Concrete Admixture Blend Optimization

{ "metadata": { "name": "Concrete Admixture Blend Optimization", "description": "Mixture simplex lattice design for supplementary cementitious material proportions" }, "factors": [ { "name": "fly_ash", "levels": [ "0", "100" ], "type": "continuous", "unit": "%" }, { "name": "silica_fume", "levels": [ "0", "100" ], "type": "continuous", "unit": "%" }, { "name": "slag", "levels": [ "0", "100" ], "type": "continuous", "unit": "%" } ], "fixed_factors": { "cement_base": "350 kg/m3", "water_cement_ratio": "0.45" }, "responses": [ { "name": "compressive_strength_28d", "optimize": "maximize", "unit": "MPa" }, { "name": "workability", "optimize": "maximize", "unit": "mm_slump" } ], "settings": { "operation": "mixture_simplex_lattice", "test_script": "use_cases/304_concrete_admixture_blend/sim.sh" } }

============================================================ MULTI-OBJECTIVE OPTIMIZATION Method: Derringer-Suich Desirability Function ============================================================ Overall desirability: D = 0.9338 Response Weight Desirability Predicted Direction --------------------------------------------------------------------- compressive_strength_28d 2.0 1.0000 67.08 MPa ↑ workability 1.0 0.8142 172.13 mm_slump ↑ Recommended settings: fly_ash = 0 % silica_fume = 0 % slag = 0 % (from RSM model prediction) Trade-off summary: compressive_strength_28d: 67.08 (best observed: 51.40, sacrifice: -15.68) workability: 172.13 (best observed: 156.20, sacrifice: -15.93) Model quality: compressive_strength_28d: R² = 0.0253 (linear) workability: R² = 0.1187 (linear) Top 3 observed runs by overall desirability: 1. Run #4 (D=0.5283): fly_ash=0, silica_fume=0, slag=100 2. Run #3 (D=0.5254): fly_ash=0, silica_fume=50, slag=50 3. Run #6 (D=0.5098): fly_ash=50, silica_fume=50, slag=0

=== Main Effects: compressive_strength_28d === Factor Effect Std Error % Contribution -------------------------------------------------------------- silica_fume 9.9333 2.2248 55.5% fly_ash 4.4333 2.2248 24.8% slag 3.5333 2.2248 19.7% === ANOVA Table: compressive_strength_28d === Source DF SS MS F p-value ----------------------------------------------------------------------------- fly_ash 2 16.7417 8.3708 silica_fume 2 120.7017 60.3508 slag 2 17.7417 8.8708 Error (Lenth PSE) 0 0.0000 0.0000 Total 5 148.4883 29.6977 Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design) === Summary Statistics: compressive_strength_28d === fly_ash: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 46.2333 3.1021 43.2000 49.4000 100 1 41.8000 0.0000 41.8000 41.8000 50 2 43.9000 10.6066 36.4000 51.4000 silica_fume: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 40.4667 3.5907 36.4000 43.2000 100 1 46.1000 0.0000 46.1000 46.1000 50 2 50.4000 1.4142 49.4000 51.4000 slag: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 46.4333 4.8087 41.8000 51.4000 100 1 43.2000 0.0000 43.2000 43.2000 50 2 42.9000 9.1924 36.4000 49.4000 === Main Effects: workability === Factor Effect Std Error % Contribution -------------------------------------------------------------- silica_fume 60.0667 13.5186 50.5% fly_ash 37.4667 13.5186 31.5% slag 21.4167 13.5186 18.0% === ANOVA Table: workability === Source DF SS MS F p-value ----------------------------------------------------------------------------- fly_ash 2 1081.6433 540.8217 silica_fume 2 4530.8483 2265.4242 slag 2 642.2833 321.1417 Error (Lenth PSE) 0 0.0000 0.0000 Total 5 5482.5750 1096.5150 Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design) === Summary Statistics: workability === fly_ash: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 106.9333 14.6889 95.5000 123.5000 100 1 144.4000 0.0000 144.4000 144.4000 50 2 111.6500 63.0032 67.1000 156.2000 silica_fume: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 141.3667 16.5597 123.5000 156.2000 100 1 101.8000 0.0000 101.8000 101.8000 50 2 81.3000 20.0818 67.1000 95.5000 slag: Level N Mean Std Min Max ------------------------------------------------------------ 0 3 104.4333 38.7172 67.1000 144.4000 100 1 123.5000 0.0000 123.5000 123.5000 50 2 125.8500 42.9214 95.5000 156.2000

=== Optimization: compressive_strength_28d === Direction: maximize Best observed run: #1 fly_ash = 50 silica_fume = 0 slag = 50 Value: 51.4 RSM Model (linear, R² = 0.7886, Adj R² = 0.4715): Coefficients: intercept +33.5375 fly_ash -11.3125 silica_fume -14.5325 slag -7.6925 Predicted optimum (from linear model, at observed points): fly_ash = 0 silica_fume = 0 slag = 100 Predicted value: 51.6900 Surface optimum (via L-BFGS-B, linear model): fly_ash = 0 silica_fume = 0 slag = 0 Predicted value: 67.0750 Model quality: Good fit — general trends are captured, some noise remains. Factor importance: 1. silica_fume (effect: 11.1, contribution: 43.5%) 2. slag (effect: 8.9, contribution: 34.9%) 3. fly_ash (effect: 5.5, contribution: 21.5%) === Optimization: workability === Direction: maximize Best observed run: #5 fly_ash = 0 silica_fume = 100 slag = 0 Value: 156.2 RSM Model (linear, R² = 0.5994, Adj R² = -0.0016): Coefficients: intercept +86.0625 fly_ash -24.6075 silica_fume -12.9475 slag -48.5075 Predicted optimum (from linear model, at observed points): fly_ash = 0 silica_fume = 100 slag = 0 Predicted value: 146.2300 Surface optimum (via L-BFGS-B, linear model): fly_ash = 0 silica_fume = 0 slag = 0 Predicted value: 172.1250 Model quality: Moderate fit — use predictions directionally, not precisely. Factor importance: 1. slag (effect: 56.9, contribution: 35.6%) 2. silica_fume (effect: 53.9, contribution: 33.7%) 3. fly_ash (effect: 49.1, contribution: 30.7%)