Wastewater Treatment Optimization

{ "metadata": { "name": "Wastewater Treatment Optimization", "description": "Plackett-Burman screening of 7 factors (5 continuous, 2 ordinal) for BOD removal and sludge volume in wastewater treatment" }, "factors": [ { "name": "ph_level", "levels": [ "6", "9" ], "type": "continuous", "unit": "pH" }, { "name": "retention_time", "levels": [ "4", "12" ], "type": "continuous", "unit": "hours" }, { "name": "aeration_rate", "levels": [ "2", "6" ], "type": "continuous", "unit": "L/min" }, { "name": "flocculant_dose", "levels": [ "10", "50" ], "type": "continuous", "unit": "mg/L" }, { "name": "temperature", "levels": [ "15", "30" ], "type": "continuous", "unit": "C" }, { "name": "mixing_intensity", "levels": [ "low", "high" ], "type": "ordinal", "unit": "" }, { "name": "filter_grade", "levels": [ "coarse", "fine" ], "type": "ordinal", "unit": "" } ], "fixed_factors": { "plant_capacity": "10000 m3/day" }, "responses": [ { "name": "bod_removal", "optimize": "maximize", "unit": "%" }, { "name": "sludge_volume", "optimize": "minimize", "unit": "mL/L" } ], "settings": { "operation": "plackett_burman", "test_script": "use_cases/309_wastewater_treatment/sim.sh" } }

============================================================ MULTI-OBJECTIVE OPTIMIZATION Method: Derringer-Suich Desirability Function ============================================================ Overall desirability: D = 0.6791 Response Weight Desirability Predicted Direction --------------------------------------------------------------------- bod_removal 2.0 0.7253 91.31 % ↑ sludge_volume 1.0 0.5952 136.59 mL/L ↓ Recommended settings: ph_level = 6.236 pH retention_time = 4.875 hours aeration_rate = 5.735 L/min flocculant_dose = 16.37 mg/L temperature = 17.96 C mixing_intensity = low filter_grade = coarse (from RSM model prediction) Trade-off summary: bod_removal: 91.31 (best observed: 96.00, sacrifice: +4.69) sludge_volume: 136.59 (best observed: 86.00, sacrifice: +50.59) Model quality: bod_removal: R² = 1.0000 (linear) sludge_volume: R² = 1.0000 (linear) Top 3 observed runs by overall desirability: 1. Run #5 (D=0.5587): ph_level=9, retention_time=12, aeration_rate=6, flocculant_dose=10, temperature=15, mixing_intensity=low, filter_grade=coarse 2. Run #4 (D=0.4636): ph_level=6, retention_time=4, aeration_rate=6, flocculant_dose=10, temperature=30, mixing_intensity=high, filter_grade=coarse 3. Run #2 (D=0.4207): ph_level=6, retention_time=4, aeration_rate=6, flocculant_dose=50, temperature=15, mixing_intensity=low, filter_grade=fine

=== Main Effects: bod_removal === Factor Effect Std Error % Contribution -------------------------------------------------------------- ph_level 7.4250 2.0251 30.0% flocculant_dose 3.9750 2.0251 16.0% mixing_intensity 3.8750 2.0251 15.6% temperature 3.6750 2.0251 14.8% aeration_rate -3.3250 2.0251 13.4% retention_time 2.0250 2.0251 8.2% filter_grade -0.4750 2.0251 1.9% === ANOVA Table: bod_removal === Source DF SS MS F p-value ----------------------------------------------------------------------------- ph_level 1 110.2612 110.2612 2.993 0.1177 retention_time 1 8.2013 8.2013 0.223 0.6483 aeration_rate 1 22.1113 22.1113 0.600 0.4584 flocculant_dose 1 31.6012 31.6012 0.858 0.3785 temperature 1 27.0112 27.0112 0.733 0.4141 mixing_intensity 1 30.0312 30.0312 0.815 0.3901 filter_grade 1 0.4512 0.4512 0.012 0.9143 ph_level*retention_time 1 22.1113 22.1113 0.600 0.4584 ph_level*aeration_rate 1 8.2013 8.2013 0.223 0.6483 ph_level*flocculant_dose 1 27.0113 27.0113 0.733 0.4141 ph_level*temperature 1 31.6013 31.6013 0.858 0.3785 ph_level*mixing_intensity 1 0.4513 0.4513 0.012 0.9143 ph_level*filter_grade 1 30.0313 30.0313 0.815 0.3901 retention_time*aeration_rate 1 110.2612 110.2612 2.993 0.1177 retention_time*flocculant_dose 1 30.0312 30.0312 0.815 0.3901 retention_time*temperature 1 0.4513 0.4513 0.012 0.9143 retention_time*mixing_intensity 1 31.6012 31.6012 0.858 0.3785 retention_time*filter_grade 1 27.0112 27.0112 0.733 0.4141 aeration_rate*flocculant_dose 1 0.4513 0.4513 0.012 0.9143 aeration_rate*temperature 1 30.0313 30.0313 0.815 0.3901 aeration_rate*mixing_intensity 1 27.0112 27.0112 0.733 0.4141 aeration_rate*filter_grade 1 31.6012 31.6012 0.858 0.3785 flocculant_dose*temperature 1 110.2613 110.2613 2.993 0.1177 flocculant_dose*mixing_intensity 1 8.2013 8.2013 0.223 0.6483 flocculant_dose*filter_grade 1 22.1113 22.1113 0.600 0.4584 temperature*mixing_intensity 1 22.1113 22.1113 0.600 0.4584 temperature*filter_grade 1 8.2013 8.2013 0.223 0.6483 mixing_intensity*filter_grade 1 110.2613 110.2613 2.993 0.1177 Error (Lenth PSE) 9 331.5769 36.8419 Total 7 229.6687 32.8098 Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design) === Interaction Effects: bod_removal === Factor A Factor B Interaction % Contribution ------------------------------------------------------------------------ retention_time aeration_rate -7.4250 10.0% flocculant_dose temperature 7.4250 10.0% mixing_intensity filter_grade -7.4250 10.0% ph_level temperature 3.9750 5.3% retention_time mixing_intensity 3.9750 5.3% aeration_rate filter_grade 3.9750 5.3% ph_level filter_grade -3.8750 5.2% retention_time flocculant_dose 3.8750 5.2% aeration_rate temperature -3.8750 5.2% ph_level flocculant_dose 3.6750 4.9% retention_time filter_grade -3.6750 4.9% aeration_rate mixing_intensity -3.6750 4.9% ph_level retention_time 3.3250 4.5% flocculant_dose filter_grade -3.3250 4.5% temperature mixing_intensity 3.3250 4.5% ph_level aeration_rate -2.0250 2.7% flocculant_dose mixing_intensity 2.0250 2.7% temperature filter_grade -2.0250 2.7% ph_level mixing_intensity 0.4750 0.6% retention_time temperature 0.4750 0.6% aeration_rate flocculant_dose -0.4750 0.6% === Summary Statistics: bod_removal === ph_level: Level N Mean Std Min Max ------------------------------------------------------------ 6 4 79.9000 2.1087 77.4000 82.1000 9 4 87.3250 5.9461 83.0000 96.0000 retention_time: Level N Mean Std Min Max ------------------------------------------------------------ 12 4 82.6000 3.0033 79.0000 86.3000 4 4 84.6250 8.0500 77.4000 96.0000 aeration_rate: Level N Mean Std Min Max ------------------------------------------------------------ 2 4 85.2750 7.4410 79.0000 96.0000 6 4 81.9500 3.7171 77.4000 86.3000 flocculant_dose: Level N Mean Std Min Max ------------------------------------------------------------ 10 4 81.6250 2.9216 77.4000 84.0000 50 4 85.6000 7.5820 79.0000 96.0000 temperature: Level N Mean Std Min Max ------------------------------------------------------------ 15 4 81.7750 2.2066 79.0000 84.0000 30 4 85.4500 7.9173 77.4000 96.0000 mixing_intensity: Level N Mean Std Min Max ------------------------------------------------------------ high 4 81.6750 4.1724 77.4000 86.3000 low 4 85.5500 7.0098 81.1000 96.0000 filter_grade: Level N Mean Std Min Max ------------------------------------------------------------ coarse 4 83.8500 8.4354 77.4000 96.0000 fine 4 83.3750 2.2911 81.1000 86.3000 === Main Effects: sludge_volume === Factor Effect Std Error % Contribution -------------------------------------------------------------- aeration_rate -57.0000 15.0330 40.0% mixing_intensity 52.5000 15.0330 36.8% retention_time -14.0000 15.0330 9.8% flocculant_dose 9.0000 15.0330 6.3% temperature 5.0000 15.0330 3.5% filter_grade 4.5000 15.0330 3.2% ph_level 0.5000 15.0330 0.4% === ANOVA Table: sludge_volume === Source DF SS MS F p-value ----------------------------------------------------------------------------- ph_level 1 0.5000 0.5000 0.007 0.9367 retention_time 1 392.0000 392.0000 5.227 0.0481 aeration_rate 1 6498.0000 6498.0000 86.640 0.0000 flocculant_dose 1 162.0000 162.0000 2.160 0.1757 temperature 1 50.0000 50.0000 0.667 0.4353 mixing_intensity 1 5512.5000 5512.5000 73.500 0.0000 filter_grade 1 40.5000 40.5000 0.540 0.4811 ph_level*retention_time 1 6498.0000 6498.0000 86.640 0.0000 ph_level*aeration_rate 1 392.0000 392.0000 5.227 0.0481 ph_level*flocculant_dose 1 50.0000 50.0000 0.667 0.4353 ph_level*temperature 1 162.0000 162.0000 2.160 0.1757 ph_level*mixing_intensity 1 40.5000 40.5000 0.540 0.4811 ph_level*filter_grade 1 5512.5000 5512.5000 73.500 0.0000 retention_time*aeration_rate 1 0.5000 0.5000 0.007 0.9367 retention_time*flocculant_dose 1 5512.5000 5512.5000 73.500 0.0000 retention_time*temperature 1 40.5000 40.5000 0.540 0.4811 retention_time*mixing_intensity 1 162.0000 162.0000 2.160 0.1757 retention_time*filter_grade 1 50.0000 50.0000 0.667 0.4353 aeration_rate*flocculant_dose 1 40.5000 40.5000 0.540 0.4811 aeration_rate*temperature 1 5512.5000 5512.5000 73.500 0.0000 aeration_rate*mixing_intensity 1 50.0000 50.0000 0.667 0.4353 aeration_rate*filter_grade 1 162.0000 162.0000 2.160 0.1757 flocculant_dose*temperature 1 0.5000 0.5000 0.007 0.9367 flocculant_dose*mixing_intensity 1 392.0000 392.0000 5.227 0.0481 flocculant_dose*filter_grade 1 6498.0000 6498.0000 86.640 0.0000 temperature*mixing_intensity 1 6498.0000 6498.0000 86.640 0.0000 temperature*filter_grade 1 392.0000 392.0000 5.227 0.0481 mixing_intensity*filter_grade 1 0.5000 0.5000 0.007 0.9367 Error (Lenth PSE) 9 675.0000 75.0000 Total 7 12655.5000 1807.9286 Note: Error estimated using Lenth's pseudo-standard-error (unreplicated design) === Interaction Effects: sludge_volume === Factor A Factor B Interaction % Contribution ------------------------------------------------------------------------ ph_level retention_time 57.0000 13.3% flocculant_dose filter_grade -57.0000 13.3% temperature mixing_intensity 57.0000 13.3% ph_level filter_grade -52.5000 12.3% retention_time flocculant_dose 52.5000 12.3% aeration_rate temperature -52.5000 12.3% ph_level aeration_rate 14.0000 3.3% flocculant_dose mixing_intensity -14.0000 3.3% temperature filter_grade 14.0000 3.3% ph_level temperature 9.0000 2.1% retention_time mixing_intensity 9.0000 2.1% aeration_rate filter_grade 9.0000 2.1% ph_level flocculant_dose 5.0000 1.2% retention_time filter_grade -5.0000 1.2% aeration_rate mixing_intensity -5.0000 1.2% ph_level mixing_intensity -4.5000 1.1% retention_time temperature -4.5000 1.1% aeration_rate flocculant_dose 4.5000 1.1% retention_time aeration_rate -0.5000 0.1% flocculant_dose temperature 0.5000 0.1% mixing_intensity filter_grade -0.5000 0.1% === Summary Statistics: sludge_volume === ph_level: Level N Mean Std Min Max ------------------------------------------------------------ 6 4 152.0000 52.6181 86.0000 214.0000 9 4 152.5000 38.0745 114.0000 205.0000 retention_time: Level N Mean Std Min Max ------------------------------------------------------------ 12 4 159.2500 41.5321 114.0000 214.0000 4 4 145.2500 48.6098 86.0000 205.0000 aeration_rate: Level N Mean Std Min Max ------------------------------------------------------------ 2 4 180.7500 34.1992 143.0000 214.0000 6 4 123.7500 29.7139 86.0000 148.0000 flocculant_dose: Level N Mean Std Min Max ------------------------------------------------------------ 10 4 147.7500 52.3601 86.0000 214.0000 50 4 156.7500 37.7216 114.0000 205.0000 temperature: Level N Mean Std Min Max ------------------------------------------------------------ 15 4 149.7500 7.8049 143.0000 161.0000 30 4 154.7500 64.3500 86.0000 214.0000 mixing_intensity: Level N Mean Std Min Max ------------------------------------------------------------ high 4 126.0000 32.9545 86.0000 161.0000 low 4 178.5000 35.9861 147.0000 214.0000 filter_grade: Level N Mean Std Min Max ------------------------------------------------------------ coarse 4 150.0000 49.1460 86.0000 205.0000 fine 4 154.5000 42.3045 114.0000 214.0000

=== Optimization: bod_removal === Direction: maximize Best observed run: #4 ph_level = 9 retention_time = 4 aeration_rate = 2 flocculant_dose = 50 temperature = 30 mixing_intensity = low filter_grade = coarse Value: 96.0 RSM Model (linear, R² = 1.0000, Adj R² = 1.0000): Coefficients: intercept +83.6125 ph_level +0.0125 retention_time -1.1625 aeration_rate -2.7125 flocculant_dose +2.6625 temperature +2.7625 mixing_intensity +2.0625 filter_grade -1.0125 Predicted optimum (from linear model, at observed points): ph_level = 9 retention_time = 4 aeration_rate = 2 flocculant_dose = 50 temperature = 30 mixing_intensity = low filter_grade = coarse Predicted value: 96.0000 Surface optimum (via L-BFGS-B, linear model): ph_level = 9 retention_time = 4 aeration_rate = 2 flocculant_dose = 50 temperature = 30 mixing_intensity = 1.0000 filter_grade = -1.0000 Predicted value: 96.0000 Model quality: Excellent fit — surface predictions are reliable. Factor importance: 1. temperature (effect: 5.5, contribution: 22.3%) 2. aeration_rate (effect: -5.4, contribution: 21.9%) 3. flocculant_dose (effect: 5.3, contribution: 21.5%) 4. mixing_intensity (effect: 4.1, contribution: 16.6%) 5. retention_time (effect: 2.3, contribution: 9.4%) 6. filter_grade (effect: -2.0, contribution: 8.2%) 7. ph_level (effect: 0.0, contribution: 0.1%) === Optimization: sludge_volume === Direction: minimize Best observed run: #8 ph_level = 9 retention_time = 12 aeration_rate = 6 flocculant_dose = 10 temperature = 15 mixing_intensity = low filter_grade = coarse Value: 86.0 RSM Model (linear, R² = 1.0000, Adj R² = 1.0000): Coefficients: intercept +152.2500 ph_level +14.2500 retention_time -13.0000 aeration_rate -3.5000 flocculant_dose +25.2500 temperature +17.7500 mixing_intensity -14.0000 filter_grade +7.0000 Predicted optimum (from linear model, at observed points): ph_level = 9 retention_time = 12 aeration_rate = 6 flocculant_dose = 50 temperature = 30 mixing_intensity = high filter_grade = fine Predicted value: 214.0000 Surface optimum (via L-BFGS-B, linear model): ph_level = 6 retention_time = 12 aeration_rate = 6 flocculant_dose = 10 temperature = 15 mixing_intensity = 1.0000 filter_grade = -1.0000 Predicted value: 57.5000 Model quality: Excellent fit — surface predictions are reliable. Factor importance: 1. flocculant_dose (effect: 50.5, contribution: 26.6%) 2. temperature (effect: 35.5, contribution: 18.7%) 3. ph_level (effect: 28.5, contribution: 15.0%) 4. mixing_intensity (effect: -28.0, contribution: 14.8%) 5. retention_time (effect: 26.0, contribution: 13.7%) 6. filter_grade (effect: 14.0, contribution: 7.4%) 7. aeration_rate (effect: -7.0, contribution: 3.7%)