An estimated method of urban concentration distribution for a mobile sensing system
Introduction
Particulate matter with diameters less than is associated with increasing rates of morbidity and mortality, particularly in cardiopulmonary disease and lung cancer [1]. In developing countries, it has been found to be the primary pollutant in urban areas [2]. A fine-grained distribution could offer well-informed air quality information for ecologists to locate the pollutant resource and analyze the possible influenced factors [3], yet for ordinary people to guide their daily lives.
Nowadays, air quality is monitored by networks of static measurement stations operated by official authorities. These stations are highly reliable and can accurately measure a wide range of air pollutants. However, their high acquisition and maintenance costs limit the number of installations. As a result, very little is known about the spatial distribution of air pollutants in urban environments and there is a lack of accurate fine-grained distribution.
Recently, a few systems based on mobile elements (MEs) [4], [5], have been proposed as an attractive solution for environmental data collection, such as Common sense, CitiSense, U-Air and Gotcha [6], [7], [8], [9]. These systems distinguished themselves from the traditional fixed air quality monitoring stations [10] which provide coarse-grained concentration distribution with a resolution of more than kilometers. However, as prototype systems, they mainly focus on networking infrastructure construction by adding more points of interests rather than simulating the particle transport informedly. The algorithm of unsampled area inference still lacks intensive research.
To this end, we try to simulate the fine particle transport in a probabilistic manner. The transport of small particles suspended in the air can be seen as a Brownian Motion [11], which has been served as a mathematical model for stochastic process since last century [12]. Random walk as an ideal mathematic model of Brownian motion from statistical physics had been successfully applied in physics, computer science, ecology, economics and the analysis of diffusion and dispersion process [13], [14]. The fundamental motivation underlying our methodology is that, the diffusion probability of certain direction is potentially affected by numerous meteorological variables. We discover the probabilities by leveraging an improved random walk which has diffusion preference inspired by biased random walk [15].
In this paper, we propose PCEM to infer the fine-grained concentration distribution based on a mobile sensing system. Those probabilities are calculated as statistical results by using quadratic programming rather than a roughly estimation based on an amount of empirical parameters and meteorological factors such as traffic volumes, street geometry, temperature, wind direction and the emission volumes for each vehicles. A heuristic function is also constructed to guide the proposed algorithm finding the most suitable original data to estimate concentration for unsampled area.
To validate our algorithm, we divide the testing area into amounts of grids and let mobile sensors to collect concentration randomly in the testing area. Compared with traditional atmospheric models, this way of data collection can improve resolution level by 100 times. The degree of correlation between estimated concentration and real measured data is more than 0.9565. During six month’s experiments, the mean absolute estimated error of proposed algorithm can be reduced by 15.4% compared with AirCloud, 41.0% and 51.4% compared against ANN and multi-variable linear regression (MLR), respectively. The root mean squared error remains lowest during this period. The robustness of PCEM is also verified by adding 1%, 5% and 10% errors into original data. The increment of mean absolute error is about 1.45% which performs far more better than ANN and MLR. These results strongly demonstrate that PCEM is robust and can be applied into various scenarios. Furthermore, the results could also display the geographical features of selected area.
Our contributions can be summarized as follows,
- •
An improved random walk approach is advised to simulate the transport.
- •
The proposed PCEM can provide a fine-grained concentration distribution which can be adopted to monitor other particle transport in an open-air flow.
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A prototype system of BlueAer is implemented to validate our PCEM. The result shows PCEM can reach up to 100 times higher resolution and has a good performance in terms of accuracy and robustness.
The rest of this paper is organized as follows. Related work is discussed in Section 2. Section 3 introduces assumptions and notations used in this work. In Section 4, the proposed PCEM algorithm is presented in detail. A prototype experimental system is developed in Section 5 to validate our PCEM. The performance of proposed algorithm is evaluated in Section 6. Section 7 analyzes the results and discusses the potential findings from a fine-grained concentration distribution. Finally, the conclusions and future work of this paper are discussed in Section 8.
Section snippets
Related work
Since many government activities and interactions have been conducted in emission monitoring area, a growing number of approaches have attempted to provide concentration information.
Most of research preferred, or partly referred to, statistic approaches when exploring concentration distribution. Chaloulakoua et al. [16] employ regression model to analyze the relationship between meteorological factors and concentration. Similarity, Karaca et al. [17] use statistical and
Preliminaries
In this paper, we define several assumptions as follows.
- (1)
The weather condition can be seen as equivalent in a regional area over a period of time.
- (2)
A grid with a resolution of hundred meters would be regard as a point in terms of geography.
- (3)
Particles can only transport from local grid to the nearest neighbors after one step.
- (4)
Different directions have different transport probabilities, and the preference is a comprehensive result affected by numerous effected factors.
- (5)
The concentration remains
Methodology
In this part, the main idea of proposed PCEM would be introduced in detail. PCEM consists of two steps: constructing a mathematical modeling of the particle transport followed by the inference of concentration of undetected grids.
Experiments
In this section, a prototype system: BlueAer is developed to verify the proposed PCEM. As Fig. 4 shows, it mainly includes three parts: sensors calibration, data collection, data processing and visualization.
Performance evaluation
In this section, we evaluate the performance of PCEM in terms of accuracy and robustness. The algorithm accuracy can be assessed by estimated error between the inference value and the actual data. The actual data is collected by vehicles with built-in sensors. The robustness of algorithm is also verified by adding different portion of error data into the collected original data set.
Discussion
In this section, we will discuss several interesting points discovered in the result fine-grained concentration distribution.
Conclusions and future work
In this paper, we embrace the idea of random walk and proposed a novel algorithm PCEM to offer a fine-grained concentration distribution in an urban area. The proposed algorithm has been validated through experiments in terms of accuracy and robustness.
Compared with the traditional model based on fixed monitoring sites, PCEM can offer the concentration in a 100 times higher resolution level. The average estimate error rate of PCEM is 5.669%, which reduces 41.0% compared with ANN.
Acknowledgments
We sincerely thank Professor Weigang Sun for shepherding our paper. This work is supported by National Natural Science Foundation of China under Grant Nos. 61190113, 61401135 and 61471150.
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