Computational Intelligence and Neuroscience

Volume 2017, Article ID 2843651, 11 pages

https://doi.org/10.1155/2017/2843651

## A New Hybrid Model FPA-SVM Considering Cointegration for Particular Matter Concentration Forecasting: A Case Study of Kunming and Yuxi, China

^{1}School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China^{2}North Automatic Control Technology Research Institute, Taiyuan, Shanxi 030006, China

Correspondence should be addressed to Weide Li; nc.ude.uzl@ilediew

Received 3 February 2017; Revised 7 June 2017; Accepted 6 July 2017; Published 28 August 2017

Academic Editor: Thomas DeMarse

Copyright © 2017 Weide Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Air pollution in China is becoming more serious especially for the particular matter (PM) because of rapid economic growth and fast expansion of urbanization. To solve the growing environment problems, daily PM2.5 and PM10 concentration data form January 1, 2015, to August 23, 2016, in Kunming and Yuxi (two important cities in Yunnan Province, China) are used to present a new hybrid model CI-FPA-SVM to forecast air PM2.5 and PM10 concentration in this paper. The proposed model involves two parts. Firstly, due to its deficiency to assess the possible correlation between different variables, the cointegration theory is introduced to get the input-output relationship and then obtain the nonlinear dynamical system with support vector machine (SVM), in which the parameters c and g are optimized by flower pollination algorithm (FPA). Six benchmark models, including FPA-SVM, CI-SVM, CI-GA-SVM, CI-PSO-SVM, CI-FPA-NN, and multiple linear regression model, are considered to verify the superiority of the proposed hybrid model. The empirical study results demonstrate that the proposed model CI-FPA-SVM is remarkably superior to all considered benchmark models for its high prediction accuracy, and the application of the model for forecasting can give effective monitoring and management of further air quality.

#### 1. Introduction

Air pollution has a great impact on humans and environment [1, 2]. The information on meteorological pollution, caused by CO, NO, NO_{2}, SO_{2}, O_{3}, and particulate matter (PM_{2.5} and PM_{10}), is urgent due to the harmful effects on human health [3]. Especially in recent years, regions of China have suffered the hazy weather including Jianghuai, North China, Huanghuai, south of the Yangtze River, and other areas. The affected regions are about 25% of the country, and the affected population is above six hundred million [4]. Furthermore, the hazy weather is harmful to the respiratory and cardiovascular system of human which would induce chronic disease and cancer. In addition, it would affect mental and reproductive health. And related studies found that extreme particulate matter (PM_{2.5} and PM_{10}) was one of the main factors of hazy weather [5]. So it is urgent to monitor the particulate matter and its forecasting is an important work. In view of this situation, this paper introduces a new hybrid model to forecast the daily particulate matter of Kunming and Yuxi, China.

In recent period, there are lots of researchers concentrating on the technique of predicting the PM concentration. The extreme particulate matter is an open, nonlinear, dynamic, and complex system. So it is difficult to derive an accurate formula to predict the value of PM. Fortunately, a data-driven, empirically based or “black-box” modeling approach which is designed to identify relationships between input and output without considering the mechanism of generating particulate matter can be employed to predict the PM concentration. With the development of artificial intelligence, machine learning techniques such as ANN and SVM have been applied into the time series of air pollution matter. Grivas and Chaloulakou provided reliable predictions of PM_{10} hourly concentrations by evaluating the potential of various developed neural network models [6]. Cai et al. applied artificial network to predict hourly air pollutant concentrations of Guangzhou, China [7]. Caselli et al. developed the back-propagation neural network to predict the daily PM_{10} concentration before 1, 2, and 3 days [8]. De Gennaro et al. developed an artificial neural network (ANN) to forecast PM_{10} daily concentration in two contrasted environments in NE Spain [9]. Ding et al. predicted air pollutant concentration using a feedforward neural network inspired by the mechanism of the human brain [10]. Meanwhile, the method of support vector machine is widely employed in predicting the air pollutant concentrations. Suárez Sánchez et al. proposed a regression model of air quality by using the support vector machine (SVM) technique in the Aviles urban area (Spain) at local scale [11]. García Nieto et al. presented a method of daily air pollution modeling by using support vector machine (SVM) technique in Oviedo urban area (Northern Spain) at local scale [12]. But it is difficult for one single machine learning algorithm to achieve high precise prediction [13]. So researchers combined different algorithms to get hybrid models to forecast the air pollution matter (CO, NO, NO_{2}, SO_{2}, O_{3}, and particulate matter). Díaz-Robles et al. proposed a hybrid model combining ARIMA and ANN to improve forecast accuracy for the air quality of Temuco, Chile [14]. Feng et al. used artificial neural network to predict ozone concentration on single site with a better forecast accuracy in huge data set condition [15]. Fu et al. introduced a feedforward neural network with rolling mechanism and grey model to forecast air PM_{2.5} and PM_{10} concentrations in Hangzhou, Shanghai, and Nanjing, China [16]. Niu et al. introduced a hybrid model based on CCEMD, GWO, and SVM for daily PM_{2.5} concentration forecasting in Harbin and Chongqing, China [4]. Xu et al. proposed a hybrid model named ICEEMD-WOA-SVM for forecasting major pollutants (CO, NO, NO_{2}, SO_{2}, O_{3}, and particulate matter) in Harbin, Chongqing, and Taiyuan, China [17]. Inspired by above researches, this paper proposes a new hybrid model with different algorithms to improve the accuracy of prediction.

As the traditional methods, many researchers established the models only using one time series. So these models may reduce the accuracy of the prediction with using insufficient information. Fortunately, Engle and Granger provided the cointegration theory to overcome the problems of nonstationarity of the time series and deal with the “spurious regression” [18]. And the forecast based on cointegration theory can put two or more sequences into the models and enhance the performance of the models. Because of its great effect, the theory has been studied in economics extensively during the past decades. Nevertheless, this theory started applying to the engineering research. Using the cointegration theory, Belloumi examined the causal relationship between per capita energy consumption and per capita gross domestic product for Tunisia during the 1971–2014 period [19]. Shahbaz et al. reexamined the relationship between electricity consumption, economic growth, and employment in Portugal using the cointegration [20]. Jahangir Alam et al. investigated the possible existence of dynamic causality between energy consumption, electricity consumption, carbon emissions, and economic growth in Bangladesh [21]. Saboori et al. established a long run as well as causal relationship between economic growth and carbon dioxide (CO_{2}) emissions for Malaysia [22]. Dogan analyzed the short and long run estimates as well as the causality relationships between economic growth, electricity consumption from renewable sources, and electricity consumption from nonrenewable sources for Turkey in a multivariate model wherein capital and labor are included as additional variables [23]. In the study of hydrology, Zhang et al. introduced CI to reveal the long-term balance relationship and short-term fluctuations of the original and decomposed runoff and sediment load time series [24]. In meteorology, de Cian et al. presented an empirical study of the relationship between residential energy demand and temperature [25]. For these reasons, this paper tries to make use of the cointegration theory to find the causal relationship of PM_{2.5} and PM_{10} of Kunming and Yuxi.

In machine learning, support vector machine (SVM) has greater performance to depict nonlinear relationship. But the accuracy of SVM depends on two parameters and the optimized methods for selecting the parameters are complex and changeable. Hu et al. proposed a hybrid forecasting approach that consists of the empirical wavelet transform, coupled simulated annealing, and least square support vector machine for enhancing the accuracy of short-term wind speed forecasting [26]. Zhang et al. built a predictive model based on support vector regression and differential evolution algorithm to forecast the electricity load [27]. Liang et al. proposed a hybrid model based on wavelet transform and least squares support vector machine, which is optimized by an improved cuckoo search to predict the short-term electric load [28]. Wu and Peng built a novel hybrid approach for wind power generation forecasting in the light of cloud-based evolutionary algorithm and least squares support vector machine [29]. Santamaría-Bonfil et al. proposed a hybrid methodology based on support vector regression and genetic algorithm for wind speed forecasting [30]. W. Sun and J. Sun presented a novel hybrid model based on least squares support vector machine optimized by cuckoo search to monitor and control the PM_{2.5} concentration [31]. Sreekumar et al. presented three forecasting models, namely, three-day trained support vector regression model and parameter optimized SVR using genetic algorithm and that using particle swarm optimization in the fields of power system [32]. This paper introduces a new optimized method using flower pollination algorithm to obtain the suitable parameters for support vector regression, and this algorithm is more efficient than traditional methods such as GA and PSO [33].

Targeting at improving the predictive accuracy of PM_{2.5} and PM_{10} concentration, a hybrid model based on cointegration theory (CI), support vector machine (SVM), and flower pollination algorithm (FPA) is established. Firstly, the cointegration theory is utilized to get the causal relationship among four particular matter sequences of Kunming and Yuxi. Then the SVM technique optimized by FPA which can achieve a balance between exploration and exploitation is built to forecast particular matter (PM_{2.5} and PM_{10} concentrations) [33]. The data sets of particular matter from two cities (Kunming and Yuxi) in Yunnan Province are collected to evaluate the effectiveness of the proposed model. The remaining part of the article is organized as follows. Section 2 mainly introduces the techniques of cointegration theory, support vector machine, and flower pollination algorithm. Next, the data of study areas, evaluation criteria, and the results of proposed hybrid model are introduced in Section 3. At last, the conclusion and future work are displayed in Section 4.

#### 2. Mathematical Methods

##### 2.1. Cointegration Theory (CI)

The cointegration theory is proposed by Engle and Granger to overcome the “spurious regression” of time series [18]. Cointegration mainly depicts the long-term balance relationships among nonstationary time series [24]. If a nonstationary time series is stationary after the times differencing, the time series is said to be integrated of order , represented as . Apparently, is the stationary time series.

The Augment Dickey-Fuller (ADF) test is one of the most popular tests to determine the stationarity of variable series [34]. The ADF test depends on the flowing regression formula:where *α* is the constant term; *β*, *δ*, are the parameters; is the first differencing of ; is the time; and is the white noise term. Meanwhile, the lag length is determined by the AIC and SC.

Engle and Granger proposed E-G test to examine the cointegration between two time series [18]. Firstly, the test establishes a regression model of the data by OLS and obtains the residues . Then, it tries to verify the residues time series using the ADF test. If the residue is stationary, the two time series have a casual relationship on short and long run.

The Johansen test is proposed by Soren Johansen to test cointegration of several time series of [35]. The test permits more than one cointegrating relationship. There are two types of Johansen test (trace and eigenvalue). The null hypothesis for the trace and eigenvalue tests is that the number of cointegration vectors is versus the alternative where . Both the Johansen tests are based on the vector autoregressive model.

##### 2.2. Support Vector Machine (SVM)

The support vector machine is a popular technique and its fundamental theory are introduced by Vapnik [36]. One of the advantages of SVM is minimization of structural risks, which minimize the upper-bound generalization error rather than the local training error [37]. The SVM purses the best trade-off between the model’s empirical error and the model complexity [30]. The regression formula is defined aswhere is the bias term; is the feature. And of formula is optimized aswhere is the complexity penalization term, and , correspond to the dual variables for the active constraints [38].

The technique converts nonlinear problem into linear problem using the kernel function . In this paper, the RBF is adopted, which can be expressed by

Finally, the nonlinear formula can be obtained by

##### 2.3. Flower Pollination Algorithm (FPA)

The novel swarm intelligence (SI) technique of FPA is first proposed by Yang [33]. Flower pollination is an intriguing process in the natural word. Its evolutionary characteristics can be used to design new algorithms.

The main purpose of a flower is ultimately reproduction via pollination. Pollination can take two major forms: abiotic and biotic. About 90% of flowering plants belong to biotic pollination; that is, pollen is transferred by a pollinator such as insects and animals. About 10% of pollination takes abiotic form which does not require any pollinators. The flower constancy may have evolutionary advantages because this will maximize the transfer of flower pollen to the same or conspecific plants, thus maximizing the reproduction of the same flower species [33].

Pollination can be achieved by self-pollination or cross-pollination. Cross-pollination, or allogamy, means pollination can occur from pollen of a flower of a different plant, while self-pollination is the fertilization of one flower from pollen of the same flower or different flowers of the same plant. Biotic cross-pollination may occur at long distance, and the pollinators can fly a long distance, which is considered as the global pollination. The algorithm idealizes the characteristics of pollination process, flower constancy, and pollinator behavior as the following rules:(1)Biotic and cross-pollination are considered as global pollination process with pollen-carrying pollinators performing Levy flights.(2)Abiotic and self-pollination are considered as local pollination.(3)Flower constancy can be considered as the reproduction probability which is proportional to the similarity of two involved flowers.(4)Local pollination and global pollination are controlled by a switch probability . Due to the physical proximity and other factors such as wind, local pollination can have a significant faction in the overall pollination activities.

There are two key steps in the algorithm, the global pollination and local pollination. In the global pollination step, pollen can travel over a long distance because insects can fly and move on a longer range. The first rule plus flower constancy can be represented mathematically aswhere is the pollen at iteration , and is the current best solution found among all solutions at the current iteration. The parameter is the strength of pollination which drew from a Levy distribution . The local pollination (Rule 2) and flower constancy can be represented as where and are random pollen from the different flowers of the same plant species; *ε* is from a uniform distribution in . And works better for most applications from lots of simulations. The flower pollination algorithm (FPA) is presented in Figure 1.