1. Introduction
In recent years, due to climate change, industrial production, and population growth, the air quality has deteriorated in many parts of the world. This decline in air quality has seriously affected economic development and public health. Fortunately, with gradual improvements in air quality monitoring systems, many countries have established multilevel air quality monitoring networks. The air pollutants of concern mainly include gaseous compounds such as carbon monoxide (CO), sulpfur dioxide (SO
2), nitrogen oxides (NO
x), ozone (O
3), and fine particulate matter (PM
2.5 and PM
10) [
1,
2,
3]. In particular, the PM
2.5 and PM
10 concentrations have considerable impacts on human health [
4]. Hence, it is crucial to forecast the ambient air quality and air quality index to ensure timely and proper responses to heavily polluted weather and to provide guidance for joint emission reduction measures to reduce regional air pollution. In addition, improving the accuracy of air quality analysis and forecasting can help governments to improve the reliability of environmental management and decision-making, and enable timely and effective prevention and control measures to minimize the harm caused by air pollution to people. However, many factors affect air quality—including environmental factors such as temperature, humidity, and wind speed; and human factors such as traffic conditions and pollution source emissions—which increases the difficulty of accurately predicting air quality. Therefore, it is particularly important to establish an air quality prediction system that can achieve excellent performance.
Traditional air quality prediction methods mainly include numerical prediction and regression statistics [
5]. Numerical air quality models are based on atmospheric dynamics and employ the monitoring information from multiple environmental monitoring stations to establish meteorological emission and chemical models, and thus, simulate the migration, exchange, diffusion, and emission of pollutants [
6]. However, numerical prediction methods are subject to complex prior knowledge, use unreliable and limited data, and have various usage constraints [
7]. Moreover, the requirements for the input data are relatively strict, rendering it difficult to accurately predict air quality in real time [
8]. Thus, it is theoretically difficult to simulate the real atmospheric environment. In contrast, the regression statistics-based approach avoids complex theoretical models and instead leverages statistical models to predict air quality based on analyses of historical air quality data. Compared with numerical prediction methods, which are based primarily on historical meteorological data and the regular analysis of pollutant monitoring concentrations, meteorological forecast products are utilized to predict pollutant concentrations [
9]. Nevertheless, the complex linear or nonlinear relationships between the various factors affecting both air quality and the concentrations of air pollutants are challenging to describe with a definite mathematical model.
Statistics-based air quality prediction models are relatively simple to implement, as the relationships between pollutant concentrations and meteorological factors are established on the basis of statistics. As air pollutant concentration data are nonlinear and irregular, the above-mentioned methods cannot meet the requirements of practical applications to obtain sufficiently accurate and reliable prediction results. However, while the prediction performances of statistics-based methods need to be improved, these models can be applied to predict the air quality in smaller areas, and thus, can provide a certain theoretical basis for future predictions using machine learning and deep learning models. Currently, with the rapid development and application of the Internet of Things and sensor technologies, atmospheric data collected by various sensors and related data collection equipment in cities provide the necessary sources of data for air quality prediction. Since traditional shallow learning models still encounter bottlenecks in utilizing big data, new air quality prediction methods need the support of data-driven models [
10]. Recently, many machine and deep learning approaches, such as decision trees (DTs) [
11,
12], support vector regression (SVR) [
13,
14,
15], long short-term memory (LSTM) [
16,
17,
18], and random forest models [
19,
20], have been adapted to air quality forecasting. In addition, a universal and effective deep learning air model was proposed to resolve the interpolation, prediction, and feature analysis of air quality at a fine resolution [
21] via the embedded feature selection and semisupervised learning of different layers in a deep learning network. This model utilizes relevant information from unlabelled air quality data to improve the interpolation and prediction performance. Moreover, in 2020, a hybrid deep learning model that combines LSTM and convolutional neural networks was developed to improve the air quality prediction accuracy [
22]. It can consider the spatial correlation characteristics of air pollutants to achieve high prediction performance. Furthermore, in regard to spatiotemporal correlations, a deep learning model was provided in [
23] for daily PM
2.5 concentration forecasting.
Although machine and deep learning models can rapidly forecast air quality with high accuracy, under many complex air quality conditions, feature extraction is not a simple task, as it requires the artificial design of an effective feature set to predict the training results. Therefore, for long-term air quality predictions and addressing the uncertainties and nonlinear problems in prediction systems, employing machine learning prediction models remains challenging. For instance, an LSTM network cannot model and analyze the complex spatial and temporal correlations with air quality, and its nonlinear spatial dependence is an important factor affecting the air quality prediction performance. Nevertheless, with the rise of artificial neural networks (ANNs), which are data-driven and have various advantages, including data adaptation, parameter self-learning, and combined memory, a number of researchers have attempted to apply various neural network models to predict air quality. For example, a hybrid multilayer perceptron (MLP) and linear regression model was developed on the basis of principal component analysis to analyze air pollution [
24]. In [
25], a feedforward backpropagation neural network (BPNN) and regression model were combined to predict seasonal indoor PM
2.5–10 and PM
2.5 concentrations, and another BPNN-based approach was developed in [
26] for regional multi-step-ahead PM
2.5 forecasting. ANNs were likewise used in a highly polluted region to predict the concentrations of all types of pollutants on subsequent days [
1]. Moreover, based on a supervised learning neural network, a modified depth-first search method was employed to estimate PM
10 concentrations in [
27], and Zhang et al. developed an Elman neural network (ENN)-based model for estimating air quality [
28]. In addition, fuzzy neural networks [
29] and recurrent neural networks [
30,
31] have been widely used in air quality prediction.
ANNs can reliably and accurately map the correlations between inputs and outputs, and thus have been extensively applied to the prediction of air quality. However, because each ANN model has unique advantages and limitations, it is difficult to select the most suitable model for all air quality time series. In addition, the above-mentioned models focus only on the signal transmission between neurons and ignore the nonlinear relationship in the dendritic structure of each neuron, which has been verified in biological neurons [
32]. Moreover, most training algorithms easily fall into local optima and are sensitive to the initial state with gradient descent information [
33,
34]. To overcome these limitations and consider the calculation efficiency, in this study, a novel dendritic neural regression model (DNR) is proposed to estimate air quality. It is an improved version of our previously proposed dendritic neural model (DNM), which has been successfully applied to morphological hardware realization [
35], classification [
36,
37,
38,
39,
40], and time series prediction [
41,
42]. Due to the plasticity of dendrites and the nonlinear characteristics of synapses, the DNM can effectively simulate the processes by which biological neurons transmit information and has the capability to fit complex nonlinear functions well. However, since the original DNM network was designed for classification problems, adaptive pruning is needed in the calculation process to improve the calculation efficiency, especially in the processing of high-dimensional data classification; consequently, the computational complexity is excessively high, leading to a long computation time. In the proposed DNR network, we employ a single-branch approach to reduce the computational complexity, and utilize a new weight to control the strength of the branch. In addition, because DNR is used to predict air quality, for which the weight space to be trained is vast and complex, a global optimization algorithm with stronger search capabilities is needed to replace the traditional gradient descent-based algorithm. In this study, to further enhance the air quality prediction performance of DNR, a scale-free network-based differential evolution (SFDE) algorithm is proposed to optimize the weight and threshold of DNR [
43]. This scale-free local search method can ensure the diversity of individuals and avoid local optima, thereby helping the differential evolution (DE) algorithm reach the global optimum.
Moreover, one-dimensional air quality time series data can be unpredictable and irregular, and some information is hidden in high dimensions. According to Takens’s theory [
44], phase space reconstruction (PSR) can extend one-dimensional data into high-dimensional space. If this high-dimensional data space exhibits chaotic characteristics, it is predictable. Therefore, before DNR is implemented for the air quality prediction, first, mutual information (MI) and false nearest neighbors (FNN) methods are utilized to calculate the time delay and embedding dimensions of the dataset. Then, PSR is performed to transform the one-dimensional PM
2.5 and PM
10 time series data into predictable multidimensional spatial vector data, and the maximum Lyapunov exponent (MLE) is used to validate the chaotic peculiarity. Finally, the resulting vectors are used as the training samples of DNR, and the trained DNR network is employed to perform the air quality prediction. For a fair comparison, three PM
2.5 and three PM
10 concentration datasets from the past two years were selected for experiments to evaluate DNR’s prediction performance, and each group of experiments was run independently 30 times. Our extensive experimental and statistical results confirm that the air quality estimations of the proposed DNR network are superior to those of its competitors. The novelty and primary contributions of this study are as follows:
A single-branch dendritic neural regression-based approach is proposed to estimate air quality.
To enhance the prediction performance of DNR, a customized SFDE algorithm is proposed to optimize DNR.
Extensive experiments demonstrate that DNR can more accurately and stably predict the PM2.5 and PM10 concentrations than the existing methods.
Two nonparametric statistical tests further verify that the proposed DNR network is superior to nine of its competitors.
The remainder of this paper is organized as follows:
Section 2 mainly introduces the related methods and techniques, including the proposed DNR network, SFDE algorithm, chaotic time series theory, and PSR. The relevant details of the experiments are introduced in
Section 3, including a brief description of the experimental data, the experimental setup, the evaluation criteria of the prediction methods, and the experimental results, which are presented and discussed in detail.
Section 4 presents a conclusion and summarizes the prospects for future work.