A novel ‘Comb Separator’ was developed and tested with the aim of improving sewer solids capture efficiency and reducing blockages on the screen. Experimental results were compared against the industry standard ‘Hydro-Jet™’ screen. Analysing the parameter sensitivity of a hydraulic screen is a standard practice to get better understanding of the device performance. In order to understand the uncertainties of the Comb Separator's input parameters, it is necessary to undertake sensitivity analysis; this will assist in making informed decisions regarding the use of this device. Such analysis will validate the device's performance in urban sewerage overflow scenarios. The methodology includes multiple linear regression and sampling using the standard Latin hypercube sampling technique to perform sensitivity analysis on different experimental parameters, such as flowrate, effective comb spacing, device runtime, weir opening and comb layers. The input parameters ‘weir opening’ and ‘comb layers’ have an insignificant influence on capture efficiency; hence, they were omitted from further analysis. Among the input parameters, ‘effective spacing’ was the most influential, followed by ‘inflow’ and ‘runtime’. These analyses provide better insights about the sensitivities of the parameters for practical application. This will assist device managers and operators to make informed decisions.

## INTRODUCTION

During continuous downpours of rain, existing urban sewer systems are not able to carry the excess water. This results in this excess water, which carries significant amounts of sewer solids, flowing into the open creek system. The sewer solids are inevitably dispersed, suspended or washed into the rivers, where they settle, creating odours and a toxic/corrosive environment in the mud deposits at the bottom. Furthermore, these solids create unaesthetic situations either by their general appearance (increasing dirtiness) or through the actual presence of specific, objectionable items, such as floating debris, sanitary discards/faecal matter, scum, or even parts of car tyres. To overcome such challenges, options include the development of wet detention ponds (Dan'azumi *et al.* 2013), wet temporary holding tanks at sewerage treatment plants, real-time control of sewer systems, enlarged upstream sewers to provide transient storage, separation of storm and sewage flows, and various screening devices in combined sewer overflow (CSO) chambers. In most cases, screening is the only economically viable method adopted in the hydraulic system (Faram *et al.* 2001). The hydraulic design of an efficient sewer network is of pivotal importance (Duque *et al.* 2016). A deterioration model could provide insight for prioritising inspection of existing sewer overflow sites (Rokstad & Ugarelli 2015).

Analysing the parameter sensitivity of a hydraulic device such as a Comb Separator has been a standard practice of hydraulic engineers for many years (Johnson 1996; Jetmarova *et al.* 2015). It is essential to generate an accurate simulation of the input models (Méndez *et al.* 2013) in sensitivity testing. Such analysis qualitatively or quantitatively explains the sources of variation (Saltelli 2004). A comprehensive review of the application of sensitivity analysis in environmental models is presented by Hamby (1995). Sensitivity analysis of the input parameters of the Comb Separator device provides a better understanding of them. This includes their influence on the outcome capture efficiency, identifying which parameter is the most important, the relative importance of each input parameter, and identification of those parameters requiring further research.

One of the most frequently used devices is the rotary screen proposed by Moffa (1997). This consists of a large rotating drum that is slightly angled to maximise dewatering. The angle of the drum ensures effective dewatering, as the screenings travel up the drum, where they are removed from the unit. Metcalf & Eddy (1991) proposed a centrifugal screen, with a series of screens attached to a cage that rotates around a vertical axis. The sewage overflow enters from the bottom and travels upward to a deflection plate at the top of the unit, and sewage solids are collected from outside the cage. In addition to these, Faram *et al.* (2001) tested the Hydro-Jet™ device that has been installed in the USA, Australia and mainland Europe. A detailed review of different types of screens can be found in the work of Saul (2008) and Madhani & Brown (2011) have provided a recent update of this literature.

The literature suggests that screens need to be ‘self-cleansing’ mechanisms; otherwise they are subject to blinding when placed in remote unmanned sewer environments (Aziz *et al.* 2013). Most ‘conventional’ screening systems utilise electro-mechanical components to facilitate such a process. However, given the harsh unmanned remote environment of sewer overflow device locations, this is clearly not ideal. Blocking and seizure of moving parts, as well as electrical failure, are common maintenance problems, which in many cases lead to an onerous maintenance commitment (Aziz *et al.* 2014). To overcome these drawbacks, a new overflow screening device, known as the ‘Comb Separator’, was proposed and tested at Swinburne University of Technology. The new device is self-cleansing and low maintenance, with fewer operating costs. A detailed description of this device can be found in the work of Aziz *et al.* (2014, 2015).

*et al.*1999; Andoh & Saul 2000; Faram & Andoh 2000). After assessing the available documentation on the evaluation process of the Hydro-Jet, the current research considers this is the benchmark device to consider in a comparative analysis of the proposed research screening system. The methodology adopted for this research is shown in the flowchart (see Figure 1). Both the Comb Separator and the Hydro Jet were developed with the aim of improving sewer solids capture efficiency and functional effectiveness of the screening device, and with lower maintenance costs. The capture efficiency of the Comb Separator varies more than that of the Hydro-Jet. To gain a better understanding of the fluctuating capture efficiency, it is important to perform a thorough sensitivity analysis of the input parameters of the Comb Separator.

The sensitivity of input parameters is of paramount importance for the Comb Separator, as this device will be located in remote, unstaffed locations. Moreover, sensitivity analysis will help to answer the following questions:

What is the input parameter that most influences sewer solids capture efficiency?

Which parameters are insignificant to model output, and thus can be omitted from further analysis?

How is it determined whether a model maintains the underlying input–output relationship when expanding the dataset using a sampling technique?

Which, if any, input parameters interact with each other?

Uncertainty analysis does not provide any meaningful results that assist in designing input variables (Hall *et al.* 2009). Hence, the focus of this paper is limited to sensitivity analysis. The key objectives of the sensitivity analyses of the Comb Separator device are listed as follows:

To develop a robust understanding of the meaningful input parameters.

To undertake a performance comparison of the proposed Comb Separator with a standard Hydro-Jet device under low flow (up to 60 L/s) conditions.

To comprehend the impact of experimental design parameters (runtime, flow discharge, effective comb spacing, weir opening and comb layers) on sewer solids capture efficiency.

To understand the relative significance of the input parameters, and to identify which parameter is the most influential in the development of output results.

This paper continues on to discuss the screening mechanism of the Comb Separator device, followed by sensitivity analysis and a review of the results.

## SCREENING MECHANISM OF THE COMB SEPARATOR

Q1 = 1 sewer overflow occurring in 1 year

Q1/2 = 2 sewer overflow occurring in 1 year

Q1/4 = 4 sewer overflow occurring in 1 year

*et al.*2015).

## SENSITIVITY ANALYSIS

*et al.*2008). SaSAT produces input parameter samples for an external model. These samples, in conjunction with outputs (responses) created from the outer model (for example, regression model), perform the sensitivity analysis. The data generation process using SaSAT is shown in Figure 5.

In the current investigation, 42 sets of experimental data were collected for the Comb Separator at five different experimental conditions to develop a MLR model. The statistical properties of data collection are summarised in Table 1. SPSS Version 22 (IBM Corp. 2013) was used as a tool for analysing MLR modelling. The MLR model shows the relation of the input parameters to output capture efficiency. However, experimental investigations are limited by the physical challenges of generating a massive experimental dataset. This is an inherent limitation in visualising a range of experimental conditions. To overcome this limitation, a sampling technique was used that allows for expansion of the data series without compromising the relationship between input and output model parameters. The standard Latin hypercube sampling (LHS) technique (Iman & Helton 1981) was used to generate 10,000 sets of data without compromising the relationship between the input–output parameters. SaSAT tools were used (see Table 2).

Input parameter | Units | Minimum | Maximum | Average | Standard deviation |
---|---|---|---|---|---|

Runtime | min | 6 | 27 | 17.04 | 7.05 |

Flow | m/s | 20 | 67 | 43.51 | 15.65 |

Effective spacing | mm | 1.5 | 4.8 | 3.05 | 1.31 |

Weir opening | mm | 470 | 970 | 765.45 | 251.62 |

Layers of combs | No. | 2 | 3 | 2.6 | 0.49 |

Input parameter | Units | Minimum | Maximum | Average | Standard deviation |
---|---|---|---|---|---|

Runtime | min | 6 | 27 | 17.04 | 7.05 |

Flow | m/s | 20 | 67 | 43.51 | 15.65 |

Effective spacing | mm | 1.5 | 4.8 | 3.05 | 1.31 |

Weir opening | mm | 470 | 970 | 765.45 | 251.62 |

Layers of combs | No. | 2 | 3 | 2.6 | 0.49 |

Change statistics | ||||||||
---|---|---|---|---|---|---|---|---|

Predictors | R | R square | Adjusted R | R square change | F change | df1 | df2 | Sig. F change |

Model 1: Considering five parameters | ||||||||

Layers of combs, runtime, flow, weir opening, effective spacing | 0.753 | 0.567 | 0.507 | 0.567 | 9.438 | 5 | 36 | 0 |

Model 2: Considering three parameters | ||||||||

Runtime, flow, effective spacing | 0.741 | 0.549 | 0.513 | 0.549 | 15.419 | 3 | 38 | 0 |

Change statistics | ||||||||
---|---|---|---|---|---|---|---|---|

Predictors | R | R square | Adjusted R | R square change | F change | df1 | df2 | Sig. F change |

Model 1: Considering five parameters | ||||||||

Layers of combs, runtime, flow, weir opening, effective spacing | 0.753 | 0.567 | 0.507 | 0.567 | 9.438 | 5 | 36 | 0 |

Model 2: Considering three parameters | ||||||||

Runtime, flow, effective spacing | 0.741 | 0.549 | 0.513 | 0.549 | 15.419 | 3 | 38 | 0 |

Key considerations for developing the methodology are listed below:

Develop meaningful and simplified inputs for the model considering the key input parameters' influence on the output capture efficiency.

Develop a MLR model and check for the necessary assumptions for validation of the model.

To gain a better understanding of the input–output relationship through expanding the dataset without compromising the input–output relationship (Aziz

*et al.*2015). The LHS technique is highly recommended in the scientific literature for parameter sampling (Loh 1995; Keramat & Kielbasa 1997; Chrisman 2014).The sampling dataset was allowed to generate 10,000 sample data, some noise data also eliminated based on unrealistic input spacing, flow discharge, runtime and capture efficiency.

Further details of data expansion are provided in the following sections.

## DEVELOPMENT OF MLR MODEL

MLR is a statistical technique that uses several explanatory (independent) variables to predict the outcome of a response (dependent) variable. The goal of MLR is to model the relationship between independent (input or predictor variables) and dependent variables.

_{i}is the outcome (dependent) variable, b

_{0}is the constant, b

_{1}is the coefficient of the first predictor (input) X

_{1i}, b

_{2}is the coefficient of the second predictor (input) X

_{2i}, b

_{n}is the coefficient of the nth predictor (X

_{ni}), and ᶓ is the difference between the predictor and the observed value of Y for the i

^{th}participant. In the case studied here, the model becomes The proposed model includes a b-value for both predictors and the constant. If the b-values are calculated, predictions can be made of the capture efficiencies using all five input (predictor) variables. Efficient design of the model input (predictors) parameters is important, because the values of the regression coefficient depend upon the variables in the model. Predictors (or inputs) variables should be selected based on past research to make sure all the key input variables are included in the model generation.

## VALIDITY OF MODEL ASSUMPTIONS

According to Berry (1993), there are a few criteria that need to be satisfied to use MLR model:

Variable type: It should be ensured that all input parameters (predictor variables) used in the experimental data are quantitative or categorical, and the output parameter (outcome variable) is quantitative and continuous.

Non-zero variance: The experimental data suggest that all the input parameters are non-zero values, so the predictor variables satisfy this criterion.

No perfect multicollinearity: Of the three key input parameters (predictors) selected for the model, there should not be a perfect linear relationship between two or more. Data were checked for multicollinearity, and it was found that no linear relationship exists between any two input parameters.

Predictors are uncorrelated with ‘external variables’: This criterion means that weir opening and comb layers should not correlate with runtime, flow and effective spacing predictors; nor should they influence capture efficiency. Neither weir opening nor comb layers influenced the other predictor variables or outcome variable; hence this criterion was satisfied.

Homoscedasticity: The data should not show any homoscedasticity. The scatter plot of the regression standardised residual against the regression standardised predicted values looks like a random array of dots evenly dispersed around zero, which confirms there is no homoscedasticity in the dataset used.

Normally distributed errors: The residuals in the model are random and normally distributed with a mean of zero. This criterion assumes that the residuals/errors are frequently zero, or very close to zero, and only occasionally are there differences much greater than zero. The histogram and normal probability plot are used to assess this criterion.

## RESULTS AND DISCUSSION

### Comb Separator performed better than Hydro-Jet at low flows

### Input parameters are almost identical using MLR and LHS

*et al.*2008).

Pearson's correlation coefficient suggests that effective spacing has a large positive correlation (*r* = 0.68) with the outcome, capture efficiency. Flow discharge has a negative correlation (*r* = −0.53) with capture efficiency, and runtime has a positive correlation (*r* = 0.49). All these results are statistically significant with *P* < 0.001 (see Table 3).

Correlations | |||||
---|---|---|---|---|---|

Capture efficiency (%) | Runtime (min) | Flow (L/s) | Effective spacing (mm) | ||

Pearson correlation | Capture efficiency (%) | 1.00 | 0.49 | − 0.53 | 0.68 |

Runtime (min) | 0.49 | 1.00 | 0.01 | 0.01 | |

Flow (L/s) | − 0.53 | 0.01 | 1.00 | 0.01 | |

Effective spacing (mm) | 0.68 | 0.01 | 0.01 | 1.00 | |

Sig. (1-tailed) | Capture efficiency (%) | 0.00 | 0.00 | 0.00 | |

Runtime (min) | 0.02 | 0.12 | 0.31 | ||

Flow (L/s) | 0.00 | 0.12 | 0.18 | ||

Effective spacing (mm) | 0.00 | 0.31 | 0.18 |

Correlations | |||||
---|---|---|---|---|---|

Capture efficiency (%) | Runtime (min) | Flow (L/s) | Effective spacing (mm) | ||

Pearson correlation | Capture efficiency (%) | 1.00 | 0.49 | − 0.53 | 0.68 |

Runtime (min) | 0.49 | 1.00 | 0.01 | 0.01 | |

Flow (L/s) | − 0.53 | 0.01 | 1.00 | 0.01 | |

Effective spacing (mm) | 0.68 | 0.01 | 0.01 | 1.00 | |

Sig. (1-tailed) | Capture efficiency (%) | 0.00 | 0.00 | 0.00 | |

Runtime (min) | 0.02 | 0.12 | 0.31 | ||

Flow (L/s) | 0.00 | 0.12 | 0.18 | ||

Effective spacing (mm) | 0.00 | 0.31 | 0.18 |

### Effective spacing, flow discharge and runtime are the key input parameters for the Comb Separator

The initial input parameter design considers all 16 input parameters that could influence pollutant capture efficiency (Aziz *et al.* 2013). Out of these 16 input parameters, physical analysis of the experimental data highlights that only five key input parameters have major influences on capture efficiency (Aziz *et al.* 2015). Further analysis on sensitivity testing only considers five input parameters, including runtime (min), flow discharge (L/s), weir opening (mm), effective spacing (mm) and layers of combs (number).

In the current research, forced entry (or Enter as it is known in SPSS (Statistical Package for the Social Science)) was used as the method by which all predictors are forced into the model simultaneously. Unlike the hierarchical method, the forced entry method makes no decisions about the order in which variables are entered. Table 2 shows the results for two MLR models, with five and three input parameters. In developing the MLR model initially, all input parameters that could have any influence on the output capture efficiency were considered. Trials were done in the MLR analysis, in which all predictors were entered into the model and outputs were examined to see which predictors contributed substantially to the model's ability to predict capture efficiency. In the initial model, all five input parameters – being runtime (min), flow discharge (L/s), weir opening (mm), effective spacing (mm) and layers of combs (number) – were considered. After a few different trials with the input parameters, it was found that the weir opening and comb layers were insignificant input (predictor) parameters, as they had little influence on the output sewage solid capture efficiency. The regression correlation coefficient R defines the correlation coefficients between the predictors and the outcome. R values vary from 0.753 to 0.741, from the first model to the second model, which is an insignificant difference between the two datasets. For the first model, R^{2} had a value of 0.567, which means that the five input parameters’ combined prediction accuracy on capture efficiency is 56.7%. However, in the second model with three parameters, the R^{2} value is 0.549, which means the three input parameters’ combined prediction accuracy on capture efficiency is 54.9%. Therefore two input parameters – weir opening and comb layers – account for only 1.8% influence on output predicting capture efficiency.

The final MLR considered three input parameters: runtime (min), flow (L/s) and effective spacing (mm), and excluded comb layers (number) and weir opening (mm). The adjusted R^{2} provides some idea of how well our model generalises; ideally, we would have liked its value to be the same, or very close to, the value of R^{2}. In this case the difference of R^{2} between the final model and the initial model was small (0.549 − 0.513 = 0.036). This shrinkage means that if the model were derived from the population rather than from a sample, it would account for approximately 3.6% less variance in the outcome (see Table 2).

### Effective spacing has a positive co-relation with capture efficiency

### Increasing flow discharge reduces capture efficiency

### Overflow event duration increases sewage capture efficiency

## CONCLUSION

A series of laboratory trials with different runtimes, flow, effective spacing, layers of combs and weir openings were tested. Sensitivity analyses of these input parameters were performed to identify their influences on sewage overflow capture efficiency. The sensitivity analysis was aimed at developing a robust understanding of the relationships between the input (predictors) and output (outcome) variables. The MLR model was initially considered, using five input parameters. After significant trial and error, it was found that the two input parameters – weir opening and comb layers – could be excluded, because these two parameters only contribute to 1.8% of prediction accuracy.

The MLR model (Equation (4)) and the LHS sampling technique (Equation (5)) are almost identical. This ensured that the model retained the underlying input and output relationship when expanding the dataset from 42 sets to 10,000 sets. Sensitivity analysis delivered a cleaner understanding of the relative importance (rank) of the input parameters. It was found that effective spacing (mm) is the most influential parameter, followed by flowrate (L/s) and runtime (min). The sampling technique also provides better understanding of the input–output relations; for example, 1 unit (mm) increase in effective spacing is likely to increase output capture efficiency by 5.32%.

These sensitivity analysis results will be immensely valuable in developing a practice manual for the proposed device. This sensitivity analysis of input parameters is relatively easy to understand and explain compared with other data-driven models. Further attempts to understand the performance of the proposed Comb Separator could focus mainly on three parameters: effective spacing (mm), flow (L/s) and runtime (min). These sensitivity analysis results will help device operators and managers to make informed decisions in the management of different sewerage overflow events. The hydraulic experiments suggest good application potential for the proposed device in the urban sewer system. Further experiments are recommended to improve the understanding of the input parameters in high flows.