# An Artificial Neural Network for Simulation of an Upflow Anaerobic Filter Wastewater Treatment Process

## Abstract

**:**

^{2}) was 0.66. The results of simulation of all 125 possible combinations of the 3 mechanical parameters and identical influent wastewater flow profiles were ranked according to total calorific value reduction. A t-test of the difference between the mean calorific value reduction of the two highest ranked experiments showed that the means are significantly different (p-value = 0.011). Thus, the model has the capacity to distinguish differences in the equipment design parameters. Consequently, the values of the three mechanical feature parameters from the highest ranked simulated experiment are recommended for use in the design of the industrial scale upflow anaerobic filter (UAF) for wastewater treatment.

## 1. Introduction

- An efficient experimental plan that can be implemented in field conditions;
- The accuracy of the artificial neural network predictive model;
- The selection of mechanical constructive parameters based on significant differences in the performance results obtained by simulation.

## 2. Materials and Methods

#### 2.1. Problem Solving Approach

- Installation of a bioreactor testing and data acquisition system at an industrial site;
- Preparation of an experimental plan to vary the operational parameters such that the test system is exposed to the full range of possible industrial conditions;
- Operation of the test system according to the experimental plan to acquire raw data;
- Restructuring and pre-treatment of the raw dataset according to the requirements of ANN models and to describe individual experiments according to the experimental plan;
- Construction of an artificial neural network model;
- Training and validation of the ANN model using supervised learning;
- Use of the ANN model to simulate test cases where mechanical parameters are varied within the range of tested values;
- Ranking of the simulation results in terms of the predicted performance of the upflow anaerobic filter bioreactor;
- Selection of the mechanical parameters according to the ranking of the simulation results.

#### 2.2. Direct Experimental Data

#### 2.3. Surrogate Data

#### 2.4. Mock Experiments

- $C{V}_{red}$ = a vector of calorific value reductions for a single mock experiment;
- ${Q}_{i}$ = the influent flow rate on the ith day;
- ${C}_{i}$ = the change in the calorific value of the influent stream on the ith day of the reference experiment;
- ${S}_{i}$ = the spherical diameter effects on calorific value reduction on the ith day;
- ${M}_{i}$ = the material type effects on calorific value reduction on the ith day;
- ${H}_{i}$ = the height-to-diameter effects on calorific value reduction on the ith day.

#### 2.5. Experiment Plan to Obtain the Mock Experimental Dataset

#### 2.6. Data Preprocessing

`ks_2samp`[39] on two samples was computed to test the null hypothesis that the training and validation response datasets were drawn from the same source. The null hypothesis can be rejected at the 99.9% confidence level if the K-S statistic is greater than the critical value (D) of 0.12. The calculated K-S statistic of 0.051 is less than the critical value (p-value = 0.53). Thus, the training and the validation response value datasets have the same distribution and were drawn from the same source.

`shuffle`parameter was set to

`False`when the temporal features of an experiment were preserved and to

`True`when the temporal features of an experiment were not included in the dataset.

`Random_state`was set to 42 to assure that the preshuffling operation was always the same.

#### 2.7. Predictive Models

#### 2.7.1. Polynomial Model

#### 2.7.2. Multilayer Perceptron (MLP) Model

`None`so that the unit weights were reinitialized before every model build, train, and test operation.

`rho`) was set as high as 0.99 which is higher than the default value of 0.90. The momentum applied to the optimizer was set as high as 0.9.

`use_bias`and

`bias_initializer`were set to

`True`and

`zeros`, respectively. The

`TruncatedNormal`initializer with a mean set to 0.0 and stddev set to 0.1 was used to set the initial weights of the hidden layers. The final hyperparameters settings were as follows:

`learning rate`= $1\times {10}^{-4}$,

`rho`= 0.99, momentum = 0.05,

`epsilon`= $1\times {10}^{-7}$,

`centered`= True. The learning rate was 10 times less and the momentum slightly more than the default values.

`R${}^{2}$`) and the slope of the regression line. There were small differences in the accuracy of the predictions between different model rebuilding operations. The models with more than 512 units per layer were frequently less accurate than the other models. The models with between 32 and 512 units per layer and between 2 and 6 hidden layers yielded similar and acceptable results.

#### 2.8. Use of the Model for Simulation

## 3. Results

^{2}), and the slope of the regression line of predicted and true values. Both the polynomial and the MLP models were built, trained and validated separately using both the unshuffled time series and preshuffled data sets. The plots of predicted versus true values are shown in Figure 3 (unshuffled) and Figure 4 (preshuffled).

#### 3.1. Polynomial Model

#### 3.2. MLP Model

#### 3.3. Time-Series Effects

#### 3.4. Model Selected for Use in Simulation

#### 3.5. Evaluation of the Experimental Plan

#### 3.6. Use of the MLP for Simulation

## 4. Discussion

#### 4.1. Comparison to Existing Methods

#### 4.2. Contribution of the Proposed Method

#### 4.3. Future Implementation

## 5. Conclusions

- The predictions made using the MLP were more accurate than those made using the polynomial model (coefficients of determination (R${}^{2}$), respectively, of 0.66 and 0.37);
- The MLP model used for simulation should be defined by architecture and not by a particular set of hidden-layer unit weight initializations;
- The reloaded MLP model can be used for simulation using previously unseen input vectors;
- The differences in the predictions are significant (p-value < 0.02, range = mean ± 20% of the full range);
- The ranked order of simulation results can be used to select the set of mechanical specifications that will result in the highest equipment performance;
- A practical on-site data collection plan can be used to reduce the resource requirements for new process development.

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Reference dataset of 170 sampled values of calorific value reduction $\Delta CV$ ($\mathrm{J}\xb7{\mathrm{L}}^{-1}$). Red diamonds: direct measurements (n = 21); blue dots: surrogate values (n = 170).

**Figure 2.**Daily calorific value reduction ($CVdt$). Reference experiment and surrogate data for 1530 sample points from the mock experiment plan. On the righthand side, there are the binned calorific value reductions of the corresponding mock experiments. Black crosses show the reference data points.

**Figure 3.**True versus predicted values (unshuffled, true times series data); polynomial model: blue; MLP model: red.

**Figure 4.**True versus predicted values (preshuffled data); True versus predicted values (preshuffled data); Polynomial model: blue; MLP model: red.

**Figure 5.**Decrease of MAE during training and validation of the MLP model. Training loss: green; Test loss: black.

**Figure 7.**Box plot of the predicted calorific value reduction. Results of 125 simulated experiments using the MLP model. The boxes enclose all values in the 25th through the 75th percentiles. The whisker reach is set to two times the range of boxes. The green lines show the mean of the simulation runs.

**Table 1.**Experimental plan (mock experiments). Three levels for each mechanical factor. The same influent profile was used in all the mock experiments. $ESD$: equivalent spherical diameter (in mm); $MAT$: packing material type (TWD: torrefied wood chips, PUF: polyurethane foam, PVC: polyvinyl chloride); $HDR$: bed height/diameter ratio. The response data are median (mean ± SD) $CVdt$ values (daily calorific value reduction) computed for each mock experiment distribution (see Figure 2).

Experiment Number | ESD | MAT | HDR | CVdt | Rank |
---|---|---|---|---|---|

E1 | 4 | PVC | 0.5 | 48.5 (46.4 ± 22.9) | 9 |

E2 (reference experiment) | 12 | TWD | 1.8 | 71.4 (75.9 ± 30.4) | 4 |

E3 | 36 | PUF | 3.6 | 79.6 (80.2 ± 50.4) | 2 |

E4 | 4 | TWD | 3.6 | 60.9 (61.8 ± 16.9) | 6 |

E5 | 12 | PUF | 0.5 | 43.8 (49.7 ± 27.4) | 8 |

E6 | 36 | PVC | 1.8 | 92.7 (91.0 ± 35.5) | 1 |

E7 | 4 | PUF | 1.8 | 51.3 (54.0 ± 19.3) | 7 |

E8 | 12 | PVC | 3.6 | 62.2 (69.1 ± 18.6) | 5 |

E9 | 36 | TWD | 0.5 | 82.5 (79.4 ± 44.7) | 3 |

Type of Numerical Model | RMSE (%) | R^{2} | Slope |
---|---|---|---|

Fourth degree polynomial, true time series | 14.9 | 0.29 | 0.24 |

Fourth degree polynomial, shuffled time series | 14.0 | 0.37 | 0.35 |

4-layer MLP, true time series | 12.7 | 0.48 | 0.38 |

4-layer MLP, shuffled time series | 10.1 | 0.66 | 0.67 |

Experiment Combination Description | RMSE | R^{2} |
---|---|---|

Experimental plan as described above (9 experiments) | 0.101 | 0.66 |

Experimental plan with experiment E3 removed | 0.096 | 0.72 |

Experimental plan with 1 experiment removed at random | 0.156 | 0.13 |

Mechanical Predictors (Factors) | Tested Values (Levels) |
---|---|

Packing diameter—ESD [mm] | 4, 8, 12, 24, 36 |

Type of packing material—MAT | 1, 1.85, 2.7, 6.85, 11 |

Fixed bed H/D ratio—HDR | 0.5, 1.15, 1.8, 2.9, 4 |

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**MDPI and ACS Style**

McCormick, M.
An Artificial Neural Network for Simulation of an Upflow Anaerobic Filter Wastewater Treatment Process. *Sustainability* **2022**, *14*, 7959.
https://doi.org/10.3390/su14137959

**AMA Style**

McCormick M.
An Artificial Neural Network for Simulation of an Upflow Anaerobic Filter Wastewater Treatment Process. *Sustainability*. 2022; 14(13):7959.
https://doi.org/10.3390/su14137959

**Chicago/Turabian Style**

McCormick, Mark.
2022. "An Artificial Neural Network for Simulation of an Upflow Anaerobic Filter Wastewater Treatment Process" *Sustainability* 14, no. 13: 7959.
https://doi.org/10.3390/su14137959