Comparison of the Prediction Accuracy of Total Viable Bacteria Counts in a Batch Balloon Digester Charged with Cow Manure: Multiple Linear Regression and Non-Linear Regression Models
Abstract
:1. Introduction
1.1. Mathematical Models Used to Predict Biogas Production in Anaerobic Digestion Process
1.2. Objectives of the Study
- i.
- To develop both multiple linear regression and non-linear regression models to predict the total viable bacteria counts with the number of days, daily slurry temperature and pH as predictors for a balloon digester charged with cow manure.
- ii.
- To use the 2D multi-contour surface plots derived from the developed mathematical models to illustrate the variation in each of the predictors with the total viable bacteria counts.
- iii.
- To exploit the 2D multi-contour surface plots for both the multiple linear regression and non-linear regression models to simulate design experiment’s data for each predictor with the desired targets while the others are held constant.
- iv.
- To compare the prediction accuracies of the multiple linear regression and the non-linear regression models.
2. Methodology of the Study
2.1. Materials and Experimental Setup
2.2. Methods
2.2.1. Raw Anaerobic Digestion Material (Cow Manure)
2.2.2. Physicochemical Analysis of the Slurry Samples
- i.
- Calculation of the ammonium (NH4) level of sample
- ii.
- Determination of percentage of moisture content of samples
- iii.
- Determination of percentage of dry matter (total solids)
- iv.
- Determination of percentage of volatile solid content and ash content
- v.
- Determination of pH, ambient temperature, slurry temperature and biogas yield
- vi.
- Microbial analysis of samples
2.2.3. Statistical Analysis
2.2.4. Development of Non-Linear Regression Model
2.2.5. Development of Multiple Linear Regression Model
2.2.6. Measurement Accuracies and Uncertainties
3. Results and Discussion
3.1. Profiles of Ambient Temperature and Input and Output Parameters during Anaerobic Digestion
3.2. Characteristics of the Cow Manure and Physicochemical Properties during Digestion
3.3. ReliefF Test Used in Ranking of the Predictors to the Total Viable Bacteria Counts
3.4. 2D Multi-Contour Surface Plots to Simulate the Variation in the Response with Each Predictor
2D Multi-Contour Surface Plots with the Developed Models
3.5. Testing of the Accuracy of the Developed Models
3.5.1. Testing of the Accuracy from Non-Linear and Multiple Linear Regression Models
3.5.2. ANOVA Statistics to Confirm Model Accuracy with Testing Dataset
3.6. Validation of the Developed Mathematical Models
ANOVA Statistics to Confirm the Accuracy of the Developed Models with the Validation Dataset
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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A. Devices and Materials Employed in Both the Physical and Chemical Analysis | ||
Item | Device and Materials | Quantity |
1 | Centrifugal tubes | 10 |
2 | Nessler’s reagent | - |
3 | Hexios, Thermo-Spectronics Spectrometer | 1 |
4 | Distilled water | - |
5 | Dish | 1 |
6 | Electric oven | 1 |
7 | PHH-SD1 pH meter | 1 |
8 | TMC6-HD copper pipe temperature sensors | 4 |
9 | Portable biogas analyser, IRCD4 | 1 |
10 | Tryptic soy broth medium | - |
11 | Physical saline | - |
12 | Triplicates of microbiological media (nutrient agar and anaerobic agar) | - |
13 | Fridge | 1 |
14 | Weight balance | 1 |
15 | Incubator | 1 |
16 | muffle furnace | 1 |
B. Devices, Sensors, and Materials Used in the Experimental Setup | ||
Item | Device and Materials | Quantity |
1 | Balloon digester | 1 |
2 | Feedstock of cow manure (slurry) | 2500 L |
2 | An open surface concrete structure | 1 |
3 | A black wooden board (insulation cover) | 1 |
4 | Portable biogas analyser, IRCD4 | 1 |
5 | TMC6-HD copper pipe temperature sensors | 4 |
6 | Hobo-UX120 four external channel data logger | 1 |
7 | PHH-SD1 pH meter | 1 |
8 | Slurry measuring cylinder (250 L) | 1 |
9 | ZAN-TECHS gas flow meters with data logger | 1 |
10 | Control flow valve | 1 |
11 | Biogas circulation pump | 1 |
12 | Connecting biogas tubing or pipe | 1 |
13 | Biogas collection chamber | 1 |
14 | Weatherproof data loggers’ enclosure | 1 |
15 | A zinc roof open structure (protection of digester, ambient temperature sensor and data loggers) | 1 |
Parameters | Sample A | Sample B | Sample C | Sample D | Sample E | Mean | Standard Deviation |
---|---|---|---|---|---|---|---|
Percentage of moisture content | 89.12 | 91.23 | 91.19 | 89.96 | 90.78 | 90.38 | 0.886 |
Percentage of total solids | 10.88 | 8.77 | 8.81 | 10.04 | 9.22 | 9.55 | 0.975 |
Percentage of volatile solids | 65.76 | 68.25 | 72.65 | 71.55 | 73.04 | 70.25 | 3.138 |
Percentage of ash content | 34.24 | 31.75 | 27.35 | 28.45 | 26.96 | 29.75 | 3.138 |
Ammonium (NH4) level (mg/mL) | 2.19 | 2.01 | 2.25 | 2.28 | 2.20 | 2.18 | 0.105 |
pH | 6.83 | 6.82 | 6.59 | 6.76 | 6.46 | 6.69 | 0.162 |
Input Parameters | Input Symbols | Scaling Attribute | Scaling Values | Output |
---|---|---|---|---|
Constant | 1 | Log of total bacteria counts (y) Determination coefficient (r2) = 0.959, Mean absolute error (MAE) = 0.180, p-value = 0.602 | ||
Number of days | x1 | 0.0047 | ||
Daily slurry temperature | x2 | 0.4947 0.0521 | ||
pH | x3 | −0.1445 2.2002 |
Inputs | Input Symbols | Scaling Attribute | Scaling Values | Output |
---|---|---|---|---|
Constant | 1 | 1.2067 | Log of total bacteria counts (y) Determination coefficient (r2) = 0.920, Mean absolute error (MAE) = 0.206, p-value = 0.514 | |
Number of days | x1 | −0.0172 | ||
Daily slurry temperature | x2 | 0.1205 | ||
pH | x3 | 0.3871 |
Quantity | Type A Uncertainty | Type B Uncertainty | Combined Uncertainty |
---|---|---|---|
Ambient temperature (°C) | ±0.200 | ±0.120 | ±0.320 |
Biogas flow rates measurements (L/min) | ±0.010 | ±0.006 | ±0.016 |
pH measurements | ±0.130 | ±0.003 | ±0.133 |
Slurry temperature (°C) | ±0.200 | ±0.120 | ±0.320 |
Percentage total solids content | ±0.850 | ±0.105 | ±0.955 |
Percentage total volatile content | ±0.850 | ±1.405 | ±2.255 |
Percentage ash content | ±0.850 | ±1.203 | ±2.053 |
Ammonium level (mg/mL) | ±0.060 | ±0.020 | ±0.080 |
Chosen Input x1 (Number of Days) | Predicted y with 2D Simulation Response Surface Model (Log of Bacteria counts) | Predicted y 2D Simulation with Multiple Linear Regression Model (Log of Bacteria Counts) | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts |
---|---|---|---|---|
10 | 6.036 | 5.961 | 6.035 | 5.960 |
30 | 5.580 | 5.617 | 5.579 | 5.616 |
50 | 5.188 | 5.273 | 5.187 | 5.272 |
70 | 4.847 | 4.929 | 4.847 | 4.928 |
90 | 4.548 | 4.585 | 4.548 | 4.584 |
110 | 4.284 | 4.241 | 4.284 | 4.240 |
130 | 4.049 | 3.897 | 4.049 | 3.896 |
150 | 3.839 | 3.553 | 3.838 | 3.552 |
170 | 3.649 | 3.209 | 3.649 | 3.208 |
Chosen Input x2 (Daily Slurry Temperature) | Predicted y with Response Surface Model (Log of Bacteria Counts) | Predicted y with Multiple Linear Regression Model (Log of Bacteria Counts) | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts |
---|---|---|---|---|
17 | 4.277 | 4.567 | 4.277 | 4.567 |
18 | 4.482 | 4.688 | 4.482 | 4.687 |
19 | 4.672 | 4.808 | 4.671 | 4.808 |
20 | 4.842 | 4.928 | 4.847 | 4.929 |
21 | 5.010 | 5.049 | 5.010 | 5.049 |
22 | 5.162 | 5.170 | 5.163 | 5.169 |
23 | 5.305 | 5.290 | 5.304 | 5.290 |
24 | 5.438 | 5.411 | 5.437 | 5.410 |
25 | 5.563 | 5.531 | 5.562 | 5.531 |
Chosen Input x3 (pH) | Predicted y with Response Surface Model (Log of Bacteria Counts) | Predicted y with Multiple Linear Regression Model (Log of Bacteria Counts) | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts | Modelled with Non-Linear Regression Model Total Log of Bacteria Counts |
---|---|---|---|---|
5.50 | 4.691 | 4.542 | 4.691 | 4.541 |
5.75 | 4.727 | 4.639 | 4.727 | 4.638 |
6.00 | 4.765 | 4.735 | 4.765 | 4.735 |
6.25 | 4.805 | 4.832 | 4.805 | 4.832 |
6.50 | 4.847 | 4.929 | 4.847 | 4.928 |
6.75 | 4.891 | 5.026 | 4.891 | 5.025 |
7.00 | 4.938 | 5.122 | 4.937 | 5.122 |
7.25 | 4.987 | 5.219 | 4.986 | 5.219 |
7.50 | 5.038 | 5.316 | 5.038 | 5.315 |
Statistics Based on Targets and Model Outputs Using the Non-Linear Regression Model | |||||
Source | Sum of Square (SS) | Degree of Freedom (df) | Mean Square (MS) | F | Prob > F |
Columns | 0.0674 | 1 | 0.0674 | 0.27 | 0.6017 |
Error | 53.2762 | 216 | 0.2467 | ||
Total | 53.3436 | 217 | |||
Statistics Based on Targets and Model Outputs with the Multiple Linear Regression Model | |||||
Source | Sum of Square (SS) | Degree of Freedom (df) | Mean Square (MS) | F | Prob > F |
Columns | 0.1115 | 1 | 0.1115 | 0.43 | 0.5140 |
Error | 56.3962 | 216 | 0.2611 | ||
Total | 56.5077 | 217 |
Number of Days (x1) | Slurry Temperature (x2) | PH (x3) | Determined Log of Bacteria Counts (y) | Predicted Log of Total Viable Bacteria Counts with Response Surface Model | Predicted Log of Total Viable Bacteria with Multiple Linear Regression Model |
---|---|---|---|---|---|
2 | 18.358 | 5.847 | 5.682 | 5.731 | 5.648 |
11 | 17.236 | 5.496 | 5.102 | 5.217 | 5.222 |
16 | 17.212 | 5.790 | 5.077 | 5.182 | 5.246 |
20 | 18.439 | 5.716 | 5.188 | 5.309 | 5.297 |
31 | 18.059 | 5.954 | 5.170 | 5.078 | 5.154 |
36 | 18.235 | 5.922 | 5.222 | 5.009 | 5.077 |
52 | 18.019 | 5.949 | 4.704 | 4.692 | 4.787 |
73 | 23.758 | 7.367 | 5.554 | 5.542 | 5.666 |
80 | 21.691 | 6.580 | 5.005 | 4.976 | 4.992 |
95 | 23.954 | 6.505 | 5.291 | 5.069 | 4.977 |
123 | 24.270 | 7.48 | 4.990 | 4.628 | 4.472 |
145 | 22.786 | 7.519 | 4.383 | 4.408 | 4.369 |
153 | 25.875 | 7.550 | 4.811 | 4.741 | 4.616 |
161 | 25.040 | 7.550 | 4.180 | 4.290 | 4.148 |
168 | 23.178 | 7.534 | 4.123 | 4.214 | 4.027 |
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Tangwe, S.; Mukumba, P.; Makaka, G. Comparison of the Prediction Accuracy of Total Viable Bacteria Counts in a Batch Balloon Digester Charged with Cow Manure: Multiple Linear Regression and Non-Linear Regression Models. Energies 2022, 15, 7407. https://doi.org/10.3390/en15197407
Tangwe S, Mukumba P, Makaka G. Comparison of the Prediction Accuracy of Total Viable Bacteria Counts in a Batch Balloon Digester Charged with Cow Manure: Multiple Linear Regression and Non-Linear Regression Models. Energies. 2022; 15(19):7407. https://doi.org/10.3390/en15197407
Chicago/Turabian StyleTangwe, Stephen, Patrick Mukumba, and Golden Makaka. 2022. "Comparison of the Prediction Accuracy of Total Viable Bacteria Counts in a Batch Balloon Digester Charged with Cow Manure: Multiple Linear Regression and Non-Linear Regression Models" Energies 15, no. 19: 7407. https://doi.org/10.3390/en15197407