Railway Freight Demand Forecasting Based on Multiple Factors: Grey Relational Analysis and Deep Autoencoder Neural Networks
Abstract
:1. Introduction
- Stronger representation learning ability: Deep automatic encoders can adaptively learn high-level feature representations. This makes it possible to distinguish the differences between the categories and to improve the accuracy of the model;
- Non-linear modeling capability: Deep automatic encoders adopt a multilayered non-linear transformation, which can better approximate the non-linear function, thus improving the performance of the model;
- Stronger generalization ability: Deep automatic encoders can map raw data to higher-level, more abstract representation spaces, improving the model’s generalizability.
2. Methodology
2.1. The Problem Formulation
2.2. The GRA-DAE-NN Model
- Step 1. Determine the characteristic sequence ;
- Step 2. Determine the correlation factor sequence ;
- Step 3. The reference and comparison sequences are normalized. The dimensionless characteristic sequence and the dimensionless correlation factor , ;
- Step 4. Find the correlation coefficient between the reference sequence and comparison sequence .
- a.
- Encoder
- b.
- Decoder
- c.
- Training process
2.3. Prediction Method Based on GRA-DAE-NN
3. Case Study
3.1. Data Source
3.2. Parameter Settings
3.3. Analysis and Comparison of Forecast Results
3.3.1. Results of Explanatory Variables Select
3.3.2. Forecast Results Analysis
3.3.3. Results Comparison between GRA-DAE-NN and Baseline Models
- (1)
- ARIMA (autoregressive integrated moving average): ARIMA regards the data series formed by the prediction object over time as a random sequence and uses a certain mathematical model to approximate the series [39];
- (2)
- SVR (support vector regression): SVR is a time series model that uses the relationship between historical and future data to predict future data [40];
- (3)
- GRU (gated recurrent unit): GRU is a learning algorithm based on a recurrent neural network, which has a sequence-to-sequence structure and is usually used for time series analysis [41];
- (4)
- FC-LSTM (fully connected LSTM): It is a classic RNN that learns time series and predicts through fully connected neural networks. In this paper, the hidden layer is set to be two layers; the hidden units are 32 and 64, respectively, the learning rate is 0.001, and the batch size is 64 [42];
- (5)
- DNN (deep neural network): It uses DNN to extract railway freight demand characteristics and predict railway freight demand [43];
- (6)
- FNN (feedforward neural networks): FNN is the most basic type of neural network, consisting of an input layer, hidden layer, and output layer, suitable for most classification and regression problems [44];
- (7)
- GRNN (general recurrent neural networks): GRNN calculates the correlation density function between variables and carries out regression, making it suitable for time series prediction [45].
3.3.4. Ablation Study
3.3.5. Explanatory Variable Analysis
4. Conclusions
- The improved GRA-DAE-NN model has high predictive accuracy and interpretability for predicting the trend of target changes and can select explanatory variables related to railway freight demand for better prediction. It can not only accurately predict the trend of changes in railway freight demand but also determine the key factors and contribution priorities that affect its changes;
- According to the analysis of the influencing factors by GRA, the core indicators in the explanatory variables for railway freight demand prediction, such as coal production, petroleum production, grain production, daily production of freight locomotives, etc., have the best explanatory power for the trend changes in railway freight demand. Railway policymakers can focus on these indicators to adjust their transportation organization strategies in response to changing demand;
- Through a case study of the Chinese railway freight market from 2000 to 2018 and comparisons with other mainstream prediction models, it is found that the improved GRA-DAE-NN model has higher prediction accuracy. The prediction accuracy of the GRA-DAE-NN model is 97.79%, higher than that of other models such as ARIMA, SVR, FC-LSTM, DNN, FNN, and GRNN, which have prediction accuracies of 94.04%, 95.38%, 96.65%, 95.52%, 92.58%, and 97.32%, respectively. The ablation experiment confirmed the efficiency of the GRA module. After using GRA to filter the explanatory variables, the prediction model exhibited greater precision.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Classify | Influence Factor | |
---|---|---|
Demand | Macroeconomy | Gross domestic product (GDP) () |
Total value of agricultural output () | ||
Total retail sales of consumer goods () | ||
Total volume of merchandise imports and exports () | ||
Related Industry Production | Coal production () | |
Petroleum production () | ||
Steel production () | ||
Main non-ferrous metal production () | ||
Grain production () | ||
Express delivery volume of the year () | ||
Competitive Context | Freight traffic of highways () | |
Freight traffic of shipping () | ||
Civil air cargo volume () | ||
Supply | Investment in fixed assets in railway transportation () | |
Length of railroad lines in service () | ||
National railway electrification mileage () | ||
Mileage of double track of national railways () | ||
National railway locomotive inventory () | ||
National railway freight wagon inventory () | ||
Number of railway employees () | ||
Wagon static load () | ||
Daily production of freight locomotives () |
Demand-Side Influencing | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | |
Macroeconomy | Gross domestic product (GDP) (billion CNY) | 10,028.01 | 11,086.31 | 12,171.74 | 13,742.20 | 16,184.02 | 18,731.89 | 21,943.85 | 27,009.23 | 31,924.46 | 34,851.77 |
Total value of agricultural output (billion CNY) | 1387.36 | 1446.28 | 1493.15 | 1487.01 | 1813.84 | 1961.34 | 2152.23 | 2444.47 | 2767.99 | 2998.38 | |
Total retail sales of consumer goods (billion CNY) | 3910.57 | 4305.54 | 4813.59 | 5251.63 | 5950.10 | 6835.26 | 7914.52 | 9357.16 | 11,483.01 | 13,304.82 | |
Total volume of merchandise imports and exports (billion DOLLAR) | 474.29 | 644.37 | 814.45 | 984.52 | 1154.60 | 1421.91 | 1760.40 | 2173.83 | 2563.26 | 2207.54 | |
Related Industry Production | Coal production (ten thousand tons) | 138,418.50 | 147,152.70 | 155,040.00 | 183,489.90 | 212,261.10 | 236,514.60 | 252,855.10 | 269,164.30 | 280,200.00 | 297,300.00 |
Petroleum production (ten thousand tons) | 16,300.00 | 16,395.90 | 16,700.00 | 16,960.00 | 17,587.30 | 18,135.30 | 18,476.60 | 18,631.80 | 19,044.00 | 18,949.00 | |
Steel production (ten thousand tons) | 13,146.00 | 16,067.61 | 19,251.59 | 24,108.01 | 31,975.72 | 37,771.14 | 46,893.36 | 56,560.87 | 60,460.29 | 69,405.40 | |
Main non-ferrous metal production (ten thousand tons) | 783.81 | 883.71 | 1012.00 | 1228.06 | 1441.12 | 1635.00 | 1916.27 | 2379.15 | 2553.63 | 2648.54 | |
Grain production (ten thousand tons) | 46,217.52 | 45,263.67 | 45,705.75 | 43,069.53 | 46,946.95 | 48,402.19 | 49,804.23 | 50,413.85 | 53,434.29 | 53,940.86 | |
Express delivery volume of the year (ten thousand piece) | 11,031.40 | 12,652.70 | 14,036.20 | 17,237.80 | 19,772.00 | 22,880.30 | 26,988.04 | 120,189.56 | 151,329.30 | 185,785.81 | |
Competitive Context | Freight traffic of highways (ten thousand tons) | 1,038,813 | 1,056,312 | 1,116,324 | 1,159,957 | 1,244,990 | 1,341,778 | 1,466,347 | 1,639,432 | 1,916,759 | 2,127,834 |
Freight traffic of shipping (ten thousand tons) | 122,391 | 132,675 | 141,832 | 158,070 | 187,394 | 219,648 | 248,703 | 281,199 | 294,510 | 318,996 | |
Civil air cargo volume (ten thousand tons) | 197 | 171 | 202 | 219 | 277 | 307 | 349 | 402 | 408 | 446 | |
Demand-Side Influencing | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | ||
Macroeconomy | Gross domestic product (GDP) (billion CNY) | 41,211.93 | 48,794.02 | 53,858 | 59,296.32 | 64,356.31 | 68,885.82 | 74,639.51 | 83,203.59 | 91,928.11 | |
Total value of agricultural output (billion CNY) | 3590.907 | 4033.962 | 4484.572 | 4894.394 | 5185.112 | 5420.534 | 5565.989 | 5805.976 | 6145.26 | ||
Total retail sales of consumer goods (billion CNY) | 15,800.8 | 18,720.58 | 21,443.27 | 24,284.28 | 27,189.61 | 30,093.08 | 33,231.63 | 36,626.16 | 38,098.69 | ||
Total volume of merchandise imports and exports (billion DOLLAR) | 2972.761 | 3641.938 | 3866.8 | 4160.3 | 4303 | 3956.901 | 3684.914 | 4107.164 | 4622.415 | ||
Related Industry Production | Coal production (ten thousand tons) | 342,844.7 | 351,600 | 394,512.8 | 397,432.2 | 387,391.9 | 374,654.2 | 339,437 | 352,356.2 | 368,121 | |
Petroleum production (ten thousand tons) | 20,301.4 | 20,287.6 | 20,747.8 | 20,991.9 | 21,142.9 | 21,455.6 | 19,957.6 | 19,150.6 | 18,907.8 | ||
Steel production (ten thousand tons) | 80,276.58 | 88,619.57 | 95,577.83 | 108,200.54 | 112,513.12 | 103,468.41 | 104,813.45 | 104,642.05 | 110,551.65 | ||
Main non-ferrous metal production (ten thousand tons) | 3120.98 | 3628.94 | 3990.33 | 4412.13 | 4828.81 | 5155.82 | 5345.11 | 5498.31 | 5702.68 | ||
Grain production (ten thousand tons) | 55,911.31 | 58,849.33 | 61,222.62 | 63,048.2 | 63,964.83 | 66,060.27 | 66,043.51 | 66,160.72 | 65,789.22 | ||
Express delivery volume of the year (ten thousand piece) | 233,891.99 | 367,311.08 | 568,547.99 | 918,674.89 | 1,395,925.3 | 2,066,636.84 | 3,128,315.11 | 4,005,591.91 | 5,071,042.8 | ||
Competitive Context | Freight traffic of highways (ten thousand tons) | 2,448,052 | 2,820,100 | 3,188,475 | 3,076,648 | 3,113,334 | 3,150,019 | 3,341,259 | 3,686,858 | 3,956,871 | |
Freight traffic of shipping (ten thousand tons) | 378,949 | 425,968 | 458,705 | 559,785 | 598,283 | 613,567 | 638,238 | 667,846 | 702,684 | ||
Civil air cargo volume (ten thousand tons) | 563 | 557 | 545 | 561 | 594 | 629 | 668 | 706 | 739 |
Supply | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 |
Investment in fixed assets in railway transportation (billion CNY) | 2622.18 | 3000.12 | 3548.88 | 4581.20 | 5902.80 | 7509.50 | 9336.90 | 11,746.40 | 14,873.80 | 19,392.00 |
Length of railroad lines in service (ten thousand km) | 6.87 | 7.01 | 7.19 | 7.30 | 7.44 | 7.54 | 7.71 | 7.80 | 7.97 | 8.55 |
National railway electrification mileage (ten thousand km) | 1.89 | 2.09 | 2.14 | 2.21 | 2.26 | 2.34 | 2.74 | 2.80 | 2.90 | 3.60 |
Mileage of double track of national railways (ten thousand km) | 2.54 | 2.66 | 2.71 | 2.77 | 2.78 | 2.85 | 2.92 | 2.98 | 3.06 | 3.30 |
National railway locomotive inventory | 14,472 | 14,955 | 15,159 | 15,456 | 16,066 | 16,547 | 16,904 | 17,311 | 17,336 | 17,825 |
National railway freight wagon inventory | 439,943 | 453,620 | 459,017 | 510,327 | 526,894 | 541,824 | 564,899 | 577,521 | 591,793 | 601,412 |
Number of railway employees | 1,871,000 | 1,789,271 | 1,758,421 | 1,727,735 | 1,698,667 | 1,665,588 | 1,652,720 | 1,741,029 | 1,732,909 | 1,850,147 |
Wagon static load (ton) | 57.90 | 58.10 | 58.20 | 58.30 | 59.30 | 60.10 | 60.90 | 61.30 | 62.00 | 62.60 |
Daily production of freight locomotives (ten thousand ton-km) | 99.40 | 99.90 | 102.20 | 105.80 | 108.70 | 110.60 | 114.30 | 120.40 | 123.60 | 128.60 |
Supply | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |
Investment in fixed assets in railway transportation (billion CNY) | 24,143.10 | 30,239.60 | 36,485.40 | 43,574.70 | 50,126.50 | 55,159.00 | 59,650.10 | 63,168.40 | 63,563.60 | |
Length of railroad lines in service (ten thousand km) | 9.12 | 9.32 | 9.76 | 10.31 | 11.18 | 12.10 | 12.40 | 12.70 | 13.17 | |
National railway electrification mileage (ten thousand km) | 4.20 | 4.60 | 5.10 | 5.60 | 6.50 | 7.50 | 8.00 | 8.70 | 9.20 | |
Mileage of double track of national railways (ten thousand km) | 3.70 | 3.90 | 4.40 | 4.80 | 5.70 | 6.50 | 6.80 | 7.20 | 7.60 | |
National railway locomotive inventory | 18,349 | 19,590 | 19,625 | 19,686 | 19,990 | 21,366 | 21,453 | 21,420 | 21,000 | |
National railway freight wagon inventory | 622,284 | 651,175 | 670,801 | 715,492 | 716,578 | 768,516 | 788,626 | 808,736 | 839,213 | |
Number of railway employees | 1,756,385 | 1,761,542 | 1,793,267 | 1,796,382 | 1,902,500 | 1,874,448 | 1,874,131 | 1,848,032 | 1,833,800 | |
Wagon static load (ton) | 63.10 | 63.60 | 64.00 | 64.40 | 64.60 | 65.00 | 65.20 | 65.60 | 65.70 | |
Daily production of freight locomotives (ten thousand ton-km) | 135.00 | 138.50 | 138.30 | 139.70 | 143.40 | 139.90 | 135.50 | 145.70 | 147.90 |
Classify | Influence Factor | Spearman Correlation | Pearson Correlation | GRA Correlation | |
---|---|---|---|---|---|
Demand | Macroeconomy | 0.898 | 0.847 | 0.835158 | |
0.896 | 0.869 | 0.876404 | |||
0.889 | 0.811 | 0.816226 | |||
0.946 | 0.948 | 0.870163 | |||
Related Industry Output | 0.926 | 0.964 | 0.960872 | ||
0.789 | 0.840 | 0.933033 | |||
0.926 | 0.943 | 0.87682 | |||
0.898 | 0.872 | 0.859417 | |||
0.856 | 0.871 | 0.946216 | |||
0.898 | 0.593 | 0.674058 | |||
Competitive Context | 0.892 | 0.890 | 0.902842 | ||
0.898 | 0.860 | 0.860545 | |||
0.880 | 0.919 | 0.915448 | |||
Supply | 0.860 | 0.796 | 0.780757 | ||
0.898 | 0.778 | 0.93183 | |||
0.898 | 0.769 | 0.85042 | |||
0.898 | 0.714 | 0.885377 | |||
0.860 | 0.886 | 0.941648 | |||
0.896 | 0.866 | 0.948876 | |||
0.883 | 0.707 | 0.718661 | |||
0.898 | 0.936 | 0.925272 | |||
0.946 | 0.963 | 0.955143 |
Year | Real Value (Million Tons) | Fitting Value (Million Tons) | Absolute Error (Million Tons) | Relative Error (%) | |
---|---|---|---|---|---|
learning sample | 2000 | 1785.81 | 1905.94 | 120.13 | 6.73% |
2001 | 1931.89 | 1974.28 | 42.39 | 2.19% | |
2002 | 2049.56 | 2089.23 | 39.67 | 1.94% | |
2003 | 2242.48 | 2246.98 | 4.5 | 0.20% | |
2004 | 2490.17 | 2554.49 | 64.32 | 2.58% | |
2005 | 2692.96 | 2769.64 | 76.68 | 2.85% | |
2006 | 2882.24 | 2973.19 | 90.95 | 3.16% | |
2007 | 3142.37 | 3074.19 | 68.18 | 2.17% | |
2008 | 3303.54 | 3250.96 | 52.58 | 1.59% | |
2009 | 3333.48 | 3225.78 | 107.7 | 3.23% | |
2010 | 3642.71 | 3705.18 | 62.47 | 1.72% | |
2011 | 3932.63 | 3814.85 | 117.78 | 2.99% | |
2012 | 3904.38 | 3901.8 | 2.58 | 0.07% | |
2013 | 3966.97 | 3931.83 | 35.14 | 0.89% | |
2014 | 3813.34 | 3770.43 | 42.91 | 1.13% | |
2015 | 3358.01 | 3489.44 | 131.43 | 3.91% | |
2016 | 3331.86 | 3436.69 | 104.83 | 3.15% | |
2017 | 3688.65 | 3700.59 | 11.94 | 0.32% | |
predicted | 2018 | 4026.31 | 3976.89 | 49.42 | 1.23% |
Approach | MAPE (%) | MAE (Million Tons) | RMSE (Million Tons) |
---|---|---|---|
ARIMA | 5.96% | 173.97 | 189.20 |
SVR | 4.62% | 134.86 | 142.86 |
GRU | 6.94% | 202.58 | 223.76 |
FC-LSTM | 3.35% | 78.60 | 81.63 |
DNN | 4.68% | 107.42 | 111.42 |
FNN | 7.42% | 216.59 | 254.41 |
GRNN | 2.68% | 74.23 | 79.62 |
The improved GRA-DAE-NN | 2.21% | 64.51 | 74.98 |
Year | Real Value (Million Tons) | Relative Error (%) | ||
---|---|---|---|---|
GRA-DAE-NN | DAE-NN | |||
learning sample | 2000 | 1785.81 | 6.73% | 12.92% |
2001 | 1931.89 | 2.19% | 3.35% | |
2002 | 2049.56 | 1.94% | 2.31% | |
2003 | 2242.48 | 0.20% | 0.27% | |
2004 | 2490.17 | 2.58% | 2.41% | |
2005 | 2692.96 | 2.85% | 3.43% | |
2006 | 2882.24 | 3.16% | 3.72% | |
2007 | 3142.37 | 2.17% | 1.30% | |
2008 | 3303.54 | 1.59% | 3.05% | |
2009 | 3333.48 | 3.23% | 0.99% | |
2010 | 3642.71 | 1.72% | 2.72% | |
2011 | 3932.63 | 2.99% | 3.82% | |
2012 | 3904.38 | 0.07% | 0.11% | |
2013 | 3966.97 | 0.89% | 0.97% | |
2014 | 3813.34 | 1.13% | 4.77% | |
2015 | 3358.01 | 3.91% | 6.03% | |
2016 | 3331.86 | 3.15% | 6.62% | |
2017 | 3688.65 | 0.32% | 0.82% | |
predicted | 2018 | 4026.31 | 1.23% | 4.40% |
Average | - | 2.21% | 3.37% |
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Share and Cite
Liu, C.; Zhang, J.; Luo, X.; Yang, Y.; Hu, C. Railway Freight Demand Forecasting Based on Multiple Factors: Grey Relational Analysis and Deep Autoencoder Neural Networks. Sustainability 2023, 15, 9652. https://doi.org/10.3390/su15129652
Liu C, Zhang J, Luo X, Yang Y, Hu C. Railway Freight Demand Forecasting Based on Multiple Factors: Grey Relational Analysis and Deep Autoencoder Neural Networks. Sustainability. 2023; 15(12):9652. https://doi.org/10.3390/su15129652
Chicago/Turabian StyleLiu, Chengguang, Jiaqi Zhang, Xixi Luo, Yulin Yang, and Chao Hu. 2023. "Railway Freight Demand Forecasting Based on Multiple Factors: Grey Relational Analysis and Deep Autoencoder Neural Networks" Sustainability 15, no. 12: 9652. https://doi.org/10.3390/su15129652