PM${}_{2.5}$ concentration prediction is an important task in atmospheric environment research, so many prediction models have been established, such as machine learning algorithm, which shows remarkable generalization ability. The time series data composed of PM${}_{2.5}$ concentration have the implied structural characteristics such as the sequence characteristic in time dimension and the high dimension characteristic in dynamic-mode space, which makes it different from other research data. However, when the machine learning algorithm is applied to the PM${}_{2.5}$ time series prediction, due to the principle of input data composition, the above structural characteristics can not be fully reflected. In our study, a neighbor structural information extraction algorithm based on dynamic decomposition is proposed to represent the structural characteristics of time series, and a new hybrid prediction system is established by using the extracted neighbor structural information to improve the accuracy of PM${}_{2.5}$ concentration prediction. During the process of extracting neighbor structural information, the original PM${}_{2.5}$ concentration series is decomposed into finite dynamic modes according to the neighborhood data, which reflects the time series structural characteristics. The hybrid model integrates the neighbor structural information in the form of input vector, which ensures the applicability of the neighbor structural information and retains the composition form the original prediction system. The experimental results of six cities show that the hybrid prediction systems integrating neighbor structural information are significantly superior to the traditional models, and also confirm that the neighbor structural information extraction algorithm can capture effective time series structural information.

An accurate, reliable and stable air quality prediction system is conducive to the public health and management of atmospheric ecological environment; therefore, many models, individual or hybrid, have been implemented widely to deal with the prediction problem. However, many of these models do not take into consideration or extract improperly the period information in air quality index (AQI) time series, which impacts the models’ learning efficiency greatly. In this paper, a period extraction algorithm is proposed by using a Luenberger observer, and then a novel period-aware hybrid model combined the period extraction algorithm and tradition time series models is build to exploit the comprehensive forecasting capacity to the AQI time series with nonlinear and non-stationary noise. The hybrid model requires a multi-phase implementation. In the first step, the Luenberger observer is used to estimate the implied period function in the one-dimensional AQI series, and then the analyzed time series is mapped to the period space through the function to obtain the period information sub-series of the original series. In the second step, the period sub-series is combined with the original input vector as input vector components according to the time points to establish a new data set. Finally, the new data set containing period information is applied to train the traditional time series prediction models. Both theoretical proof and experimental results obtained on the AQI hour values of Beijing, Tianjin, Taiyuan and Shijiazhuang in North China prove that the hybrid model with period information presents stronger robustness and better forecasting accuracy than the traditional benchmark models.

PM_2.5 (Particulate Matter less than 2.5 micrometers) is the main cause of haze weather, especially high concentrations of PM_2.5 can have a significant impact on normal production and daily life. The developed heavy industry in North China has led to poor air quality, characterized by high concentrations of pollutants and frequent pollution incidents. The research on the prediction of PM_2.5 concentration in North China is of great significance for the prevention and control of air pollution nationwide. In this article, hourly PM_2.5 data from six important cities in North China, namely Beijing, Tianjin, Shijiazhuang, Taiyuan, Jinan, and Zhengzhou, were used as the basic dataset. Empirical Mode Decomposition (EMD), Long Short-Term Memory (LSTM), Support Vector Machine (SVM), and Autoregressive Integrated Moving Average (ARIMA) were mixed to establish a PM_2.5 hourly prediction model (Hybrid-EMD_HL). The selection of different analysis models based on the time-frequency characteristics of high-frequency and low-frequency subsequences helps to improve the adaptability of data and models, deeply mine data information, and fully express the inherent characteristics of one-dimensional time series, which improves the prediction accuracy. Firstly, nonlinear and non-stationary PM_2.5 time-series data were decomposed into Intrinsic Mode Functions (IMFs) and residuals at different frequencies using EMD technology. Then, based on the frequency characteristics of the subseries, LSTM and ARIMA model were used to predict the high-frequency and low-frequency parts, respectively. Finally, the SVM (Support Vector Machine) model was used to integrate the high and low frequency prediction results to obtain the final result. The simulation experiment was verified by algorithm performance indicators. Compared with the single prediction model, the hybrid prediction model significantly improved the prediction accuracy of PM_2.5 concentration. Specifically, in multiple data experiments, the directional indicator DA of hybrid prediction model is higher than 0.69, showing better direction prediction ability, which is of practical significance for the prevention and control of air pollution in North China.