1. Introduction
As China’s economy grows steadily and industrialization increases, the air pollutants emitted by certain cities have exceeded the tolerable capacity of the environment, leading to a deterioration in ambient air quality. Air pollution has become a serious challenge to social development and ecosystem health. Fine particulate matter (PM2.5), respirable particulate matter (PM10), carbon monoxide (CO), nitrogen dioxide (NO
2), ozone (O
3), and sulfur dioxide (SO
2) are six major air pollutants [
1]. Their excessive emissions pose a serious threat to human health, triggering a wide range of diseases affecting the cardiovascular, cerebral, and respiratory systems and causing persistent damage to the human body [
2].
According to the Atmospheric Environment Quality Standards (GB3095-2012) set by the Ministry of Ecology and Environment of China, the AQI converts advanced air pollutant quality data into a number, and the concentration of air pollutants in major urban areas exceeds regulatory limits [
3]. The AQI ranges from 0 to 500, with 0 representing normal air quality and 500 being the most hazardous air quality. The AQI classifies air quality into six main levels of different health impacts, providing key information about the state of air quality to the public by reflecting the potential impact of different pollution levels on health. Air quality is influenced by various factors. Changes in past pollutant emission intensity and meteorological conditions provide important reference data for predicting future air quality [
4]. Meteorological conditions play a crucial role, both directly and indirectly, in the emission, diffusion, formation, and deposition of atmospheric pollutants and are the main driving factors for regional air pollution changes [
5]. Therefore, it is crucial to improve the stability and accuracy of air quality prediction caused by the complex problems of nonlinearity and non-stationarity in the AQI due to factors such as meteorological conditions and pollutant type [
6].
Research on air quality mainly includes numerical simulation methods, statistical modeling theory, and artificial intelligence methods [
7,
8,
9]. Numerical simulation relies on the physical and chemical processes of the atmosphere, combined with meteorological principles and mathematical methods, to simulate large-scale air quality in both horizontal and vertical dimensions. Statistical modeling theory is based on the assumption of data distribution, aimed at explaining causal relationships and emphasizing parameter inference [
10]. Machine learning, especially deep learning methods in artificial intelligence, can learn parameters through algorithmic formulas based on input characteristics, identify trends and features in large amounts of data, and make predictive inferences. Taking into account the characteristics of atmospheric pollutants and the influence of various factors such as weather, it has partially addressed the problems of nonlinear fitting, non-stationarity, and complexity in air quality time series, demonstrating superior predictive performance [
11]. Traditional machine learning techniques such as Random Forest (RF) [
12] and Extreme Gradient Booster (XGBoost) [
13] have been widely applied in the field of air quality prediction. Due to the advantages of deep learning in feature extraction and mining, more and more research is focusing on recursive neural networks and their variant models such as Long Short-Term Memory Networks (LSTMs) [
14], Gated Recurrent Units (GRUs) [
15], Bidirectional Long Short-Term Memory Networks (Bi-LSTMs) [
16], Bidirectional Gated Recurrent Units (Bi-GRUs) [
17], and Convolutional Long Short-Term Memory Networks (CNN-LSTMs) [
18]. Seng et al. [
14] proposed a multi-index comprehensive prediction model based on an LSTM, using data on the concentration of major pollutants at representative sites in Beijing, and demonstrated its effectiveness in air quality prediction. Athira et al. [
19] used the AirNet dataset of meteorological characteristics and air quality to predict and evaluate atmospheric environmental quality using RNN, LSTM, and GRU models. Compared with traditional models such as ARIMA, they have stronger advantages in terms of evaluation indicators such as R
2, MAE, and RMSE. Prihatno et al. [
16] proposed a multi-density layer model based on a Bi-LSTM to more accurately predict PM2.5 concentration levels in air quality pollutants. Zhang et al. [
17] proposed a Bi-GRU model based on spatial geographic location information. The combination of historical air quality monitoring data and meteorological monitoring data has improved the prediction accuracy of recurrent neural networks in air quality. However, a single predictive model may be limited by specific algorithms or model structures and may not be able to adapt well to complex data patterns or relationships. In addition, when facing multi-source data, it may not be possible to capture complex patterns in the data, and the data may be incomplete, making it difficult to fully utilize information. Therefore, how to improve the accuracy of prediction methods has become a key issue in current air quality prediction research.
A Convolutional Neural Network (CNN) can capture uneven changes in air pollution data, effectively extract data features, expand the scope of analysis, and evaluate the connectivity between features. The memory units in an LSTM make neural networks more suitable for time series analysis and modeling. The CNN-LSTM model combines the advantages of both methods and adaptively extracts features layer by layer, enhancing the network’s learning ability and more effectively extracting information from time series data. Yan et al. [
18] combined the advantages of CNNs and LSTMs to establish a CNN-LSTM coupled prediction model based on multi-temporal seasonal station data from Beijing. Compared with traditional single prediction models, it significantly reduces AQI errors. To further improve the accuracy of AQI prediction, Zhang et al. [
20] utilized the effective feature extraction function of a CNN for data feature extraction, constructed a feature vector sequence, and fed it into the LSTM network to learn the variation patterns of air quality data, demonstrating the performance advantages of the CNN-LSTM model. Additionally, attention mechanisms have greatly improved the computational efficiency and accuracy of models in feature extraction and parallel computing. They can also capture the time dependence and correlation between long-term data indicators. In recent years, they have been widely used by scholars. Long et al. [
21] proposed an improved Informer [
22] model based on the Transformer [
23] architecture. The Informer model, which improves the self-attention mechanism, has strong advantages in feature extraction and parallel decoding, enhancing the accuracy of air quality prediction.
In addition to the rapid development of artificial intelligence-related prediction models, the effective preprocessing of datasets plays an important role in extracting data features, reducing the complexity of time series data and modeling, and improving prediction accuracy. The application of the modal function helps to deeply analyze and reveal the periodicity, trend, and abnormal changes of air quality series, and signal decomposition methods can obtain more accurate prediction accuracy [
24]. Huang et al. [
25] proposed an Improved Particle Swarm Optimization algorithm (IPSO) based on the Empirical Mode Decomposition (EMD) method of the LSTM to optimize the parameters of the LSTM for air quality modeling. However, to address the issues of mode mixing and end effects in EMD and other decomposition methods, scholars have gradually developed and applied the VMD [
26]. VMD is a non-recursive modal signal processing technique that decomposes time series into multiple relatively smooth subsequences with different frequency scales, which can reduce the non-stationarity and complexity of time series. VMD is highly robust to noise and can effectively overcome mode mixing and achieve suitable decomposition results. Wu et al. [
27] proposed a VMD-LSTM mixed air quality prediction model, which utilizes VMD to decompose the original AQI sequence into subsequences with different frequencies and rearranges these subsequences using sample entropy, addressing issues of over-decomposition and a large amount of calculation.
Data preprocessing techniques may encounter challenges related to local optimization and slow convergence during post-processing. Moreover, improper parameter selection can degrade the quality of decomposition results, thereby impacting the accuracy of air quality prediction models [
28]. The swarm intelligence optimization algorithm has a strong ability to seek optimality by imitating the search behavior of population predation in nature and is frequently employed to optimize model hyperparameters. By integrating the swarm intelligence optimization algorithm with signal decomposition techniques such as VMD, the challenge of hyperparameter setting is effectively mitigated, and the performance of the integrated model is enhanced [
29]. Shao et al. [
30] introduced an adaptive parameter search technique for VMD based on the DBO algorithm to optimize VMD parameters, which exhibits a fast iteration rate and yields good optimization effects. Additionally, they employed the Informer and XGBoost methods to handle high-frequency and low-frequency feature data of approximate entropy classification and ultimately superimposed the reconstructed predicted values to achieve high prediction accuracy. Wang et al. [
31] utilized the multi-objective Gray Wolf Optimization (GWO) algorithm [
32] in conjunction with the VMD method to effectively extract the intrinsic information of PM2.5 data, thereby reducing the computational complexity of the model and enabling timely detection and warning of air pollution. Chang et al. [
33] merged wavelet decomposition [
34] and the Particle Swarm algorithm (PSO) [
35] to introduce a hybrid framework model for predicting the accuracy of major air pollutants. Liu et al. [
36] employed the Sparrow Search Algorithm (SSA) [
37] to optimize LSTM parameters, resulting in improved prediction performance compared with that of a standalone neural network model in terms of MAPE, RMSE, MAE, and R
2 metrics. Xu et al. [
38] utilized the Whale Optimization Algorithm (WOA) [
39] to optimize SVM parameters, leading to the development of a hybrid ICEEMD-WOA-SVM warning model, which was empirically validated in the cities of Taiyuan, Harbin, and Chongqing. Subsequent developments in algorithmic models should integrate multiple algorithms to enhance prediction accuracy and generalization while capturing data features.
Current research on air quality forecasting encounters several challenges. Firstly, the nonlinearity, complexity, and nonsmoothness characteristics of the air quality series make it challenging for a single feature to capture the overall changes. Various influencing factors, such as common atmospheric pollutants and meteorology, should be considered in the prediction of the AQI [
40]. Secondly, some commonly used original data decomposition methods, such as VMD, often rely on trial-and-error methods based on subjective experience, making it difficult to find appropriate parameters, which may reduce the quality of decomposition results due to improper parameter selection, thus affecting the prediction accuracy of the model [
41]. Additionally, while most optimization algorithms are utilized for refining prediction models, significant potential remains for data preprocessing. Due to the complexity and instability of the time series data of the main air quality influencing factors, data preprocessing techniques, although generally capable of mining the potential characteristics of air pollutants to improve the prediction accuracy [
42], suffer from the issues of falling into local optima and slow convergence [
43]. Based on the above issues, this paper proposes a coupled DVMD-Informer-CNN-LSTM model based on the optimization of VMD parameters by DBO, which combines Informer and CNN-LSTM models for application in air quality prediction. The model uses the correlation coefficient method to select the main influential features from meteorological data and atmospheric pollutants, with VMD optimized by the improved Dung Beetle Algorithm (DBO). Envelope entropy is used as the fitness value to determine the penalty factor and the number of Intrinsic Mode Function (IMF) decomposition layers for the variational mode fraction. Compared with the aforementioned GWO, PSO, SSA and WOA, DBO shows significant competitive performance in terms of both accuracy and stability of the solution accuracy and realizes the accurate decomposition of complex data. Compared with the relevant benchmark models set in this paper, the proposed DVMD-Informer-CNN-LSTM air quality prediction model is innovative and accuracy-enhancing in terms of parameter optimization, model architecture, and prediction performance. The contributions of this paper can be summarized as follows:
(1) To effectively capture and process complex features of air quality data and enhance AQI prediction accuracy. A DVMD-Informer-CNN-LSTM multi-factor coupled integration framework model based on DBO, VMD, Informer, and CNN-LSTM is proposed. This model can better capture the long and short-term dependencies in the time series through the improved Informer algorithm, which includes a long- and short-term global self-attention mechanism, as well as the CNN-LSTM algorithm to enhance the model’s ability to process sequence data. The Informer model is specifically chosen for its efficiency in handling high-frequency data, which often contains complex patterns and significant noise. Informer’s probabilistic sparse self-attention mechanism reduces computational complexity while maintaining robust performance, making it highly suitable for high-frequency datasets. Secondly, a multi-level feature extraction strategy is employed to process the original time series data through various feature extraction modules. This strategy significantly reduces the prediction error stemming from the dataset’s complexity by extracting features at different levels from both high- and low-frequency data following the information entropy decomposition. The CNN-LSTM model is utilized for low-frequency data due to its ability to capture features and temporal dependencies through CNN and LSTM layers. This combination is particularly effective for low-frequency data. Finally, the parallel decoder structure enables the distributed processing of different prediction tasks simultaneously, enhancing the parallelism and efficiency of the model. This accelerates the training and inference speed of the model while maintaining high prediction accuracy, demonstrating the model’s practical value.
(2) A DBO-based optimization algorithm is employed to adjust the adaptive parameters of the VMD. The DBO algorithm, known for its rapid iteration rate and effective optimization, optimizes the penalty factor and the number of decomposition layers of the VMD. Envelope entropy is used as the adaptive value, while information entropy serves as the boundary between high-frequency and low-frequency data. This method prevents modal mixing and pseudo-componentization during VMD decomposition, enabling more precise parameter identification. It minimizes errors due to subjective parameter adjustments and integrates model fusion to significantly enhance prediction accuracy.
(3) Using 26,110 data points from 13 major air quality monitoring stations in Beijing from 2021 to 2023, the proposed DVMD-Informer-CNN-LSTM air quality multi-factor coupled comprehensive prediction model and 11 benchmark models were applied to improve the accuracy, stability, and interpretability of the model through data preprocessing. The evaluation metrics, including , , and , demonstrate the accuracy and adaptability of the model.
The remainder of the paper is organized as follows:
Section 2 outlines the algorithmic principles and detailed implementation steps of the DVMD-Informer-CNN-LSTM coupled model.
Section 3 concentrates on presenting the numerical experimental results required for the model. This section includes discussions on the data sources and preprocessing methods, correlation analysis of key factors affecting air quality, parameter optimization and data decomposition of the VMD by DBO, standardization of the experimental setup, and accuracy assessment of the results.
Section 4 summarizes the advantages and limitations of the proposed model and offers an overview of future research prospects.
2. Models and Algorithms
2.1. Variational Modal Decomposition (VMD)
Given the highly nonlinear and nonsmooth uncertainty inherent in AQI, efficient dataset preprocessing can enhance data feature extraction and diminish time series data and modeling complexity, thereby enhancing prediction accuracy.
Several signal decomposition techniques have been successfully employed in time series prediction, including Discrete Wavelet Transform (DWT) [
44], EMD [
26], and Ensemble Empirical Mode Decomposition (EWT) [
45]. While DWT is effective in capturing signal changes at different scales, it relies on predefined wavelet bases, which may not adapt well to the intrinsic characteristics of complex signals, potentially leading to suboptimal decomposition for highly irregular data. EMD is a widely used technique that decomposes a signal into Intrinsic Mode Functions (IMFs). However, it often suffers from mode mixing and end effects, which can compromise the accuracy and reliability of the decomposition. EWT was developed to mitigate some of these issues but remains computationally intensive and susceptible to reconstruction errors.
VMD offers significant advantages over DWT, EMD, and EWT. Unlike DWT, VMD does not require predefined basis functions and instead uses adaptive basis functions that better fit the data’s inherent properties. VMD effectively addresses the mode mixing and end effects associated with EMD by iteratively searching for modes with minimal interference and distinct frequency bands. This results in more precise and stable decomposition outcomes, which are crucial for accurate AQI prediction. Moreover, VMD’s robustness to noise ensures reliable performance even with noisy datasets, enhancing the overall prediction accuracy. Therefore, we chose VMD for its ability to adaptively decompose complex signals, handle noise effectively, and produce stable and accurate components suitable for subsequent predictive modeling.
VMD is a method grounded in variational methods that decomposes nonlinear and nonsmooth signals into multiple IMFs [
26]. Fundamentally, VMD aims to minimize interference between each IMF and other frequency bands via iterative optimization. This prevents information overlap and enhances robustness to noise and interference. In comparison to other techniques, VMD demonstrates superior accuracy, faster computation speed, and better noise immunity when handling data center frequency components.
where
and
denote the modal components and center frequency;
is the Dirac function;
is the original signal; and
is used for the convolution operation.
Solving variational constrained problems, penalty factor
and Lagrange multiplier
are introduced to transform the constrained variational problem into an unconstrained variational problem. The augmented Lagrange expression is derived as:
The modal and center frequencies are updated using the multiplier alternating direction method to seek the saddle points of the augmented Lagrangian function,
,
and
with the following expressions:
where
is the noise tolerance,
is the number of iterations, and the Fourier transforms correspond to
,
,
, and
are
,
,
, and
.
2.2. DBO-Optimized VMD (DVMD)
Unlike existing optimization algorithms such as GWO, PSO, SSA, and WOA, among others, the Dung Beetle Optimization Algorithm (DBO) considers both global exploration and local exploitation while exhibiting fast convergence speed and high solution accuracy. The optimization technique of adaptive parameter finding can better optimize the penalty factor and the number of intrinsic modes of VMD, and through the dung beetle’s positional changes, the global optimal position and the adaptation value can be obtained, thereby facilitating accurate AQI decomposition prediction.
The population-based DBO algorithm, proposed by Xue in November 2022 [
46], draws inspiration from the dung beetle’s behaviors of rolling, dancing, foraging, stealing, and reproducing. To simulate the rolling behavior, the dung beetle is required to move in a specified direction throughout the search space.
where
denotes the current iteration number,
denotes the information of dung beetle
at the
th iteration,
ranges from 0 to 0.2, and
denotes the deflection coefficient.
denotes the worst-case global position and denotes the change in light intensity.
When the dung beetle is prevented from moving forward by an obstacle, a dance behavior repositioning is required, and updating the rolling ball dung beetle position can be expressed as follows:
where
denotes the difference between the position of the
dung beetle at the
th iteration and its position at the
th iteration, and
is the angle of deflection belonging to 0 to
. The position of the dung beetle is not updated when
,
, and
.
Dung beetles will hide dung balls for spawning, and a boundary selection strategy is needed to determine the spawning boundary to simulate the spawning region, which can be expressed as follows:
where
denotes the current local optimal position,
and
denote the lower and upper limits of the spawning area, respectively,
,
denote the maximum number of iterations, and
and
denote the lower and upper limits of the optimization.
is the position information of the
th female sphere at the
th iteration, denotes two independent random vectors of size
, and
denotes the dimension of the optimization problem.
Dung beetles have a foraging behavior that searches for physical objects, and the optimal foraging boundary can be expressed as follows:
where
is the global optimal location,
and
denote the lower and upper bounds of the optimal foraging area, respectively,
denotes a random number, and
denotes a random vector belonging to (0, 1).
Some dung beetles have the behavior of stealing dung balls from other dung beetles, and the update of the location of the area of theft can be expressed as follows:
where
is a normally distributed random vector of size
and
is a constant value.
The dung beetle population contains
individuals, and each individual
represents a candidate solution. At the
th iteration, the position vector of the
th agent is represented by 1, where
is the dimension of the search space, and the allocation ratio is not specified and can be set according to the actual application problem. In
Figure 1, the size of the dung beetle population was chosen to be 30. Green, yellow, blue, and red rectangles represent the number of dung beetles rolling, laying eggs, foraging, and stealing, with numbers 6, 6, 7, and 11, respectively. The sum of the numbers corresponds to the population size, and the percentages are about 20%, 20%, 25% and 35%.
To summarize, the DBO algorithm, as a novel optimization technique, confronts an optimization problem comprising six main steps: initializing the dung beetle population and the parameters of the DBO algorithm; calculating the fitness values of all the individuals according to the objective function; updating the positions of all the dung beetles; determining whether each individual crosses the boundary; updating the current optimal solution and its fitness value; iteratively performing the aforementioned steps until the termination criterion is met; and finally outputting the global optimal solution and its corresponding fitness value (
Figure 2). In the aforementioned model, the number of decomposition layers (k) and the penalty factor parameter (α) of VMD are optimized using DBO. The number of modes k and the penalty factor α have the most significant influence on the VMD decomposition outcomes. Elevated values of k may result in an overdecomposition of the original signal, yielding spurious components. Conversely, lower values of k may result in the underdecomposition of the signal, thus leading to modal aliasing. The size of the penalty parameter determines the size of the bandwidth of each component; a larger value will make the modal function narrower, resulting in loss of bandwidth information, while a smaller value will carry too much interference information, resulting in redundancy. Determining the inherent relationship between these two parameters, optimizing, and validating the appropriate [k, α] values constitute the crucial aspect of VMD decomposition. Envelope entropy can more effectively reflect the sparse characteristics of the initial signal: when the modal component contains less feature information, the envelope entropy is higher; conversely, when there is less noise and more feature information in the IMF, the envelope entropy is lower. This property can be leveraged as the target fitness function for DBO optimization, as depicted below:
is a sequence of probability distributions obtained by normalizing , and represents the envelope signal of the Hilbert demodulated signal.
The DBO algorithm is employed for global optimization of the two parameters, k and α, of the VMD simultaneously to achieve adaptive decomposition of the air quality sequence. We adopted the optimization of VMD for data decomposition, specifically to manage the inherent complexities of AQI time series data. The detailed process is as follows: First, the time series is decomposed by setting the number of decomposition modes and penalty parameters, yielding multiple mode functions. To prevent data leakage, we meticulously followed standard procedures for time series prediction, ensuring the independence of training and test data. During the decomposition, we referenced the relevant literature [
47] and employed cross-validation techniques to ensure that test data were not exposed during model training. In the air quality prediction model presented in this study, the DVMD algorithm is employed to achieve precise decomposition of complex data. In our approach, we employed a static integration method to combine the predictive outputs of the Informer and CNN-LSTM models. The predictions from each model are weighted and averaged to obtain the final AQI prediction. The choice of static integration was based on its simplicity and proven effectiveness in our preliminary tests. Although dynamic integration methods, which adaptively adjust weights based on performance metrics, can potentially offer better accuracy, our experiments indicated that the static integration already provided sufficient predictive precision.
2.3. Informer
Due to the attention mechanism in feature extraction, parallel computation has significantly improved the model’s computational efficiency and accuracy, and significant progress has been made this year. The Informer model with an improved self-attention mechanism has a strong advantage in feature extraction and parallel decoding and can capture the temporal dependence and correlation between long-time data indicators, which improves the prediction accuracy of the AQI.
The Informer model was proposed by Zhou et al. [
22] in 2020 and introduces an enhanced self-attention mechanism that excels in processing long sequences. High-frequency data, characterized by significant noise and complex patterns, benefits from the Informer model’s ability to efficiently capture long-term dependencies and correlations between data points and can effectively capture the precise long-term correlation coupling between outputs and inputs due to the existence of quadratic time complexity, high memory utilization, and limitations inherent in the architecture of codecs in the traditional Transformer model. The Informer model proposed the ProbeSparse sparse self-attention mechanism, which achieves O(LlogL) in time complexity and memory usage. In addition, self-attention can highlight the dominant attention by halving the cascaded layer inputs and efficiently handling extremely long input sequences, improving the inference speed of long sequences. The Informer model architecture is shown in
Figure 3, where the probabilistic sparse self-attention mechanism is used instead of regular self-attention. The encoder on the left receives a large number of green long sequence inputs so that the blue trapezoid is a self-attention extracting operation, and to greatly reduce the network size, the robustness is enhanced by using cascading to extract the main attention. The decoder on the right also receives long sequential inputs, fills the target element with zeros, measures the weighted self-attention composition of the feature map, and generates the orange predicted output element.
The Informer model solves the time complexity problem of self-attentive dot product computation in optimization problems using the probabilistic sparse self-attention algorithm in the encoder. The dot product computation is performed by sampling each point with the equation shown below [
48]:
, , and are three matrices of the same size obtained by linearly transforming the input feature variables, where , , . are the input dimensions, are obtained by probabilistic sparsification , and Softmax is the activation function.
An extraction operation is used to prioritize superior features with dominant features and produce a focused self-attentive feature map in the next layer. It drastically cuts down the time dimension of the input. The public presentation is as follows:
where
denotes the multi-head probabilistic sparse self-attention module,
is a one-dimensional convolutional filter executed in the time dimension using the activation function ELU, and MaxPool is the maximum pooling layer with a step size of 2. After
downsampling the stacked layers, the memory usage will be reduced to
, with
being a very small value.
The decoder gets a long input sequence and places a zero at the predicted target location. The decoder is passed through the attention layers to produce the expected output. Each decoder layer performs a feature extraction operation based on the input in the direction of the target, a two-layer stack of multi-head attention mechanism level composed decoders that use probabilistic sparse self-attention in the first layer to compute the current output using only a priori data. The multi-head probabilistic sparse self-attention obtains a long input sequence in the second stage and sets zero at the projected target point. The projected output is then generated by masking the attention layers in the last step. Each decoding layer performs feature extraction operations in the target direction based on the given input to complete the decoding process. In the proposed air quality prediction model, Informer is used to predict the high-frequency components of the DBO-optimized VMD.
2.4. CNN-LSTM Model
Convolutional Neural Networks have been widely used for time series data analysis due to their powerful feature extraction properties, which capture the temporal dependence present in AQI data by extracting the relationships in the spatial structure of multi-dimensional time series data [
49]. Memory units in the LSTMs make the neural networks more suitable for time series analysis and modeling, and the layer-by-layer adaptive feature extraction gives the networks a stronger learning ability to acquire information in time series more efficiently. The CNN-LSTM hybrid model, which can combine the advantages of CNN and LSTM, enables the model to better handle the data of AQI and make predictions.
The network structure of CNNs mainly contains an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer. In addition to this, CNNs share a convolutional kernel in different regions, and the same convolutional kernel has the same weight parameters, which realizes weight sharing. The pooling layer can also be mainly used for feature dimensionality reduction to reduce the number of parameters and decrease the network complexity. Long Short-Term Memory Neural Networks can be a good solution to the long-distance dependency problem. The network structure mainly contains an input layer, an LSTM layer, a fully connected layer, and an output layer [
50]. In the LSTM network structure, three gate units are added inside the neurons to control the transmission of information, i.e., input gate, forgetting gate, and output gate, by gating the memory units. The problem of information loss and stability in long-time sequence propagation is solved, and the problems of gradient vanishing and gradient explosion, which exist in recurrent neural networks such as an RNN, are solved. The structure of the constructed CNN-LSTM framework is shown in
Figure 4.
In the CNN-LSTM model, the convolutional layer of the CNN is used for extracting local features from time series data. For the pooling layer to further obtain the hidden information and reduce the feature dimensions, the pooled information is used to learn the long-term dependencies in the data through the LSTM network to obtain the features with long-term dependencies. By calculating the loss function to update each hidden layer and selecting a suitable optimization algorithm to improve the prediction of the model, the CNN-LSTM is found to have a higher accuracy rate in AQI prediction compared with other algorithms. In the new model proposed in this paper, the low-frequency components of the DVMD decomposition are predicted using the well-performing CNN-LSTM model.
2.5. DVMD-Informer-CNN-LSTM Model
To improve the air quality prediction accuracy, based on the optimization performance of the DVMD algorithm, the DVMD algorithm, Informer algorithm, and CNN-LSTM algorithm are coupled, and the DVMD-Informer-CNN-LSTM combined air quality prediction model is proposed. The selection of DVMD, Informer, and CNN-LSTM as the prediction models is based on a comprehensive consideration of model performance, complexity, computational resources, and diversity. In terms of model performance, these proposed models have shown excellent performance in previous studies, especially in processing time series data with high prediction accuracy. Under limited computing resources, a combination of models that can complete training and prediction in a reasonable time was selected to improve the robustness and generalization ability of the prediction results.
The model consists of three parts: data preprocessing, parameter optimization decomposition, and coupled model prediction and the flow chart is shown in
Figure 5. The core of the model uses the DBO algorithm to optimize the decomposition modes and penalty factor parameters in the VMD model, adopts the envelope entropy as the adaptation value, and reflects the high-frequency and low-frequency data values of the approximate entropy decomposition of the tiny fluctuation and nonlinear change characteristics in the time series, which are inputted into the Informer and the CNN-LSTM model for the combined prediction. The new model solves the problems of prediction bias due to data complexity and insufficient feature capture, neglecting the influence of factors other than time series, and poor accuracy due to human intervention that exists in the field of traditional air quality prediction. The specific steps to realize the model are as follows.
Step 1: Data preprocessing. Collect the data of six major air pollutants and key meteorological features as the original dataset, and perform data standardization and linear interpolation to fill in the missing values of the data and remove the outliers, data smoothing, and other preprocessing operations on the data.
Step 2: Data feature selection. The Spearman correlation coefficient method is used to screen the meteorological characteristics and the six major air pollutants data for the importance of their influence characteristics, to determine the key influencing factors and use them as inputs to the dataset, to reduce the complexity of the data, and to provide a basis for the subsequent improvement of the model prediction accuracy.
Step 3: Model parameter optimization. After verifying the efficiency and performance of the DBO algorithm. The DVMD algorithm is applied to optimize the decomposition mode k and penalty factor, and the IMF components are obtained by decomposing the historical AQI data. According to the approximate entropy value of each IMF component, the m IMF components are divided into f low-frequency decomposition data and m-f high-frequency decomposition data, which provide the basis for subsequent model selection and prediction.
Step 4: Feature input and prediction output. The n influential features and the historical data of AQI obtained after feature screening are used as the feature inputs of the model and the prediction outputs of the model. The Informer model is constructed to predict the f low-frequency decomposition data, and the CNN-LSTM prediction model is constructed to predict the m-f high-frequency decomposition parts. Finally, the prediction results of the m components are reconstructed and superimposed to generate the final prediction results.
Step 5: Model evaluation. The prediction ability of the DVMD-Informer-CNN-LSTM model and the proposed 11 comparative models is measured using MAE, RMSE, and R2 evaluation metrics. The VMD decomposition method enhanced by the DBO optimization algorithm has been successfully applied to air quality prediction models.