## 2 Materials and Methods
### System Architecture and Design Methodology
The direct average of the four SPLs is then computed as [18; 19]:  
\[\overline{L}(t_{n})=\frac{1}{4}\sum\limits_{j=1}^{4}L_{j}(t_{n}) \tag{2}\]  
Figure 3 shows a typical mean SPL time history (red circle) as a function of the effective propagation length, \(d=C_{air}t\), \(15\leq d\leq 100\) m, where \(C_{air}=(331.3+0.606\ \theta)\) m/s is the sound speed in air and \(\theta\) is the temperature in degrees Celsius (\({}^{\circ}\)C) [27]. The choice for this range can be explained by the fact that for \(d<15\) m (i.e., below 44 msec at \(\theta=20\ ^{\circ}\)C), the recorded signal was dominated by the sound which was coming directly from the speaker. This sound was yet to be reflected by the screen multiple times to form a fully diffused sound field to carry useful information on the screen condition. For \(d>100\) m (0.29 s at \(\theta=20\ ^{\circ}\)C), the acoustic signal was attenuated well below the background noise floor so that it could not be used in the analysis. It was found that a change in the air temperature had little or no effect on the measured sound pressure level time history \(\overline{L}(d)\) for a given screen condition. In order to simplify the process of analysing the meaning of this graph, a least mean squares curve fitting method [28] was adopted to provide an analytical fit to the recorded sound pressure level data. In this study, the following polynomial equation was used:  
\[\overline{L}_{n}=a_{0}+b_{0}\sqrt{d_{n}} \tag{3}\]  
Figure 2: Basic operation block diagram of the system. where  
\[b_{0}=\frac{\sum\sqrt{d_{n}L_{n}}-\frac{\sum\overline{L}_{n}\Sigma\sqrt{d_{n}}}{ \left(\sum d_{n}-\frac{\sum\sqrt{d_{n}}\Sigma\sqrt{d_{n}}}{N}\right)}}{\left( \sum d_{n}-\frac{\sum\sqrt{d_{n}}\Sigma\sqrt{d_{n}}}{N}\right)} \tag{4}\]  
\[a_{0}=\frac{\sum\overline{L}_{n}-b_{0}\sum\sqrt{d_{n}}}{N} \tag{5}\]  
Here \(\overline{L}_{n}\) is the sound pressure level recorded at the time instance \(t_{nr}\), \(d_{n}\) is the distance, \(n\) is the integer in the time step, \(a_{0}\) is the SPL level at the intercept point when \(d_{n}=0\) and \(b_{0}\) is the gradient of the curve. This method enabled us to identify the optimal values for the \(a_{0}\) and \(b_{0}\) coefficients for the best fit of a set of data. Figure 3 presents an example of experimental data and corresponding polynomial fit obtained using the LMS method. The coefficients \(a_{0}\) and \(b_{0}\) have a clear physical meaning. The slope of the curve (\(b_{0}\)) gives good indication of the conditions of the screen. A smaller absolute value of \(b_{0}\) indicates a smaller acoustic absorption of the screen, which results in a longer reverberation time in the CSO chamber. This means that the CSO screen condition is cleaner. On the contrary, a larger absolute value of \(b_{0}\) suggests that the CSO screen becomes contaminated with organic wastewater porous debris which absorbs sound better. This is an indicator that the screen is getting blinded. In this case, the acoustic attenuation in the chamber increases and so does the reverberation time. The coefficient \(a_{0}\) corresponds to the intercept point of the SPL curve when \(d\) is zero. This coefficient changes consistently with a change in \(b_{0}\) and it is an estimate of the maximum sound pressure level in the CSO. It is controlled by the power of the sound radiated by the speaker, the absorption area of the screen and walls in the CSO chamber and its volume.