Summary
This experiment investigates laser cutting parameter optimization. Definitive screening design to optimize edge quality and kerf width in laser cutting.
The design varies 5 factors: power (W), ranging from 40 to 80, speed (mm/s), ranging from 100 to 500, frequency (Hz), ranging from 5000 to 25000, focus offset (mm), ranging from -3 to 3, and gas pressure (bar), ranging from 2 to 8. The goal is to optimize 2 responses: edge quality (score) (maximize) and kerf width (mm) (minimize). Fixed conditions held constant across all runs include material thickness = 2.
The Definitive Screening Design produces 11 experimental runs.
Key Findings
For edge quality, the most influential factors were power (21.9%), frequency (21.6%), speed (19.3%). The best observed value was 74.72 (at power = 40, speed = 500, frequency = 25000).
For kerf width, the most influential factors were frequency (33.2%), focus offset (22.1%), gas pressure (22.1%). The best observed value was 0.1498 (at power = 80, speed = 500, frequency = 5000).
Recommended Next Steps
- Consider whether any fixed factors should be varied in a future study.
- The screening results can guide factor reduction — drop factors contributing less than 5% and re-run with a smaller, more focused design.
Experimental Setup
Factors
| Factor | Low | High | Unit |
|---|
power | 40 | 80 | W |
speed | 100 | 500 | mm/s |
frequency | 5000 | 25000 | Hz |
focus_offset | -3 | 3 | mm |
gas_pressure | 2 | 8 | bar |
Fixed: material_thickness = 2
Responses
| Response | Direction | Unit |
|---|
edge_quality | ↑ maximize | score |
kerf_width | ↓ minimize | mm |
Configuration
{
"metadata": {
"name": "Laser Cutting Parameter Optimization",
"description": "Definitive screening design to optimize edge quality and kerf width in laser cutting"
},
"factors": [
{
"name": "power",
"levels": [
"40",
"80"
],
"type": "continuous",
"unit": "W"
},
{
"name": "speed",
"levels": [
"100",
"500"
],
"type": "continuous",
"unit": "mm/s"
},
{
"name": "frequency",
"levels": [
"5000",
"25000"
],
"type": "continuous",
"unit": "Hz"
},
{
"name": "focus_offset",
"levels": [
"-3",
"3"
],
"type": "continuous",
"unit": "mm"
},
{
"name": "gas_pressure",
"levels": [
"2",
"8"
],
"type": "continuous",
"unit": "bar"
}
],
"fixed_factors": {
"material_thickness": "2"
},
"responses": [
{
"name": "edge_quality",
"optimize": "maximize",
"unit": "score"
},
{
"name": "kerf_width",
"optimize": "minimize",
"unit": "mm"
}
],
"settings": {
"operation": "definitive_screening",
"test_script": "use_cases/301_laser_cutting_parameters/sim.sh"
}
}
Experimental Matrix
The Definitive Screening Design produces 11 runs. Each row is one experiment with specific factor settings.
| Run | power | speed | frequency | focus_offset | gas_pressure |
|---|
| 1 | 80 | 100 | 5000 | -3 | 8 |
| 2 | 40 | 100 | 25000 | 3 | 2 |
| 3 | 40 | 500 | 25000 | 3 | 2 |
| 4 | 80 | 500 | 5000 | -3 | 8 |
| 5 | 40 | 500 | 25000 | -3 | 8 |
| 6 | 40 | 100 | 5000 | -3 | 8 |
| 7 | 80 | 500 | 5000 | 3 | 2 |
| 8 | 40 | 100 | 25000 | -3 | 8 |
| 9 | 80 | 100 | 5000 | 3 | 2 |
| 10 | 80 | 500 | 25000 | 3 | 2 |
| 11 | 60 | 300 | 15000 | 0 | 5 |
Step-by-Step Workflow
1
Preview the design
$ doe info --config use_cases/301_laser_cutting_parameters/config.json
2
Generate the runner script
$ doe generate --config use_cases/301_laser_cutting_parameters/config.json \
--output use_cases/301_laser_cutting_parameters/results/run.sh --seed 42
3
Execute the experiments
$ bash use_cases/301_laser_cutting_parameters/results/run.sh
4
Analyze results
$ doe analyze --config use_cases/301_laser_cutting_parameters/config.json
5
Get optimization recommendations
$ doe optimize --config use_cases/301_laser_cutting_parameters/config.json
6
Multi-objective optimization
With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.
$ doe optimize --config use_cases/301_laser_cutting_parameters/config.json --multi
7
Generate the HTML report
$ doe report --config use_cases/301_laser_cutting_parameters/config.json \
--output use_cases/301_laser_cutting_parameters/results/report.html
Features Exercised
| Feature | Value |
|---|
| Design type | definitive_screening |
| Factor types | continuous (all 5) |
| Arg style | double-dash |
| Responses | 2 (edge_quality ↑, kerf_width ↓) |
| Total runs | 11 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: edge_quality
Top factors: power (21.9%), frequency (21.6%), speed (19.3%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| power | 2 | 180.8072 | 90.4036 | | |
| speed | 2 | 121.5503 | 60.7751 | | |
| frequency | 2 | 170.5501 | 85.2750 | | |
| focus_offset | 2 | 114.9533 | 57.4766 | | |
| gas_pressure | 2 | 114.9533 | 57.4766 | | |
| Error | (Lenth | PSE) | 0 | 51.6150 | 0.0000 |
| Total | 10 | 754.4292 | 75.4429 | | |
Response: kerf_width
Top factors: frequency (33.2%), focus_offset (22.1%), gas_pressure (22.1%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| power | 2 | 0.0029 | 0.0014 | | |
| speed | 2 | 0.0001 | 0.0001 | | |
| frequency | 2 | 0.0115 | 0.0057 | | |
| focus_offset | 2 | 0.0051 | 0.0026 | | |
| gas_pressure | 2 | 0.0051 | 0.0026 | | |
| Error | (Lenth | PSE) | 0 | 0.0329 | 0.0000 |
| Total | 10 | 0.0577 | 0.0058 | | |
Multi-Objective Optimization
When responses compete, Derringer–Suich desirability finds the best compromise.
Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.
Overall Desirability
D = 0.8085
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|
edge_quality |
1.5 |
|
74.72 0.9545 74.72 score |
↑ |
kerf_width |
1.0 |
|
0.25 0.6302 0.25 mm |
↓ |
Recommended Settings
| Factor | Value |
|---|
power | 40 W |
speed | 100 mm/s |
frequency | 25000 Hz |
focus_offset | 3 mm |
gas_pressure | 2 bar |
Source: from observed run #11
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|
kerf_width | 0.25 | 0.15 | +0.10 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|
| #10 | 0.7450 | power=80, speed=100, frequency=5000, focus_offset=-3, gas_pressure=8 |
| #5 | 0.6618 | power=60, speed=300, frequency=15000, focus_offset=0, gas_pressure=5 |
Model Quality
| Response | R² | Type |
|---|
kerf_width | 0.4329 | linear |
Full Multi-Objective Output
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.8085
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
edge_quality 1.5 0.9545 74.72 score ↑
kerf_width 1.0 0.6302 0.25 mm ↓
Recommended settings:
power = 40 W
speed = 100 mm/s
frequency = 25000 Hz
focus_offset = 3 mm
gas_pressure = 2 bar
(from observed run #11)
Trade-off summary:
edge_quality: 74.72 (best observed: 74.72, sacrifice: +0.00)
kerf_width: 0.25 (best observed: 0.15, sacrifice: +0.10)
Model quality:
edge_quality: R² = 0.3568 (linear)
kerf_width: R² = 0.4329 (linear)
Top 3 observed runs by overall desirability:
1. Run #11 (D=0.8085): power=40, speed=100, frequency=25000, focus_offset=3, gas_pressure=2
2. Run #10 (D=0.7450): power=80, speed=100, frequency=5000, focus_offset=-3, gas_pressure=8
3. Run #5 (D=0.6618): power=60, speed=300, frequency=15000, focus_offset=0, gas_pressure=5
Full Analysis Output
=== Main Effects: edge_quality ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
power 13.7340 2.6189 21.9%
frequency 13.5300 2.6189 21.6%
speed 12.0760 2.6189 19.3%
focus_offset 11.6260 2.6189 18.6%
gas_pressure 11.6260 2.6189 18.6%
=== ANOVA Table: edge_quality ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
power 2 180.8072 90.4036
speed 2 121.5503 60.7751
frequency 2 170.5501 85.2750
focus_offset 2 114.9533 57.4766
gas_pressure 2 114.9533 57.4766
Error (Lenth PSE) 0 51.6150 0.0000
Total 10 754.4292 75.4429
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Summary Statistics: edge_quality ===
power:
Level N Mean Std Min Max
------------------------------------------------------------
40 5 59.6320 8.3505 48.6300 70.5300
60 1 51.1300 0.0000 51.1300 51.1300
80 5 64.8640 8.5834 54.3600 74.7200
speed:
Level N Mean Std Min Max
------------------------------------------------------------
100 5 61.2900 8.3051 48.6300 70.5300
300 1 51.1300 0.0000 51.1300 51.1300
500 5 63.2060 9.4470 54.3600 74.7200
frequency:
Level N Mean Std Min Max
------------------------------------------------------------
15000 1 51.1300 0.0000 51.1300 51.1300
25000 5 59.8360 8.6889 48.6300 71.5500
5000 5 64.6600 8.3948 54.3600 74.7200
focus_offset:
Level N Mean Std Min Max
------------------------------------------------------------
-3 5 61.7400 6.9846 54.3600 70.5300
0 1 51.1300 0.0000 51.1300 51.1300
3 5 62.7560 10.5397 48.6300 74.7200
gas_pressure:
Level N Mean Std Min Max
------------------------------------------------------------
2 5 62.7560 10.5397 48.6300 74.7200
5 1 51.1300 0.0000 51.1300 51.1300
8 5 61.7400 6.9846 54.3600 70.5300
=== Main Effects: kerf_width ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
frequency 0.0674 0.0229 33.2%
focus_offset 0.0449 0.0229 22.1%
gas_pressure 0.0449 0.0229 22.1%
power 0.0333 0.0229 16.4%
speed 0.0123 0.0229 6.1%
=== ANOVA Table: kerf_width ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
power 2 0.0029 0.0014
speed 2 0.0001 0.0001
frequency 2 0.0115 0.0057
focus_offset 2 0.0051 0.0026
gas_pressure 2 0.0051 0.0026
Error (Lenth PSE) 0 0.0329 0.0000
Total 10 0.0577 0.0058
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Summary Statistics: kerf_width ===
power:
Level N Mean Std Min Max
------------------------------------------------------------
40 5 0.2591 0.0887 0.1498 0.3472
60 1 0.2651 0.0000 0.2651 0.2651
80 5 0.2924 0.0764 0.2492 0.4284
speed:
Level N Mean Std Min Max
------------------------------------------------------------
100 5 0.2741 0.1130 0.1498 0.4284
300 1 0.2651 0.0000 0.2651 0.2651
500 5 0.2774 0.0402 0.2492 0.3472
frequency:
Level N Mean Std Min Max
------------------------------------------------------------
15000 1 0.2651 0.0000 0.2651 0.2651
25000 5 0.2421 0.0771 0.1498 0.3472
5000 5 0.3095 0.0749 0.2492 0.4284
focus_offset:
Level N Mean Std Min Max
------------------------------------------------------------
-3 5 0.2982 0.0905 0.1866 0.4284
0 1 0.2651 0.0000 0.2651 0.2651
3 5 0.2533 0.0703 0.1498 0.3472
gas_pressure:
Level N Mean Std Min Max
------------------------------------------------------------
2 5 0.2533 0.0703 0.1498 0.3472
5 1 0.2651 0.0000 0.2651 0.2651
8 5 0.2982 0.0905 0.1866 0.4284
Optimization Recommendations
=== Optimization: edge_quality ===
Direction: maximize
Best observed run: #11
power = 40
speed = 500
frequency = 25000
focus_offset = 3
gas_pressure = 2
Value: 74.72
RSM Model (linear, R² = 0.4612, Adj R² = -0.0775):
Coefficients:
intercept +61.2373
power +2.4900
speed -1.1400
frequency +4.5525
focus_offset +1.8988
gas_pressure -1.8988
Predicted optimum (from linear model, at observed points):
power = 80
speed = 500
frequency = 25000
focus_offset = 3
gas_pressure = 2
Predicted value: 70.9373
Surface optimum (via L-BFGS-B, linear model):
power = 80
speed = 100
frequency = 25000
focus_offset = 3
gas_pressure = 2
Predicted value: 73.2173
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. focus_offset (effect: 10.0, contribution: 26.0%)
2. gas_pressure (effect: 10.0, contribution: 26.0%)
3. frequency (effect: 8.1, contribution: 21.1%)
4. speed (effect: 5.5, contribution: 14.4%)
5. power (effect: 4.8, contribution: 12.5%)
=== Optimization: kerf_width ===
Direction: minimize
Best observed run: #3
power = 80
speed = 500
frequency = 5000
focus_offset = 3
gas_pressure = 2
Value: 0.1498
RSM Model (linear, R² = 0.2681, Adj R² = -0.4639):
Coefficients:
intercept +0.2748
power +0.0372
speed +0.0061
frequency +0.0325
focus_offset -0.0196
gas_pressure +0.0196
Predicted optimum (from linear model, at observed points):
power = 80
speed = 500
frequency = 5000
focus_offset = -3
gas_pressure = 8
Predicted value: 0.3248
Surface optimum (via L-BFGS-B, linear model):
power = 40
speed = 100
frequency = 5000
focus_offset = 3
gas_pressure = 2
Predicted value: 0.1598
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. focus_offset (effect: 0.2, contribution: 21.0%)
2. gas_pressure (effect: 0.2, contribution: 21.0%)
3. speed (effect: 0.2, contribution: 19.7%)
4. power (effect: 0.2, contribution: 19.6%)
5. frequency (effect: 0.2, contribution: 18.8%)