The Integrated ANN-NPRT-HUB Algorithm for Rail-Transit Networks of Smart Cities: A TOD Case Study in Chengdu

: Rail-transit hub classiﬁcation in TOD refers to the categorization of transit stations based on their level of connectivity and ridership and the potential for development around them as part of a Transit-Oriented Development (TOD) strategy. TOD, as an essential concept in developing smart cities and public transportation accessibility, has attracted the focus of many policymakers. To this end, many research projects have been dedicated to classifying the rail-transit stations, although the necessity of integrated models for rail-transit hubs could have been mentioned in previous papers. Therefore, this parametric case study is directed to apply the Node–Place–Ridership–Time (NPRT) model to provide a logical classiﬁcation model for Chengdu rail-transit hubs at the junctions of high-speed railway and subway stations. Multiple Linear Regression (MLR) provided a series of equations, including the effective parameters of the NPRT model. These equations were then veriﬁed by the Artiﬁcial Neural Network (ANN) to provide the effect of each node and place values on the integrated ridership of rail-transit hubs in different time periods. The results proved the consistent contribution of the integrated ANN-NPRT-HUB algorithm to the TOD concept for smart cities.


Introduction
A rail-transit hub is a transportation center where different modes of rail-based transportation intersect and connect, such as commuter trains, subways, light rail, and highspeed trains. These hubs are designed to facilitate the transfer of passengers and goods between different rail lines and modes of transportation and provide access to other forms of transportation, such as buses, taxis, and bicycles. Rail-transit hubs are typically located in urban areas and are often designed as multi-level structures with multiple platforms, tracks, and concourses. They may also include retail, dining, and other amenities to serve the needs of passengers and visitors. Examples of well-known rail-transit hubs include Grand Central Terminal in New York City, Gare du Nord in Paris, and Shinjuku Station in Tokyo. These hubs are critical transportation network components, providing a convenient and efficient way for people to move within and between cities and regions. Rail transit networks highlight the efficiency of public transportation in reducing air pollution and urban traffic loads, especially in developed cities such as Beijing, Shanghai, Chengdu, and New York [1][2][3].
A smart city is a concept that refers to the integration of technology and data-driven solutions to improve the quality of life, sustainability, and efficiency of urban areas. It uses transportation systems. Classifying rail-transit hubs is crucial for understanding their characteristics and functionalities and guiding effective station design and infrastructure development. By categorizing hubs based on size, capacity, connectivity, and accessibility, planners and designers can make informed decisions regarding platform design, pedestrian flow management, parking facilities, and integration with other transportation modes. Additionally, hub classification is vital in determining land use patterns and enabling tailored land use policies and regulations that promote transit-supportive development, including mixed-use developments, higher density, and pedestrian-friendly environments. Understanding transit ridership and demand patterns is facilitated through station and hub classification, allowing researchers to analyze location, connectivity, proximity to residential and commercial areas, and parking availability, providing valuable insights for investment prioritization, resource allocation, and service planning. Moreover, hub classification helps identify disparities in transit access, facilitating efforts to address inequities through station improvements, equitable resource distribution, and targeted investments in underserved areas. Lastly, it supports performance evaluation by comparing metrics such as ridership, efficiency, service quality, and customer satisfaction across hub categories, allowing for benchmarking and targeted interventions to enhance the overall performance of rail transit systems.
This research considered the Chengdu rail transit network as the case study to investigate the NPRT algorithm for classifying the rail-transit hubs and study the correlations between the NPRT effective parameters. The Min-Max normalization method and the integrated NPRT values provided a reliable database for this study. Moreover, an Artificial Neural Network (ANN) was applied to predict and evaluate the results of our proposed NPRT-HUB model. The outcomes of this research aimed to provide new insight into the TOD concept with an exclusive focus on rail transit networks. These results can be implemented by municipal governments, city planners, and policymakers to adapt and improve the efficiency of their rail transit networks.

Approach
This research is a case study on the Chengdu city rail transit network. Four hub district sizes were identified according to the results of questionnaires and statistical data collected from the riders, residents, and real estate. Each hub includes active rail transit stations which connect the whole district to the hub center. The hubs' arrangement was assigned according to the counterclockwise direction starting from North. Regarding the statistical data and the questionnaire results, after several trials of integrating the stations' data and applying the Min-Max normalization method, a 3000 m radius was set as the right active radius for the hubs. Table 1 presents more details for our case study hubs. The Chengdu rail transit network, including four hubs, is shown in Figure 1. We integrated the stations' data and applied Min-Max normalization to provide a reliable database for each hub. We integrated the stations' data and applied Min-Max normalization to provide a reliable database for each hub.
In this study, we employed a comprehensive methodology to analyze and classify rail-transit hubs using various data analysis techniques. First, we applied Min-Max Normalization to standardize the range of our data attributes, ensuring fair comparisons and preventing any attribute from dominating the classification process due to its scale. This normalization technique transformed the attribute values to a standard range between 0 and 1.
To determine the relative importance of attributes in the classification task, we utilized the Improved Entropy Weight (IEW) method. We assessed their diversity and randomness by calculating the entropy for each attribute. Lower entropy values indicated attributes with higher uniformity and specific information for classification. We assigned weights to the attributes based on these values, emphasizing those with lower entropy values. The attribute weights were then normalized to ensure meaningful comparisons and summing up to 1.
Next, we employed the Multiple Linear Regression (MLR) algorithms to build a classification model for rail-transit hubs. MLR allowed us to learn the linear relationship between input features (attributes) and the target variable (rail-transit hub classification). The attribute weights obtained from the IEW method were incorporated into the MLR In this study, we employed a comprehensive methodology to analyze and classify rail-transit hubs using various data analysis techniques. First, we applied Min-Max Normalization to standardize the range of our data attributes, ensuring fair comparisons and preventing any attribute from dominating the classification process due to its scale. This normalization technique transformed the attribute values to a standard range between 0 and 1.
To determine the relative importance of attributes in the classification task, we utilized the Improved Entropy Weight (IEW) method. We assessed their diversity and randomness by calculating the entropy for each attribute. Lower entropy values indicated attributes with higher uniformity and specific information for classification. We assigned weights to the attributes based on these values, emphasizing those with lower entropy values. The attribute weights were then normalized to ensure meaningful comparisons and summing up to 1.
Next, we employed the Multiple Linear Regression (MLR) algorithms to build a classification model for rail-transit hubs. MLR allowed us to learn the linear relationship between input features (attributes) and the target variable (rail-transit hub classification). The attribute weights obtained from the IEW method were incorporated into the MLR model, giving higher importance to attributes with lower entropy during the training process.
To evaluate the performance of the MLR model, we utilized several metrics. Mean Squared Error (MSE) measured the average squared difference between the predicted and actual classification values, reflecting the model's accuracy. R 2 (coefficient of determination) indicated the proportion of variance in the target variable that the MLR model could explain. Adjusted R 2 adjusted for the number of predictors, considering the model's complexity and preventing overfitting.
We calculated the Variance Inflation Factor (VIF) to assess multicollinearity, which helped identify attributes with high intercorrelations that might impact the model's stability and interpretability. Additionally, we employed statistical tests such as the F-Test and T-Test to evaluate the overall significance of the MLR model and the individual significance of the attribute coefficients, respectively. Finally, ANN was applied to predict and verify the results.
By integrating Min-Max Normalization, IEW, MLR, MSE, R 2 , Adjusted R 2 , VIF, F-Test, and T-test into our analysis pipeline, we gained insights into the classification of railtransit hubs. These techniques allowed us to preprocess and normalize the data, determine attribute weights, build a classification model, assess its performance and significance, and address potential multicollinearity issues. This comprehensive approach provided a robust framework for analyzing and classifying rail-transit hubs.
This study advocates for a paradigm shift in the classification model by acknowledging and incorporating the time value. By completing three-dimensional models with time as a main dimension, the accuracy and precision of predictions can be significantly improved while also unraveling more profound correlations between various indicators. This approach aligns the classification model with the dynamic nature of real-world data, facilitating a more sophisticated understanding of evolving patterns and trends and ultimately leading to more reliable and insightful analyses.
Using mathematical concepts allows for a systematic and quantitative approach to the classification process. By leveraging mathematical models, factors such as connectivity, accessibility, and spatial patterns can be precisely analyzed and incorporated into the classification framework. This objective and data-driven methodology enhances the accuracy and reliability of the classification results. Moreover, the integration of ANN adds a powerful ML component to the classification process. ANN can effectively learn and recognize complex patterns and relationships within the data, enabling the identification of subtle nuances and hidden features that may not be readily apparent through traditional methods. This combination of mathematical concepts and ANN creates a sophisticated and advanced approach to classifying rail-transit hubs, facilitating a deeper understanding of their characteristics and aiding in the planning and development of transit-oriented communities. Therefore, using mathematical concepts and ANN in classifying rail-transit hubs within the context of TOD represents a cutting-edge and innovative approach that enhances decision-making and fosters sustainable urban development. Figure 2 presents the research framework applied in this study.

NPRT Indicators
A list of NPR (node, place, and ridership) indicators are provided in Table 2. As mentioned before, the ridership value of each hub cannot be considered a constant or independent value since the number of people using the subway is different during working days and weekends. Moreover, on weekdays, three primary time categories lead to different ridership rates on the day. Therefore, we applied four time classes, T1 to T4, on weekdays and weekends to consider our hubs' ridership value. Table 2 presents normalized integrated time classes applied in this research.

NPRT Indicators
A list of NPR (node, place, and ridership) indicators are provided in Table 2. As mentioned before, the ridership value of each hub cannot be considered a constant or Buildings 2023, 13,1944 6 of 24 independent value since the number of people using the subway is different during working days and weekends. Moreover, on weekdays, three primary time categories lead to different ridership rates on the day. Therefore, we applied four time classes, T1 to T4, on weekdays and weekends to consider our hubs' ridership value. Table 2 presents normalized integrated time classes applied in this research.  Table 3 fully describes the node and place value indicators, including relevant subbranches. The node value has been divided into eight sections from N1 to N8, represented by the principal concepts of TOD mentioned as sub-branches in this table. Moreover, P1 to P9 also provide nine sub-values of Place value.   Normalized integrated node, place, and ridership values collected from all stations in each Hub area are presented in Tables 4-6, respectively.

Information Entropy Weighting (IEW)
Information Entropy Weighting (IEW) [15] was applied to compose the N1 − N8 and P1 − P9 value indexes into one integrated value of node and place, respectively. To this end, we could process the composed indicators to implement the database analysis started by the decision matrix presented in Equation (1). m stations and n node value indicators of each hub are consisted in X. X pq represents the value of indicator q at station p. Equation (2) shows the decision matrix normalization: The proportion of station p for indicator q is calculated by Equation (3): To compute the entropy value e q of indicator q, we can apply Equation (4): The imbalance coefficient is shown in Equation (5): Equation (10) provides the weight of indicator q indicated by W q . The result of Equation (6) is used in Equation (7) to compose the N p (node value index) for station p.
To normalize the node value index in [0, 1], we apply Equation (8), in which N denotes the index in the array of node values, m indicates the number of stations, and p is the target station:

Multiple Linear Regression (MLR)
In this study, we applied Multiple Linear Regression (MLR) to investigate the relationships between the effective parameters (factor variable and multiple variables) on our TOD models and equations.
Regarding the linear Equation (9), a 1 and a 2 can be determined by applying linear regression of multiple variables using machine learning techniques.
The MLR equations are a regression analysis applying the least-square function to model the argument relationships. This function provides a linear combination of one or more effective parameters, known as regression coefficients [16].
The corresponding model for our n-dimensional feature sample data using linear regression is presented in Equation (10): A simplified equation considering x 0 = 1 would be: The matrix form provides a more concise understanding of the above equations: where In Equation (13) (14) and (15), respectively.
Applying Equations (16) and (17) and parameter estimation of the MLR model leads to minimizing of the loss function. Then, Thus, the following multilinear regression model is achieved.

Machine Learning Application in TOD
An Artificial Neural Network (ANN), as an application of Machine Learning (ML), is widely used to predict outcomes, classify the results, and check the accuracy of research achievements. Seven main steps create the primary process of ANN applications: importing the data, cleaning the data, splitting the data into training/test sets, model creation, model training, predictions, and model evaluation and improvement.
The ANN structure is created by three main layers, shown in Figure 3. For simplicity, the activation function is not shown in the figure; therefore, we use the same one between two adjacent layers.
is widely used to predict outcomes, classify the results, and check the accuracy of research achievements. Seven main steps create the primary process of ANN applications: importing the data, cleaning the data, splitting the data into training/test sets, model creation, model training, predictions, and model evaluation and improvement.
The ANN structure is created by three main layers, shown in Figure 3. For simplicity, the activation function is not shown in the figure; therefore, we use the same one between two adjacent layers. The ANN structure directs the input to output in one-way information processing. After receiving the input data by the ANN, the error value is calculated. Each layer contains groups of neurons that have their importance determined by assigned weight. The backpropagation algorithm leads to learning and solving errors based on the data of the input and output layers. Mean Square Error (MSE) provides a valuable loss function for regression problems to predetermine the logical minimum error [16][17][18].
In this research, the neurons' activation function ( ) supports the Rectified Linear Unit ( ) function, as shown in Figure 4. The ANN structure directs the input to output in one-way information processing. After receiving the input data by the ANN, the error value is calculated. Each layer contains groups of neurons that have their importance determined by assigned weight. The backpropagation algorithm leads to learning and solving errors based on the data of the input and output layers. Mean Square Error (MSE) provides a valuable loss function for regression problems to predetermine the logical minimum error [16][17][18].
In this research, the neurons' activation function ( f ) supports the Rectified Linear Unit (ReLU) function, as shown in Figure 4.
Buildings 2023, 13, x FOR PEER REVIEW 11 of 25 Based on the existing applications of deep learning methods [19][20][21][22][23][24], this study applied the MSE loss function, shown in Figure 5. Moreover, adaptive moment estimation (ADAM) was used to optimize the convergence and enhance the model accuracy. Based on the existing applications of deep learning methods [19][20][21][22][23][24], this study applied the MSE loss function, shown in Figure 5. Moreover, adaptive moment estimation (ADAM) was used to optimize the convergence and enhance the model accuracy.
Based on the existing applications of deep learning methods [19][20][21][22][23][24], this study applied the MSE loss function, shown in Figure 5. Moreover, adaptive moment estimation (ADAM) was used to optimize the convergence and enhance the model accuracy.

Model Evaluation Method
As mentioned before, to verify the Multiple Linear regression (MLR) equations' accuracies of fit in the regression method, we used the Mean Square Error (MSE), presented in Equation (21).
The Multiple Determination Coefficients ( ), a valuable indicator to evaluate the convergence of MLR equations, reflects the proportions described by the estimated regression equations in the variance of the factor variable , calculated as the proportion of progression squares to the sum of total squares [25].
Regarding Equations (22)- (24), shows the model forecast value, stands for the average of , indicates the Regression Sum of Squares, represents the Error Sum of Squares, and denotes the Total Sum of Squares [16,17,25].

Model Evaluation Method
As mentioned before, to verify the Multiple Linear regression (MLR) equations' accuracies of fit in the regression method, we used the Mean Square Error (MSE), presented in Equation (21).
The Multiple Determination Coefficients R 2 , a valuable indicator to evaluate the convergence of MLR equations, reflects the proportions described by the estimated regression equations in the variance of the factor variable y, calculated as the proportion of progression squares to the sum of total squares [25].
Regarding Equations (22)- (24),ŷ i shows the model forecast value, y stands for the average of y, SSR indicates the Regression Sum of Squares, SSE represents the Error Sum of Squares, and SST denotes the Total Sum of Squares [16,17,25].

The NPRT Variables' Correlations
We applied Python as a high-level programming language for creating our ANN-NPRT-HUB algorithm and investigated the correlations between independent values (node and place) and dependent values (integrated ridership-time). Using Python's pandas and numpy libraries, the correlations between the positive or negative variables were obtained and presented in Table 7. A positive correlation is a statistical measure that signifies a simultaneous increase in one variable as the other variable also experiences an increase. This phenomenon implies that the two variables exhibit a coherent behavior, moving in the same direction. Conversely, a negative correlation denotes an inverse relationship, wherein an increase in one variable corresponds to a decrease in the other variable. This indicates a tendency for the variables to move in opposite directions. A correlation coefficient is employed to ascertain the magnitude of the correlation, offering a numerical representation of the relationship between the variables. The correlation coefficient ranges from −1 to 1, providing valuable insights into the strength and direction of the correlation. A correlation coefficient close to 1 or −1 implies a robust correlation, with the variables exhibiting a highly consistent pattern of behavior. In contrast, a coefficient closer to 0 suggests a weaker correlation, indicating that the variables have less synchrony in their variations. Using the correlations between the values provided in Table 7, we can adjust and improve the efficiency of each rail-transit hub by increasing or decreasing the corresponding value(s). The correlation between variables can provide valuable insights into optimizing the efficiency of rail-transit hubs. By focusing on these critical factors, improvements can be targeted where they have the most significant impact.

MLR Equations for the ANN-NPRT-HUB Model
This research applied Multiple Linear Regression (MLR) to extract eight regression equations for the proposed ANN-NPRT-HUB model. A comprehensive form for the MLR equations is presented in Equation (25). This equation is made of three main terms. α indicates the intercept, while β and γ represent the coefficients of node and place values, respectively. To determine the three parameters of α, β, and γ, from the sklearn.linear_model of Python, we imported the LinearRegression function.
Appendix A provides a list of constants and variable coefficients for the dependent variable of IT1 to OT4. The complete results of our MLR models are presented in Table 8. The Ad.R 2 indicates how well the model fits the data, with a value of 1 indicating a perfect fit. Generally, a value of Ad.R 2 greater than 0.2 is considered acceptable for the fitted model. In statistical analysis, the significance level of a result is typically represented by the p value, where a smaller p value corresponds to a more substantial effect of the independent variable on the dependent variable. The coefficient of variation (CV) indicates the impact of an independent variable on a dependent variable. A higher CV value indicates a more substantial influence of the independent variable on the dependent variable. And a negative CV implies a negative correlation between the independent and dependent variables.
Applying the constant and coefficient values from Table 8 to Equation (25), we can construct a series of eight MLR equations for the rail-transit hubs provided in Table 9. Table 9. Extracted MLR Equations.

General MLR Equation (25)
Extracted MLR Equations from Table 8 Ridership Multiple Linear Regression (MLR) equations can be highly beneficial for analyzing ridership in rail-transit hubs. MLR models provide a statistical framework for understanding the relationships between multiple independent variables and the dependent variable of ridership. By considering various factors influencing ridership, MLR equations offer valuable insights into understanding and forecasting the demand for rail-transit services.

Classification Results
Applying the MLR equations of Table 9 and the NP (Node, Place) values, we can achieve the actual ridership values of the NPRT model for rail-transit hubs. Moreover, we used the ANN to predict the NPRT model results presented in this research. Table 10 shows a list of predicted values provided by the ANN and the MLR equations' actual results. In this table, p denotes the predicted value. The ANN-predicted ridership for individual rail-transit hubs holds significant importance in various technical aspects. It primarily enables effective demand forecasting, capacity planning, resource allocation, service optimization, revenue estimation, and decision-making. Leveraging the capabilities of ANN models empowers transit authorities to make well-informed decisions to enhance operational efficiency, improve the passenger experience, and ensure the sustainable growth and development of rail transit systems.
In Table 10, the predicted ridership by the ANN is based on the underlying patterns and associations discovered during the model training. By leveraging the power of the ANN, which excels in capturing intricate relationships in complex datasets, transit authorities gain insights into the anticipated demand for each rail-transit hub. Figure 6 illustrates a comparison between the actual NPRT-HUB results created by MLR equations and the predicted ones by the ANN. As mentioned before, the predicted classes can be distinguished by the letter p before the name of the class. This figure shows that the ANN could logically predict the NPRT model ridership values. For example, the ANN predicted that the class IT 1 covers 19% of the ridership of HUB#1 (North Railway Station), while the actual MLR value is 17%. This logical prediction comes true while looking at the other hubs' classes, such as POT 2 and OT 2 for HUB#4 (East Railway Station), with values of 24% and 23%, respectively. Therefore, applying the ANN in classifying and assessing the efficiency of rail-transit hubs could bring new insight into TOD.
ANNs can be helpful for city planners in assessing the rail-transit hubs because they can assist in identifying significant patterns and relationships within large and complex datasets. In the case of rail-transit hubs, ANNs can be used to analyze data on passenger flows, station usage, train schedules, and other factors that affect the efficiency and effectiveness of a hub. Using ANNs, city planners can create predictive models to help them make informed decisions about optimizing a rail-transit hub's performance. For example, ANNs can forecast passenger demand at different times of the day or during special events, allowing transit planners to adjust train schedules and allocate resources accordingly. ANNs can also identify patterns in passenger behavior, such as how they move through a station or which routes they tend to take, which can inform decisions about station design and layout. In addition to these practical applications, ANNs can also be used to test hypothetical scenarios and predict the potential impact of different planning decisions. For example, planners can use ANNs to simulate the effects of adding new train lines or changing the location of a station, helping them make informed decisions that will benefit both passengers and the city as a whole. ANNs can be helpful for city planners in assessing the rail-transit hubs because they can assist in identifying significant patterns and relationships within large and complex datasets. In the case of rail-transit hubs, ANNs can be used to analyze data on passenger flows, station usage, train schedules, and other factors that affect the efficiency and effectiveness of a hub. Using ANNs, city planners can create predictive models to help them make informed decisions about optimizing a rail-transit hub's performance. For example, ANNs can forecast passenger demand at different times of the day or during special events, allowing transit planners to adjust train schedules and allocate resources accordingly. ANNs can also identify patterns in passenger behavior, such as how they move through a station or which routes they tend to take, which can inform decisions about station design and layout. In addition to these practical applications, ANNs can also be used to test hypothetical scenarios and predict the potential impact of different planning decisions. For example, planners can use ANNs to simulate the effects of adding new train lines or changing the location of a station, helping them make informed decisions that will benefit both passengers and the city as a whole.
Rail-transit hub classification empowers city planners and policymakers to optimize network efficiency. It guides network optimization, service planning, infrastructure development, land use decisions, and policy formulation. By using the results of hub classification, cities can create more efficient and sustainable rail transit networks that cater to the diverse needs of their residents and visitors. Classification helps identify key hub types, such as significant transfer or high-demand ones, which require specific infrastructure and operational considerations. Planners can strategically allocate resources, prioritize investments, and optimize service frequencies to ensure efficient connectivity and minimize delays and congestion. For example, a city may identify a particular hub as a central transfer point between multiple rail lines and allocate additional platform space and staffing to facilitate smooth transfers and reduce overcrowding. Hub classification assists in determining service patterns and frequencies based on hub types. Planners can Rail-transit hub classification empowers city planners and policymakers to optimize network efficiency. It guides network optimization, service planning, infrastructure development, land use decisions, and policy formulation. By using the results of hub classification, cities can create more efficient and sustainable rail transit networks that cater to the diverse needs of their residents and visitors. Classification helps identify key hub types, such as significant transfer or high-demand ones, which require specific infrastructure and operational considerations. Planners can strategically allocate resources, prioritize investments, and optimize service frequencies to ensure efficient connectivity and minimize delays and congestion. For example, a city may identify a particular hub as a central transfer point between multiple rail lines and allocate additional platform space and staffing to facilitate smooth transfers and reduce overcrowding. Hub classification assists in determining service patterns and frequencies based on hub types. Planners can allocate more frequent service to high-demand hubs, ensuring efficient transportation access for a larger population.
Conversely, lower-demand hubs may receive less frequent service, optimizing resource utilization. For instance, a city may identify specific hubs as high-demand destinations due to their proximity to employment centers or popular tourist attractions. Higher service frequencies can be scheduled during peak hours to accommodate commuter and tourist travel.
By understanding the characteristics of different hub types, city planners can make informed decisions about infrastructure development and station design. For example, if a hub is classified as a major transfer point, planners can allocate sufficient space for platform-to-platform transfers, install clear wayfinding signage, and ensure adequate ac-cessibility features. This promotes smooth passenger flow and minimizes bottlenecks, contributing to overall network efficiency. Rail-transit hub classification informs land use and development strategies around hubs. Planners can identify hubs with potential for transit-oriented development (TOD) and focus on creating vibrant, mixed-use neighborhoods with a high-density residential and commercial mix. This fosters a walkable environment, reducing the dependence on private vehicles and enhancing the efficiency of the overall transit network. For instance, a city may classify a hub near a university as a potential hub for mixed-use development, with student housing, retail establishments, and recreational facilities. Hub classification provides valuable data for policymakers to make informed decisions regarding transit policies and investments. It helps prioritize funding and resources for infrastructure improvements, station upgrades, and system expansion. Planners can identify hubs in underserved areas and allocate targeted investments to enhance accessibility and connectivity. Additionally, policymakers can use hub classification results to shape transportation policies, such as promoting transit-oriented development, implementing fare integration systems, or introducing innovative mobility solutions.
ANNs can analyze diverse data sets obtained from railway transportation hubs, including passenger flow, peak hours, and travel patterns. By utilizing this data, ANNs can effectively detect areas of congestion and optimize transportation planning, enabling city authorities to make well-informed decisions regarding infrastructure development, scheduling, and resource allocation. Additionally, ANNs can be leveraged to develop predictive models anticipating the demand for transportation services. By analyzing historical data and current trends, cities can optimize the deployment of transportation resources, such as trains, buses, and shared mobility services, ensuring efficient and reliable mobility options for residents and visitors.
Moreover, ANNs can monitor and analyze real-time data from railway transportation hubs, encompassing train arrival and departure times, passenger volumes, and service disruptions. This valuable information empowers city authorities to respond to dynamic conditions promptly, improve service reliability, and deliver timely updates to passengers, thus significantly enhancing the overall transportation experience.
In the context of sustainable urban development, integrating Transit-Oriented Development (TOD) with ANN-based classification of railway transportation hubs becomes pivotal. By strategically designing compact and mixed-use neighborhoods around transit stations, cities can effectively diminish reliance on private vehicles, foster the adoption of walking and cycling, and foster vibrant communities. ANN plays a critical role in identifying optimal locations for TOD by considering crucial factors such as population density, land use patterns, and proximity to transit infrastructure.
This research explored and incorporated the time dimension into the classification model, recognizing its critical importance in enhancing predictive accuracy. By conducting an in-depth review of existing research works [5,26,27], it became evident that two and three-dimensional models lacked the crucial element of time. Thus, the necessity arose to complete these models by incorporating time as a main dimension, providing a more comprehensive and precise analysis.
One of the key benefits of integrating time into the classification model is the ability to establish stronger correlations between indicators. As time plays a significant role in various processes and trends, taking it into account enables a more accurate understanding of the relationships between different indicators. This, in turn, leads to improved predictions and a deeper insight into the dynamics of the phenomena under investigation.
By acknowledging the importance of the time value, this study tried to bridge the gap between traditional static models and the dynamic nature of real-world data. The classification model's capabilities are significantly enhanced by considering time as a main dimension, paving the way for more sophisticated and reliable analysis.

Conclusions
This research study aimed to analyze and assess Chengdu rail-transit hubs using the integrated Node, Place, Ridership, and Time (NPRT) method. The investigation employed a temporal segmentation into four distinct time periods, uncovering a direct correlation between ridership and time. Combining mathematical techniques and machine learning, we developed a series of eight Multiple Linear Regression (MLR) equations for each hub. These MLR equations incorporated node and place values as independent variables to examine their influence on ridership throughout different time periods. Integrating MLR analysis into planning, resource allocation, and policy formulation processes facilitates well-informed decision-making, optimized ridership levels, and enhanced efficiency of rail-transit systems. The identified correlations highlight the significance of NPRT models as valuable tools for policymakers and city planners in evaluating the effectiveness of rail transportation hubs. In Transit-Oriented Development (TOD) context, evaluating factors like station location, ridership, and connectivity is essential for efficiency. NPRT models contribute to establishing development objectives and formulating effective strategies. Moreover, the inclusion of Artificial Neural Networks (ANNs) in assessing rail-transit hubs provides valuable insights that inform decision-making and support the creation of transportation systems that are efficient, effective, and sustainable.

Possible Directions for Future Studies
This study conducted a case study on Chengdu rail-transit hubs to investigate the effect of node and place values on ridership in different time periods. Although the study provided accurate results, applying other methods, such as Partial Differential Equations (PDE), to study the correlations between dependent and independent variables sounds interesting for future studies. Utilizing PDEs for studying correlations between variables in a rail-transit hub classification model provides a powerful and flexible approach to analyzing the complex dynamics of the system, making predictions, optimizing operations, and validating the model against real-world data.
Additionally, future research should consider the significance of the economy; ecology; and sociodemographic factors, such as the proportion of people using public transportation, the frequency of household outings, and the distribution of age groups concerning the NPRT model for rail-transit hubs. Moreover, applying train schedules, infrastructure capacity, and operational efficiency can improve the limitations of the 3D indicators presented in this study.