Subway network passenger spatio-temporal path estimation method fusing incremental learning

Abstract

The application discloses a subway network passenger travel space-time path estimation method based on fusion incremental learning. The method obtains passenger entry and exit card swiping records through an AFC system of a subway network, combines with ATS train operation data, constructs a space-time network and generates a passenger feasible space-time path set. Taking a passenger of a single feasible space-time path as a sample basis, a Gaussian mixture distribution model is used to model a walking time distribution. For a multi-space-time path passenger, the posterior probability of each space-time path is calculated by combining with a Bayesian theorem, and dynamic estimation of a passenger path selection probability is realized. Through an incremental learning mechanism, model parameters are adaptively adjusted according to the confidence of the space-time path, and the model is updated in real time to adapt to changes in passenger behavior patterns. The application solves the problems of small sample size, poor scalability and high computational complexity in the prior art, can efficiently and dynamically estimate passenger space-time paths, and provides decision support for subway operation management.

Description

Technical Field

[0001] This invention relates to the field of traffic engineering and intelligent transportation systems, and in particular to a method for estimating the spatiotemporal paths of passengers in a subway network by incorporating incremental learning. Background Technology

[0002] With the acceleration of urbanization, subway networks have become a core component of public transportation in large and medium-sized cities. However, under the condition of a fully operational subway network, operators struggle to accurately grasp the spatiotemporal distribution characteristics of passengers within the network, primarily due to a lack of complete passenger transfer path information. Accurately acquiring passenger travel path information, especially precisely identifying passenger spatiotemporal trajectories (including the lines they travel on and the specific trains they take), is crucial for improving the accuracy of dynamic passenger flow distribution prediction and meeting the precision requirements of OD dynamic demand analysis and transfer flow prediction. Furthermore, accurate inference of passenger spatiotemporal paths can provide important decision support for subway operation management, such as optimizing capacity resource allocation and train operation adjustments by assessing the real-time load factors of each line and train.

[0003] In the field of subway passenger spatiotemporal path inference, existing research methods mainly include Logit models, Bayesian networks, dynamic path correction strategies considering station congestion, and reinforcement learning-based methods. The Logit model is a classic discrete choice model that treats passenger path selection as a probabilistic decision-making process based on utility maximization. It infers the most likely travel path by calculating the utility value of each path and converting it into selection probabilities. However, the Logit model suffers from difficulties in parameter calibration. Bayesian methods utilize AFC card swipe data and ATS train operation data, dynamically updating the posterior probability of path selection using the Bayesian formula. While possessing strong theoretical interpretability, they are highly dependent on prior knowledge, and their prediction accuracy is limited when the sample size is small. Furthermore, Bayesian methods are based on static data, requiring long training times and making it difficult to achieve high-frequency and rapid data updates.

[0004] Spatiotemporal path estimation methods considering station congestion are based on AFC card swipe data and ATS train operation data. They employ techniques such as travel time back-calculation, congestion rate modeling, and multi-path matching, making them suitable for complex transfer scenarios in megacity subway networks. However, this method also relies on prior knowledge, and the accuracy of back-inference and path matching degree selection needs improvement. Reinforcement learning-based spatiotemporal path estimation methods learn optimal decision-making strategies by simulating the interaction between an agent and its environment, modeling the passenger travel process as a Markov decision process. This method requires a large amount of data and computational resources, has a long training cycle, and is often combined with heuristic algorithms to improve efficiency.

[0005] While existing technologies have achieved some success in passenger spatiotemporal path estimation, several key shortcomings remain. For example, both traditional Logit models and Bayesian methods rely on prior knowledge, and insufficient prior knowledge of the samples limits the model's accuracy and adaptability. Furthermore, existing technologies exhibit lag in model parameter updates, often relying on periodic batch updates and failing to achieve real-time iteration, thus lacking adaptive capabilities. These drawbacks restrict the widespread adoption of existing technologies in practical applications. Summary of the Invention

[0006] The present invention aims to provide a method for estimating the spatiotemporal paths of passengers in subway networks by incorporating incremental learning, in order to solve the problems of small sample size, poor scalability and high computational complexity of existing passenger spatiotemporal path estimation techniques.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for estimating the spatiotemporal paths of passengers in a subway network by incorporating incremental learning, comprising the following steps:

[0008] S1. Generation of Feasible Spatiotemporal Path Sets for Passengers Based on Spatiotemporal Network: Passengers' entry and exit card swipe records are obtained through the AFC system of the metro network, and ATS timetable data is collected at the same time to construct a spatiotemporal network of train operation and passenger travel, and generate a set of feasible spatiotemporal paths for passengers; based on the number of feasible spatiotemporal paths for passengers, they are divided into single spatiotemporal path passengers and multi-spatiotemporal path passengers.

[0009] S2. Spatiotemporal Path Travel Time Breakdown: Based on the passenger's travel process, the spatiotemporal path travel time can be broken down into four parts: the time for entering the origin station (including waiting), the time for boarding, the time for walking (including waiting) at the transfer station (if there is a transfer in the travel process), and the time for exiting the destination station; and the time of each segment in the spatiotemporal path is read based on each passenger's AFC entry and exit time and ATS timetable data.

[0010] S3. Modeling of walking time distribution based on Gaussian mixture distribution: Based on the exit walking time information of passengers on a single spatiotemporal path, the exit walking time distribution is modeled using a Gaussian mixture distribution model. The number of sub-distributions, weights, mean and variance of the Gaussian mixture distribution model are calculated to generate the walking time distribution of passengers exiting the station. The station entry walking (including waiting) time can be estimated using the same method, or approximated by the station exit walking time distribution and the entry waiting time adopts a uniform distribution that follows the departure interval.

[0011] S4. Passenger spatiotemporal path probability calculation based on Bayes' theorem: For each spatiotemporal path, the time distribution of each segment is convolved to generate the theoretical total travel time distribution of the spatiotemporal path. Then, based on the actual travel time in the passenger's AFC card swipe data, the posterior probability of the passenger choosing the spatiotemporal path is calculated using Bayes' theorem.

[0012] S5. Incremental Learning and Adaptive Adjustment: Spatiotemporal paths with a posterior probability greater than 80% are marked as high-confidence spatiotemporal paths, spatiotemporal paths with a posterior probability between 50% and 80% are marked as medium-confidence spatiotemporal paths, and spatiotemporal paths with a posterior probability less than 50% are marked as low-confidence spatiotemporal paths. Different update weights are assigned to spatiotemporal path samples with different confidence levels. An exponential decay learning strategy is adopted to update the parameters of a Gaussian mixture distribution and update the probability of spatiotemporal paths.

[0013] Specifically, in step S1, single-temporal-space path passengers are used to extract the characteristics of walking time (including waiting time) to enter the station and walking time to exit the station. Single-temporal-space path passengers include both passengers without transfers and passengers with transfers.

[0014] Specifically, in step S3, the Gaussian mixture distribution model estimation includes parameter initialization, EM algorithm iteration, and model convergence determination. Parameter initialization includes mean initialization, variance initialization, and weight initialization. Mean initialization adopts the farthest point initialization strategy, variance initialization adopts the calculation of the scalar variance of each Gaussian component, and weight initialization adopts the uniform initialization strategy.

[0015] Specifically, in step S3, the number of sub-distributions of the Gaussian mixture distribution is analyzed using the Akaike Information Criterion, the Bayesian Information Criterion, and the KS test. When the sample size is small, the Akaike Information Criterion is used to score models with different numbers of Gaussian sub-distributions, and the model with the smallest Akaike Information Criterion value is selected as the optimal parameter structure for the station. When the sample size is large, the Bayesian Information Criterion is used to score models with different numbers of Gaussian sub-distributions, and the model with the smallest Bayesian Information Criterion value is selected as the optimal parameter structure for the station. The KS test is used to evaluate whether the Gaussian mixture distribution can reasonably fit the actual walking time distribution after the number of components is determined.

[0016] Specifically, in step S3, the EM algorithm iteration includes an E step and an M step. The E step calculates the probability that each sample belongs to a different Gaussian component, and the M step uses the response obtained in the E step to re-estimate the model parameters. The model convergence determination uses the change in the log-likelihood value as the basis for convergence determination.

[0017] Specifically, in step S4, the convolution operation integrates and fuses the temporal probability density functions of each stage through a sliding stacking algorithm, accurately synthesizing the complete probability distribution of the total time spent when a passenger selects a specific spatiotemporal path, preserving the randomness characteristics of the distribution of each sub-stage and truly reflecting the cumulative effect of uncertainty in the travel process.

[0018] Specifically, in step S5, when updating the posterior probability of each passenger's spatiotemporal path, the Gaussian mixture distribution parameters of the corresponding stations in the spatiotemporal path can be dynamically updated.

[0019] Specifically, in step S5, based on different confidence levels, the initial learning rate of the high-confidence spatiotemporal path is 1, and the initial learning rate of the medium-confidence spatiotemporal path is 0.15, and an exponential decay factor is introduced.

[0020] The principle and beneficial effects of this technical solution:

[0021] This invention constructs a spatiotemporal network of passenger travel by combining data from the Automatic Fare Collection (AFC) system and the Automatic Train Control (ATS) system, and uses a Gaussian Mixture Model (GMM) and Bayes' theorem to estimate and dynamically update passenger spatiotemporal paths. First, this invention generates a set of feasible spatiotemporal paths for passengers using a search algorithm, covering both single-spatiotemporal and multi-spatiotemporal path passengers. Data from single-spatiotemporal path passengers is used to extract key features, such as entry and waiting times, and transfer walking times, which provide basic sample data support for subsequent path estimation. The path selection probability of multi-spatiotemporal path passengers is the focus of this research. Second, this invention uses a Gaussian mixture distribution to model passenger exit walking time, accurately describing the distribution of walking time through parameter initialization, EM algorithm iteration, and model convergence determination. This process not only considers the diversity of passenger behavior but also ensures the stability and adaptability of the model through model selection and goodness-of-fit tests (such as the Akaike Information Criterion, Bayesian Information Criterion, and KS Test). Based on Bayes' theorem, this invention further calculates the posterior probability of each spatiotemporal path, thereby achieving dynamic estimation of the passenger's spatiotemporal path. This process combines prior knowledge and actual observation data, effectively reflecting the probability of passengers choosing different paths.

[0022] Compared to traditional methods, this invention considers not only passengers without transfers but also passengers with single-spatiotemporal routes involving transfers, significantly expanding the sample size of basic information and thus improving the accuracy of route estimation. Through an incremental learning mechanism, real-time updates of model parameters are achieved. Upon receiving new passenger data, the model can immediately adjust its parameters without periodic batch updates, thereby adapting to gradual changes in passenger behavior patterns. This invention employs an exponential decay learning strategy, assigning different update weights to samples with different confidence levels. This ensures the model's rapid response to new data while avoiding model bias caused by excessive single updates. Furthermore, this invention is applicable to subway networks of different sizes. Even at stations with small sample sizes, model stability and adaptability can be ensured through model selection and goodness-of-fit testing. Attached Figure Description

[0023] Figure 1 Flowchart of a method for estimating the spatiotemporal paths of passengers in a subway network;

[0024] Figure 2This is a schematic diagram of the spatiotemporal path;

[0025] Figure 3 This is a schematic diagram of a Gaussian mixture distribution;

[0026] Figure 4 Schematic diagram of GMM models with different component numbers;

[0027] Figure 5 This is a schematic diagram showing the actual walking time distribution upon exiting the station;

[0028] Figure 6 Select a flowchart for the optimal model;

[0029] Figure 7 This is a schematic diagram of the convolution process;

[0030] Figure 8 Design a graph for incremental learning. Detailed Implementation

[0031] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0032] Example 1:

[0033] like Figure 1 The method for estimating the spatiotemporal paths of passengers in a subway network by incorporating incremental learning includes the following steps:

[0034] 1. Generation of Feasible Spatiotemporal Path Sets for Passengers Based on Spatiotemporal Networks

[0035] After passengers generate entry and exit card records through the AFC system, the system captures and records information such as the passenger's departure station, destination station, boarding time, and transfer stations. At the same time, it collects ATS operation data from the subway network to obtain complete train timetable information for each train, including the arrival and departure times of each train at each station.

[0036] Using two types of information as data input, a spatiotemporal network of train operation and passenger travel is constructed. A path search method is then used to filter feasible spatiotemporal paths, generating a set of feasible spatiotemporal paths for each passenger. Specifically, for each passenger, all feasible spatiotemporal paths are traversed by combining their AFC card swipe data and ATS train data, and all feasible spatiotemporal paths are saved.

[0037] Passengers are categorized into single-spatiotemporal-path passengers and multi-spatiotemporal-path passengers based on the number of feasible spatiotemporal paths. For single-spatiotemporal-path passengers, their actual spatiotemporal paths are known, forming the data sample basis for this method. Combined with ATS train timetable data, information on entry and waiting time, transfer walking and waiting time, and exit walking time can be extracted. The research objective of this method is to determine the probability of each spatiotemporal path chosen by multi-spatiotemporal-path passengers.

[0038] like Figure 2 As shown, passenger number 1 is a single-temporal-space path passenger, while passenger number 2 has three temporal-space paths and is a multi-temporal-space path passenger.

[0039] It is worth noting that passengers with a single spatiotemporal route in this method can include passengers with or without transfers. This method considers passengers with single spatiotemporal routes who have transfers, which can expand the sample size of the basic information for this method.

[0040] 2. Spatiotemporal Path Travel Time Breakdown

[0041] Based on the passenger's travel process, the travel time for each spatiotemporal path is broken down. The total travel time for passengers without transfers is broken down into three parts: walking time to enter the station (including waiting time), travel time, and walking time to exit the terminal station. The total travel time for passengers with one transfer is broken down into four parts: walking time to enter the origin station (including waiting time), travel time, walking time to the transfer station (including waiting time), and walking time to exit the terminal station. The information for passengers with multiple transfers is similarly broken down.

[0042] Of the travel time components, the travel time can be directly read using ATS, while the walking time or walking (including waiting time) is distributed and statistically analyzed based on the time information of a single spatiotemporal path.

[0043] 3. Modeling of walking time distribution based on Gaussian mixture distribution (GMM)

[0044] Taking the exit walking time of each station as an example, we model the walking time distribution. The entry walking time (including waiting time) of the starting station can be modeled using the same method. Details are as follows.

[0045] Because passengers' walking time upon exiting the station may vary due to individual differences, forming multiple speed groups, a mixture of Gaussian distributions may occur, such as... Figure 3 As shown, the model assumes that the data is composed of a mixture of multiple Gaussian distribution components (sub-distributions). By weighting and superimposing the Gaussian distribution components, a multimodal and asymmetric data distribution can be effectively described. Using a Gaussian mixture distribution can better describe the distribution of passenger exit walking time.

[0046] Based on the exit walking time of passengers along a single spatiotemporal path, a Gaussian mixture distribution model is used for modeling. The number of sub-distributions, weights, mean, and variance of the Gaussian mixture distribution model are calculated to generate the exit walking time distribution of passengers leaving the station. The specific modeling method is as follows.

[0047] (1) Parameter initialization

[0048] In Gaussian mixture models, the number of sub-distributions (K value) directly determines the model's ability to represent the data structure. Insufficient sub-distributions prevent the model from fully characterizing complex distributions; excessive sub-distributions may lead to overfitting and decreased generalization ability. Therefore, we evaluate models with different K values ​​to select the optimal K value that best reflects the real data structure. Here, we try different sub-distribution numbers K (K = 1, 2, 3, 4) to initialize the Gaussian mixture model parameters.

[0049] First, we initialize the mean. In the Gaussian mixture model, the mean μ... k The initial mean represents the center position of each sub-distribution and has a decisive impact on the convergence spatiotemporal path and clustering effect of the entire model. If the initial means are too close to each other, multiple components are likely to fall into the same data cluster, thereby reducing the model's expressive power; conversely, if the initial means are reasonably distributed, it will help the model capture the different potential structures in the data, improving the convergence speed and the final fitting quality.

[0050] This invention employs an improved farthest-point initialization strategy. The basic idea is to preferentially select the sample furthest from the existing cluster center as the next initial mean, thereby maximizing the "coverage" between components in the initial stage. The specific steps are as follows:

[0051] ① Determine the first cluster center: Randomly select a sample point from the dataset as the first cluster center.

[0052] ② Select the next cluster center: For each remaining data point x i Calculate the shortest Manhattan distance D(x) to the selected cluster centers mentioned above. i ), calculate the sum of the shortest distances from all data points to the selected cluster centers, denoted as . Then, the probability of each point being selected as the next cluster center is calculated using the following probability formula.

[0053]

[0054] ③ Select the point with the highest probability as the cluster center μ k A higher probability indicates that the corresponding value is farther away from the data center, which can better expand the distribution of cluster centers. Therefore, the farthest point, i.e., the point with the highest probability, is selected as the new cluster center μ. k This helps avoid cluster centers being concentrated in the same data area, thereby improving cluster quality.

[0055] Repeat the above steps until K initial cluster centers μ1, μ2…μ are selected. k .

[0056] Then, variance initialization is performed. It describes the "diffusion range" of each component, which directly determines the breadth and boundaries of the data it covers. In a Gaussian mixture distribution model, if the initial variance is set too small, the component will be unable to absorb any samples in the early stages, thus rapidly collapsing and failing; conversely, if the variance is set too large, it may cause serious overlap between different components, affecting the convergence accuracy.

[0057] For each Gaussian component k, its covariance matrix is ​​typically calculated. However, since the data in this invention represents passengers' exit walking time and does not involve other feature dimensions, it falls under the one-dimensional case. Therefore, the covariance matrix degenerates into a scalar variance in this situation, and its calculation method is shown in the following formula:

[0058]

[0059] Where |C k | represents the set of samples assigned to the k-th class, C k This represents the number of samples in this category.

[0060] Finally, the weights are initialized. The mixture weights (π) in the Gaussian mixture model... k This reflects the proportion of each component in the overall distribution. During model initialization, the weight settings affect the response of samples to each component in the EM algorithm, thus influencing the direction of model learning. Considering the lack of prior knowledge about the actual proportion of each component in the initial state, this invention adopts the most common uniform initialization strategy, namely:

[0061]

[0062] Under this assumption, all sub-distributions have equal weights in the early stages of the iteration, and the weight ratios are adjusted subsequently through data-driven adjustments.

[0063] The Gaussian subdistribution under different K values ​​is as follows Figure 4 As shown.

[0064] Since it is impossible to directly determine the number K of the optimal sub-distribution that best matches the actual walking time distribution, three commonly used goodness-of-fit testing tools are introduced: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov–Smirnov Test (KS Test). By comprehensively considering the model's fitting accuracy and complexity, candidate models are screened to determine the optimal K value of the Gaussian mixture distribution, so as to ensure that the finally selected Gaussian mixture distribution has stability, interpretability, and statistical consistency.

[0065] like Figure 5As shown, for subway stations with a small sample size (e.g., less than 200), the AIC score is used to evaluate the model under different K values, and the model with the smallest AIC value is selected as the optimal parameter structure for that station. For stations with a large sample size (e.g., more than 200), the BIC score is used to evaluate the model under different K values, and the model with the smallest BIC value is selected as the optimal parameter structure for that station, to ensure the convergence stability and rationality of the modeling under large samples. The KS test is a non-parametric statistical test method for continuous distributions. This test is often used to compare whether a single sample conforms to a known distribution. That is, the cumulative frequency distribution of the sample data is compared with a specific theoretical distribution; if the difference between the two is small, it is inferred that the sample comes from a specific distribution cluster. In this invention, the KS test is used as a model validation tool to evaluate whether the Gaussian mixture distribution can reasonably fit the actual exit walking time distribution after the number of components is determined, such as... Figure 6 As shown.

[0066] (2) EM algorithm iteration

[0067] After parameter initialization, the model needs to iterate continuously using the EM algorithm to gradually approximate the true distribution of the data. In the initial GMM model of this invention, the observed value of a sample is the exit walking time, and its component (i.e., which type of passenger) is determined. Through the EM iteration process, the model can gradually learn these potential distribution characteristics under unsupervised conditions, enabling subsequent group modeling of complex behaviors.

[0068] ①Step E

[0069] The purpose of the E-step is to calculate the probability that each sample belongs to a different Gaussian component under the current parameters. This probability is usually called the "responsibility" or "posterior responsibility". In a Gaussian mixture distribution, the E-step essentially "soft-assigns" samples to various sub-distributions, with the weights determined by their similarity.

[0070] This approach avoids the "either / or" limitations of hard clustering algorithms, better reflecting the characteristics of passenger groups in reality, whose behavior is ambiguous and whose speeds are mixed. Each response value can be understood as "the probability of a sample belonging to a certain group," and these probabilities will serve as the weighting basis for the next parameter update.

[0071] In step E of this invention, based on the currently initialized mean μ k ,variance and weight π k The probability of each data point belonging to each component is calculated using the following Bayesian formula. These probabilities reflect the confidence level of each data point belonging to each component.

[0072]

[0073] These responsiveness metrics are used in the M-step to recalculate the model's parameters (mean, variance, weights).

[0074] ②M step

[0075] The task of the M step is to use the response scores obtained in the E step to re-estimate the model parameters to improve the overall log-likelihood. The update method for each parameter (mean, variance, weight) is derived from the "weighted maximum likelihood estimation", which involves using all samples with their corresponding response scores as weights in the statistic calculation.

[0076] This process demonstrates the model's adaptive learning ability to the data: the higher the responsiveness, the greater the contribution of the sample to the parameters, thus gradually guiding each component to concentrate towards its "representative group." The M-step continuously adjusts the model structure, enabling the model to better fit the data and approach more reasonable behavioral patterns.

[0077] The formula for recalculating the model parameters (mean, variance, weights) using the data obtained from the E-step is shown below.

[0078] Weight update:

[0079]

[0080] Mean update:

[0081]

[0082] Variance update:

[0083]

[0084] (3) Model convergence determination

[0085] Since the EM algorithm is an iterative optimization process, reasonable termination conditions need to be set to prevent invalid computations or overfitting. A common strategy is to track the change in log-likelihood value in each iteration; once the change falls below a set threshold, the model is considered converged. This invention uses the change in log-likelihood value as the basis for convergence judgment. If the difference between the log-likelihood values ​​of two iterations is very small (less than the set threshold), it indicates that the model optimization is already very small, and further iterations will not significantly improve the model's fit. At this point, the algorithm can stop iterating.

[0086] Maximum likelihood (MLF) measures the probability of observed data occurring given certain parameters. In a Gaussian mixture model (Gaussian mixture model), the likelihood is a weighted sum of the probability densities of all components. The EM algorithm maximizes the log-likelihood function by iteratively updating model parameters (such as the mean, variance, and weights of each Gaussian component). In each iteration, the responsibility probability of each data point belonging to each Gaussian component is calculated, and these probabilities are used to update the model parameters.

[0087] After each iteration, the algorithm calculates the current log-likelihood value. The log-likelihood value is the logarithm of the likelihood function, providing a very intuitive metric during the optimization process. By calculating the log-likelihood value, it's possible to determine whether the model has improved after each iteration.

[0088] The specific formula for calculating the log-likelihood value l(θ) is as follows:

[0089]

[0090] Among them, (x i |μ k ,∑ k Let x be the probability density function of the k-th Gaussian component. i This is the travel time data for the i-th passenger.

[0091] The specific convergence criterion formula is as follows:

[0092]

[0093] Where, l(θ) (t) ) and l(θ (t-1) Let ) represent the log-likelihood values ​​for round t and round (t-1), respectively. It is a predetermined small threshold, set to 1×10 -3 .

[0094] In addition, to avoid excessive iteration, a maximum number of iterations of 100 is set. When the maximum number of iterations is reached, the algorithm will be forcibly stopped.

[0095] At this point, the passenger walking time distribution obtained using a single spatiotemporal path has been calculated, and the estimation framework for each component of the total travel time has been established.

[0096] 4. Calculation of passenger spatiotemporal path probability based on Bayes' theorem

[0097] Based on the walking travel time distribution of the origin and destination stations in the spatiotemporal path, and combined with the travel time and transfer walking (including waiting time), a convolution is performed to generate the theoretical total travel time distribution of the spatiotemporal path.

[0098] Convolution operations, through a sliding stacking algorithm, integrate and fuse the temporal probability density functions of each stage to accurately synthesize the complete probability distribution of the total time spent by passengers when choosing a specific spatiotemporal path. This operation can preserve the randomness characteristics of the distribution in each sub-stage (such as the distribution skew caused by differences in walking speed). Compared with simple linear stacking, the convolution result more realistically reflects the cumulative effect of uncertainty in the travel process.

[0099] Taking passenger data from Dinggonglu North Station to Nanchang West Station in the Nanchang Metro as an example, according to the spatiotemporal path generation rules, there are four feasible spatiotemporal paths. We will perform convolutional analysis using one of these spatiotemporal paths as an example. Figure 7 The convolution process is illustrated below.

[0100] Read the actual total travel time T for each passenger from the AFC card swipe data. obs (seconds), in the theoretical distribution corresponding to the i-th feasible spatiotemporal path, directly read its corresponding likelihood value, indicating "given the i-th spatiotemporal path, the time taken is exactly T". obs The probability of "T" is: P(T) obs path i ).

[0101] To transform these likelihood values ​​into posterior probabilities of spatiotemporal paths, this invention employs Bayes' theorem, as shown in the following equation.

[0102]

[0103] P(T obs path i ): That is, the likelihood value mentioned above.

[0104] P(path i Prior probability: Represents the "subjective" probability that each feasible spatiotemporal path is selected before any temporal information is observed. In this invention, to reflect the lack of preference for each candidate spatiotemporal path, it is assumed that all feasible spatiotemporal paths have equal prior probability; that is, if the i-th passenger has M feasible spatiotemporal paths, then:

[0105]

[0106] P(T obs Marginal likelihood (): representing the likelihood based solely on the total time T. obs The overall probability that can be observed. According to the law of total probability shown in 4-16, we get:

[0107]

[0108] P(path i |T obs ): Posterior probability

[0109] Substituting the above terms into Bayes' formula, due to the prior probability... The numerator and denominator cancel each other out, and we can directly obtain the simplified form of the following equation:

[0110]

[0111] The resulting set of posterior probabilities not only satisfies the normalization condition formula, but also intuitively reflects the relative probability of each spatiotemporal path under the same observation conditions. The posterior probability of each spatiotemporal path is calculated using Bayes' theorem to generate the selection probability of that spatiotemporal path.

[0112] 5. Incremental learning and adaptive adjustment

[0113] like Figure 8 As shown, since passengers with multiple spatiotemporal paths lack directly observable real spatiotemporal path labels, traditional supervised learning cannot be carried out using hard labels. Therefore, a "soft recognition mechanism" based on spatiotemporal path probability is introduced, that is, based on the estimation of spatiotemporal path selection probability, candidate spatiotemporal paths with high confidence are extracted as pseudo-label inputs.

[0114] Spatiotemporal paths with a posterior probability greater than 80% are labeled as high-confidence spatiotemporal paths, those with a posterior probability between 50% and 80% are labeled as medium-confidence spatiotemporal paths, and those with a posterior probability less than 50% are labeled as low-confidence spatiotemporal paths. During the parameter update phase, different update weights are assigned to samples of different confidence levels. High-confidence samples can be used entirely to update model parameters, with an initial learning rate set to η = 1. Medium-confidence samples undergo parameter fine-tuning with a fixed learning rate (e.g., η = 0.15), ensuring the model can quickly adapt to new data without deviating excessively from existing knowledge in a single update. Simultaneously, during parameter update iterations, the method employs an exponential decay learning strategy to decay the learning rate. An exponential decay factor ρ∈(0,1) is introduced to gradually reduce the weight of older data in the Gaussian mixture distribution, allowing the model to adaptively "forget" older data and relatively strengthen the weight of more recent data. This balances historical data with the latest observations while preventing drastic model fluctuations due to a single new data point.

[0115] Specifically, after estimating the spatiotemporal path selection probability for each passenger, if a spatiotemporal path is marked as a "high-confidence spatiotemporal path" or a "medium-confidence spatiotemporal path," the responsivity of the corresponding K sub-distributions for this spatiotemporal path is calculated based on the current GMM parameters of its origin or destination station. The passenger's travel characteristics are then assigned to the sub-distribution with the highest responsivity, achieving a targeted update of the Gaussian mixture distribution. The update method involves adjusting the weights of the sub-distributions of the Gaussian mixture distribution and the sufficient statistics (i.e., mean, first moment, and second moment). Let the sufficient statistics be... Updated as

[0116] The formula is adjusted as follows:

[0117] (1) Selected component k * The statistical update is shown in Equation 1:

[0118]

[0119] (2) Unselected component j≠k * The statistical update is shown in Equation 2:

[0120]

[0121] After the walking time distribution of the station is updated, when the posterior probability of the passenger's spatiotemporal path is recalculated, the posterior probability of each spatiotemporal path will also change due to the change in the theoretical total travel time distribution.

[0122] Once all passenger spatiotemporal path data has been processed or no new data is input, an iteration is manually completed. To ensure model accuracy, the maximum number of iterations is set to 10, or the iteration is terminated when no new high-confidence samples are added for two consecutive rounds.

[0123] This update mechanism ensures continuous optimization of the model, making the spatiotemporal path estimation results increasingly closer to real passenger behavior.

[0124] Example 2: Alternative Strategies for Confidence Utilization

[0125] Probability weight adjustment scheme: The discrete three-level confidence level division is eliminated, and a continuous probability weight mechanism is adopted instead. Updating the weights is directly equivalent to the posterior probability value.

[0126] Path chain propagation scheme: A path association graph is established. When a path is determined to have high confidence, its topologically adjacent paths (paths sharing more than 70% of the sites) automatically acquire a base confidence level of 40%. By setting a propagation attenuation factor β = 0.6, the confidence level decreases and diffuses along the path chain.

[0127] Example 3: Alternative Architecture for Incremental Learning Mechanism

[0128] Sliding window online learning solution: The sample-by-sample update mechanism is replaced with a time-driven sliding window update. The window length T is set to 10 minutes, and the window sliding step δt is set to 1 minute. The accumulated passenger data (e.g., 50-200 records) within each window triggers a batch update.

[0129] The above descriptions are merely embodiments of the present invention, and common technical solutions or characteristics known in the schemes are not described in detail here. For those skilled in the art, various modifications and improvements can be made without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application shall be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A subway network passenger travel space-time path estimation method based on fusion incremental learning, characterized in that, The method comprises the following steps: S1, generating a set of feasible space-time paths of passengers based on a space-time network: obtaining the AFC system of the subway network to obtain the entry and exit card records of passengers, collecting ATS train schedule data, constructing a space-time network of train operation and passenger travel, and generating a set of feasible space-time paths of passengers; according to the number of feasible space-time paths of passengers, the passengers are divided into single space-time path passengers and multi-space-time path passengers; S2, space-time path travel time splitting: according to the travel process of passengers, the space-time path travel time is split into four parts: the walking time at the starting station, the riding time, the walking time at the transfer station, and the walking time at the ending station; and according to the AFC entry and exit time of each passenger and the ATS train schedule data, the time of each segment in the space-time path of the passenger is read; wherein the walking time at the starting station and the walking time at the transfer station both include waiting time; S3, modeling the walking time distribution based on Gaussian mixture distribution: based on the exit walking time information of single space-time path passengers, the exit walking time distribution is modeled by using a Gaussian mixture distribution model, the number of sub-distributions, the weight, the mean and the variance of the Gaussian mixture distribution model are calculated, the walking time distribution of the passengers at the station is generated, the walking time distribution at the station can be estimated by using the same method, the walking time at the station includes waiting time, or the walking time at the station is approximated to the walking time distribution at the station, and the waiting time at the station is uniformly distributed according to the interval between the trains; S4, calculating the probability of the space-time path of passengers based on the Bayes theorem: for each space-time path, the time distribution of each segment is convolved to generate the theoretical total travel time distribution of the space-time path, and then the posterior probability of the passenger selecting the space-time path is calculated by using the Bayes theorem according to the actual travel time in the AFC card data of the passenger; S5, incremental learning and adaptive adjustment: the space-time paths with a posterior probability greater than 80% are marked as high-confidence space-time paths, the space-time paths with a posterior probability between 50% and 80% are marked as medium-confidence space-time paths, and the space-time paths with a posterior probability less than 50% are marked as low-confidence space-time paths; different update weights are given to the space-time path samples with different confidence levels, an exponential decay type learning strategy is adopted, the parameters of the Gaussian mixture distribution are updated, and the probability of the space-time path is updated; In step S3, the Gaussian mixture distribution model estimation includes parameter initialization, EM algorithm iteration and model convergence determination, the parameter initialization includes mean initialization, variance initialization and weight initialization, the mean initialization adopts the farthest point initialization strategy, the variance initialization adopts the scalar variance calculation of each Gaussian component, and the weight initialization adopts the uniform initialization strategy. In step S3, the number of sub-distributions of the Gaussian mixture distribution is analyzed by using Akaike information criterion, Bayesian information criterion and KS test; when the sample number is small, the Akaike information criterion is used to score the models with different numbers of Gaussian sub-distributions, and the model with the minimum Akaike information criterion value is selected as the optimal parameter structure of the station; when the sample number is large, the Bayesian information criterion is used to score the models with different numbers of Gaussian sub-distributions, and the model with the minimum Bayesian information criterion value is selected as the optimal parameter structure of the station; the KS test is used to evaluate whether the Gaussian mixture distribution can reasonably fit the actual walking time distribution after determining the number of components; In step S3, the EM algorithm iteration includes an E step and an M step, the E step calculates the probability of each sample belonging to different Gaussian components, and the M step estimates the model parameters using the responsivity obtained by the E step; the change amount of the log-likelihood value is used as the basis for convergence judgment for model convergence determination; In step S4, the convolution operation integrates and fuses the time probability density functions of each stage by using a sliding superposition algorithm, accurately synthesizes the complete probability distribution form of the total time consumption of passengers selecting a specific space-time path, and retains the randomness characteristics of each sub-stage distribution and truly reflects the uncertainty accumulation effect in the travel process.

2. The metro network passenger spatio-temporal path estimation method of claim 1, wherein: In step S1, the single space-time path passenger is used to extract the characteristics of the inbound walking time and the outbound walking time, the inbound walking time includes the waiting time, and the single space-time path passenger includes both non-transfer passengers and transfer passengers.

3. The metro network passenger spatio-temporal path estimation method of claim 1, wherein: In step S5, when updating the space-time path posterior probability of each passenger, the Gaussian mixture distribution parameters of the corresponding stations in the space-time path are dynamically updated.

4. The metro network passenger spatio-temporal path estimation method of claim 1, wherein: In step S5, according to different confidence levels, the initial learning rate of the high-confidence space-time path is 1, the initial learning rate of the medium-confidence space-time path is 0.15, and an exponential decay factor is introduced.

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