# Prediction of Wastewater Treatment Plant Performance Using Multivariate Statistical Analysis: A Case Study of a Regional Sewage Treatment Plant in Melaka, Malaysia

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2}= 0.85), p-value < 0.05, and residual values were uniformly distributed above and below the zero baselines. Therefore, the coefficients of the WWQI model are directly dependent on influent biological oxygen demand (BOD), effluent BOD, influent chemical oxygen demand (COD), and effluent COD values. The experimental results showed that the model performed well and can be used to predict WWQI for each WWTP individually and provide better achievements.

## 1. Introduction

_{3}), nitrate (NO

_{3}), and phosphorous (P), while the pH and temperature need to be accurately monitored. The dynamical behavior of sewage treatment plants is due to the nonlinearity and variations in physical properties in terms of environmental conditions, wide variation in flow rate, and various concentrations of influent composition. In the long term, it will cause difficulties in monitoring, analyzing, and controlling the actual situation of WWTP [8]. Due to the lack of instrumentation, control, and automation technologies, the diagnosis of process performances and plant operations are still conducted by human operators. Various process monitoring and control systems have been introduced such as SMAC (smart control of wastewater system) [9], SCADA (supervisory control and data acquisition) [10], LabView software [11], and biosensor monitoring [12].

^{3}per day. Wastewater predictions for the wastewater quality index (WWQI) are used by government bodies to indicate the quality of the wastewater quality effluent ranging from poor to excellent [14]. This is vital as Malaysia’s effluent standards allow for the discharging of treated wastewater to the river, reservoir, and well when it meets the specific criteria for BOD, COD, suspended solids (SS), oil and grease (O&G), ammoniacal nitrogen, nitrate, and phosphorous [15].

## 2. Materials and Methods

#### 2.1. Site Description

^{3}per day of treated effluent. This plant has been functional since 2017. The plant is a sequence batch reactor (SBR) system consisting of preliminary, secondary, and tertiary treatment systems. Screening and grit removal was designed for preliminary treatment, and the SBR tank process was for secondary treatment. For tertiary treatment, effluents flow to the disinfection process, and the final effluent is discharged to a nearby drain.

#### 2.2. Collecting Data

#### 2.3. Wastewater Quality Index (WWQI)

#### 2.4. Principal Component Analysis (PCA)

_{j}can be expressed as the linear combination of the measured variables, x, and associated weighting factors loading, v, as presented in Equations (7)–(10) [33]:

_{j}= v

_{j}x

_{1}+ v

_{2}x

_{2}+ … v

_{jm}x

_{1m}

_{j}= v

_{j}

^{T}x

_{j}

^{T}is a vector containing all the jth loadings, and l

_{j}has the greatest variance subject to two conditions:

_{j}

^{T}v

_{j}= 1

_{j}

^{T}v

_{i}= 0 (i < j)

#### 2.5. Multiple Linear Regression Analysis (MLR)

^{2}), Pearson (R), and standard error are the governing factors for indicating the strength of the model. The strength of the pairwise correlations was evaluated using Pearson’s correlation coefficients which have a value between +1 and −1, where +1 indicates total positive linear correlation, 0 indicates no linear correlation, and −1 indicates total negative linear correlation. A higher R

^{2}indicates that the model has a strong predictive power [38]. The performance of the developed models was assessed by R

^{2}and the root mean squared error (RMSE). The p-value will rule the decision by choosing variables that have a significant value (p < 0.05). For all calculations, the XLSTAT software (Addinsoft company, Paris, Ile-de-France, France) and Statgraphics Centurion XVI (Statgraphics Technologies, Inc., The Plains, VA, USA) were used. Both models were compared to study the accuracy of their prediction. The comparison was performed on the basis of the relevant statistical metrics such as the correlation coefficient, R

^{2}value, mean square error, and standard error.

## 3. Results

#### 3.1. Wastewater Quality Index (WWQI)

#### 3.2. Principal Component Analysis (PCA)

#### 3.3. Multiple Linear Regression (MLR)

#### 3.3.1. XLSTAT Modeling

^{2}to less than 0.85. There are several factors that affect the model’s performance such as data variation and data quantity. According to Abba et al. [23], for a good analysis of any data intelligence model, the efficiency performance should include a larger value of goodness-of-fit (R

^{2}) and lower absolute error measure (e.g., RMSE). Further examination of the models revealed that MLR projected values had a high level of accuracy, as shown in Figure 5.

^{2}values are summarized in Table 4. A linear relationship was observed (R

^{2}= 0.85, p < 0.05), and regression analysis coefficients for the model are shown in Table 5. This model can be used to estimate the value of WWQI and to predict the wastewater treatment plant performance immediately. When R

^{2}is more than 0.85, this shows that the model appears to be confirmed, indicating that this technique is suitable for modeling WWQI [46].

^{2}.

#### 3.3.2. Statgraphic Modeling

^{2}score for the stratigraphic model reveals that the model as fitted explains 85.72% of the WWQI variability, compared to the XLSTAT model, which explains 85.60%. The modified R

^{2}statistic is 85.60 for both models, which are suited for comparing models with varied numbers of independent variables. The standard error of the estimated value for Statgraphic and XLSTAT models is 3.43 and 3.40, respectively.

^{2}value. Still, these findings do not differ from those of other researchers. Sarkheil et al. [21] confirmed that the dominant pollutant in both Fuzzy WWQI and aggregative weighted WWQI methodologies was the BOD parameter, which is 65.38% of the analysis, while the COD parameter is dominant about 34% of the time. Previous studies have supported the application of XLSTAT and Statgraphic in the modeling regression process [52,53].

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Site location with 100 km bar distance and (

**b**) layout of centralized sewage treatment plant in Melaka, Malaysia.

**Figure 3.**Boxplots of the wastewater parameters; from left to right: influent BOD, effluent BOD, influent COD, and effluent COD.

**Figure 4.**The principal component analysis diagram for the active variables and active observations; PCA 1 for effluent parameters and PCA 2 for influent parameters.

**Figure 7.**Comparison of the model for the measured and predicted value for the WWQI model; (

**a**) XLSTAT analysis and (

**b**) Statgraphic analysis.

Variable | Description | Unit | Minimum | Maximum | Mean | Std. Deviation (±) | Malaysia Effluent Standard (A) |
---|---|---|---|---|---|---|---|

BOD | Influent BOD | mg/L | 6.00 | 350.00 | 133.76 | 66.34 | - |

COD_{i} | Influent COD | mg/L | 30.00 | 1323.00 | 307.62 | 213.98 | - |

TSS_{i} | Influent TSS | mg/L | 15.00 | 903.00 | 148.48 | 137.08 | - |

Ammonia_{i} | Influent ammonia | mg/L | 8.00 | 38.00 | 20.64 | 6.49 | - |

pH_{i} | Influent pH | - | 6.40 | 8.20 | 7.00 | 0.30 | - |

O&G_{i} | Influent O&G | mg/L | 1.00 | 135.00 | 32.12 | 24.28 | - |

BOD_{e} | Effluent BOD | mg/L | 2.00 | 18.00 | 3.68 | 2.30 | 20 |

COD_{e} | Effluent COD | mg/L | 20.00 | 76.00 | 34.07 | 10.64 | 120 |

TSS_{e} | Effluent TSS | mg/L | 2.00 | 42.00 | 11.06 | 7.59 | 5 |

Ammonia_{e} | Effluent Ammonia | mg/L | 1.00 | 45.00 | 7.62 | 6.75 | 5 |

pH_{e} | Effluent pH | - | 6.00 | 8.50 | 7.02 | 0.33 | 6–9 |

OG_{e} | Effluent O&G | mg/L | 1.00 | 7.00 | 2.07 | 1.08 | 5 |

Temp_{e} | Effluent Temp | °C | 29.00 | 32.00 | 29.55 | 0.59 | 40 |

Nitrate_{i} | Influent Nitrate | mg/L | 1.00 | 11.00 | 1.05 | 0.74 | - |

Nitrate_{e} | Effluent Nitrate | mg/L | 1.00 | 24.00 | 1.57 | 2.46 | 20 |

MLSS | MLSS | mg/L | 2918.00 | 9905.00 | 5858.94 | 2226.53 | - |

WWQI | WWQI | - | 36.30 | 86.80 | 74.30 | 9.10 | - |

Quality Range | WWQI | Category |
---|---|---|

Excellent | 95–100 | Very close to natural or pristine levels |

Good | 80–94 | Rarely depart from natural or desirable levels |

Fair | 65–79 | Sometimes depart from natural or desirable levels |

Marginal | 45–64 | Often depart from natural or desirable levels |

Poor | 0–44 | Quality is almost always threatened or impaired |

F1 | F2 | F3 | F4 | F5 | F6 | F7 | |
---|---|---|---|---|---|---|---|

Eigenvalue | 3.466 | 2.710 | 1.520 | 1.268 | 1.067 | 1.031 | 1.008 |

Variability (%) | 20.389 | 15.944 | 8.941 | 7.462 | 6.274 | 6.067 | 5.930 |

Cumulative (%) | 20.389 | 36.333 | 45.273 | 52.735 | 59.009 | 65.076 | 71.006 |

Source | DF | Sum of Squares | Mean Squares | F | Pr > F | R^{2} | Adjusted R^{2} |
---|---|---|---|---|---|---|---|

Model | 4 | 2.511 | 0.628 | 530.587 | <0.0001 | 0.856 | 0.856 |

Error | 353 | 0.418 | 0.001 | ||||

Total Corrected | 357 | 2.928 |

Source | Value | Standard Error | t-Value | p-Level |
---|---|---|---|---|

Intercept | 0.993 | 0.007 | 138.313 | <0.0001 |

BOD_{i} | 0.000018 | 0.000033 | 0.563 | 0.574 |

COD_{i} | 0.000018 | 0.000010 | 1.813 | 0.071 |

BOD_{e} | −0.009 | 0.001 | −8.972 | <0.0001 |

COD_{e} | −0.007 | 0.000 | −31.286 | <0.0001 |

Source | DF | Sum of Squares | Mean Squares | F | Pr > F | R^{2} | Adjusted R^{2} |
---|---|---|---|---|---|---|---|

Model | 3 | 25,103.2 | 8367.72 | 708.59 | <0.0001 | 85.7245 | 85.6035 |

Error | 354 | 4180.38 | 11.809 | ||||

Total Corrected | 357 | 29,283.5 |

Source | Value | Standard Error | t-Value | p-Level |
---|---|---|---|---|

Intercept | 99.4487 | 0.65471 | 151.898 | <0.0001 |

COD_{i} | 0.002145 | 0.000854 | 2.5107 | 0.0125 |

BOD_{e} | −0.872038 | 0.097284 | −8.96375 | <0.0001 |

COD_{e} | −0.66303 | 0.0211011 | −31.4215 | <0.0001 |

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**MDPI and ACS Style**

Rahmat, S.; Altowayti, W.A.H.; Othman, N.; Asharuddin, S.M.; Saeed, F.; Basurra, S.; Eisa, T.A.E.; Shahir, S.
Prediction of Wastewater Treatment Plant Performance Using Multivariate Statistical Analysis: A Case Study of a Regional Sewage Treatment Plant in Melaka, Malaysia. *Water* **2022**, *14*, 3297.
https://doi.org/10.3390/w14203297

**AMA Style**

Rahmat S, Altowayti WAH, Othman N, Asharuddin SM, Saeed F, Basurra S, Eisa TAE, Shahir S.
Prediction of Wastewater Treatment Plant Performance Using Multivariate Statistical Analysis: A Case Study of a Regional Sewage Treatment Plant in Melaka, Malaysia. *Water*. 2022; 14(20):3297.
https://doi.org/10.3390/w14203297

**Chicago/Turabian Style**

Rahmat, Sofiah, Wahid Ali Hamood Altowayti, Norzila Othman, Syazwani Mohd Asharuddin, Faisal Saeed, Shadi Basurra, Taiseer Abdalla Elfadil Eisa, and Shafinaz Shahir.
2022. "Prediction of Wastewater Treatment Plant Performance Using Multivariate Statistical Analysis: A Case Study of a Regional Sewage Treatment Plant in Melaka, Malaysia" *Water* 14, no. 20: 3297.
https://doi.org/10.3390/w14203297