# Air pollutant source estimation from sensor networks

## Date

2024

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## Abstract

A computationally efficient model for the estimation of unknown source parameters using the Gaussian plume model, linear least square optimization, and gradient descent is presented in this work. This thesis discusses results for simulations of a two-dimensional field using advection-diffusion equations underlining the benefits of plume solutions when compared to other methods. The Gaussian plume spread for pollutant concentrations has been studied in this work and modeled in Matlab to estimate the pollutant concentration at various wireless sensor locations. To set up the model simulations, we created a field in Matlab with several pollutant-measuring sensors and one or two pollutant-emitting sources. The forward model estimated the concentration measured at the sensors when the sources emit the pollutants. These pollutants were programmed in Matlab to follow Gaussian plume equations while spreading. The initial work estimated the concentration of the pollutants with varying sensor noise, wind speed, and wind angles. The varying noise affects the sensors' readings whereas the wind speed and wind angle affect the plume shape. The forward results are then applied to solving the inverse problem to determine the possible sources and pollutant emission rates in the presence of additive white Gaussian noise (AWGN). A vector of possible sources within a region of interest is minimized using L2 minimization and gradient descent methods. Initially, the input to the inverse model is random a guess for the source location coordinates. Then, initial values for the source emission rates are calculated using the linear least squares method since the sensor readings are proportional to the source emission rates. The accuracy of this model is calculated by comparing the predicted source locations with the true locations of the sources. The cost function reaches a minimum value when the predicted sensor concentrations are close to the true concentration values. The model continues to minimize the cost function until it remains fairly constant. The inverse model is initially developed for a single source and later developed for two sources. Different configurations for the number of sources and locations of the sensors are considered in the inverse model to evaluate the accuracy. After verifying the inverse algorithm with synthetic data, we then used the algorithm to estimate the source of pollution with real air pollution sensor data collected by Purple Air sensors. For this problem, we extracted data from Purpleair.com from 4 sensors around the Woolsey forest fire area in California in 2018 and used its data as input to the inverse model. The predictions suggested the source was located close to the true high-intensity forest fire in that area. Later, we apply a neural network method to estimate the source parameters and compare estimates of the neural network with the results from the inverse problem using the physical model for the synthetic data. The neural vii model uses sequential neural network techniques for training, testing, and predicting the source parameters. The model was trained with sensor concentration readings, source locations, wind speeds, wind angles, and corresponding source emission rates. The model was tested using the testing data set to compare the predictions with the true source locations and emission rates. The training and testing data were subjected to feature engineering practices to improve the model's accuracy. To improve the accuracy of the model different configurations of activation functions, batch size, and epoch size were used. The neural network model was able to obtain an accuracy above 90% in predicting the source emission rates and source locations. This accuracy varied depending upon the type of configuration used such as single source, multiple sources, number of sensors, noise levels, wind speed, and wind angle used. In the presence of sensor noise, the neural network model was more accurate than the physical inverse model in predicting the source location based on a comparison of R2 scores for fitting the predicted source location to the true source location. Further work on this model's accuracy will help the development of a real-time air quality wireless sensor network application with automatic pollutant source detection.

## Description

## Rights Access

## Subject

Gaussian plume model

neural networks

air pollutants monitoring

sensor networks

Internet of Things