Technical Summary: Civil Aviation Passenger Traffic Forecasting Using a Hybrid SSA and Sparrow-Search-Optimized MLP-BP Model

1. Problem Statement

Accurate forecasting of civil aviation passenger traffic is critical for airline operations, route network planning, and capacity allocation. However, post-pandemic demand fluctuations have introduced significant challenges, characterized by high volatility, non-stationarity, seasonality, and nonlinearity. Traditional statistical methods (e.g., ARIMA) struggle with nonlinear data, while standard neural networks (e.g., MLP-BP) often suffer from random initialization issues, slow convergence, and a tendency to get trapped in local optima. These limitations lead to forecasting errors that result in either wasted capacity (overestimation) or missed revenue opportunities (underestimation), with potential economic impacts ranging from millions of dollars in operating costs to service disruptions. Existing hybrid models often fail to achieve global optimization or effectively extract multi-scale features from non-stationary time series.

2. Methodology

The study proposes a hybrid forecasting framework, SSA-MLP-BP-SpSA, which integrates three core components: Singular Spectrum Analysis (SSA), a Multilayer Perceptron trained by Backpropagation (MLP-BP), and the Sparrow Search Algorithm (SpSA).

2.1 Data Preprocessing: Singular Spectrum Analysis (SSA)

SSA is employed to decompose the original non-stationary time series into interpretable components, effectively separating signal from noise. The process involves four steps:

1. Embedding: Mapping the original time series into a trajectory matrix.
2. Decomposition: Performing Singular Value Decomposition (SVD) on the trajectory matrix.
3. Grouping: Grouping the resulting elementary matrices into disjoint subcollections to isolate specific features.
4. Reconstruction: Using diagonal averaging to reconstruct the time series into distinct components:
   • Trend Component (IMF4): Reflects long-term growth and fleet planning cycles.
   • Seasonal Components (IMF2, IMF3): Capture periodic peaks such as the Spring Festival and summer travel seasons.
   • Noise/High-Frequency Components (IMF1, Residual): Represent irregular fluctuations and random disturbances.

2.2 Prediction Model: MLP-BP

A Multilayer Perceptron (MLP) with a feedforward architecture is used to model the decomposed components. The network structure consists of an input layer, two hidden layers (16 and 32 neurons respectively), and an output layer.

• Activation: The ReLU function is used in hidden layers to mitigate gradient vanishing.
• Training: The Backpropagation (BP) algorithm is used for error backpropagation and weight updates.
• Optimization: The Adam optimizer is utilized for iterative parameter updates.

2.3 Parameter Optimization: Sparrow Search Algorithm (SpSA)

To address the limitations of standard BP training (local optima and instability), the SpSA is introduced to globally optimize the MLP-BP network's initial weights and biases.

• Mechanism: The algorithm simulates sparrow foraging behavior with a population of "discoverers" (guiding the search), "followers" (tracking discoverers), and "sentinels" (reconnaissance/warning).
• Fitness Function: The Root Mean Square Error (RMSE) or Mean Absolute Error (MAE) of the network serves as the fitness function to be minimized.
• Process: SpSA iteratively updates sparrow positions (network parameters) based on fitness values until convergence, ensuring the MLP-BP starts training from a globally optimized state.

2.4 Overall Framework

The modeling workflow proceeds as follows:

1. Standardize and normalize the raw monthly passenger data (2005–2024).
2. Decompose the data using SSA into trend, seasonal, and noise components.
3. Train separate MLP-BP models for each decomposed component.
4. Optimize the MLP-BP parameters using SpSA.
5. Reconstruct the final forecast by integrating the predictions of all components.
6. Evaluate performance using $R^2$, MAE, and RMSE.

3. Key Contributions

1. Hybrid Framework Development: A unified framework combining time-series decomposition, nonlinear learning, and intelligent optimization is developed specifically for the volatile, seasonal, and post-pandemic uncertain nature of civil aviation traffic.
2. Interpretability via SSA: The introduction of SSA allows for the extraction of distinct trend, seasonal, and irregular components. This enhances the interpretability of the forecasting process, linking specific model outputs to operational decisions like fleet planning (trend) and peak scheduling (seasonality).
3. Global Optimization: The employment of SpSA to optimize MLP-BP parameters reduces the risk of local optima and improves model stability under highly fluctuating demand conditions.
4. Empirical Validation: The model is validated using monthly passenger data from China (2005–2024), demonstrating practical value for capacity planning and operational management.

4. Results

The study utilized monthly passenger data from the Civil Aviation Administration of China (CAAC) from 2005 to 2024, splitting the data into an 80% training set and a 20% test set.

• Performance Metrics: The proposed SSA-MLP-BP-SpSA model achieved an $R^2$ of 0.987 and an RMSE of 179.71 on the test set.
• Comparative Analysis:
  • Vs. Single Models: The hybrid model significantly outperformed the standalone MLP-BP model (which had an $R^2$ of 0.628 and RMSE of 3206.193).
  • Vs. Partial Hybrids: It surpassed models using only decomposition (SSA-MLP-BP, $R^2$ 0.761) or only optimization (MLP-BP-SpSA, $R^2$ 0.832).
  • Vs. Other Neural Networks: In comparisons with SSA-preprocessed BiLSTM, GRU, and LSTM models, the SSA-MLP-BP-SpSA model demonstrated superior accuracy and stability, particularly during critical market inflection points and periods of sharp fluctuation.
• Error Distribution: The model exhibited a narrow 95% confidence interval and concentrated residuals in the low-value range, indicating high statistical stability and effective error control.
• Turning Points: The model successfully captured major turning points, such as the rapid growth phases and seasonal peaks, with minimal deviation compared to actual values.

5. Significance and Claims

The authors claim that the proposed approach offers reliable support for civil aviation demand forecasting, addressing the specific challenges of non-stationarity and nonlinearity in the post-pandemic era.

• Operational Decision Support: The model is positioned as a tool to assist airlines and airport operators in:
  • Short-term: Adjusting capacity and scheduling flights during peak periods (e.g., Spring Festival, summer travel) to reduce resource misallocation.
  • Medium-to-Long-term: Informing fleet planning and airport infrastructure expansion based on accurate trend identification.
• Economic Impact: The study suggests that reducing forecasting errors (e.g., from ~15-20% in traditional models to <1.2% in the proposed model) can save airlines millions of dollars annually by optimizing fuel procurement, crew scheduling, and inventory management, while simultaneously improving flight load factors and customer satisfaction.
• Limitations: The authors acknowledge that the model has high computational complexity, limiting its application in high-frequency real-time scenarios. They also note that the current study uses aggregate monthly data and does not explicitly incorporate exogenous variables (e.g., macroeconomic indicators, policy changes) or route-level heterogeneity. Future work is suggested to focus on parallel computing, adaptive update mechanisms, and the integration of multi-source data.