE
multivariate	True	Model parameter correlations
n_ei_candidates	24	Expected improvement candidates
gamma	0.25	Good/bad split threshold
seed	42	Reproducibility

3.2 Explore/Exploit Balance

Trials 1-15:   Random sampling (exploration)
Trials 16-150: TPE-guided sampling (exploitation with adaptive exploration)

TPE dynamically balances exploration vs exploitation based on:
- Parzen estimator of "good" trials (top 25%)
- Expected improvement acquisition function
- Multivariate modeling of parameter correlations

3.3 Optimization Flow

┌─────────────────────────────────────────────────────────────────────┐
│                    TPE OPTIMIZATION LOOP                            │
├─────────────────────────────────────────────────────────────────────┤
│                                                                      │
│  FOR trial = 1 to 150:                                              │
│  │                                                                   │
│  ├─ 1. SAMPLE PARAMETERS                                            │
│  │      └─ trial 1-15: Random (uniform)                             │
│  │      └─ trial 16+: TPE (Expected Improvement)                    │
│  │                                                                   │
│  ├─ 2. UPDATE NX GEOMETRY                                           │
│  │      └─ Import expressions to M1_Blank.prt                       │
│  │      └─ Rebuild geometry with DoUpdate()                         │
│  │                                                                   │
│  ├─ 3. EXTRACT MASS                                                 │
│  │      └─ MeasureManager.NewMassProperties()                       │
│  │      └─ Write _temp_mass.txt                                     │
│  │                                                                   │
│  ├─ 4. RUN FEA SIMULATION                                           │
│  │      └─ Update FEM mesh                                          │
│  │      └─ Solve Nastran SOL 101 (4 subcases)                       │
│  │      └─ Generate .op2 results                                    │
│  │                                                                   │
│  ├─ 5. EXTRACT OBJECTIVES                                           │
│  │      └─ Parse OP2 with ZernikeExtractor                          │
│  │      └─ Compute relative filtered RMS                            │
│  │      └─ Read mass from temp file                                 │
│  │                                                                   │
│  ├─ 6. COMPUTE WEIGHTED SUM                                         │
│  │      └─ WS = 5*obj40 + 5*obj60 + 2*mfg + 1*mass                  │
│  │                                                                   │
│  ├─ 7. ARCHIVE IF BEST                                              │
│  │      └─ Copy iteration folder to best_design_archive/            │
│  │                                                                   │
│  └─ 8. UPDATE OPTUNA STUDY                                          │
│         └─ Record trial value and user attributes                   │
│                                                                      │
│  END FOR                                                             │
│                                                                      │
│  SAVE FINAL RESULTS                                                  │
│                                                                      │
└─────────────────────────────────────────────────────────────────────┘

---

4. Result Extraction Methods

4.1 Zernike WFE Extraction

Attribute	Value
Extractor	ZernikeExtractor.extract_relative()
Module	optimization_engine.extractors.extract_zernike
Source	.op2 file from NX Nastran
Output	nm (nanometers)

Algorithm:

1. Parse OP2 displacement results for target and reference subcases
2. Fit Zernike polynomials (Noll indexing, J1-J50)
3. Compute difference: \Delta Z_j = Z_j^{target} - Z_j^{ref}
4. Filter low orders (J1-J4 for operational, J1-J3 for manufacturing)
5. Compute RMS: \text{RMS} = \sqrt{\sum_{j} \Delta Z_j^2}

4.2 Part Mass Extraction

Attribute	Value
Extractor	MeasureManager.NewMassProperties()
Source	M1_Blank.prt (NX part file)
Output	kg (kilograms)

Algorithm:

1. Get all solid bodies from M1_Blank part
2. Create mass properties measurement with 99% accuracy
3. Extract mass from measureBodies.Mass
4. Write to _temp_mass.txt in iteration folder

Code:

# Mass extraction (in solve_simulation.py)
measureManager = part.MeasureManager
uc = part.UnitCollection
mass_units = [uc.GetBase("Area"), uc.GetBase("Volume"),
              uc.GetBase("Mass"), uc.GetBase("Length")]
measureBodies = measureManager.NewMassProperties(mass_units, 0.99, bodies)
mass_kg = measureBodies.Mass

---

5. Baseline Design (V11-V15 Best)

5.1 Source

Attribute	Value
Study	m1_mirror_adaptive_V14
Trial	#725
Iteration	iter242
Source	FEA
Archived	2025-12-12

5.2 Baseline Objectives

Objective	Value	Target	Status
40-20	5.99 nm	4.0 nm	Above target
60-20	13.10 nm	10.0 nm	Above target
MFG	26.28 nm	20.0 nm	Above target
Mass	91.02 kg	-	Baseline
Weighted Sum	121.72	-	-

5.3 Baseline Parameters

Parameter	Value	Units
lateral_inner_angle	27.70	deg
lateral_outer_angle	13.03	deg
lateral_outer_pivot	11.24	mm
lateral_inner_pivot	8.16	mm
lateral_middle_pivot	22.88	mm
lateral_closeness	9.84	mm
whiffle_min	58.63	mm
whiffle_outer_to_vertical	77.96	deg
whiffle_triangle_closeness	67.33	mm
blank_backface_angle	4.31	deg
inner_circular_rib_dia	537.86	mm

---

6. Study File Structure

m1_mirror_cost_reduction/
│
├── 1_setup/                              # INPUT CONFIGURATION
│   ├── model/                            # NX Model Files
│   │   ├── ASSY_M1.prt                   # Assembly
│   │   ├── M1_Blank.prt                  # Mirror blank (mass source)
│   │   ├── M1_Blank_fem1.fem             # FEM mesh
│   │   ├── M1_Blank_fem1_i.prt           # Idealized part
│   │   ├── M1_Vertical_Support_Skeleton.prt
│   │   ├── M1_Vertical_Support_Skeleton_fem1.fem
│   │   ├── M1_Vertical_Support_Skeleton_fem1_i.prt
│   │   ├── ASSY_M1_assyfem1.afm          # Assembly FEM
│   │   └── ASSY_M1_assyfem1_sim1.sim     # Simulation file
│   └── optimization_config.json          # Study configuration
│
├── 2_iterations/                         # FEA iteration folders
│   └── iter{N}/                          # Per-trial working directory
│       ├── [model files]                 # Copied NX files
│       ├── params.exp                    # Expression values
│       ├── _temp_mass.txt                # Extracted mass
│       ├── _temp_part_properties.json    # Full mass properties
│       ├── *.dat                         # Nastran input deck
│       ├── *.op2                         # Results (binary)
│       ├── *.f06                         # Results (text)
│       └── results/                      # Processed outputs
│
├── 3_results/                            # OUTPUT
│   ├── study.db                          # Optuna SQLite database
│   ├── optimization.log                  # Execution log
│   ├── optimization_summary.json         # Final results summary
│   └── best_design_archive/              # Archived best designs
│       └── {timestamp}/                  # Per-improvement snapshot
│           ├── [model files]
│           ├── params.exp
│           └── _archive_info.json
│
├── run_optimization.py                   # Main entry point
└── README.md                             # This documentation

---

7. Quick Start

7.1 Run Commands

# Navigate to study
cd C:\Users\antoi\Atomizer\studies\m1_mirror_cost_reduction

# Activate environment
conda activate atomizer

# Run optimization (150 trials)
python run_optimization.py --start --trials 150

# Resume if interrupted
python run_optimization.py --start --trials 150 --resume

# Single test trial
python run_optimization.py --test

7.2 Command Line Options

Option	Default	Description
--start	-	Required to begin optimization
--trials	100	Number of FEA trials to run
--resume	False	Resume from existing study.db
--test	False	Run single test trial

---

8. Expected Runtime

Phase	Time per Trial	Total (150 trials)
Geometry update	~45s	~1.9 hr
FEA solve	~90s	~3.8 hr
Extraction	~15s	~0.6 hr
Total	~2.5 min	~6-7 hours

---

9. Configuration Reference

File: 1_setup/optimization_config.json

Section	Key	Description
optimization.algorithm	TPE	Single-objective optimizer
optimization.n_trials	150	Total trials planned
optimization.n_startup_trials	15	Random exploration phase
optimization.multivariate	true	Model correlations
design_variables[]	11 params	5 enabled, 6 fixed
objectives[]	4 objectives	WFE (3) + Mass (1)
nx_settings.nx_install_path	DesigncenterNX2512	NX version

---

10. Success Criteria

Metric	Target	Priority
Mass reduction	>3 kg (to <88 kg)	Primary
40-20 degradation	<2 nm increase	Secondary
60-20 degradation	<3 nm increase	Secondary
MFG impact	Acceptable increase	Tertiary

---

11. References

• Optuna Documentation: Tree-structured Parzen Estimator (TPE)
• Noll, R.J. (1976). Zernike polynomials and atmospheric turbulence. JOSA.
• V11-V15 Campaign: Previous optimization studies establishing baseline

---

Generated by Atomizer Framework - M1 Mirror Cost Reduction Study