Introduction
As industrialization accelerates, human society’s demand for energy continues to rise. However, this increase in energy demand is accompanied by worsening air pollution issues, particularly the rising concentration of PM2.5 (fine particulate matter), posing a significant threat to public health. Due to its small particle size, PM2.5 can penetrate deep into the lungs and even enter the bloodstream, closely associated with various respiratory and cardiovascular diseases [1]. Consequently, monitoring and predicting PM2.5 concentrations has become a critical task in urban environmental management. Accurate prediction of PM2.5 concentrations can greatly assist in environmental quality assessment, the establishment and improvement of public health warning systems, and the formulation of strategies for air pollution control [2, 3].
Recent studies have highlighted the significant constraints imposed by climate change and smog pollution on high-quality economic development in China. The urgency of addressing these environmental challenges is underscored by the adverse effects on public health and economic stability, particularly in urban areas where PM2.5 levels are critically high. According to recent findings, low-carbon city pilot (LCCP) policies have shown potential for synergistically governing carbon and smog emissions, thus aiding cities in achieving dual environmental and economic benefits [4]. These policies have been instrumental in reducing energy consumption intensities and optimizing industrial structures, which are crucial steps toward sustainable urban development.
Furthermore, the development of public transportation systems has been identified as a crucial strategy for improving urban air quality. The “Transit Metropolis” construction demonstration project, a significant initiative in China, has been effective in reducing private car ownership and upgrading industrial structures, thereby contributing positively to air quality [5]. This policy’s success provides a compelling context for our model’s application. The significance of this research is further magnified by the pressing need to implement effective air quality management practices in light of the ongoing challenges posed by rapid urbanization and industrialization in major Chinese cities. By providing a robust tool for predicting PM2.5 concentrations, this paper assists policymakers and urban planners in crafting strategies that align with sustainability goals.
Current research indicates that PM2.5 concentration prediction techniques primarily fall into two categories: models based on physical laws and data-driven intelligent algorithms. Physical models often require researchers to have an extensive background in atmospheric science, understanding the chemical and physical evolution processes and the trans-regional migration of the atmosphere [6]. These models use meteorological data and environmental information to make predictions through complex numerical calculations. Although suitable for long-term forecasting, these models involve cumbersome computational processes and require high-quality data [7]. In contrast, data-driven intelligent algorithms, by mining statistical information and features from historical data, can establish a mapping relationship between historical data and forecasting targets. These methods can effectively predict PM2.5 concentrations even with incomplete historical data and are more cost-effective. Traditional statistical methods like Markov chains [8] and Autoregressive Integrated Moving Average (ARIMA) models [9], as well as machine learning approaches such as Support Vector Machines [10], have been widely adopted in the field of PM2.5 prediction.
The Transformer, known for its capability to learn complex patterns and features from time series and its ability to capture long-distance dependencies, has been applied in time series forecasting [11]. The Informer model introduces the ProbSparse self-attention mechanism, which reduces computational complexity by calculating attention only for a subset of key elements. Autoregressive sparsification further reduces the attention scores that need to be calculated, focusing only on those most likely to be important. This reduces the computational burden and improves the model’s efficiency and performance in handling long sequences. The Informer model optimizes the encoding of time features, ensuring the model better understands and utilizes temporal information, which is particularly important for time series forecasting. This encoding approach helps the model capture seasonal and trend dynamics in the time series [12]. With increasing demands for prediction accuracy, more research is exploring hybrid forecasting models to more accurately capture the temporal characteristics of PM2.5 concentration variations and enhance prediction accuracy.
In the data preprocessing stage, to mitigate the effects of the nonlinearity, volatility, and instability of PM2.5 concentration data on the forecasting models, researchers often employ decomposition algorithms. These algorithms can break down complex raw data into several more stable subsequences, thereby reducing the non-stationary characteristics of the data. Widely used decomposition algorithms include Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT), and Variational Mode Decomposition (VMD). For instance, some studies have used EMD to split PM2.5 data into multiple intrinsic mode components and residue components, which are then sequentially fed into a GRU neural network for training [13]. The Empirical Wavelet Transform (EWT) algorithm can adaptively partition the Fourier spectrum and select appropriate wavelet filter banks. Research has been conducted using EWT to obtain several PM2.5 time series components and then construct predictors based on the Echo State Network (ESN) for each decomposed sublayer within each cluster group to perform multi-step forecasting calculations and form the final predictions [14]. Although EMD and EWT have demonstrated certain effects in enhancing prediction accuracy, they also have issues with endpoint effects and mode mixing. To overcome these issues, some studies have used VMD for data decomposition, inputting each decomposed subsequence (including the residual sequence) into a GRU, and then calculating the prediction loss of the subsequences [15], achieving relatively good results. However, the selection of VMD parameters remains a challenge. In other forecasting fields, some studies have adjusted VMD parameters through optimization algorithms and combined them with Convolutional Neural Networks and Bidirectional Long Short-Term Memory networks (CNN-BILSTM) to predict decomposed components, proving the effectiveness of this method in parameter selection [16].
In the feature selection stage of PM2.5 concentration forecasting, selecting highly correlated and significant features is crucial for enhancing the model’s prediction speed and accuracy. There are numerous methods for feature selection, including Mutual Information (MI) and Random Forest (RF) [13], which have proven effective in identifying features strongly correlated with PM2.5 concentrations. For example, some studies have used a method combining Variance Inflation Factor and Mutual Information (VIF-MI) to select features, demonstrating that this method can effectively reduce model complexity and enhance prediction efficiency [17]. While feature selection can improve prediction accuracy [18], although single-objective feature selection methods are effective in reducing redundancy and error, they often overlook the interrelationships among multiple objectives, which may not achieve the optimal overall effect. To this end, in the field of wind speed forecasting, some research has proposed a method based on K-means clustering and the non-dominated sorting differential evolution algorithm (FWNSDEC), a multi-objective feature selection method that integrates the advantages of different algorithms and shows better prediction performance than single feature selection methods [19].
After a systematic review of the literature, several research gaps seem to await further supplementation and exploration. Firstly, while previous studies have successfully applied various decomposition techniques to predict PM2.5 concentrations, common algorithms like EMD and EWT still have issues with endpoint effects and mode mixing, and parameter selection for various decomposition algorithms remains a challenge; single-objective feature selection has been applied in the field of PM22.5 concentration prediction, but integrating the interrelationships among multiple objectives to further reduce redundancy and error could potentially yield better prediction results; moreover, the error series generated in predictions also contains some potential features, and in some prediction fields, error correction has been proven to improve prediction accuracy to some extent [20, 21], but existing PM2.5 concentration predictions have paid little attention to post-model processing, especially error correction model with decomposition (ECD). Based on the above analysis, this paper proposes an integrated forecasting framework. The first step of the framework uses the RIME algorithm to select parameters for Variational Mode Decomposition (VMD) to stabilize the fluctuations in PM2.5 data. Then, by integrating similar components using sample entropy, high, medium, and low-frequency data components are formed. Next, an optimized multi-objective feature selection algorithm (MOFS) is used, combining the functions of filters and wrappers, to precisely select the best input feature set. Finally, an optimized Informer model is used to predict different frequency data components and error correction is combined to obtain the final prediction results. The specific research contributions include:
1) In the data preprocessing stage, the RIME algorithm is innovatively used to select the parameters for Variational Mode Decomposition (VMD), enhancing the effectiveness of VMD decomposition and reducing the volatility of the raw data. This is crucial as the RIME algorithm simulates the movement and interaction of frostbite particles, exhibiting high exploratory capabilities, especially important when dealing with long-duration data containing complex patterns and trends, such as PM2.5 concentrations. The forward greedy selection mechanism ensures that the algorithm always chooses solutions with higher fitness during updates, which helps continuously optimize the quality of results in long-term series analysis. Additionally, this selection mechanism aids in rapid convergence, particularly when dealing with large datasets, effectively reducing computational time and resource consumption. Unlike traditional methods that often struggle with parameter selection [13, 16], the RIME-enhanced VMD stabilizes data fluctuations and reduces mode mixing issues inherent in techniques like EMD and EWT. This approach has not been observed in previous PM2.5 concentration forecasting literature.
2) For the first time, Multi-Objective Feature Selection (MOFS) is introduced into the field of PM2.5 concentration prediction. MOFS optimizes the objective functions of both the designed filter and wrapper, thus integrating the advantages of these two different feature selection criteria. The Minimum Redundancy Maximum Relevance (mRMR) and Time Series Cross-Validation (TSCV) are used as the filter and wrapper objective functions, respectively. This approach selects the best feature inputs from multiple meteorological factors and historical data, enhancing the model’s prediction speed and accuracy. By employing MOFS, our model effectively addresses the limitations seen in traditional methods like Mutual Information and Random Forest, which do not consider the multivariate interrelationships crucial for understanding complex environmental data [13, 18].
3) Innovatively, an optimized Informer model is introduced into the field of PM2.5 concentration prediction. This paper compares it with common models such as LSTM, CNN, and Bi-LSTM. Studies [22, 23] have utilized LSTM and CNN for short-term PM2.5 forecasting, demonstrating their effectiveness in capturing linear relationships but often struggling with complex nonlinear patterns and long-term dependencies that are critical in environmental datasets. Similarly, Bi-LSTM models have improved upon LSTM by processing data in both forward and backward states but still face limitations in handling very long sequences and high computational loads. The ProbSparse self-attention mechanism and time feature encoding of the Informer model ensure that the model can understand and utilize time information effectively while reducing computational complexity, helping to capture the dynamic changes in the PM2.5 concentration time series. Experimental results show that the model used in this study achieved the best results across all three evaluation metrics.
4) Error correction techniques are seldom applied in the field of PM2.5 concentration prediction, particularly the error correction model with decomposition (ECD), which is introduced into the hybrid model proposed in this paper to further enhance prediction accuracy.
5) Aligning with global and national initiatives to combat air pollution, our model’s capabilities support the objectives of policies like China’s “Transit Metropolis” policy and LCCP, which aim to achieve dual environmental and economic benefits [4, 5]. Our research not only provides technological insights but also offers practical tools for policymakers to assess and refine strategies aimed at reducing PM2.5 levels and their associated health risks. The hybrid model proposed in this paper considers potential issues to various stages of prediction, combining the advantages of each module to accurately predict PM2.5 concentrations. This enriches the technological tools in the field, providing valuable quantitative references for environmental quality assessment, the establishment and improvement of public health warning systems, and the formulation of strategies for air pollution control.
Materials and Methods
Rime Optimization Algorithm
The Rime Optimization Algorithm was proposed by Hang Su in February 2023. It is inspired by the growth mechanism of rime frost. The algorithm simulates the movement of soft rime frost particles and introduces a frost impulse search strategy for algorithmic search. The components of the algorithm are as follows:
1) Initialization of rime frost cluster. Where i represents the index of a RIME agent and j the sequence number of rime frost particles, R denotes the population, and F(Si) is used to represent the growth state of each individual, i.e., the fitness value of an agent in metaheuristic algorithms.
2) Soft rime frost search strategy. Reflecting the five movement characteristics of rime frost particles, this simplifies the simulation of each rime frost particle’s condensation process and calculates the position of the rime frost particles as shown in Equation (3).
Where Rijnew is the new position of the updated particle. Rbest,j is the particle of the best rime frost agent R within the rime frost population j. The parameter r is a random number within the range (1, 1) and r1 controls the direction of particle movement. cosθ changes with the iteration number as shown in Equation (4). β is the environmental factor, which follows the iteration number to simulate the impact of the external environment and ensures the convergence of the algorithm as shown in Equation (5). h is the adhesion factor, a random number within the range (0, 1), controlling the distance between the centers of two rime frost particles. Ubij and Lbij define the upper and lower limits of the escape space, restricting the particle’s effective movement area. E is the adhesion coefficient, influencing the probability of agent cohesion and increasing with the iteration number, as shown in Equation (6).
Where t,T represent the current iteration number and the maximum iteration number, respectively.
Where the default value of w is 5, it is used to control the number of segments of β.
3) Hard-rime puncture mechanism. Inspired by the piercing phenomenon, a hard-rime puncture mechanism is proposed to update the algorithm among agents, enabling the exchange of algorithmic particles to enhance the convergence of the algorithm and the ability to escape local optima. The particle interchange formula is shown in Equation (7).
Where Fnormr(Si) denotes the normalized value of the current agent’s fitness.
4) Positive Greedy Selection Mechanism. The idea is to compare the fitness value of an agent after the update with the value before the update. If the updated fitness is superior, a replacement occurs, and the solutions of both agents are swapped.
Variational Mode Decomposition (VMD)
Variational Mode Decomposition (VMD) decomposes a complex signal into a predetermined number of band-limited Intrinsic Mode Functions (IMFs) through a variational approach. The core advantage of VMD is its ability to adaptively determine the central frequency and bandwidth of each component, effectively isolating different frequency components of the signal.
In practical applications, the performance of VMD depends on the appropriate selection of the modal number K and penalty factor α. Suitable K and α can decompose the signal more effectively and enhance the forecasting performance. To effectively select these two parameters, this paper utilizes RIME with the objective of minimizing the sample entropy value for optimization.
Sample Entropy
Sample Entropy (SampEn) is a tool used to measure the complexity of a time series, quantifying the rate of new information production within the series. Compared to other measures of complexity, Sample Entropy has the advantages of being computationally straightforward, independent of data length, and insensitive to noise. Its primary purpose is to determine the frequency of similar patterns within a time series. A lower Sample Entropy indicates a higher frequency of repeating patterns and, consequently, a lower complexity. Conversely, a higher Sample Entropy suggests that the time series is more complex and unpredictable. In this paper, Sample Entropy is used to measure the complexity of the components, and on this basis, components of high, medium, and low frequencies are constructed.
Multi-Objective Feature Selection (MOFS)
Filter objective function: mRMR (minimum Redundancy Maximum Relevance) obtains an optimal feature set by considering both relevance and redundancy, improving machine learning efficiency without sacrificing a significant amount of accuracy. In mRMR, mutual information coefficients are used to calculate the relationship between variables. The specific calculation method is shown in Equation (8), where p(x) and p(y) represent the marginal probability density of variables x and y, respectively; p(x, y) represents the joint probability density of x and y; and I(x, y) represents the mutual information coefficient value between x and y, with higher values indicating stronger relevance.
Therefore, for a given feature set S, the redundancy and relevance within the set can be measured by Equations (9) and (10), respectively.
Based on the mRMR criterion, the filter objective function can be constructed to obtain both minimal redundancy and maximal relevance, as computed by Equation (11).
Wrapper objective function: Mean Squared Error (MSE) is commonly used to measure the magnitude of error between predicted and actual values. To achieve a more scientifically valid error metric, MSE is combined with time series cross-validation techniques to derive the wrapper objective function, as shown in Equation (12). In the equation, n represents the number of samples in each subset, and v represents the number of validation sets. yi,t and ŷi,t (S) respectively represents the actual value and the predicted value with the given feature set S for the ith sample in the subset. The paper sets the number of cross-validations to 10. As Kernel Extreme Learning Machine (KELM) is efficient and provides good fitting results, it is used as the predictor for the wrapper.
Thus, the combined filter-wrapper objective function can be formulated as shown in Equation (13):
Informer
Informer, introduced by Zhou et al. (2021), represents a significant advancement in the field of time-series forecasting, particularly for long sequences. Building on the well-established Transformer architecture, the Informer introduces several key innovations that address the limitations of its predecessor, especially in handling sequences that are orders of magnitude longer than those typically processed by standard Transformers.
Enhanced Attention Mechanism
One of the most critical challenges addressed by the Informer is the inefficiency of the Transformer’s self-attention mechanism when dealing with long sequences. The standard self-attention has a quadratic computational complexity with respect to the sequence length, which makes it impractical for long sequence forecasting due to excessive memory and computational resource requirements.
ProbSparse Self-Attention Mechanism
The Informer mitigates this issue through its ProbSparse self-attention mechanism, which strategically reduces the number of attention calculations required. This is achieved by identifying and attending only to a sparse subset of the most informative key-query pairs, rather than exhaustively computing attention weights across all pairs.
Complexity Reduction
Here, in Equation (14), Q is a matrix of queries, K is a matrix of keys, V is a matrix of values, and dk is the scaling factor determined by the dimensionality of the keys. The Informer’s attention mechanism significantly reduces computational complexity by sparsifying the matrix Q.
In the conventional Transformer, the computation of QKT has a complexity of O(n2), where n is the sequence length. The Informer, by contrast, reduces this to O(nlogn), thereby enabling the processing of significantly longer sequences.
Sparsity Measure
The significance of queries is ascertained using a sparsity measure, which is essential for the ProbSparse technique:
Where qi is a specific query and LK is the length of the key sequence.
Self-Attention Distilling Encoder
Traditional Transformer encoders are limited by the memory constraints imposed by long input sequences. The Informer’s encoder circumvents this limitation through a process called Self-Attention Distilling.
Distillation Mechanism
[Xjt]AB is the attention block. By applying a convolutional layer followed by a downsampling operation, the Informer encoder is able to reduce the temporal dimension of the data while preserving essential information, thus facilitating the processing of long sequences without a proportional increase in memory usage.
Generative Decoding for Forecasting
The Informer’s decoder extends the Transformer’s capabilities by incorporating a Generative Inference approach designed to efficiently generate predictions for long sequences.
Generative Inference Process
X tde = Concat X( ttoken , X 0t ) ∈R(Ltoken +Ly )⋅dmodel
where Xtde feed de represents the input of the decoder, Xttoken token is the beginning token of the sequence, and X0t is the placeholder of the target sequence. This process allows the Informer to generate forecasts without the need to recompute attention weights for the entire sequence, thereby avoiding the performance bottleneck encountered by standard Transformer decoders during long sequence generation.
Proposed Model
The hybrid model proposed in this paper consists of four modules: optimized decomposition, feature selection, deep learning prediction, and error correction. Fig. 1 illustrates the flowchart of this hybrid model.
Step 1: Optimized Decomposition.
The raw PM2.5 data sequence is decomposed using Variational Mode Decomposition (VMD) optimized by the RIME algorithm. This step extracts useful information by calculating Sample Entropy (SE) for each component derived from the decomposition. Based on these calculations, the main frequency components – high, medium, and low – are reconstructed to capture the different dynamic characteristics of PM2.5 concentration changes.
Step 2: Multi-objective Feature Selection.
This step involves using a multi-objective feature selection strategy to filter meteorological elements and endogenous variables from the decomposed frequency components. This process aims to select the most influential feature subsets from complex data, creating an optimal feature combination for each frequency component. This approach simplifies the data for the prediction model, reduces the computational burden, and enhances prediction accuracy.
Step 3: Deep Learning Prediction.
The Informer model’s hyperparameters are optimized using the RIME algorithm. Predictions are then made for all sub-sequences, and the results from each component are linearly combined to produce preliminary prediction results and an error sequence.
Step 4: Error Correction.
The error sequence is decomposed using VMD, and each error sub-sequence is predicted using the Informer model. The results are then summed to obtain an error prediction result. The error sequence is added to the initial prediction results to obtain the final PM2.5 concentration prediction results.
Results and Discussion
Data
As the capital of China, Beijing is not only the center for politics, culture, education, and international exchange, but it is also a highly populated and industrialized metropolis. In the past few years, Beijing has frequently faced severe air pollution issues, particularly concerning high concentrations of PM2.5, which have significantly impacted the quality of life and health of urban residents. Therefore, predicting PM2.5 concentrations in Beijing holds particular importance.
The data used in this study are sourced from the public datasets provided by the China National Meteorological Information Center, specifically from the monitoring station numbered 1011A located near the Beijing Olympic Sports Center. The data encompass meteorological features and common pollutants, including PM2.5 measurements, collected from May 13, 2014, at 8:00 AM to October 10, 2020, at 11:00 PM, with data sampled every hour. Considering the significant seasonal variations in PM2.5 concentrations in the Beijing area, to improve prediction accuracy, the original dataset is divided into four subsets corresponding to the seasons: spring, summer, autumn, and winter.
Each dataset includes meteorological features such as temperature, solar zenith angle, cloud opacity, dew point temperature, wind speed at 10 m height, wind direction at 10 m height, relative humidity, and atmospheric precipitable water. The selected common pollutants for the study are SO2, NO2, CO, O3, and PM10. The data splitting strategy for model training involves using the first 70% of the data as the training set, the following 20% as the validation set, and the last 10% as the test set.
Evaluation Metrics
This paper selects three evaluation metrics, including Root Mean Square Error RMSE, Mean Absolute Error MAE, and the coefficient of determination R2. Their calculation formulas are as follows:
Optimized Decomposition Results
In Variational Mode Decomposition (VMD), the number of decomposition layers, K, and the penalty factor, ɑ, are critical factors affecting the performance of the algorithm and significantly influencing the outcomes of the decomposition. The decomposition layer K refers to the number of modes preset during the VMD process. If K is set too low, multiple modes may be merged; if K is too high, it may treat noise or irrelevant information as independent modes, increasing computational complexity and potentially introducing errors.
The penalty factor ɑ serves as a balance parameter for the constraints and is used to adjust the decomposition precision and smoothness in VMD. The value of ɑ determines the bandwidth during modal extraction, and the optimal value of ɑ can vary significantly depending on the type of signal and the level of noise. A larger ɑ results in smoother modal components but might overlook some subtle signal features; conversely, a smaller ɑ could lead to overly wide bandwidths, causing unclear boundaries between modes. In this case study, the RIME optimization algorithm is effectively used for parameter tuning. Arranged according to the seasons – spring, summer, autumn, and winter – the obtained values of K are 6, 6, 6, and 7, respectively, while the values of ɑ are 100, 100, 200, and 100, respectively.
Feature Selection Results
The results of feature selection for the four datasets corresponding to the seasons of spring, summer, autumn, and winter are shown in Table 1, where a checkmark (✔) indicates that the feature was selected. The results in Table 1 illustrate that the features required for each seasonal dataset vary. Since PM10 includes PM2.5, the correlation between them might be high, making this feature frequently used. Additionally, wind speed can influence the dispersion and dilution of pollutants, and typically, higher wind speeds help reduce PM2.5 concentrations. When humidity is high, atmospheric particulates can grow through vapor absorption and chemical reactions, potentially increasing PM2.5 concentrations, which might explain why meteorological features such as Height 10 m, wind speed, and Relative humidity are often selected.
Comparative Experiments
We initially conducted forecasts using undecomposed data for the four seasons – spring, summer, autumn, and winter – employing predictive models such as Bi-LSTM, LSTM, CNN, and Informer, with their parameters optimized using the RIME algorithm. According to the results shown in Table 2, the Informer model consistently demonstrated the best predictive performance across all original datasets.
Further, the data for the four seasons were processed through modal decomposition, and the same four benchmark predictive models – Bi-LSTM, LSTM, CNN, and Informer – were applied again. After modal decomposition, the predictive results of each mode were summed to derive the final forecast for each season. As indicated by the results in Table 2, the Informer model continued to exhibit the best forecasting performance on the seasonally decomposed datasets. Therefore, in this case study, employing the Informer as the forecasting model is an appropriate choice.
Comparison of Feature Selection Methods
Building on the decomposition of the original time series, this study combines Multi-objective Feature Selection (MOFS) for predicting PM2.5 concentrations and compares the results with those obtained using two common single-objective optimization algorithms. The results demonstrate that the MOFS method outperforms the others when predicting summer data using the Informer model. Specifically, the Root Mean Square Error (RMSE) for MOFS is 42.1987, which is significantly lower than that of the Random Forest (RF) method at 65.3129 and the Mutual Information (MI) method at 68.4523, indicating superior performance. Similarly, in the prediction of winter data, the MOFS method excels, with a Coefficient of Determination (R²) reaching 0.9712, compared to 0.9258 for RF and 0.9207 for MI.
Table 1.
Multi-objective feature selection results and feature abbreviations.
Therefore, compared to traditional single-objective feature selection methods, the multi-objective feature selection approach exhibits better performance. It effectively identifies the appropriate feature subsets, thereby enhancing the accuracy of predictions. Table 3 displays the error metrics of the predictions using the MOFS method post-modal decomposition, alongside those using MI and RF methods. Fig. 2 illustrates the prediction results for each model after RIME optimization using the MOFS approach.
Table 2.
Benchmark model predictions before and after decomposition.
Table 3.
Results of prediction error metrics based on MI, RF, and MOFS.
Error Correction with Decomposition
The error sequence is decomposed using Variational Mode Decomposition (VMD), and each decomposed error subsequence is then predicted using the Informer model. The predictions of these subsequences are summed to derive the error prediction results. The error sequence is then added to the initial prediction results to yield the final PM2.5 concentration predictions.
To validate the adaptability of the proposed model, forecasts were also carried out using data collected from monitoring stations coded 1052A in Baoding and 1352A in Guangzhou. Baoding, located to the south of Beijing, shares a similar geographical position and is likewise subjected to severe smog pollution, characteristic of this region. Both cities are influenced by surrounding industrial zones and agricultural activities; however, Baoding also possesses its own unique sources of pollution, such as significant industrial emissions. In contrast, Guangzhou is situated in the southern part of China, within the Pearl River Delta, and experiences a subtropical monsoon climate that is markedly different from Beijing’s temperate monsoon climate. The high temperatures and humidity typical of Guangzhou, combined with the complex interactions between land and sea, pose distinct challenges for air quality models. These conditions are invaluable for testing the adaptability of the model under varying climatic conditions and diverse pollution sources. Table 4 displays the final prediction results of the model proposed in this paper, and Fig. 3 illustrates a comparison of the prediction results before and after error correction. It is evident that the model proposed in this paper exhibits excellent accuracy and performance, effectively accomplishing the task of accurately predicting PM2.5 concentrations.
Fig. 3.
Comparison of partial prediction results before and after error correction (Beijing 1011A, Autumn).
Table 4.
Final predictions of the proposed model.
Conclusions
Accurate prediction of PM2.5 concentrations is of paramount importance for public health and environmental protection, as the level of these concentrations directly relates to air quality and has become a global focal point due to its impact on human health. Long-term exposure to high concentrations of PM2.5 increases the risk of respiratory and cardiovascular diseases, especially in urban areas. Thus, predicting PM2.5 is crucial for environmental monitoring, pollution alerts, and health risk assessments.
To address the nonlinearity and complexity of predicting PM2.5 concentrations, this paper presents a novel hybrid model for PM2.5 concentration prediction. This model initially decomposes the historical PM2.5 data using VMD, optimized by the RIME algorithm, to extract several intrinsic modal components and a residual component. Subsequently, based on sample entropy values, these components are restructured into high, medium, and low-frequency components. Then, the MOFS method is employed to select the most influential feature subsets from meteorological conditions and historical data. Finally, the optimized Informer model is used for concentration prediction and error correction to obtain the final prediction results.
Experimental results demonstrate that this model surpasses other single and hybrid models in all evaluation metrics. These achievements indicate that RIME effectively selects the key parameters for VMD, enhancing the applicability and decomposition efficiency of VMD in processing PM2.5 data while also reducing the volatility and chaos of the original data. The MOFS method integrates the advantages of wrappers and filters, providing a more stable and reasonable feature combination compared to standalone feature selection algorithms, thereby reducing model complexity and enhancing prediction efficiency and accuracy. Additionally, RIME effectively explores the hyperparameter space of the Informer model, aiding the model in achieving higher prediction accuracy and stability. The optimized Informer, combined with an error correction model with decomposition (ECD), achieves accurate PM2.5 concentration predictions. The hybrid model proposed in this paper considers potential issues in the prediction process and combines the strengths of each module to accurately predict PM2.5 concentrations, enriching the technological tools in this field and providing valuable quantitative references for public health and environmental protection.
