Summary
This experiment investigates lithium-ion battery cell design. Latin Hypercube sampling with 25 runs across 6 continuous factors and 3 responses for battery cell design space exploration.
The design varies 6 factors: cathode thickness (microns), ranging from 50 to 150, anode thickness (microns), ranging from 60 to 120, electrolyte conc (M), ranging from 0.8 to 1.4, separator porosity (%), ranging from 30 to 60, charge rate (C), ranging from 0.5 to 3, and tab width (mm), ranging from 10 to 30. The goal is to optimize 3 responses: energy density (Wh/kg) (maximize), power density (W/kg) (maximize), and cycle life (cycles) (maximize). Fixed conditions held constant across all runs include cell format = pouch, temperature = 25C.
Latin Hypercube Sampling was used to space 25 runs across the 6-dimensional factor space with good coverage and minimal gaps, making it ideal for computer experiments where the response surface may be complex.
Key Findings
For energy density, the most influential factors were cathode thickness (16.7%), anode thickness (16.7%), electrolyte conc (16.7%). The best observed value was 255.3 (at cathode thickness = 88.666, anode thickness = 64.4416, electrolyte conc = 1.10351).
For power density, the most influential factors were cathode thickness (16.7%), anode thickness (16.7%), electrolyte conc (16.7%). The best observed value was 971.0 (at cathode thickness = 141.048, anode thickness = 117.242, electrolyte conc = 0.882444).
For cycle life, the most influential factors were cathode thickness (16.7%), anode thickness (16.7%), electrolyte conc (16.7%). The best observed value was 1382.0 (at cathode thickness = 58.8445, anode thickness = 89.643, electrolyte conc = 1.32052).
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 |
|---|
cathode_thickness | 50 | 150 | microns |
anode_thickness | 60 | 120 | microns |
electrolyte_conc | 0.8 | 1.4 | M |
separator_porosity | 30 | 60 | % |
charge_rate | 0.5 | 3 | C |
tab_width | 10 | 30 | mm |
Fixed: cell_format = pouch, temperature = 25C
Responses
| Response | Direction | Unit |
|---|
energy_density | ↑ maximize | Wh/kg |
power_density | ↑ maximize | W/kg |
cycle_life | ↑ maximize | cycles |
Configuration
{
"metadata": {
"name": "Lithium-Ion Battery Cell Design",
"description": "Latin Hypercube sampling with 25 runs across 6 continuous factors and 3 responses for battery cell design space exploration"
},
"factors": [
{
"name": "cathode_thickness",
"levels": [
"50",
"150"
],
"type": "continuous",
"unit": "microns"
},
{
"name": "anode_thickness",
"levels": [
"60",
"120"
],
"type": "continuous",
"unit": "microns"
},
{
"name": "electrolyte_conc",
"levels": [
"0.8",
"1.4"
],
"type": "continuous",
"unit": "M"
},
{
"name": "separator_porosity",
"levels": [
"30",
"60"
],
"type": "continuous",
"unit": "%"
},
{
"name": "charge_rate",
"levels": [
"0.5",
"3"
],
"type": "continuous",
"unit": "C"
},
{
"name": "tab_width",
"levels": [
"10",
"30"
],
"type": "continuous",
"unit": "mm"
}
],
"fixed_factors": {
"cell_format": "pouch",
"temperature": "25C"
},
"responses": [
{
"name": "energy_density",
"optimize": "maximize",
"unit": "Wh/kg"
},
{
"name": "power_density",
"optimize": "maximize",
"unit": "W/kg"
},
{
"name": "cycle_life",
"optimize": "maximize",
"unit": "cycles"
}
],
"settings": {
"operation": "latin_hypercube",
"test_script": "use_cases/310_battery_cell_design/sim.sh"
}
}
Experimental Matrix
The Latin Hypercube Design produces 25 runs. Each row is one experiment with specific factor settings.
| Run | cathode_thickness | anode_thickness | electrolyte_conc | separator_porosity | charge_rate | tab_width |
|---|
| 1 | 65.6351 | 63.9888 | 1.30765 | 46.3955 | 1.3796 | 24.2822 |
| 2 | 104.166 | 94.6012 | 1.06568 | 52.9393 | 2.90325 | 21.9379 |
| 3 | 101.301 | 82.7625 | 0.981162 | 33.9942 | 2.51865 | 24.677 |
| 4 | 68.4509 | 91.2914 | 1.34648 | 36.3178 | 2.64256 | 25.2067 |
| 5 | 147.576 | 96.1159 | 1.17579 | 59.5239 | 1.81519 | 11.8288 |
| 6 | 58.317 | 100.031 | 1.00438 | 50.026 | 0.817917 | 13.9392 |
| 7 | 126.821 | 102.269 | 1.27245 | 56.8717 | 1.16059 | 12.5885 |
| 8 | 89.6933 | 85.3752 | 0.800518 | 41.9681 | 2.16182 | 18.3551 |
| 9 | 71.1789 | 70.7536 | 0.89142 | 44.6153 | 2.35018 | 26.3226 |
| 10 | 134.067 | 110.784 | 0.852471 | 43.965 | 2.26496 | 22.2504 |
| 11 | 118.359 | 66.2344 | 1.21468 | 47.3311 | 0.541622 | 15.7494 |
| 12 | 55.4058 | 75.6316 | 0.827382 | 51.7424 | 1.29849 | 23.1422 |
| 13 | 106.179 | 115.765 | 1.12146 | 50.5327 | 2.7857 | 10.4056 |
| 14 | 125.293 | 60.4842 | 1.14053 | 56.2039 | 1.98645 | 29.9156 |
| 15 | 81.3182 | 79.4838 | 1.39866 | 55.0231 | 2.40745 | 20.6798 |
| 16 | 132.929 | 72.711 | 0.95198 | 48.522 | 0.978472 | 19.2565 |
| 17 | 96.7431 | 108.845 | 0.906925 | 38.4176 | 1.02098 | 17.8065 |
| 18 | 139.809 | 113.655 | 0.937822 | 31.8759 | 0.675092 | 10.9092 |
| 19 | 91.8561 | 103.563 | 1.24277 | 38.1508 | 0.755432 | 28.0338 |
| 20 | 53.5807 | 90.8434 | 1.01665 | 43.1324 | 1.59849 | 28.5603 |
| 21 | 74.367 | 105.951 | 1.0613 | 58.68 | 1.47455 | 27.0711 |
| 22 | 110.952 | 77.7994 | 1.35387 | 32.9292 | 2.89583 | 15.3865 |
| 23 | 83.9302 | 87.6369 | 1.10669 | 35.0503 | 2.03711 | 20.1105 |
| 24 | 144.381 | 119.052 | 1.18821 | 30.6455 | 1.74519 | 14.0185 |
| 25 | 115.431 | 68.8558 | 1.28145 | 40.3775 | 1.61766 | 16.4425 |
Step-by-Step Workflow
1
Preview the design
$ doe info --config use_cases/310_battery_cell_design/config.json
2
Generate the runner script
$ doe generate --config use_cases/310_battery_cell_design/config.json \
--output use_cases/310_battery_cell_design/results/run.sh --seed 42
3
Execute the experiments
$ bash use_cases/310_battery_cell_design/results/run.sh
4
Analyze results
$ doe analyze --config use_cases/310_battery_cell_design/config.json
5
Get optimization recommendations
$ doe optimize --config use_cases/310_battery_cell_design/config.json
6
Multi-objective optimization
With 3 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.
$ doe optimize --config use_cases/310_battery_cell_design/config.json --multi
7
Generate the HTML report
$ doe report --config use_cases/310_battery_cell_design/config.json \
--output use_cases/310_battery_cell_design/results/report.html
Features Exercised
| Feature | Value |
|---|
| Design type | latin_hypercube |
| Factor types | continuous (all 6) |
| Arg style | double-dash |
| Responses | 3 (energy_density ↑, power_density ↑, cycle_life ↑) |
| Total runs | 25 |
Analysis Results
Generated from actual experiment runs using the DOE Helper Tool.
Response: energy_density
Top factors: cathode_thickness (16.7%), anode_thickness (16.7%), electrolyte_conc (16.7%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| cathode_thickness | 24 | 6927.5104 | 288.6463 | | |
| anode_thickness | 24 | 6927.5104 | 288.6463 | | |
| electrolyte_conc | 24 | 6927.5104 | 288.6463 | | |
| separator_porosity | 24 | 6927.5104 | 288.6463 | | |
| charge_rate | 24 | 6927.5104 | 288.6463 | | |
| tab_width | 24 | 6927.5104 | 288.6463 | | |
| Error | (Lenth | PSE) | 0 | 0.0000 | 0.0000 |
| Total | 24 | 6927.5104 | 288.6463 | | |
Response: power_density
Top factors: cathode_thickness (16.7%), anode_thickness (16.7%), electrolyte_conc (16.7%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| cathode_thickness | 24 | 194460.9600 | 8102.5400 | | |
| anode_thickness | 24 | 194460.9600 | 8102.5400 | | |
| electrolyte_conc | 24 | 194460.9600 | 8102.5400 | | |
| separator_porosity | 24 | 194460.9600 | 8102.5400 | | |
| charge_rate | 24 | 194460.9600 | 8102.5400 | | |
| tab_width | 24 | 194460.9600 | 8102.5400 | | |
| Error | (Lenth | PSE) | 0 | 0.0000 | 0.0000 |
| Total | 24 | 194460.9600 | 8102.5400 | | |
Response: cycle_life
Top factors: cathode_thickness (16.7%), anode_thickness (16.7%), electrolyte_conc (16.7%).
ANOVA
| Source | DF | SS | MS | F | p-value |
|---|
| Source | DF | SS | MS | F | p-value |
| cathode_thickness | 24 | 233929.0400 | 9747.0433 | | |
| anode_thickness | 24 | 233929.0400 | 9747.0433 | | |
| electrolyte_conc | 24 | 233929.0400 | 9747.0433 | | |
| separator_porosity | 24 | 233929.0400 | 9747.0433 | | |
| charge_rate | 24 | 233929.0400 | 9747.0433 | | |
| tab_width | 24 | 233929.0400 | 9747.0433 | | |
| Error | (Lenth | PSE) | 0 | 0.0000 | 0.0000 |
| Total | 24 | 233929.0400 | 9747.0433 | | |
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 = 0.6654
Per-Response Desirability
| Response | Weight | Desirability | Predicted | Dir |
|---|
energy_density |
2.0 |
|
227.40 0.6204 227.40 Wh/kg |
↑ |
power_density |
1.5 |
|
855.00 0.6281 855.00 W/kg |
↑ |
cycle_life |
1.0 |
|
1324.00 0.8350 1324.00 cycles |
↑ |
Recommended Settings
| Factor | Value |
|---|
cathode_thickness | 110.185 microns |
anode_thickness | 107.589 microns |
electrolyte_conc | 1.11796 M |
separator_porosity | 42.9632 % |
charge_rate | 0.76933 C |
tab_width | 16.3121 mm |
Source: from observed run #3
Trade-off Summary
Sacrifice = how much worse than single-objective best.
| Response | Predicted | Best Observed | Sacrifice |
|---|
power_density | 855.00 | 971.00 | +116.00 |
cycle_life | 1324.00 | 1382.00 | +58.00 |
Top 3 Runs by Desirability
| Run | D | Factor Settings |
|---|
| #17 | 0.5600 | cathode_thickness=77.7647, anode_thickness=108.475, electrolyte_conc=1.16541, separator_porosity=35.3078, charge_rate=2.25613, tab_width=17.5419 |
| #23 | 0.5552 | cathode_thickness=59.7391, anode_thickness=67.1751, electrolyte_conc=0.825034, separator_porosity=54.8962, charge_rate=2.04326, tab_width=25.4971 |
Model Quality
| Response | R² | Type |
|---|
power_density | 0.2234 | linear |
cycle_life | 0.2945 | linear |
Full Multi-Objective Output
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================
Overall desirability: D = 0.6654
Response Weight Desirability Predicted Direction
---------------------------------------------------------------------
energy_density 2.0 0.6204 227.40 Wh/kg ↑
power_density 1.5 0.6281 855.00 W/kg ↑
cycle_life 1.0 0.8350 1324.00 cycles ↑
Recommended settings:
cathode_thickness = 110.185 microns
anode_thickness = 107.589 microns
electrolyte_conc = 1.11796 M
separator_porosity = 42.9632 %
charge_rate = 0.76933 C
tab_width = 16.3121 mm
(from observed run #3)
Trade-off summary:
energy_density: 227.40 (best observed: 255.30, sacrifice: +27.90)
power_density: 855.00 (best observed: 971.00, sacrifice: +116.00)
cycle_life: 1324.00 (best observed: 1382.00, sacrifice: +58.00)
Model quality:
energy_density: R² = 0.1575 (linear)
power_density: R² = 0.2234 (linear)
cycle_life: R² = 0.2945 (linear)
Top 3 observed runs by overall desirability:
1. Run #3 (D=0.6654): cathode_thickness=110.185, anode_thickness=107.589, electrolyte_conc=1.11796, separator_porosity=42.9632, charge_rate=0.76933, tab_width=16.3121
2. Run #17 (D=0.5600): cathode_thickness=77.7647, anode_thickness=108.475, electrolyte_conc=1.16541, separator_porosity=35.3078, charge_rate=2.25613, tab_width=17.5419
3. Run #23 (D=0.5552): cathode_thickness=59.7391, anode_thickness=67.1751, electrolyte_conc=0.825034, separator_porosity=54.8962, charge_rate=2.04326, tab_width=25.4971
Full Analysis Output
=== Main Effects: energy_density ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
cathode_thickness 75.9000 3.3979 16.7%
anode_thickness 75.9000 3.3979 16.7%
electrolyte_conc 75.9000 3.3979 16.7%
separator_porosity 75.9000 3.3979 16.7%
charge_rate 75.9000 3.3979 16.7%
tab_width 75.9000 3.3979 16.7%
=== ANOVA Table: energy_density ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
cathode_thickness 24 6927.5104 288.6463
anode_thickness 24 6927.5104 288.6463
electrolyte_conc 24 6927.5104 288.6463
separator_porosity 24 6927.5104 288.6463
charge_rate 24 6927.5104 288.6463
tab_width 24 6927.5104 288.6463
Error (Lenth PSE) 0 0.0000 0.0000
Total 24 6927.5104 288.6463
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Summary Statistics: energy_density ===
cathode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
101.945 1 233.1000 0.0000 233.1000 233.1000
104.128 1 191.4000 0.0000 191.4000 191.4000
107.924 1 200.8000 0.0000 200.8000 200.8000
110.147 1 211.6000 0.0000 211.6000 211.6000
114.012 1 255.3000 0.0000 255.3000 255.3000
121.463 1 211.2000 0.0000 211.2000 211.2000
125.779 1 222.7000 0.0000 222.7000 222.7000
129.083 1 204.8000 0.0000 204.8000 204.8000
132.597 1 179.4000 0.0000 179.4000 179.4000
134.262 1 227.4000 0.0000 227.4000 227.4000
140.755 1 206.3000 0.0000 206.3000 206.3000
145.805 1 199.2000 0.0000 199.2000 199.2000
148.49 1 221.9000 0.0000 221.9000 221.9000
52.6869 1 238.7000 0.0000 238.7000 238.7000
54.9796 1 230.7000 0.0000 230.7000 230.7000
58.1205 1 224.6000 0.0000 224.6000 224.6000
64.6945 1 215.7000 0.0000 215.7000 215.7000
69.8719 1 207.4000 0.0000 207.4000 207.4000
71.7682 1 209.3000 0.0000 209.3000 209.3000
75.4959 1 217.2000 0.0000 217.2000 217.2000
81.3034 1 222.1000 0.0000 222.1000 222.1000
84.4992 1 238.1000 0.0000 238.1000 238.1000
89.4723 1 204.3000 0.0000 204.3000 204.3000
91.4428 1 228.2000 0.0000 228.2000 228.2000
95.1661 1 195.4000 0.0000 195.4000 195.4000
anode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
102.599 1 227.4000 0.0000 227.4000 227.4000
104.69 1 207.4000 0.0000 207.4000 207.4000
105.731 1 230.7000 0.0000 230.7000 230.7000
108.443 1 195.4000 0.0000 195.4000 195.4000
111.747 1 204.3000 0.0000 204.3000 204.3000
113.533 1 211.2000 0.0000 211.2000 211.2000
116.616 1 238.1000 0.0000 238.1000 238.1000
118.201 1 199.2000 0.0000 199.2000 199.2000
60.8803 1 222.7000 0.0000 222.7000 222.7000
64.566 1 221.9000 0.0000 221.9000 221.9000
65.5981 1 238.7000 0.0000 238.7000 238.7000
67.6709 1 222.1000 0.0000 222.1000 222.1000
70.3588 1 200.8000 0.0000 200.8000 200.8000
74.3687 1 228.2000 0.0000 228.2000 228.2000
75.044 1 255.3000 0.0000 255.3000 255.3000
77.5215 1 209.3000 0.0000 209.3000 209.3000
81.0621 1 179.4000 0.0000 179.4000 179.4000
82.2867 1 191.4000 0.0000 191.4000 191.4000
84.0577 1 215.7000 0.0000 215.7000 215.7000
88.3285 1 224.6000 0.0000 224.6000 224.6000
88.9839 1 233.1000 0.0000 233.1000 233.1000
91.578 1 217.2000 0.0000 217.2000 217.2000
95.6724 1 204.8000 0.0000 204.8000 204.8000
97.6982 1 211.6000 0.0000 211.6000 211.6000
98.8664 1 206.3000 0.0000 206.3000 206.3000
electrolyte_conc:
Level N Mean Std Min Max
------------------------------------------------------------
0.81439 1 211.6000 0.0000 211.6000 211.6000
0.835949 1 233.1000 0.0000 233.1000 233.1000
0.867617 1 209.3000 0.0000 209.3000 209.3000
0.885037 1 224.6000 0.0000 224.6000 224.6000
0.910813 1 204.3000 0.0000 204.3000 204.3000
0.935797 1 207.4000 0.0000 207.4000 207.4000
0.966078 1 206.3000 0.0000 206.3000 206.3000
0.989442 1 228.2000 0.0000 228.2000 228.2000
0.995181 1 199.2000 0.0000 199.2000 199.2000
1.02792 1 222.7000 0.0000 222.7000 222.7000
1.06198 1 191.4000 0.0000 191.4000 191.4000
1.06495 1 221.9000 0.0000 221.9000 221.9000
1.09841 1 230.7000 0.0000 230.7000 230.7000
1.12163 1 222.1000 0.0000 222.1000 222.1000
1.15496 1 215.7000 0.0000 215.7000 215.7000
1.16531 1 255.3000 0.0000 255.3000 255.3000
1.19262 1 179.4000 0.0000 179.4000 179.4000
1.23018 1 238.1000 0.0000 238.1000 238.1000
1.25453 1 217.2000 0.0000 217.2000 217.2000
1.26309 1 204.8000 0.0000 204.8000 204.8000
1.30056 1 227.4000 0.0000 227.4000 227.4000
1.31917 1 238.7000 0.0000 238.7000 238.7000
1.33021 1 211.2000 0.0000 211.2000 211.2000
1.37282 1 200.8000 0.0000 200.8000 200.8000
1.38618 1 195.4000 0.0000 195.4000 195.4000
separator_porosity:
Level N Mean Std Min Max
------------------------------------------------------------
30.4594 1 217.2000 0.0000 217.2000 217.2000
32.1551 1 204.8000 0.0000 204.8000 204.8000
32.7145 1 211.6000 0.0000 211.6000 211.6000
33.8144 1 215.7000 0.0000 215.7000 215.7000
35.462 1 207.4000 0.0000 207.4000 207.4000
36.7677 1 230.7000 0.0000 230.7000 230.7000
38.2884 1 222.7000 0.0000 222.7000 222.7000
38.5547 1 228.2000 0.0000 228.2000 228.2000
40.2264 1 255.3000 0.0000 255.3000 255.3000
41.7408 1 238.1000 0.0000 238.1000 238.1000
42.0792 1 221.9000 0.0000 221.9000 221.9000
43.4832 1 200.8000 0.0000 200.8000 200.8000
45.0759 1 238.7000 0.0000 238.7000 238.7000
46.6538 1 209.3000 0.0000 209.3000 209.3000
47.7108 1 233.1000 0.0000 233.1000 233.1000
49.0485 1 206.3000 0.0000 206.3000 206.3000
49.9953 1 191.4000 0.0000 191.4000 191.4000
50.9625 1 211.2000 0.0000 211.2000 211.2000
51.6122 1 227.4000 0.0000 227.4000 227.4000
53.4563 1 179.4000 0.0000 179.4000 179.4000
54.2869 1 224.6000 0.0000 224.6000 224.6000
55.7534 1 195.4000 0.0000 195.4000 195.4000
57.5345 1 199.2000 0.0000 199.2000 199.2000
57.8712 1 204.3000 0.0000 204.3000 204.3000
58.8055 1 222.1000 0.0000 222.1000 222.1000
charge_rate:
Level N Mean Std Min Max
------------------------------------------------------------
0.587906 1 191.4000 0.0000 191.4000 191.4000
0.667728 1 204.3000 0.0000 204.3000 204.3000
0.701019 1 207.4000 0.0000 207.4000 207.4000
0.837148 1 224.6000 0.0000 224.6000 224.6000
0.982648 1 211.6000 0.0000 211.6000 211.6000
1.06591 1 179.4000 0.0000 179.4000 179.4000
1.19896 1 227.4000 0.0000 227.4000 227.4000
1.25955 1 204.8000 0.0000 204.8000 204.8000
1.3484 1 230.7000 0.0000 230.7000 230.7000
1.4668 1 209.3000 0.0000 209.3000 209.3000
1.54127 1 228.2000 0.0000 228.2000 228.2000
1.65494 1 238.7000 0.0000 238.7000 238.7000
1.71733 1 222.1000 0.0000 222.1000 222.1000
1.89941 1 206.3000 0.0000 206.3000 206.3000
1.98213 1 238.1000 0.0000 238.1000 238.1000
2.0668 1 200.8000 0.0000 200.8000 200.8000
2.15137 1 211.2000 0.0000 211.2000 211.2000
2.21786 1 222.7000 0.0000 222.7000 222.7000
2.3565 1 221.9000 0.0000 221.9000 221.9000
2.4617 1 255.3000 0.0000 255.3000 255.3000
2.54543 1 199.2000 0.0000 199.2000 199.2000
2.66107 1 217.2000 0.0000 217.2000 217.2000
2.78239 1 195.4000 0.0000 195.4000 195.4000
2.82007 1 215.7000 0.0000 215.7000 215.7000
2.91173 1 233.1000 0.0000 233.1000 233.1000
tab_width:
Level N Mean Std Min Max
------------------------------------------------------------
10.0438 1 204.3000 0.0000 204.3000 204.3000
10.8683 1 238.1000 0.0000 238.1000 238.1000
12.3681 1 221.9000 0.0000 221.9000 221.9000
12.8326 1 227.4000 0.0000 227.4000 227.4000
13.8905 1 217.2000 0.0000 217.2000 217.2000
14.4394 1 200.8000 0.0000 200.8000 200.8000
15.0959 1 211.6000 0.0000 211.6000 211.6000
16.3318 1 255.3000 0.0000 255.3000 255.3000
16.7086 1 207.4000 0.0000 207.4000 207.4000
17.3556 1 228.2000 0.0000 228.2000 228.2000
18.4089 1 209.3000 0.0000 209.3000 209.3000
19.4251 1 222.1000 0.0000 222.1000 222.1000
20.1536 1 233.1000 0.0000 233.1000 233.1000
20.483 1 222.7000 0.0000 222.7000 222.7000
21.8578 1 199.2000 0.0000 199.2000 199.2000
22.3346 1 211.2000 0.0000 211.2000 211.2000
22.8207 1 230.7000 0.0000 230.7000 230.7000
23.9515 1 204.8000 0.0000 204.8000 204.8000
24.4401 1 191.4000 0.0000 191.4000 191.4000
25.997 1 179.4000 0.0000 179.4000 179.4000
26.7194 1 238.7000 0.0000 238.7000 238.7000
27.4 1 206.3000 0.0000 206.3000 206.3000
27.6967 1 224.6000 0.0000 224.6000 224.6000
28.8382 1 195.4000 0.0000 195.4000 195.4000
29.6107 1 215.7000 0.0000 215.7000 215.7000
=== Main Effects: power_density ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
cathode_thickness 323.0000 18.0028 16.7%
anode_thickness 323.0000 18.0028 16.7%
electrolyte_conc 323.0000 18.0028 16.7%
separator_porosity 323.0000 18.0028 16.7%
charge_rate 323.0000 18.0028 16.7%
tab_width 323.0000 18.0028 16.7%
=== ANOVA Table: power_density ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
cathode_thickness 24 194460.9600 8102.5400
anode_thickness 24 194460.9600 8102.5400
electrolyte_conc 24 194460.9600 8102.5400
separator_porosity 24 194460.9600 8102.5400
charge_rate 24 194460.9600 8102.5400
tab_width 24 194460.9600 8102.5400
Error (Lenth PSE) 0 0.0000 0.0000
Total 24 194460.9600 8102.5400
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Summary Statistics: power_density ===
cathode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
101.945 1 783.0000 0.0000 783.0000 783.0000
104.128 1 901.0000 0.0000 901.0000 901.0000
107.924 1 875.0000 0.0000 875.0000 875.0000
110.147 1 768.0000 0.0000 768.0000 768.0000
114.012 1 664.0000 0.0000 664.0000 664.0000
121.463 1 898.0000 0.0000 898.0000 898.0000
125.779 1 740.0000 0.0000 740.0000 740.0000
129.083 1 767.0000 0.0000 767.0000 767.0000
132.597 1 971.0000 0.0000 971.0000 971.0000
134.262 1 855.0000 0.0000 855.0000 855.0000
140.755 1 870.0000 0.0000 870.0000 870.0000
145.805 1 849.0000 0.0000 849.0000 849.0000
148.49 1 801.0000 0.0000 801.0000 801.0000
52.6869 1 654.0000 0.0000 654.0000 654.0000
54.9796 1 752.0000 0.0000 752.0000 752.0000
58.1205 1 648.0000 0.0000 648.0000 648.0000
64.6945 1 742.0000 0.0000 742.0000 742.0000
69.8719 1 778.0000 0.0000 778.0000 778.0000
71.7682 1 804.0000 0.0000 804.0000 804.0000
75.4959 1 877.0000 0.0000 877.0000 877.0000
81.3034 1 737.0000 0.0000 737.0000 737.0000
84.4992 1 687.0000 0.0000 687.0000 687.0000
89.4723 1 825.0000 0.0000 825.0000 825.0000
91.4428 1 690.0000 0.0000 690.0000 690.0000
95.1661 1 940.0000 0.0000 940.0000 940.0000
anode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
102.599 1 855.0000 0.0000 855.0000 855.0000
104.69 1 778.0000 0.0000 778.0000 778.0000
105.731 1 752.0000 0.0000 752.0000 752.0000
108.443 1 940.0000 0.0000 940.0000 940.0000
111.747 1 825.0000 0.0000 825.0000 825.0000
113.533 1 898.0000 0.0000 898.0000 898.0000
116.616 1 687.0000 0.0000 687.0000 687.0000
118.201 1 849.0000 0.0000 849.0000 849.0000
60.8803 1 740.0000 0.0000 740.0000 740.0000
64.566 1 801.0000 0.0000 801.0000 801.0000
65.5981 1 654.0000 0.0000 654.0000 654.0000
67.6709 1 737.0000 0.0000 737.0000 737.0000
70.3588 1 875.0000 0.0000 875.0000 875.0000
74.3687 1 690.0000 0.0000 690.0000 690.0000
75.044 1 664.0000 0.0000 664.0000 664.0000
77.5215 1 804.0000 0.0000 804.0000 804.0000
81.0621 1 971.0000 0.0000 971.0000 971.0000
82.2867 1 901.0000 0.0000 901.0000 901.0000
84.0577 1 742.0000 0.0000 742.0000 742.0000
88.3285 1 648.0000 0.0000 648.0000 648.0000
88.9839 1 783.0000 0.0000 783.0000 783.0000
91.578 1 877.0000 0.0000 877.0000 877.0000
95.6724 1 767.0000 0.0000 767.0000 767.0000
97.6982 1 768.0000 0.0000 768.0000 768.0000
98.8664 1 870.0000 0.0000 870.0000 870.0000
electrolyte_conc:
Level N Mean Std Min Max
------------------------------------------------------------
0.81439 1 768.0000 0.0000 768.0000 768.0000
0.835949 1 783.0000 0.0000 783.0000 783.0000
0.867617 1 804.0000 0.0000 804.0000 804.0000
0.885037 1 648.0000 0.0000 648.0000 648.0000
0.910813 1 825.0000 0.0000 825.0000 825.0000
0.935797 1 778.0000 0.0000 778.0000 778.0000
0.966078 1 870.0000 0.0000 870.0000 870.0000
0.989442 1 690.0000 0.0000 690.0000 690.0000
0.995181 1 849.0000 0.0000 849.0000 849.0000
1.02792 1 740.0000 0.0000 740.0000 740.0000
1.06198 1 901.0000 0.0000 901.0000 901.0000
1.06495 1 801.0000 0.0000 801.0000 801.0000
1.09841 1 752.0000 0.0000 752.0000 752.0000
1.12163 1 737.0000 0.0000 737.0000 737.0000
1.15496 1 742.0000 0.0000 742.0000 742.0000
1.16531 1 664.0000 0.0000 664.0000 664.0000
1.19262 1 971.0000 0.0000 971.0000 971.0000
1.23018 1 687.0000 0.0000 687.0000 687.0000
1.25453 1 877.0000 0.0000 877.0000 877.0000
1.26309 1 767.0000 0.0000 767.0000 767.0000
1.30056 1 855.0000 0.0000 855.0000 855.0000
1.31917 1 654.0000 0.0000 654.0000 654.0000
1.33021 1 898.0000 0.0000 898.0000 898.0000
1.37282 1 875.0000 0.0000 875.0000 875.0000
1.38618 1 940.0000 0.0000 940.0000 940.0000
separator_porosity:
Level N Mean Std Min Max
------------------------------------------------------------
30.4594 1 877.0000 0.0000 877.0000 877.0000
32.1551 1 767.0000 0.0000 767.0000 767.0000
32.7145 1 768.0000 0.0000 768.0000 768.0000
33.8144 1 742.0000 0.0000 742.0000 742.0000
35.462 1 778.0000 0.0000 778.0000 778.0000
36.7677 1 752.0000 0.0000 752.0000 752.0000
38.2884 1 740.0000 0.0000 740.0000 740.0000
38.5547 1 690.0000 0.0000 690.0000 690.0000
40.2264 1 664.0000 0.0000 664.0000 664.0000
41.7408 1 687.0000 0.0000 687.0000 687.0000
42.0792 1 801.0000 0.0000 801.0000 801.0000
43.4832 1 875.0000 0.0000 875.0000 875.0000
45.0759 1 654.0000 0.0000 654.0000 654.0000
46.6538 1 804.0000 0.0000 804.0000 804.0000
47.7108 1 783.0000 0.0000 783.0000 783.0000
49.0485 1 870.0000 0.0000 870.0000 870.0000
49.9953 1 901.0000 0.0000 901.0000 901.0000
50.9625 1 898.0000 0.0000 898.0000 898.0000
51.6122 1 855.0000 0.0000 855.0000 855.0000
53.4563 1 971.0000 0.0000 971.0000 971.0000
54.2869 1 648.0000 0.0000 648.0000 648.0000
55.7534 1 940.0000 0.0000 940.0000 940.0000
57.5345 1 849.0000 0.0000 849.0000 849.0000
57.8712 1 825.0000 0.0000 825.0000 825.0000
58.8055 1 737.0000 0.0000 737.0000 737.0000
charge_rate:
Level N Mean Std Min Max
------------------------------------------------------------
0.587906 1 901.0000 0.0000 901.0000 901.0000
0.667728 1 825.0000 0.0000 825.0000 825.0000
0.701019 1 778.0000 0.0000 778.0000 778.0000
0.837148 1 648.0000 0.0000 648.0000 648.0000
0.982648 1 768.0000 0.0000 768.0000 768.0000
1.06591 1 971.0000 0.0000 971.0000 971.0000
1.19896 1 855.0000 0.0000 855.0000 855.0000
1.25955 1 767.0000 0.0000 767.0000 767.0000
1.3484 1 752.0000 0.0000 752.0000 752.0000
1.4668 1 804.0000 0.0000 804.0000 804.0000
1.54127 1 690.0000 0.0000 690.0000 690.0000
1.65494 1 654.0000 0.0000 654.0000 654.0000
1.71733 1 737.0000 0.0000 737.0000 737.0000
1.89941 1 870.0000 0.0000 870.0000 870.0000
1.98213 1 687.0000 0.0000 687.0000 687.0000
2.0668 1 875.0000 0.0000 875.0000 875.0000
2.15137 1 898.0000 0.0000 898.0000 898.0000
2.21786 1 740.0000 0.0000 740.0000 740.0000
2.3565 1 801.0000 0.0000 801.0000 801.0000
2.4617 1 664.0000 0.0000 664.0000 664.0000
2.54543 1 849.0000 0.0000 849.0000 849.0000
2.66107 1 877.0000 0.0000 877.0000 877.0000
2.78239 1 940.0000 0.0000 940.0000 940.0000
2.82007 1 742.0000 0.0000 742.0000 742.0000
2.91173 1 783.0000 0.0000 783.0000 783.0000
tab_width:
Level N Mean Std Min Max
------------------------------------------------------------
10.0438 1 825.0000 0.0000 825.0000 825.0000
10.8683 1 687.0000 0.0000 687.0000 687.0000
12.3681 1 801.0000 0.0000 801.0000 801.0000
12.8326 1 855.0000 0.0000 855.0000 855.0000
13.8905 1 877.0000 0.0000 877.0000 877.0000
14.4394 1 875.0000 0.0000 875.0000 875.0000
15.0959 1 768.0000 0.0000 768.0000 768.0000
16.3318 1 664.0000 0.0000 664.0000 664.0000
16.7086 1 778.0000 0.0000 778.0000 778.0000
17.3556 1 690.0000 0.0000 690.0000 690.0000
18.4089 1 804.0000 0.0000 804.0000 804.0000
19.4251 1 737.0000 0.0000 737.0000 737.0000
20.1536 1 783.0000 0.0000 783.0000 783.0000
20.483 1 740.0000 0.0000 740.0000 740.0000
21.8578 1 849.0000 0.0000 849.0000 849.0000
22.3346 1 898.0000 0.0000 898.0000 898.0000
22.8207 1 752.0000 0.0000 752.0000 752.0000
23.9515 1 767.0000 0.0000 767.0000 767.0000
24.4401 1 901.0000 0.0000 901.0000 901.0000
25.997 1 971.0000 0.0000 971.0000 971.0000
26.7194 1 654.0000 0.0000 654.0000 654.0000
27.4 1 870.0000 0.0000 870.0000 870.0000
27.6967 1 648.0000 0.0000 648.0000 648.0000
28.8382 1 940.0000 0.0000 940.0000 940.0000
29.6107 1 742.0000 0.0000 742.0000 742.0000
=== Main Effects: cycle_life ===
Factor Effect Std Error % Contribution
--------------------------------------------------------------
cathode_thickness 441.0000 19.7454 16.7%
anode_thickness 441.0000 19.7454 16.7%
electrolyte_conc 441.0000 19.7454 16.7%
separator_porosity 441.0000 19.7454 16.7%
charge_rate 441.0000 19.7454 16.7%
tab_width 441.0000 19.7454 16.7%
=== ANOVA Table: cycle_life ===
Source DF SS MS F p-value
-----------------------------------------------------------------------------
cathode_thickness 24 233929.0400 9747.0433
anode_thickness 24 233929.0400 9747.0433
electrolyte_conc 24 233929.0400 9747.0433
separator_porosity 24 233929.0400 9747.0433
charge_rate 24 233929.0400 9747.0433
tab_width 24 233929.0400 9747.0433
Error (Lenth PSE) 0 0.0000 0.0000
Total 24 233929.0400 9747.0433
Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design)
=== Summary Statistics: cycle_life ===
cathode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
101.945 1 941.0000 0.0000 941.0000 941.0000
104.128 1 1103.0000 0.0000 1103.0000 1103.0000
107.924 1 1092.0000 0.0000 1092.0000 1092.0000
110.147 1 1023.0000 0.0000 1023.0000 1023.0000
114.012 1 1217.0000 0.0000 1217.0000 1217.0000
121.463 1 1222.0000 0.0000 1222.0000 1222.0000
125.779 1 1126.0000 0.0000 1126.0000 1126.0000
129.083 1 1180.0000 0.0000 1180.0000 1180.0000
132.597 1 1310.0000 0.0000 1310.0000 1310.0000
134.262 1 1324.0000 0.0000 1324.0000 1324.0000
140.755 1 1382.0000 0.0000 1382.0000 1382.0000
145.805 1 1082.0000 0.0000 1082.0000 1082.0000
148.49 1 1070.0000 0.0000 1070.0000 1070.0000
52.6869 1 1214.0000 0.0000 1214.0000 1214.0000
54.9796 1 1197.0000 0.0000 1197.0000 1197.0000
58.1205 1 1111.0000 0.0000 1111.0000 1111.0000
64.6945 1 1207.0000 0.0000 1207.0000 1207.0000
69.8719 1 1096.0000 0.0000 1096.0000 1096.0000
71.7682 1 1187.0000 0.0000 1187.0000 1187.0000
75.4959 1 1033.0000 0.0000 1033.0000 1033.0000
81.3034 1 1177.0000 0.0000 1177.0000 1177.0000
84.4992 1 1172.0000 0.0000 1172.0000 1172.0000
89.4723 1 1212.0000 0.0000 1212.0000 1212.0000
91.4428 1 1174.0000 0.0000 1174.0000 1174.0000
95.1661 1 1230.0000 0.0000 1230.0000 1230.0000
anode_thickness:
Level N Mean Std Min Max
------------------------------------------------------------
102.599 1 1324.0000 0.0000 1324.0000 1324.0000
104.69 1 1096.0000 0.0000 1096.0000 1096.0000
105.731 1 1197.0000 0.0000 1197.0000 1197.0000
108.443 1 1230.0000 0.0000 1230.0000 1230.0000
111.747 1 1212.0000 0.0000 1212.0000 1212.0000
113.533 1 1222.0000 0.0000 1222.0000 1222.0000
116.616 1 1172.0000 0.0000 1172.0000 1172.0000
118.201 1 1082.0000 0.0000 1082.0000 1082.0000
60.8803 1 1126.0000 0.0000 1126.0000 1126.0000
64.566 1 1070.0000 0.0000 1070.0000 1070.0000
65.5981 1 1214.0000 0.0000 1214.0000 1214.0000
67.6709 1 1177.0000 0.0000 1177.0000 1177.0000
70.3588 1 1092.0000 0.0000 1092.0000 1092.0000
74.3687 1 1174.0000 0.0000 1174.0000 1174.0000
75.044 1 1217.0000 0.0000 1217.0000 1217.0000
77.5215 1 1187.0000 0.0000 1187.0000 1187.0000
81.0621 1 1310.0000 0.0000 1310.0000 1310.0000
82.2867 1 1103.0000 0.0000 1103.0000 1103.0000
84.0577 1 1207.0000 0.0000 1207.0000 1207.0000
88.3285 1 1111.0000 0.0000 1111.0000 1111.0000
88.9839 1 941.0000 0.0000 941.0000 941.0000
91.578 1 1033.0000 0.0000 1033.0000 1033.0000
95.6724 1 1180.0000 0.0000 1180.0000 1180.0000
97.6982 1 1023.0000 0.0000 1023.0000 1023.0000
98.8664 1 1382.0000 0.0000 1382.0000 1382.0000
electrolyte_conc:
Level N Mean Std Min Max
------------------------------------------------------------
0.81439 1 1023.0000 0.0000 1023.0000 1023.0000
0.835949 1 941.0000 0.0000 941.0000 941.0000
0.867617 1 1187.0000 0.0000 1187.0000 1187.0000
0.885037 1 1111.0000 0.0000 1111.0000 1111.0000
0.910813 1 1212.0000 0.0000 1212.0000 1212.0000
0.935797 1 1096.0000 0.0000 1096.0000 1096.0000
0.966078 1 1382.0000 0.0000 1382.0000 1382.0000
0.989442 1 1174.0000 0.0000 1174.0000 1174.0000
0.995181 1 1082.0000 0.0000 1082.0000 1082.0000
1.02792 1 1126.0000 0.0000 1126.0000 1126.0000
1.06198 1 1103.0000 0.0000 1103.0000 1103.0000
1.06495 1 1070.0000 0.0000 1070.0000 1070.0000
1.09841 1 1197.0000 0.0000 1197.0000 1197.0000
1.12163 1 1177.0000 0.0000 1177.0000 1177.0000
1.15496 1 1207.0000 0.0000 1207.0000 1207.0000
1.16531 1 1217.0000 0.0000 1217.0000 1217.0000
1.19262 1 1310.0000 0.0000 1310.0000 1310.0000
1.23018 1 1172.0000 0.0000 1172.0000 1172.0000
1.25453 1 1033.0000 0.0000 1033.0000 1033.0000
1.26309 1 1180.0000 0.0000 1180.0000 1180.0000
1.30056 1 1324.0000 0.0000 1324.0000 1324.0000
1.31917 1 1214.0000 0.0000 1214.0000 1214.0000
1.33021 1 1222.0000 0.0000 1222.0000 1222.0000
1.37282 1 1092.0000 0.0000 1092.0000 1092.0000
1.38618 1 1230.0000 0.0000 1230.0000 1230.0000
separator_porosity:
Level N Mean Std Min Max
------------------------------------------------------------
30.4594 1 1033.0000 0.0000 1033.0000 1033.0000
32.1551 1 1180.0000 0.0000 1180.0000 1180.0000
32.7145 1 1023.0000 0.0000 1023.0000 1023.0000
33.8144 1 1207.0000 0.0000 1207.0000 1207.0000
35.462 1 1096.0000 0.0000 1096.0000 1096.0000
36.7677 1 1197.0000 0.0000 1197.0000 1197.0000
38.2884 1 1126.0000 0.0000 1126.0000 1126.0000
38.5547 1 1174.0000 0.0000 1174.0000 1174.0000
40.2264 1 1217.0000 0.0000 1217.0000 1217.0000
41.7408 1 1172.0000 0.0000 1172.0000 1172.0000
42.0792 1 1070.0000 0.0000 1070.0000 1070.0000
43.4832 1 1092.0000 0.0000 1092.0000 1092.0000
45.0759 1 1214.0000 0.0000 1214.0000 1214.0000
46.6538 1 1187.0000 0.0000 1187.0000 1187.0000
47.7108 1 941.0000 0.0000 941.0000 941.0000
49.0485 1 1382.0000 0.0000 1382.0000 1382.0000
49.9953 1 1103.0000 0.0000 1103.0000 1103.0000
50.9625 1 1222.0000 0.0000 1222.0000 1222.0000
51.6122 1 1324.0000 0.0000 1324.0000 1324.0000
53.4563 1 1310.0000 0.0000 1310.0000 1310.0000
54.2869 1 1111.0000 0.0000 1111.0000 1111.0000
55.7534 1 1230.0000 0.0000 1230.0000 1230.0000
57.5345 1 1082.0000 0.0000 1082.0000 1082.0000
57.8712 1 1212.0000 0.0000 1212.0000 1212.0000
58.8055 1 1177.0000 0.0000 1177.0000 1177.0000
charge_rate:
Level N Mean Std Min Max
------------------------------------------------------------
0.587906 1 1103.0000 0.0000 1103.0000 1103.0000
0.667728 1 1212.0000 0.0000 1212.0000 1212.0000
0.701019 1 1096.0000 0.0000 1096.0000 1096.0000
0.837148 1 1111.0000 0.0000 1111.0000 1111.0000
0.982648 1 1023.0000 0.0000 1023.0000 1023.0000
1.06591 1 1310.0000 0.0000 1310.0000 1310.0000
1.19896 1 1324.0000 0.0000 1324.0000 1324.0000
1.25955 1 1180.0000 0.0000 1180.0000 1180.0000
1.3484 1 1197.0000 0.0000 1197.0000 1197.0000
1.4668 1 1187.0000 0.0000 1187.0000 1187.0000
1.54127 1 1174.0000 0.0000 1174.0000 1174.0000
1.65494 1 1214.0000 0.0000 1214.0000 1214.0000
1.71733 1 1177.0000 0.0000 1177.0000 1177.0000
1.89941 1 1382.0000 0.0000 1382.0000 1382.0000
1.98213 1 1172.0000 0.0000 1172.0000 1172.0000
2.0668 1 1092.0000 0.0000 1092.0000 1092.0000
2.15137 1 1222.0000 0.0000 1222.0000 1222.0000
2.21786 1 1126.0000 0.0000 1126.0000 1126.0000
2.3565 1 1070.0000 0.0000 1070.0000 1070.0000
2.4617 1 1217.0000 0.0000 1217.0000 1217.0000
2.54543 1 1082.0000 0.0000 1082.0000 1082.0000
2.66107 1 1033.0000 0.0000 1033.0000 1033.0000
2.78239 1 1230.0000 0.0000 1230.0000 1230.0000
2.82007 1 1207.0000 0.0000 1207.0000 1207.0000
2.91173 1 941.0000 0.0000 941.0000 941.0000
tab_width:
Level N Mean Std Min Max
------------------------------------------------------------
10.0438 1 1212.0000 0.0000 1212.0000 1212.0000
10.8683 1 1172.0000 0.0000 1172.0000 1172.0000
12.3681 1 1070.0000 0.0000 1070.0000 1070.0000
12.8326 1 1324.0000 0.0000 1324.0000 1324.0000
13.8905 1 1033.0000 0.0000 1033.0000 1033.0000
14.4394 1 1092.0000 0.0000 1092.0000 1092.0000
15.0959 1 1023.0000 0.0000 1023.0000 1023.0000
16.3318 1 1217.0000 0.0000 1217.0000 1217.0000
16.7086 1 1096.0000 0.0000 1096.0000 1096.0000
17.3556 1 1174.0000 0.0000 1174.0000 1174.0000
18.4089 1 1187.0000 0.0000 1187.0000 1187.0000
19.4251 1 1177.0000 0.0000 1177.0000 1177.0000
20.1536 1 941.0000 0.0000 941.0000 941.0000
20.483 1 1126.0000 0.0000 1126.0000 1126.0000
21.8578 1 1082.0000 0.0000 1082.0000 1082.0000
22.3346 1 1222.0000 0.0000 1222.0000 1222.0000
22.8207 1 1197.0000 0.0000 1197.0000 1197.0000
23.9515 1 1180.0000 0.0000 1180.0000 1180.0000
24.4401 1 1103.0000 0.0000 1103.0000 1103.0000
25.997 1 1310.0000 0.0000 1310.0000 1310.0000
26.7194 1 1214.0000 0.0000 1214.0000 1214.0000
27.4 1 1382.0000 0.0000 1382.0000 1382.0000
27.6967 1 1111.0000 0.0000 1111.0000 1111.0000
28.8382 1 1230.0000 0.0000 1230.0000 1230.0000
29.6107 1 1207.0000 0.0000 1207.0000 1207.0000
Optimization Recommendations
=== Optimization: energy_density ===
Direction: maximize
Best observed run: #5
cathode_thickness = 88.666
anode_thickness = 64.4416
electrolyte_conc = 1.10351
separator_porosity = 46.9964
charge_rate = 0.639737
tab_width = 28.2564
Value: 255.3
RSM Model (linear, R² = 0.2860, Adj R² = 0.0481):
Coefficients:
intercept +215.8525
cathode_thickness +4.0792
anode_thickness -14.8355
electrolyte_conc +0.7390
separator_porosity -0.9970
charge_rate -4.0448
tab_width +8.9658
Predicted optimum (from linear model, at observed points):
cathode_thickness = 88.666
anode_thickness = 64.4416
electrolyte_conc = 1.10351
separator_porosity = 46.9964
charge_rate = 0.639737
tab_width = 28.2564
Predicted value: 238.4380
Surface optimum (via L-BFGS-B, linear model):
cathode_thickness = 150
anode_thickness = 60
electrolyte_conc = 1.4
separator_porosity = 30
charge_rate = 0.5
tab_width = 30
Predicted value: 249.5139
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. cathode_thickness (effect: 75.9, contribution: 16.7%)
2. anode_thickness (effect: 75.9, contribution: 16.7%)
3. electrolyte_conc (effect: 75.9, contribution: 16.7%)
4. separator_porosity (effect: 75.9, contribution: 16.7%)
5. charge_rate (effect: 75.9, contribution: 16.7%)
6. tab_width (effect: 75.9, contribution: 16.7%)
=== Optimization: power_density ===
Direction: maximize
Best observed run: #4
cathode_thickness = 141.048
anode_thickness = 117.242
electrolyte_conc = 0.882444
separator_porosity = 36.4421
charge_rate = 1.10899
tab_width = 16.6578
Value: 971.0
RSM Model (linear, R² = 0.2211, Adj R² = -0.0385):
Coefficients:
intercept +795.2392
cathode_thickness -20.9859
anode_thickness +66.8319
electrolyte_conc -20.7625
separator_porosity +5.9211
charge_rate +6.3785
tab_width -34.6966
Predicted optimum (from linear model, at observed points):
cathode_thickness = 64.2473
anode_thickness = 119.509
electrolyte_conc = 0.80979
separator_porosity = 39.8316
charge_rate = 1.97884
tab_width = 23.9888
Predicted value: 881.3562
Surface optimum (via L-BFGS-B, linear model):
cathode_thickness = 50
anode_thickness = 120
electrolyte_conc = 0.8
separator_porosity = 60
charge_rate = 3
tab_width = 10
Predicted value: 950.8157
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. cathode_thickness (effect: 323.0, contribution: 16.7%)
2. anode_thickness (effect: 323.0, contribution: 16.7%)
3. electrolyte_conc (effect: 323.0, contribution: 16.7%)
4. separator_porosity (effect: 323.0, contribution: 16.7%)
5. charge_rate (effect: 323.0, contribution: 16.7%)
6. tab_width (effect: 323.0, contribution: 16.7%)
=== Optimization: cycle_life ===
Direction: maximize
Best observed run: #23
cathode_thickness = 58.8445
anode_thickness = 89.643
electrolyte_conc = 1.32052
separator_porosity = 50.3057
charge_rate = 0.5277
tab_width = 15.5953
Value: 1382.0
RSM Model (linear, R² = 0.1000, Adj R² = -0.2000):
Coefficients:
intercept +1162.8599
cathode_thickness -21.5127
anode_thickness -30.4352
electrolyte_conc +26.8319
separator_porosity -44.0003
charge_rate -9.0494
tab_width +9.9244
Predicted optimum (from linear model, at observed points):
cathode_thickness = 95.3714
anode_thickness = 65.0499
electrolyte_conc = 1.06097
separator_porosity = 31.7734
charge_rate = 1.65711
tab_width = 17.4315
Predicted value: 1223.5942
Surface optimum (via L-BFGS-B, linear model):
cathode_thickness = 50
anode_thickness = 60
electrolyte_conc = 1.4
separator_porosity = 30
charge_rate = 0.5
tab_width = 30
Predicted value: 1304.6137
Model quality: Weak fit — consider adding center points or using a different design.
Factor importance:
1. cathode_thickness (effect: 441.0, contribution: 16.7%)
2. anode_thickness (effect: 441.0, contribution: 16.7%)
3. electrolyte_conc (effect: 441.0, contribution: 16.7%)
4. separator_porosity (effect: 441.0, contribution: 16.7%)
5. charge_rate (effect: 441.0, contribution: 16.7%)
6. tab_width (effect: 441.0, contribution: 16.7%)