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Short-Term Passenger Flow Forecasting for Rail Transit considering Chaos Theory and Improved EMD-PSO-LSTM-Combined Optimization
Short-Term Passenger Flow Forecasting for Rail Transit considering Chaos Theory and Improved...
Zhao, Lixin;Jin, Hui;Zou, Xintong;Liu, Xiao
Hindawi Journal of Advanced Transportation Volume 2023, Article ID 9524966, 16 pages https://doi.org/10.1155/2023/9524966 Research Article Short-Term Passenger Flow Forecasting for Rail Transit considering Chaos Theory and Improved EMD-PSO- LSTM-Combined Optimization 1 1 1 2 Lixin Zhao , Hui Jin , Xintong Zou , and Xiao Liu Liaoning University of Technology of China, Jinzhou, Liaoning 121000, China North China University of Technology, Beijing 100000, China Correspondence should be addressed to Hui Jin; firstname.lastname@example.org Received 4 August 2022; Revised 20 January 2023; Accepted 5 April 2023; Published 3 May 2023 Academic Editor: Ren-Yong Guo Copyright © 2023 Lixin Zhao et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper proposes a prediction method based on chaos theory and an improved empirical-modal-decomposition particle- swarm-optimization long short-term-memory (EMD-PSO-LSTM)-combined optimization process for passenger fow data with high nonlinearity and dynamic space-time dependence, using EMD to process the original passenger fow data and generate several eigenmodal functions (IMFs) and residuals with diferent characteristic scales. Based on the chaos theory, each component of the PSO algorithm was improved by introducing an inertia factor to facilitate the adjustment of its search capability to improve optimization. Each subsequence of the phase-space reconstruction was built into an improved PSO-LSTM prediction model, and the output of each prediction model was summed to determine the fnal output. Experimental studies were performed using data from the North Railway Station of Chengdu Rail Transit, and the results showed that the proposed model can generate better prediction results. Te proposed model obtained root mean square error (RMSE) and mean absolute error (MAE) of 16.0908 and 11.3704, respectively. Compared with the LSTM, the improved PSO-LSTM, the improved EMD-PSO-LSTM, and the model proposed in this paper improved the RMSE values by 25.53%, 29.97%, and 58.76%, respectively, and the MAE values by 30.41%, 40.13%, and 63.08%, respectively, of the prediction results. However, short-time passenger fow prediction can be 1. Introduction a particularly challenging problem. Raw trafc-fow data are At present, urban rail transport continues to develop spatiotemporal data that simultaneously exhibit heteroge- well, as its speed, capacity, comfort, and safety help it neity and correlation, as well as strong nonlinearity and become the main mode of transport for the urban public. chaos. In addition, most existing research captures relatively Along with the gradually increasing intensity of pas- few trafc data attributes, resulting in unsatisfactory pre- senger fow, short-time passenger fow prediction has diction results. Consequently, real-time accurate short-time become particularly important, as accurate trafc pas- passenger fow prediction is critical. senger fow prediction helps urban trafc managers Short-term trafc forecasting models can be broadly better plan and manage their resources. Moreover, trafc classifed into four categories—traditional statistical learning short-time passenger fow prediction has become of algorithms, machine learning models, deep learning algo- strategic importance for the construction of urbanized rithms, and combinatorial models. Te tasks of statistical intelligent transport systems to relieve trafc pressure, learning and machine learning algorithms are similar, which adjust operating times, and plan future construction. It is involve inferring model parameters and ftting and pre- also the foundation of smart city ambitions and dicting data. However, the focus of the two difers—that is, construction. statistical learning algorithms are more concerned with the 2 Journal of Advanced Transportation nonsmooth signal processing methods—was examined for confdence of predictions, whereas machine learning algo- rithms are more concerned with the predictive efects of the rail trafc short-time passenger fow predictions. Te im- proved complete ensemble EMD with adaptive noise model. Statistical learning algorithms include autoregressive-integrated moving average (ARIMA) models (CEEMDAN) method was proposed and used for the de- , seasonal ARIMA models , and Kalman flter models composition of highway data by decomposing the time series . Te advantage of these models is that they are simple to into diferent features, which could dramatically reduce the operate; however, owing to the complexity of changes in prediction error of the mainstream model. Te improved actual passenger fow data, there can be a certain subjective CEEMDAN-fuzzy entropy (FE)-temporal convolutional factor in their establishment, which can be easily infuenced network model was shown to exhibit high predictive accuracy and strong robustness when using the US101-S highway in by a priori assumptions that can be difcult to satisfy in practice, limiting their predictive performance. California as the research object. Wang Xiao Quan et al.  proposed an SVM model for short-time trafc fow pre- Machine learning models include support vector ma- chines (SVMs) , artifcial neural networks [5, 6], and diction, incorporating the principles of chaos theory to map trafc fows into a hyper-dimensional structure by per- Bayesian networks , which can capture the nonlinear data features of short-time passenger fow using their own forming phase-space reconstruction based on its nonlinear learning abilities. Leng et al.  established an improved characteristics, and to calculate the embedding dimension neural network prediction model that was optimized using parameter by using the maximum conditional entropy a genetic optimization algorithm that not only improved the method with a time delay parameter obtained using mutual convergence of its search capability but also its prediction information techniques. Finally, the reconstructed subseries accuracy. However, traditional machine learning models were used as inputs and predicted using genetic-algorithm optimized support vector regression. Numerical experiments cannot efectively process high-dimensional data, and the complex variability of nonlinearities in time series trafc showed that the proposed method exhibited excellent pre- dictive accuracy. Lingling Wu et al.  proposed an em- data can be difcult to capture. Moreover, their predictive performance depends on expert experience, and their pirical model decomposition and diferential evolution algorithm to optimize the back propagation neural network generalization ability is weak. Consequently, many scholars have researched deep learning models to handle high- for a short-time trafc fow prediction model. Tey used the dimensional spatiotemporal trafc data. EMD algorithm to decompose diferent modal components in Based on deep learning algorithms such as recurrent the trafc timing data step-by-step, generating a series of neural networks (RNNs) [9, 10] and long short-term eigenmodal functions (IMFs) and residuals at diferent scales memory (LSTM) neural networks , Huang et al.  to remove certain noise efects, thereby improving the ac- processed information from trafc sequence data using curacy of results. Te main contributions of this paper are as follows: long-and short-time neural networks and gated recurrent units in RNNs, and performed noise reduction of raw (1) Given the nonlinear characteristics of trafc fow and passenger fow data using wavelet transforms. Zhang et al. the fact that particle swarm optimization (PSO) al-  used multigraph convolutional neural networks to gorithms usually fall into local optimality, we explore the spatial features of trafc data. However, deep combined the chaos theory and an improved EMD- learning models are prone to overftting or underftting . PSO-LSTM model to design a short-time passenger Tere is also a class of combinatorial models. Zhai fow forecasting method for urban rail transport, and et al. proposed a hybrid trafc fow prediction method by applied it to the feld of rail transit passenger fow combining the k-nearest neighbor and LSTM algorithms forecasting for the frst time. based on the spatiotemporal features of transportation data. (2) We used the EMD algorithm to decompose the Teir experimental results showed that their proposed original time series data and perform phase-space model improved by 12.59% on average compared with the reconstruction using chaos theory principles to re- comparison model. Gao et al.  proposed a new hierar- construct the useful aspects of the EMD to further chical hybrid model to forecast short-term passenger fows, explore the internal characteristics of trafc fow and with an average absolute error of approximately 10% in the improve prediction accuracy. An improved forecasting results. Moreover, experiments showed that the PSO-LSTM prediction model was then developed for prediction results of this combined model exhibited greater each reconstructed subsequence. Owing to the ten- accuracy. dency of the original model to fall into a local op- However, the collected trafc fow data can be disturbed timum, we improved it to increase its PSO-seeking by noise factors, reducing the predictive performance of the search capability, and the predictions of each com- models. To minimize the impact of external factors on ponent were summed to produce the fnal output. forecast accuracy, a prediction model that employs chaos (3) We conducted the experiments using a dataset theory can directly analyze the intrinsic regularity of trafc comprising data from the North Railway Station of fow data through a priori cognition without establishing the Chengdu Municipal Railway to validate the ef- a subjective model. Consequently, considering the charac- fectiveness of the proposed model. Te results teristics of nonlinearity and nonsmoothness in urban rail showed that the proposed model performed better trafc time series data, the empirical mode decomposition than existing methods. (EMD) algorithm—which can be applied to nonlinear and Journal of Advanced Transportation 3 n− 1 2. Methods X(t) � f (t) + RES (t). (4) i n 2.1. EMD Algorithm. EMD can be used for analyzing both i�1 linear and smooth, and nonlinear and nonsmooth signals. Te core of this approach is to gradually smoothen the signal and decompose the vibration modes in the signal into a fnite 2.2. Chaos Teory. Te study of the chaos theory began in number of components that tend to be smoothed based on 1980 with the phase-space reconstruction theory proposed diferent characteristic scales or trends. Moreover, in short- by Packard et al. Te theory states that the evolution of each component in a chaotic system is jointly dictated by the period passenger fow forecasting for rail transport, the transformation of nonlinear and nonsmooth passenger fow other individual components of these interactions, and that the variable contains information about the long-term signals into linear and smooth signals better refects their intrinsic physical meaning . Compared with other evolution of all the variables in the system. Te basic signal-processing methods, EMD methods are more in- principle of phase-space reconstruction is the delayed em- direct, intuitive, and adaptive. bedding theorem proposed by Takens . For chaotic time EMD divides the raw trafc fow signal into several series, chaotic models can be built and predicted in the so- empirical mode components (IMFs) based on its adaptive called phase space, wherein phase-space reconstruction timing analysis, each of which contains local features of based on the chaos theory is an essential component in the diferent feature scales in the previous trafc fow signal, and processing of a chaotic time series. Tere are two key index residuals (RES), which represent the mean or trend in the values in the phase-space reconstruction algorithm—the embedding dimension (d) and time delay (τ)—and in , original trafc fow signal. Each IMF must satisfy two conditions at the same time—that is, the diference between the parameters of both the embedding dimension and time the number of extremes and zeros in the domain of def- delay are only proved via theoretical studies, and no specifc nition should not exceed 1, and the mean value of the upper formula is given. In practical applications, the time delay and and lower envelope functions should be 0 . Te process is embedding dimension parameters should be calculated as follows: considering the actual situation because raw trafc fow time-series data are infuenced by external variables. Step 1: In the original trafc signal, all extreme points In a chaotic system, a set of observations that vary with are calculated, and the upper and lower envelopes are time can be obtained by examining them—noted as chaotic ftted m (t)m (t) with the cubic spline interpolation 1 2 time series Y , i � 1, 2, . . . , n—and a set of m-dimensional function to calculate the mean value m(t) of the upper vectors can be constructed using the observations, as follows: and lower envelopes. Te mean of the original signal envelope is calculated as follows: Y � y , y(i + τ), · · ·, y(i + (m − 1)τ) , (5) i i m (t) + m (t) 1 2 where τ � k∆t, k � 1, 2, . . ., ∆t denotes the time interval, Y (1) m(t) � . i denotes a sample point in the constructed phase space with m components, and m � n − (m − 1)k. If the parameters of Step 2: Subtracting the original sequence m(t) from m are chosen appropriately, then Y can represent the state X(t) to obtain a new sequence, as follows: in the original system and dynamic characteristics of pri- mary passenger fow data in the multidimensional h (t) � X(t) − m(t), (2) phase space. where h (t) satisfes the IMF condition, so that the frst f (t) IMF component is obtained. If h (t) is still 1 1 2.3. LSTM-Based Short-Time Passenger Flow Forecasting for unstable, the abovementioned process is repeated once Rail Transit. LSTM is particularly suitable for processing with h (t) instead of X(t) until the resulting average trafc data sequences with certain time intervals. In the envelope tends to 0, defning the f component as h . 1 1k LSTM neural network structure, each neuron comprises three gating units as a solution to the drawback of dis- f � h . (3) i ik appearing gradients owing to a long time series. Te LSTM model comprises four main parts—memory cells, forgetting Step 3: Te original sequence X(t) is subtracted from gate, input gate, and output gate —as shown in Figure 1. the frst IMF component to obtain the frst f (t) Te LSTM network structure is shown in Figure 2. diference sequence with the high-frequency compo- Here, the memory cell is the core component of the nent and removed RES (t). Te above processing of entire LSTM model used for storing the cell states of past RES (t) is used to obtain a second empirical modal information, and the output of the memory cell at moment t component until it is no longer possible to disaggregate can be expressed as follows: it, with the last one obtained being a residual RES (t). After decomposition, which represents the actual av- C � tan h W · h , Z + b , t c t− 1 t c erage trend of the primary series X(t), the original (6) C � f · C + i · C , sequence X(t) can be expressed as follows: t t t− 1 t t 4 Journal of Advanced Transportation c t t-1 × + tanh σσ tanh σ h h t-1 Figure 1: LSTM structure. h h t+1 t-1 t c c t-1 t × + tanh σσ σ tanh h h t-1 t Z Z t t+1 t-1 Figure 2: LSTM network structure. where Z denotes the input at the present time, i denotes the Te output gate result can be determined via three main t t input gate, which refreshes the stored information in the cell components—the previous moment’s input information, state, and C is the update to C . the information stored after the cell state is updated, and the t− 1 t Te forgetting gate is used to determine which part of the output information at the last moment. Tus, the output at information in the cell state needs to be removed by fusing moment t can be expressed as follows: information from the preceding point in time and that on O � σ