## 2 Materials and Methods
### Experimental Data Processing
#### 2.3.2 Fuzzy Rough Monotone Dependence Algorithm for Data Processing  
Obviously, the reaction mechanisms of activated sludge process is very complex, and the process parameters involved are numerous, and therefore the dimension of the obtained wastewater data is too high. This will not only lead to the occurrence of over fitting, but also cause the dimension disaster. In order to avoid these problems and not to affect the accuracy of model prediction, it is necessary to find out the parameters which have great influence on the BOD of the effluent. Therefore, the fuzzy rough monotone dependence (FRMD) [16; 24] algorithm is used for processing the data to reduce the attribute. It can be shown that there is a monotonic dependence between conditional attributes and decision attributes. Based on the FRMD algorithm, the steps of attribute reduction for wastewater data are as follows:  
Step 1: Define and initialize a two-dimensional array \(D[n,m]\) for the decision table, where the \(m^{\text{th}}\) column is the decision attribute (that is, the data of effluent water quality), and \(1^{\text{st}}\) to the \((m-1)^{\text{th}}\) columns are the conditional attributes (that is, the data of the wastewater influent);  
Step 2: Arrange the decision attribute values in ascending order, and exchange the rows of the conditional attributes corresponding to the ordered decision attribute; \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Units** & **Descriptions** \\ \hline \(\mathit{Kla_{3}}\), \(\mathit{Kla_{4}}\) & 240 & mg/day & Oxygen transfer coefficient of the 3 rd and 4 th bioreactors \\ \(\mathit{Kla_{5}}\) & 83 & mg/day & Oxygen transfer coefficient of the 5 th bioreactor \\ \(\mathit{Qint}\) & 55338 & m\({}^{3}\)/day & Internal recirculation flow rate \\ \(\mathit{Qr}\) & 18446 & m\({}^{3}\)/day & Returned sludge flow rate \\ \(\mathit{Qw}\) & 385 & m\({}^{3}\)/day & Waste sludge flow rate \\ \hline \hline \end{tabular}  
* Steps to obtain the experimental data:
* Step 1: Run a 100-day steady state simulation and repeat until the system achieves steady stability;
* Step 2: Run a 14-day simulation with the input data representing dry weather conditions and repeat until the system achieves dynamic stability;
* Step 3: Simulate BSM1 to obtain experimental data using the influent data mentioned above.  
The 2-week data (1344 groups in total with a sampling time of 15 minutes, 4 groups \(\times\) 24 hours \(\times\) 14 days \(=\) 1344 groups), of the wastewater treatment process was finally obtained. The compositions of wastewater are shown in Table 2.  
\end{table} 
Table 1: Parameters of BSM1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Unit** & **Description** \\ \hline \(S_{\text{i}}\) & mg COD/L & Soluble inert organic matter \\ \(S_{\text{s}}\) & mg COD/L & Readily biodegradable substrate \\ \(X_{\text{i}}\) & mg COD /L & Particulate inert organic matter \\ \(X_{\text{s}}\) & mg COD/L & Slowly biodegradable substrate \\ \(X_{\text{bh}}\) & mg COD /L & Active heterotrophic biomass \\ \(X_{\text{ba}}\) & mg COD/L & Active autotrophic biomass \\ \(X_{\text{p}}\) & mg COD /L & Particulate product arising from biomass decay \\ \(S_{\text{o}}\) & mg -COD/L & Oxygen (negative COD) \\ \(S_{\text{no}}\) & mg N/L & Nitrate and nitrite nitrogen \\ \(S_{\text{nh}}\) & mg N/L & NH\({}_{4}\)\({}^{+}\) and NH\({}_{3}\) nitrogen \\ \(S_{\text{nd}}\) & mg N/L & Soluble biodegradable organic nitrogen \\ \(X_{\text{nd}}\) & mg N/L & Particulate biodegradable organic nitrogen \\ \(S_{\text{alk}}\) & mole/m\({}^{3}\) & Alkalinity \\ \(TSS\) & mg \(S_{\text{S}}\)/L & Total amount of solids \\ \(Q\) & m\({}^{3}\)/day & Influent flow rate \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Components of wastewater. COD: chemical oxygen demand.