# Predicting Fibrous Filter’s Efficiency by Two Methods: Artificial Neural Network (ANN) and Integration of Genetic Algorithm and Artificial Neural Network (GAINN)

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## Abstract

In this study, we used both methods of ANN and GAINN for predicting the fibrous filter’s efficiency. In this regard, we collected the experimental penetration data for particles in the range of 10.7–191.1 nm. Experimental data were collected with different constant flow rates and from one type of N95 filtering facepiece respirator. A satisfactory number of data from experimental setup were exploited to build up a database. These methods are according to the back-propagation algorithm to map two components, namely, particle diameter and constant air flow rates into the corresponding penetration. The developed ANN and GAINN methods were capable of predicting precise values of penetration from experimental data. Also by comparing the results of these two methods, it is understandable that ANN method can predict the penetration data from examples of the experimental setup more efficiently than GAINN within an acceptable computational time.

## Keywords

Nanoparticles Filtration Artificial neural networks Genetic algorithm HVAC filters## 1 Introduction

Air pollution has become a major problem in recent years. This matter is at highest importance in protecting workers against toxic inhaled nanoparticles. Besides, removing ultrafine particles (UFPs) in residential and light-commercial central HVAC systems highlights the significance of studies in this field. These concerns necessitate evaluating the efficiency of fibrous filters, used in ventilation systems (Stephens and Siegel 2013) or in filtering facepieces (Brochot et al. 2018; Mahdavi et al. 2015; Mostofi et al. 2011, 2012). As reported in several reviews, the filtration performance is evaluated based on two parameters: the pressure drop and filtration efficiency (Abdolghader et al. 2018; Givehchi and Tan 2014; Lee and Liu 1982; Mostofi et al. 2010; Wang and Otani 2013).

As an aerosol flow approaches the surface of a fiber, particle deposit on it is caused by several mechanisms such as gravitational settling, inertial impaction, interception, diffusion and electrostatic forces.

*η*) is considered as a function of total single-fiber efficiencies \((E_{\sum } )\) and is given as (Hinds 1999):

*α*is considered as the packing density of the medium,

*L*is the thickness of the medium and \(d_{\text{f}}\) is the fiber diameter. The equation was obtained theoretically by considering the interrelationship between total single-fiber efficiency and total efficiency of a medium. Single-fiber efficiency is the ratio of the particles settled down on a unit length of fiber surface. The total single-fiber efficiency is an approximation according to the assumption that all separate mechanisms are independent and all of them are smaller than unity (Brown 1993; Kasper et al. 1978; Lee and Liu 1982; Payet et al. 1992). In this regard, it will be assumed that total single-fiber efficiency \((E_{\sum } )\) is presented by the sum of the efficiencies for each of the individual mechanisms.

Thus, it is obvious that theoretical studies are necessary to understand the performance of fibrous filters (Abdolghader et al. 2018; Givehchi and Tan 2014; Lee and Liu 1982). Also, it is important to carry out experiments to validate those theoretical studies. Meanwhile, predicting the experimental data using artificial neural networks (ANNs) is a very efficient approximation method. However, there are few studies to demonstrate that ANNs can be applied to predict the filtration efficiency of fibrous filters. Therefore, filling this gap is the prime motivation for the present study.

The objective of this work is to investigate the possibility of using two methods, artificial neural networks (ANNs), and the integration of genetic algorithm (GA) and neural network (GAINN) to predict the efficiency of the fibrous filters directly. At the next level, by comparing the results from the above-mentioned methods, we will indicate which method can be exploited to better estimate the penetration data from the examples of the experimental setup within an acceptable computational time.

## 2 Artificial Neural Network (ANN)

Artificial neural network is parallel information processing method which is capable of modeling complicated and nonlinear equations using a variety of input–output training data, obtained from accessible experiments or numerical results (Awad and Herzallah 2015; Kaushik et al. 2015; Su et al. 2014).

\(x_{1}\) and \(x_{2}\) are input data which are particle diameter and constant air flow rates, respectively, and *y* is output value which is penetration.

*y*which is called output is given as:

*f*is a transfer function which generates scalar neuron output in accordance with weight, bias and neurons input. Among different types of transfer functions, the ‘S’-shaped log-sigmoid is commonly used in feed-forward multilayer neural networks with back propagation which is given as (Madaeni et al. 2010):

In Eq. (6), *m* represents the number of output nodes, *G* denotes the number of training samples, while \(y_{{({\text{ANN}})j}} (k)\) is the expected output, and \(y_{{({\text{Experiment}})j}} (k)\) stands for the actual output (Parsian et al. 2017).

The network is trained by optimizing the weights for each node interconnection and bias terms until a satisfactory agreement is obtained among the output layer neurons and actual outputs.

The data are divided into two groups, a training data and a validating one. The validating data are used to estimate the accuracy of the model, whereas the training data are exploited to find optimal set of weights. In a case that the number of weights is bigger than the number of existing data, the error in-fitting the non-trained data reduces at first, but then increases as the network gets over-trained. In contrast, in a case that the number of weights is lower than the number of existing data, the over-fitting problem is not necessary.

## 3 Genetic Algorithm (GA)

### 3.1 GAINN

The simulation time and accuracy are the most important analytical points that should be mentioned in this study.

### 3.2 Simulation Time

Certainly, the runtime of the GAINN method is lengthier than ANN. The reason for this can relate to the structural characterization of these two methods. The neural network is a method of training based on gradient equations and derivatives and it knows the procedure to solve the problems. The GA has not been created to solve the problems, but it has been created to find the optimal answer. It obvious that the GA is a random algorithm which is searching in space; so, finding the answer by this method takes more time in comparison with the method of neural network.

### 3.3 Accuracy

According to the definition of the two methods in the previous section, the ANN will have a higher accuracy because the process of problem solving is done based on legitimate mathematical relationships. GA is a random searcher which is trying to find the answer by looking in the space of the states. The other thing about the GA is that this algorithm is the simplest algorithm in the evolutionary algorithm set which is no longer used in important and complex issues.

## 4 Experimental Procedure

*C*reflects the concentration, while the subscript d and u refer to downstream and upstream, respectively. Whereas efficiency of the filter is given (Bahloul et al. 2014):

## 5 Results and Discussion

In this study the selected constant airflow rates were: 42, 68, 85, 115, 135, 170, 210, 230, 270, 360 L/min and also particles were in the range of 10.7–191.1 nm. The penetration range depends on the particle diameter and air flow rates. The output results of both ANN and GAINN are related to the implementation of a double-layer neural network (each layer of five neurons) and 200 populations for the GA. The GA is based on production of 2000 generations and it has stopped at 8000th repetition.

These results indicate that ANN method can predict the penetration data from examples of the experimental setup more efficiently than GAINN.

## 6 Conclusion and Future Studies

ANN and GAINN methods were trained with data derived from experimental setup to determine the fibrous filters efficiency. To create a database, a sufficient number of data were performed, from which the ANN parameters (weights and biases) were adjusted. Both methods were developed to map the two components, which are particle diameter and constant air flow rates into the corresponding penetration. The developed ANN and GAINN methods were capable of predicting correct values for penetration from experimental data which have not been used in the training. By comparing the results of two methods, it is obvious that ANN can predict the penetration data from examples of the experimental setup more efficiently than GAINN within an acceptable computational time.

This study is limited to predict the efficiency of filtering facepieces in the range of particles and airflow rates that were used in experimental setup under certain condition of the experiment, so in this study current prediction model with ANN can not be used to evaluate the efficiency of other filters under different experimental conditions because it has been trained and validated for certain experimental parameters.

From this study, it can be inferred that, the developed neural network method is an effective tool for prediction of fibrous filters efficiency. In this study, the N95 filtering facepiece respirator was chosen as a fibrous filter media and good results were obtained as a result, ANN method can be extrapolated to all general filters to evaluate their removal efficiencies. Future studies are still required to predict the filtration efficiency of fibrous filters especially in HVAC filters which are the dominant systems for removing ultrafine particles in buildings. Thus, exploiting the ANN can result in a good predication to evaluate the filtration performance in HVAC filters. Also, further studies are necessary to investigate the possibility of integrating neural network with other optimization algorithms; such as particle swarm optimization (PSO) to reach more precise prediction.

## Notes

### Acknowledgements

The authors would like to express their gratitude to the Concordia University for funding this work, and Ms. Farinaz Haghighat for her valuable comments and suggestions.

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