PM_2.5浓度预测对空气污染物早期预警具有重要意义。本文提出一种改进的PM_2.5浓度多步预测模型，即多特征聚类分解(MCD)-回声状态网络(ESN)-粒子群优化(PSO)混合模型。该模型包括分解预测部分和优化预测部分。在分解部分，提出了一种由粗糙集属性约简(RSAR)、k均值聚类(KC)和经验小波变换(EWT)组成的MCD方法进行特征选择和数据分类。在MCD方法中，采用RSAR算法选择重要的空气污染物变量，使用KC算法对所得变量进行聚类，利用EWT算法将PM_2.5浓度序列的聚类结果分解为多个子层。在优化预测部分，为每个分解层分别建立ESN多步预测器，利用粒子群算法对ESN的初始参数进行优化。利用我国4个不同城市的真实PM_2.5浓度数据，验证了所提出模型的有效性。实验结果表明，所提出预测模型适用于PM_2.5浓度的多步高精度预测，具有比基准模型更优的预测性能。

Particulate matter with an aerodynamic diameter no greater than 2.5 μm (PM_2.5) concentration forecasting is desirable for air pollution early warning. This study proposes an improved hybrid model, named multi-feature clustering decomposition (MCD)–echo state network (ESN)–particle swarm optimization (PSO), for multi-step PM_2.5 concentration forecasting. The proposed model includes decomposition and optimized forecasting components. In the decomposition component, an MCD method consisting of rough sets attribute reduction (RSAR), k-means clustering (KC), and the empirical wavelet transform (EWT) is proposed for feature selection and data classification. Within the MCD, the RSAR algorithm is adopted to select significant air pollutant variables, which are then clustered by the KC algorithm. The clustered results of the PM_2.5 concentration series are decomposed into several sublayers by the EWT algorithm. In the optimized forecasting component, an ESN-based predictor is built for each decomposed sublayer to complete the multi-step forecasting computation. The PSO algorithm is utilized to optimize the initial parameters of the ESN-based predictor. Real PM_2.5 concentration data from four cities located in different zones in China are utilized to verify the effectiveness of the proposed model. The experimental results indicate that the proposed forecasting model is suitable for the multi-step high-precision forecasting of PM_2.5 concentrations and has better performance than the benchmark models.