Metro logistics system vehicle speed energy-saving control method considering cargo loading conditions

Abstract

The application aims to provide a metro logistics system vehicle speed energy-saving control method considering the loading conditions of goods, relates to the cross technical field of urban rail transit and intelligent logistics, and aims to simultaneously improve the safety and energy efficiency of freight metro vehicles when running on curves. First, based on the dynamics equation of the carrying vehicle, a multi-body dynamics model of B-type metro vehicles is established and verified through field tests on Chengdu Metro Line 1. The simulation results under different working conditions reveal the influence of the loading conditions of goods on the safety and energy efficiency of vehicle operation. Then, a surrogate model is developed using the random forest algorithm to predict the performance of vehicle operation under any working condition. Finally, a double-objective optimization model is established for a specific metro section, and the objective function is derived from the surrogate model. By applying the multi-objective evolutionary algorithm based on adaptive reference points, the optimal cruising speed of the vehicle is determined, which can greatly improve the safety and energy efficiency of metro vehicles.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit and intelligent logistics intersection technology, and in particular to a speed energy-saving control method for a subway logistics system that takes into account cargo loading conditions. Background Technology

[0002] Over-reliance on road transport has become a bottleneck restricting sustainable urban development, leading to problems such as traffic congestion, environmental pollution, and energy inefficiency. Specifically, road transport accounts for approximately 30%-40% of urban traffic congestion and generates about 25% of transportation-related greenhouse gas emissions. In recent years, with the acceleration of urbanization and the booming development of e-commerce, the negative impacts of road transport have intensified. To address this challenge, utilizing the idle capacity of subway systems during off-peak hours for freight transport—i.e., subway logistics—has become an effective solution. When transporting passengers in traditional subway systems, passengers tend to be evenly distributed within the carriages to maximize personal space. However, when vehicles are loaded with goods, the characteristics of the goods (such as size, density, and center of gravity) vary significantly and are highly complex. Since the interaction between goods and vehicles significantly affects wheel-rail forces, it is necessary to conduct in-depth research on the impact of freight loading conditions on vehicle performance in order to take targeted measures to improve the operational safety and energy efficiency of subway logistics systems.

[0003] Current research on subway logistics systems has made some progress, but mainly at the macro level, such as route planning and urban multimodal transport. Existing technologies have rarely addressed the specific operational control issues of vehicles in subway logistics systems, particularly failing to recognize that cargo loading conditions are a key factor affecting vehicle dynamics performance, a factor that underscores the fundamental difference between subway logistics systems and traditional passenger transport systems. The cargo-vehicle coupling relationship determined by loading conditions directly affects train dynamics and significantly impacts its energy consumption. Among the many factors influencing train performance, speed control is a feasible technical approach. Furthermore, mature Dynamic Track Scale (WIM) technology can accurately and in real-time monitor wheelset loads, providing the technical conditions for achieving speed control based on loading conditions. Therefore, integrating WIM systems to acquire real-time vehicle load data and optimizing vehicle speed control accordingly becomes an effective means to improve the overall performance of freight subway vehicles. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides the following technical solution:

[0005] A method for energy-saving speed control of a subway logistics system that takes into account cargo loading conditions is as follows:

[0006] S1. Based on the dynamic equations of the transport vehicle, a multibody dynamic model of a type B metro vehicle considering cargo characteristics is established using the VI-Grade simulation platform, and the accuracy of the model is verified through field testing. Based on the verified model, loading and operating conditions are designed for simulation experiments. Based on the simulation experiment results, the impact of cargo loading and vehicle operating conditions on vehicle operating safety and energy efficiency is verified.

[0007] S2 uses simulation data under several given working conditions to construct a proxy model based on random forest to predict the vehicle's operational safety and energy consumption under complex loading and operation scenarios.

[0008] S3 establishes a dual-objective optimization model for vehicle cruising speed based on the prediction results of the random forest surrogate model. It then combines the AR-MOEA multi-objective evolutionary algorithm based on adaptive reference points to optimize the vehicle cruising speed and dynamically adjust the vehicle's cruising speed under different loading and operating scenarios.

[0009] Further, refer to the appendix. Figure 3-5 The dynamic equations of the transport vehicle include lateral motion, vertical motion, roll motion, pitching motion, and yaw motion:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] Furthermore, based on the dynamic equations of the transport vehicle, the influence of cargo loading on the change of the vehicle's center of gravity is analyzed. Based on this, a multibody dynamics model of a type B metro vehicle considering cargo characteristics is established, and the accuracy of the model is verified through field testing. Loading conditions (cargo quantity h, longitudinal loading offset x, lateral loading offset y) and running conditions (track curve radius R, vehicle cruising speed v) are designed for simulation experiments to obtain the wheel load reduction rate (UN) and running resistance energy consumption (ECMR) of the vehicle under different conditions.

[0021] The EMCR is calculated using the following formula:

[0022]

[0023] In the formula, Indicates traction force. This indicates the vehicle's cruising speed.

[0024] Furthermore, the loading conditions include: the quantity of goods h ranging from 0.2 to 1.8 m, the longitudinal loading offset x ranging from -6.3 to 6.3 m, and the lateral loading offset y ranging from -0.2 to 0.2 m; the operating conditions include: the curve radius of the line ranging from 600 m to 1800 m, the superelevation of the curved track set to 120 mm, the length of the transition curve set to 100 m, and the collection of simulation data when the train passes through a curved track of 360 m in length, with the subway vehicle operating at a speed of 40 km / h to 120 km / h, testing the safety and energy efficiency indicators of the train under the above loading and operating conditions.

[0025] Furthermore, the random forest surrogate model extends the standard random forest model architecture by encoding the characteristic relationship between freight volume and longitudinal loading offset into the model. The inputs of the random forest surrogate model are curve radius R, cruising speed v, lateral loading offset y, freight quantity h, and longitudinal loading offset x, and the outputs are UN and ECMR. The random forest surrogate models used to predict UN and ECMR contain 500 and 70 trees, respectively, with maximum tree depths of 18 and 13, respectively.

[0026] Furthermore, the random forest surrogate model divides the dataset into 4500 training samples and 1125 test samples for training. During the training process, 5-fold cross-validation is used to ensure the robustness of the model. The root mean square error (RMSE) and the coefficient of determination (R²) are used to quantify the prediction accuracy of the random forest model. The lower the RMSE value, the higher the prediction accuracy of the model, and the closer the R² value is to 1.0, the better the fitting effect.

[0027] The surrogate model used to predict UN had RMSEs of 0.0061 and 0.014 on the training and test sets, respectively, with R² values ​​of 0.9949 and 0.9735. The surrogate model used to predict ECMR had RMSEs of 178.2 and 371.8 on the training and test sets, respectively, with R² values ​​of 1.0000 and 0.9999. These results validate the excellent predictive performance of the random forest surrogate model.

[0028] Furthermore, for a specific subway section, the dual-objective optimization model divides it into several operating units based on track conditions. Utilizing the varying impacts of cruising speed on vehicle performance under different operating conditions, the model performs dual-objective optimization on the cruising speed of vehicles within these operating units. Specifically, the dual-objective optimization model treats UN and ECMR as conflicting optimization objectives.

[0029]

[0030]

[0031]

[0032] In the formula, and Let UN and ECMR be the regression functions derived from the surrogate model, respectively. Indicates the vehicle's cruising speed. The vector represents the track radius, h represents the freight volume, and x and y represent the off-center freight load. Indicates the number of units within a segment and limits the effective range of cruising speed:

[0033]

[0034] In the formula, and These represent the lower and upper limits of speed, respectively.

[0035] The AR-MOEA algorithm is used to solve the Pareto solution for cruise speed under multiple operating conditions.

[0036] Furthermore, the AR-MOEA algorithm and its solution are as follows:

[0037] To solve the aforementioned dual-objective optimization model, this application employs the AR-MOEA algorithm as the basic algorithm. The AR-MOEA algorithm is an index-based multi-objective evolutionary algorithm whose core feature lies in its reference point adaptive mechanism. This mechanism enables it to automatically adapt to Pareto fronts of different shapes, effectively approximating both regular and irregular Pareto fronts without requiring prior knowledge of the front's shape. When coupled with the aforementioned random forest surrogate model, the algorithm can be used to solve for the Pareto optimal solution of vehicle cruising speed under various operating conditions.

[0038] The solution process of the AR-MOEA algorithm is as follows:

[0039] Step 1: Initialization

[0040] Step 1.1: Generate a population cluster P and predefine a set of uniformly distributed reference points Z;

[0041] Step 1.2: Initialize archive set A to the current population, and set the adaptive reference point set Z' as a copy of the uniform reference point set Z;

[0042] Step 2: Main Loop

[0043] Step 2.1: Use a binary tournament selection strategy to select the parent P' from the population P, and apply genetic operators (such as crossover, mutation, etc.) to the parent P' to generate the offspring Q;

[0044] Step 2.2: Merge the newly generated child Q into archive set A, and remove all dominated or duplicate solutions from it to update the archive set;

[0045] Step 2.3: Integrate the initial uniform reference point set Z with the archive set A to achieve adaptive adjustment of the reference point set Z';

[0046] Step 2.4: Merge the parent population with the offspring population to form a candidate solution pool;

[0047] Step 2.5: Select the optimal solution through a two-stage process: First, perform non-dominated sorting and determine the priority of solutions based on convergence; then calculate the enhanced inversion generation distance index and select the solution that is better in terms of diversity and distribution.

[0048] Step 3: Termination and Output

[0049] Step 3.1: Terminate the loop if the maximum number of iterations is reached or other stopping conditions are met;

[0050] Step 3.2: Output the final population P as an approximation of the desired Pareto front.

[0051] Compared with the prior art, the technical solution of this application has the following beneficial effects:

[0052] This invention first establishes a multibody dynamics model for a Type B metro vehicle based on the vehicle's dynamic equations, and verifies it through field testing on Chengdu Metro Line 1. Simulation results under different operating conditions reveal the impact of cargo loading characteristics on vehicle operation safety and energy efficiency. Next, a surrogate model is developed using the random forest algorithm to predict vehicle operation performance under arbitrary conditions. Finally, a dual-objective optimization model is established for a specific metro section, with its objective function derived from the surrogate model. By applying a multi-objective evolutionary algorithm based on adaptive reference points, the optimal cruising speed of the vehicle is determined, which significantly improves the operational safety and energy efficiency of the metro vehicle. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of a subway logistics system.

[0054] Figure 2 This forms the research framework for the present invention;

[0055] Figure 3 For the vehicle model, Y in the figure c Y f Y w Z represents the lateral displacement of the car body, side frame, and wheelsets. c Z f Z w ϕ represents the vertical displacement of the car body, side frame, and wheelsets. c ϕ f ϕ w M is the roll angle of the car body, side frame, and wheelsets. c M f M w For the mass of the car body, side frame and wheelsets, I cx , I fx , I wx K represents the moment of inertia of the car body, side frame, and wheelsets about the X-axis. py , K sy K represents the lateral stiffness coefficient of the primary and secondary suspension systems. pz , K sz C represents the vertical stiffness coefficient of the primary and secondary suspension systems. py C sy C represents the lateral damping coefficients of the primary and secondary suspension systems. pz C sz K represents the vertical damping coefficients of the primary and secondary suspension systems. rX H is the stiffness coefficient of the anti-roll spring. co H is the vertical distance between the center of the unloaded vehicle body and the center of the loaded vehicle body. os H is the vertical distance between the center of the unloaded vehicle body and the secondary suspension. sfH is the vertical distance between the secondary suspension and the center of the side frame. fw O represents the vertical distance between the center of the side frame and the center of the wheelset; C represents the center of gravity of the unloaded vehicle and the center of gravity of the loaded vehicle.

[0056] Figure 4 This diagram illustrates the impact of cargo loading on the vehicle's center of gravity. Figure (a) is a front view, and (b) is a side view. O, O # C is the center of gravity of the empty car body, the cargo car body, and the loaded car body, M v M represents the weight of the unloaded vehicle body and cargo. c H represents the mass of the load vehicle body, h represents the height of the cargo model, and H represents the mass of the load vehicle body. floor Let x be the vertical distance from the vehicle floor to point O, and y be the longitudinal and lateral loading offsets of the cargo. c , y c Let O be the vertical and horizontal distances from point O to point C;

[0057] Figure 5 The diagram shows the forces and moments acting on the vehicle body. , Let the left and right longitudinal forces be the secondary suspension forces of the i-th bogie. , Let the left and right lateral forces be the secondary suspension forces of the i-th bogie. , Let the left and right vertical forces be the secondary suspension forces of the i-th bogie. , For the left and right longitudinal forces of the i-th bogie anti-hunting shock absorber, The anti-roll moment of the i-th bogie;

[0058] Figure 6 For the multibody dynamics model of the transport vehicle;

[0059] Figure 7 This is a diagram of the vehicle body vibration test.

[0060] Figure 8 The diagram shows a comparison of vehicle body vibration acceleration, where (a) represents the lateral direction and (b) represents the vertical direction.

[0061] Figure 9 This is a diagram showing the offset of a subway car loading. In the diagram, O# and O represent the center of gravity of the goods and the car, M represents the mass of the goods, and l represents half the center distance of the center plate (taken as 12.6m).

[0062] Figure 10 This is a schematic diagram of traction control.

[0063] Figure 11 Figure showing the UN simulation results;

[0064] Figure 12Figures showing ECMR simulation results under different axis arrangements;

[0065] Figure 13 This is a schematic diagram of a random forest model;

[0066] Figure 14 The figure shows the parameter adjustment plots for the UN regression model. In the figure, (a) shows the effect of the number of trees on the model performance when the maximum tree depth is fixed at 50, and (b) shows the effect of the maximum tree depth on the model performance when the number of trees is given.

[0067] Figure 15 The figure shows the parameter adjustment plots for the ECMR regression model. In the figure, (a) shows the effect of the number of trees on the model performance when the maximum tree depth is fixed at 50, and (b) shows the effect of the maximum tree depth on the model performance when the number of trees is given.

[0068] Figure 16 The figure shows the performance of the UN regression model and the importance of its features. In the figure, (a) shows the predictive performance of the model on the test set; and (b) shows the importance ranking of the five input features.

[0069] Figure 17 The figure shows the performance of the ECMR regression model and the importance of its features. In the figure, (a) shows the predictive performance of the model on the test set, and (b) shows the importance ranking of the five input features.

[0070] Figure 18 This is a schematic diagram of a subway section. In the diagram, R is the curve radius, h is the quantity of goods, and x and y are the goods loading offsets.

[0071] Figure 19 Pareto front plots for different unit cruise speeds;

[0072] Figure 20 To optimize the comparison chart of vehicle operating performance under cruise speed and baseline scheme, v in the chart represents the vehicle cruise speed;

[0073] Figure 21 The diagram shows the Pareto optimal values ​​for different unit cruise speeds, where v represents the vehicle's cruise speed. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] Example 1:

[0076] This embodiment addresses the technical problem solved by this application: to cope with traffic congestion and environmental pollution caused by road logistics, it utilizes the idle capacity of the subway system during off-peak hours for freight transportation, i.e., constructing a subway logistics system, such as... Figure 1 As shown, it has become a highly promising mode of logistics transportation. Current research on subway logistics systems has made some progress, but this is mainly reflected in tactical and strategic aspects such as road network planning and urban multimodal transport. It has not yet addressed the operational control of freight subway vehicles, particularly operational optimization methods considering cargo loading conditions, resulting in a research gap in this technological field.

[0077] Given the differences in physical characteristics such as size, density, and center of gravity among various goods, and the dynamic changes in their spatial distribution due to loading and unloading operations at stations, the coupling relationship between goods and vehicles changes accordingly. This coupling relationship not only significantly affects the operational safety of subway vehicles but is also a key factor determining their energy consumption levels. Therefore, this application proposes a speed-saving control method for subway logistics systems that considers cargo loading conditions. Based on dynamic track weighing (WIM) technology to obtain train load characteristics, the method optimizes the cruising speed of subway vehicles to simultaneously improve operational safety and energy efficiency. Figure 2 As shown, based on the simulation results of multibody dynamics (MBD) under different operating conditions, a random forest (RF) surrogate model was constructed to dynamically predict vehicle operating performance. When the vehicle load data of the WIM system is received, the surrogate model inputs the prediction results into the optimization model and uses the AR-MOEA algorithm to determine the optimal cruising speed.

[0078] Example 2:

[0079] This example demonstrates the construction of dynamic equations for a transport vehicle. A model is established using the common Type B vehicle found in subway systems as the research object. Figure 3 As shown, the model consists of one load-bearing vehicle body, two side frames, and four wheelsets, with each component connected by different types of constraints. After loading cargo, the vehicle body's center of gravity moves from point O (empty state) to point C (loaded state). Figure 3 The specific definitions of the symbols are shown in Table 1.

[0080]

[0081] For a given subway car, the location of point C depends on the loading conditions, such as... Figure 4 As shown. Since subway logistics systems are mainly used for transporting small goods, goods with similar characteristics are usually placed in the same area. Therefore, this application models the goods as cuboids with uneven horizontal mass distribution and uniform vertical distribution. (The text then abruptly shifts to a seemingly unrelated topic: "From the car floor to point O...") # The vertical distance is h / 2. Based on the formula for calculating the center of gravity, the positions of point C in the three directions can be derived from the loading conditions as follows:

[0082] Vertically upwards,

[0083] (1)

[0084] Vertically,

[0085] (2)

[0086] Horizontally,

[0087] (3)

[0088] In the formula, O, O # C and M represent the center of gravity of the unloaded vehicle body, the cargo vehicle body, and the loaded vehicle body, respectively. v M and M represent the mass of the empty vehicle body and the mass of the cargo, respectively. c H represents the mass of the load vehicle body, h represents the height of the cargo model, and H represents the mass of the load vehicle body. floor The x and y values ​​represent the vertical distance from the vehicle floor to point O, respectively, and the x and y values ​​represent the longitudinal and lateral loading offsets. c and y c These represent the longitudinal and transverse distances from point O to point C, respectively.

[0089] Considering the significant impact of cargo on the vehicle's center of gravity, this application improves the dynamic equations of the load-bearing vehicle body based on existing technology. The external forces and moments acting on the load-bearing vehicle body are as follows: Figure 5 As shown, the specific symbol definitions are shown in Table 2.

[0090]

[0091] like Figure 4 As shown, the center of gravity of a loaded vehicle is affected by the loading conditions and can be determined by its displacement relative to the center of gravity of an unloaded vehicle. Let Ry be the equivalent radius of curvature of the loaded vehicle body when the vehicle travels at a cruising speed v on a right-hand track of radius R. c According to Newton's second law, the dynamic equations corresponding to the loaded vehicle body are as follows:

[0092] Lateral movement:

[0093] (4)

[0094] Vertical motion:

[0095] (5)

[0096] Side roll motion:

[0097] (6)

[0098] Nodding exercise:

[0099] (7)

[0100] Head shaking exercise:

[0101] (8)

[0102] The definitions of the remaining symbols in equations (4)-(8) are shown in Table 3.

[0103]

[0104] Since the loading conditions do not directly affect the motion equations of the side frame and wheelsets, the dynamic equations of these components are not described in detail in this embodiment.

[0105] Example 3:

[0106] This embodiment describes the construction of a simulation platform. A MBD simulation model of a subway vehicle is created using VI-Grade software, such as... Figure 6 As shown in the figure. In this application, the cargo is modeled as a cuboid with uneven horizontal mass distribution. The position of its center of gravity and the height of the cargo change with the loading conditions. The cargo is rigidly connected to the vehicle body. The primary and secondary suspensions are constructed with corresponding forces, connections and constraints. The S1002 wheel tread and UIC60 rail profile are adopted. The key parameters of the vehicle are detailed in Table 4.

[0107]

[0108]

[0109] To verify the model, a field test was conducted on Type B metro vehicles on Chengdu Metro Line 1, such as... Figure 7 As shown. In the experiment, an empty vehicle ran on a straight track at a speed of 60 km / h, and the vehicle body vibration acceleration was recorded. Since the track conditions of the Chengdu Metro are similar to the low-interference spectrum of the German high-speed railway, they were applied to the track model as external excitation. A comparison of MBD simulation and field test results is shown below. Figure 8 As shown, the two are highly consistent, indicating that the established MBD vehicle model has high accuracy.

[0110] In this embodiment, the loading conditions of the subway car are determined by the quantity of goods (denoted as h) and the loading offset (denoted as x and y), such as Figure 4As shown. The internal length, width, and height of the subway car used in this invention are 19 m, 2.8 m, and 2.1 m, respectively. Considering the space occupied by seats and the passage required for moving goods, this invention assumes that the goods can be loaded within a rectangular area with a length of 15 m and a width of 2 m. Since reducing the cargo density would worsen the safety of freight train operation, this invention reduces the cargo density by maximizing the cargo height, thereby simulating the worst operating conditions of the subway car. Based on this, when the vehicle load reaches its maximum static load of 21.12 t, the value of h is considered to be 2 m in this embodiment. Based on the setting of the geometric parameters of the cargo model, its density can be calculated as (21.12E+3) / (15‧2‧2) = 352 kg / m³. 3 Meanwhile, the minimum value of h is set to 0.2 m to ensure that the vehicle is not in an unloaded state.

[0111] The center of gravity of the goods is as follows Figure 9 It is stated that, considering that when the lateral loading offset exceeds 0.2 m, the uneven load distribution will significantly deteriorate the performance of the suspension system, the maximum value of y is taken as 0.2 m. According to the specifications issued by China Railway Corporation and the American Railway Association, the longitudinal loading offset of the vehicle must meet two basic requirements: (1) the center of gravity of the cargo should be located between the two bogies; (2) the load on each bogie should not exceed half of the maximum static load (21.12 t in this application), from which x can be calculated. max The limit (unit: m) is:

[0112] (9)

[0113] (10)

[0114] For ease of expression, this application uses x * express Based on the above analysis and the calculation results, the loading conditions of the subway car in the simulation experiment are listed in Tables 5 and 6, where x is positive indicating that the center of gravity of the cargo is closer to the front bogie, and y is positive indicating that the cargo is located on the right side of the vehicle. Since there is no cargo offset when the vehicle is fully loaded (h = 2), this application sets the maximum value of h to 1.8m.

[0115]

[0116]

[0117] The design speed of Type B metro vehicles is 120 km / h, while the minimum operating speed of metro vehicles on the main line is 40 km / h. Therefore, the cruising speed of the vehicles in this invention is designed to be 40, 60, 80, 100, and 120 km / h. Referring to existing technical requirements, this invention sets the radius of the curved track to 600, 900, 1200, 1500, and 1800 m, and the superelevation to 120 mm. Simulation data was collected when the train passed through a 360 m long curved track. In summary, the operating conditions of the metro vehicles are determined by two parameters: the radius of the curved track (denoted as R) and the cruising speed of the metro vehicles (denoted as v). The parameter value ranges are shown in Table 7.

[0118]

[0119] Example 4:

[0120] This embodiment utilizes simulation data to construct an RF proxy model to predict the operational safety and energy consumption of subway vehicles under complex loading and operation scenarios. Based on the parameter values ​​listed in Tables 5-7, a total of 5625 simulation experiments were conducted. The input variables included five parameters (R, v, x, y, h), which specifically describe the vehicle's operation and loading conditions. During the vehicle's passage through curved tracks, the maximum absolute value of the wheel load reduction rate (denoted as UN) was used to evaluate the operational safety of the subway vehicle under off-center loading conditions. Vehicle energy efficiency was assessed using ECMR, such as... Figure 10 As shown, the traction force can be adjusted in real time through the PID controller to ensure the uniform speed of the subway vehicle. Based on the energy flow within the vehicle system, the ECMR can be calculated using equation (11):

[0121] (11)

[0122] In the formula, F t This indicates the vehicle's traction force.

[0123] This application uses parallel coordinate graphs (PCP) to present simulation results and analyze the impact of loading and operating conditions on vehicle safety and energy efficiency. In PCP, each parallel axis represents a variable, and the points on each axis are marked with the corresponding variable values. The values ​​of the output variables are encoded by the color of the polyline connecting the points on each axis.

[0124] Figure 11 The distribution of UN in 5625 simulation cases was shown, through Figure 11Preliminary findings reveal the impact of each input variable on operational safety: operational safety is worst when the vehicle is roughly half-loaded; safety improves when cargo is loaded on the left side of the vehicle, closer to the lateral centerline. Furthermore, reducing the curve radius or increasing the cruising speed can mitigate the under-superelevation effect, thereby enhancing vehicle safety. However, it should be noted that the above conclusions represent overall statistical trends. To ensure actual vehicle operational safety, more advanced technologies are needed to accurately assess the vehicle's performance under each specific operating condition.

[0125] In contrast, the distribution pattern of ECMR is more difficult to observe directly. Therefore, [the study is needed to analyze the distribution patterns of ECMR]. Figure 12 The coordinate axes were adjusted to analyze ECMR from multiple perspectives. It is evident that vehicle operating energy consumption decreases as the curve radius increases. Furthermore, in most cases, loading cargo to the left rear of the vehicle improves energy efficiency. Simultaneously, both cruising speed and cargo load are positively correlated with ECMR. Although PCP can intuitively reveal the impact of various variables on vehicle performance, accurate surrogate models are still needed to achieve rapid and accurate prediction of vehicle operating indicators. Such models play a crucial role in optimizing cruising speed based on specific loading conditions.

[0126] Considering that the RF algorithm can model complex nonlinear relationships without extensive data preprocessing, and its built-in feature importance assessment function can provide importance ranking for key independent variables that affect the model prediction results, this embodiment uses the algorithm to establish a surrogate model to explore in depth the impact of loading and operating parameters on vehicle operating performance.

[0127] RF is a nonparametric prediction model consisting of M randomized classification and regression trees (CART), such as... Figure 13 As shown. For the j-th tree in the family, the predicted value at the test sample point x can be expressed as:

[0128] (12)

[0129] In the formula, variables They are independent of each other and follow the same distribution (iid), which is the same as the distribution of the general random variable Θ. They are also independent of the original training samples. ; Represents the resampled training set used to construct the j-th tree; I represents the indicator function, when the leaf node... The value is 1 when the test sample point x is included; Represents the predicted value corresponding to the leaf node; Item express Middle in unit The number of data points within.

[0130] The final prediction results of the RF model are calculated as follows:

[0131] (13)

[0132] This application utilizes the Scikit-Learn library for regression experiments. Model performance is evaluated using root mean square error (RMSE) and coefficient of determination (R²), where a lower RMSE value indicates higher model prediction accuracy, and an R² value closer to 1.0 indicates better fit. The dataset is divided into 4500 training samples and 1125 test samples, and 5-fold cross-validation is used during training to ensure model robustness. Furthermore, this embodiment extends the standard RF architecture by placing a constraint layer before the input layer, which aims to explicitly encode the feature relationships defined by equation (10) into the model.

[0133] This invention focuses on two key hyperparameters that determine model complexity (number of trees and maximum tree depth), aiming to train a model that is as simple as possible, making it easier to integrate into subsequent optimization models. Figure 14 (a) shows the R² of the UN regression model as a function of the number of trees when the maximum tree depth is fixed at 50. The results indicate that the R² values ​​for both the training and test datasets tend to stabilize when the number of trees reaches or exceeds 500. Similarly, Figure 14 (b) shows the variation of R² with maximum tree depth at three different ensemble sizes (500, 600, and 700 trees). The model performance remains stable at a maximum depth of 18 regardless of the number of trees. Therefore, the optimal RF configuration for predicting UNs is 500 trees and a maximum depth of 18. The RMSE of this model on the training and test sets are 0.0061 and 0.014, respectively, while the R² values ​​are 0.9949 and 0.9735, respectively.

[0134] Figure 15 (a) shows the relationship between R² and the number of trees in the ECMR regression model, with the maximum depth fixed at 50. The results show that the R² values ​​for both the training and test sets stabilize after the number of trees reaches 50. Given the small variation in R², the corresponding RMSE values ​​are also displayed as dashed lines for easier analysis. It can be seen that the RMSE values ​​for all datasets also stabilize after the number of trees reaches 70. Similarly, Figure 15 (b) presents how the RMSE changes with the maximum tree depth at three ensemble sizes (60, 70, and 80 trees). The results show that the model performance stabilizes when the maximum depth reaches 13, unaffected by the number of trees. Based on this, the optimal configuration for the ECMR regression model is determined to be 70 trees and a maximum depth of 13. The RMSE of this model on the training and test sets are 178.2 and 371.8, respectively, while the R² reaches 1.0000 and 0.9999, respectively.

[0135] The regression performance of the RF proxy model was evaluated based on the test dataset, and the importance of features was analyzed. Figure 16 (a) presents a graph showing the relationship between the predicted and actual values ​​of UN. The overlaid linear fit lines in the graph show a high degree of agreement, and the R² value of 0.9735 further confirms the strong linear correlation, thus verifying the model's prediction accuracy. Also see... Figure 16 (b) This figure assesses feature importance using the Mean Impurity Reduction (MDI) metric. The results show that all five input features contribute to the prediction, with feature R having the highest importance and feature x the lowest. Figure 17 As shown in (a), the predicted ECMR values ​​are in excellent agreement with the actual values, further confirmed by the superimposed linear fit lines. The R² value is 0.9999, indicating a very strong linear correlation between the two values, which fully demonstrates the model's excellent predictive accuracy. Furthermore, from... Figure 17 (b) The feature importance analysis results show that feature R plays an absolutely dominant role in the prediction, while feature x has the smallest contribution.

[0136] Example 5:

[0137] In this embodiment, to simultaneously improve the operational safety and energy efficiency of subway vehicles, a dual-objective optimization model for the cruising speed of subway vehicles is constructed based on the RF proxy model and solved using the AR-MOEA algorithm to achieve adaptive speed control. This embodiment first divides the subway section into multiple operating units according to different loading and track conditions, such as... Figure 18 As shown, the cruise speed of vehicles in these operating units is then optimized as a whole by taking advantage of the differences in the impact of cruise speed on vehicle operating performance under different loading and track conditions, thereby simultaneously minimizing the UN and ECMR indices of the entire metro section.

[0138] The decision variables for the optimization model are the cruising speeds corresponding to each pre-divided unit within the metro section. The model considers two optimization objectives: maximizing the overall operational safety of the metro section and minimizing its total energy consumption. For each operating unit, its UN and ECMR values ​​can be predicted using an established RF proxy model, determined by the corresponding loading and operating conditions. To ensure that the vehicles meet safety threshold requirements in each unit, the maximum UN value among all units is selected to evaluate the overall operational safety of the metro section, which can be expressed as:

[0139] (14)

[0140] In the formula, This represents the UN regression function derived from the surrogate model. This indicates the cruising speed of the operating unit. The vector represents the track radius, h represents the freight volume, and x and y represent the off-center freight load. This indicates the number of operating units within the segment.

[0141] The total energy consumption of this subway section can be expressed as the sum of the ECMR of all units, as shown in equation (15):

[0142] (15)

[0143] In the formula, This represents the ECMR regression function derived from the surrogate model.

[0144] Therefore, the objective function of the optimization problem can be expressed as:

[0145] (16)

[0146] To ensure vehicle operation safety and efficiency, the cruising speed of each unit must meet the following requirements:

[0147] (17)

[0148] In the formula, and These represent the lower and upper limits of speed, respectively.

[0149] This invention employs the AR-MOEA algorithm to obtain the Pareto optimal solution set for the cruising speed of subway vehicles under different operating conditions. The AR-MOEA algorithm is a multi-objective evolutionary algorithm based on indices. Its core feature lies in the reference point adaptive mechanism, which enables it to automatically adapt to Pareto fronts of different shapes. It can effectively approximate regular and irregular Pareto fronts without requiring prior knowledge of the front shape. The AR-MOEA algorithm process can be summarized into three main stages:

[0150] Step 1: Initialization

[0151] Step 1.1: Generate a population cluster P and predefine a set of uniformly distributed reference points Z;

[0152] Step 1.2: Initialize archive set A to the current population, and set the adaptive reference point set Z' as a copy of the uniform reference point set Z;

[0153] Step 2: Main Loop

[0154] Step 2.1: Use a binary tournament selection strategy to select the parent P' from the population P, and apply genetic operators (such as crossover, mutation, etc.) to the parent P' to generate the offspring Q;

[0155] Step 2.2: Merge the newly generated child Q into archive set A, and remove all dominated or duplicate solutions from it to update the archive set;

[0156] Step 2.3: Integrate the initial uniform reference point set Z with the archive set A to achieve adaptive adjustment of the reference point set Z';

[0157] Step 2.4: Merge the parent population with the offspring population to form a candidate solution pool;

[0158] Step 2.5: Select the optimal solution through a two-stage process: First, perform non-dominated sorting and determine the priority of solutions based on convergence; then calculate the enhanced inversion generation distance index and select the solution that is better in terms of diversity and distribution.

[0159] Step 3: Termination and Output

[0160] Step 3.1: Terminate the loop if the maximum number of iterations is reached or other stopping conditions are met;

[0161] Step 3.2: Output the final population P as an approximation of the desired Pareto front.

[0162] To verify the effectiveness of the proposed method, this embodiment selects a subway section with varying track and loading conditions for a case study. Based on the curve radius and cargo loading characteristics, the section is divided into 10 different units. The specific track and loading parameters for each unit are shown in Table 8. The lower and upper limits of the subway vehicle's operating speed are set to 40 km / h and 120 km / h, respectively.

[0163]

[0164] Based on the case size, the AR-MOEA algorithm is configured with parameters as shown in Table 9. Under this configuration, the proposed optimization model is solved to obtain the Pareto optimal solution set for the cruise speed of all operating units.

[0165]

[0166] Figure 19 The Pareto fronts for different unit cruise speeds are shown. For comparative analysis, the figure also presents five baseline scenarios with a fixed cruise speed throughout the entire journey (i.e., constant speeds of v = 40, 60, 80, 100, and 120 km / h respectively). Figure 19 As can be seen, compared with the baseline scheme, adaptively adjusting the cruise speed according to the track and loading conditions of each unit can significantly improve the operational safety and energy efficiency of subway vehicles.

[0167] Figure 20This demonstrates the maximum percentage reduction in UN and ECMR achievable by using the Pareto optimal solution relative to each baseline scheme, without affecting other objectives. It can be seen that compared to the most unfavorable operating condition (i.e., v = 120 km / h), UN can be reduced by a maximum of 23.57%, and ECMR by a maximum of 20.84%.

[0168] Figure 21 The Pareto optimal cruise speeds of each unit exhibit a clear distribution pattern, influenced by both track and loading conditions. For example, unit 7 (R = 1000 m, y = -0.2 m, h = 0.92 m, x = -6.3 m) employs a lower cruise speed due to its moderate track curvature and loading imbalance (particularly critical longitudinal offset). In contrast, unit 9 (R = 1600 m, y = 0.15 m, h = 0.25 m, x = 3.84 m) has a more moderate track curvature and a more balanced cargo load, allowing it to achieve a higher cruise speed.

[0169] The above optimization results show that adaptively adjusting the cruising speed according to the track and loading conditions can effectively improve the operational safety and energy efficiency of subway vehicles. In addition, the obtained Pareto optimal solution set provides significant flexibility for operational decision-making. System operators can select the corresponding speed scheme according to specific performance priorities. Under the premise of safety priority, a solution with a lower UN value can be selected; while if energy efficiency optimization is the focus, an operation scheme that minimizes ECMR can be adopted.

[0170] Example 6:

[0171] This invention proposes a novel optimization framework for adjusting the cruising speed of vehicles in a metro logistics system, aiming to simultaneously improve the operational safety and energy efficiency of vehicles under the cargo-vehicle coupling effect. Considering the changes in vehicle body mass characteristics caused by cargo loading, the dynamic equations of the loaded vehicle body are derived, and a MBD model for a type B metro vehicle is constructed and verified through field testing on Chengdu Metro Line 1. A total of 5625 MBD simulation experiments were conducted under various conditions such as loading offset, freight volume, curve radius, and cruising speed. The simulation results reveal the impact of loading and operating conditions on vehicle performance. Based on the simulation results, an RF proxy model is established, which predicts vehicle performance by inputting characteristic parameters related to loading and operating conditions. For a specific metro section, it is divided into different operating units according to loading and track parameters. A dual-objective optimization model with operational safety and energy efficiency as indicators is constructed to adjust the cruising speed of each unit. The AR-MOEA algorithm is used to solve the model. Case studies demonstrate the effectiveness of the proposed model and algorithm. The main conclusions are as follows:

[0172] (1) There is a complex nonlinear relationship between the operating parameters and the running performance of subway vehicles. Based on the MBD simulation results, several general rules can be derived: In order to improve the safety of operation, the vehicle should be kept in a half-load state; the cargo should be placed on the outside of the vehicle, and the impact of excessive height can be mitigated by appropriately increasing the cruising speed; in terms of energy efficiency, the loading on the outside still has advantages, but higher speed will lead to an increase in ECMR value; given that the cruising speed has different effects on safety and energy efficiency, it is crucial to adopt a dual-objective optimization method.

[0173] (2) The RF-based proxy model can accurately predict the operating performance of subway vehicles under any operating conditions. Feature importance analysis shows that the curve radius is the most critical factor affecting operating performance, indicating that cruise speed control should be dynamically adjusted in combination with the specific line curvature, in addition to considering loading conditions.

[0174] (3) The AR-MOEA algorithm is suitable for solving the constructed dual-objective optimization model, especially for the objective function driven by the regression model. Case studies show that adaptive adjustment of cruise speed according to track and loading conditions can significantly improve both operational safety and energy efficiency. Compared with the benchmark scheme, the proposed control strategy can reduce the wheel load reduction rate by a maximum of 23.57% and reduce the ECMR value by 20.84%.

[0175] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for energy-saving speed control of a subway logistics system considering cargo loading conditions, characterized in that, Specific methods include: S1. Based on the dynamic equations of the transport vehicle, a multibody dynamic model of a type B metro vehicle considering cargo characteristics is established using the VI-Grade simulation platform, and the accuracy of the model is verified through field testing. Based on the verified model, loading and operating conditions are designed for simulation experiments. Based on the simulation experiment results, the impact of cargo loading and vehicle operating conditions on vehicle operating safety and energy efficiency is verified. S2 utilizes simulation data under different working conditions to construct a proxy model based on random forest to predict the operational safety and energy consumption of vehicles under complex loading and operation scenarios. S3 establishes a dual-objective optimization model for vehicle cruising speed based on the prediction results of the random forest surrogate model. It then combines the AR-MOEA multi-objective evolutionary algorithm based on adaptive reference points to optimize the vehicle cruising speed and dynamically adjust the vehicle's cruising speed under different loading and operating scenarios.

2. The adaptive speed control method for a subway logistics system considering loading conditions according to claim 1, characterized in that, In step S1, the impact of cargo loading on the vehicle's center of gravity change is derived using the vehicle's dynamic equations. These dynamic equations include lateral motion, vertical motion, roll motion, pitching motion, and yaw motion.

3. The speed-saving control method for a subway logistics system considering cargo loading conditions according to claim 1, characterized in that, In step S1, the loading condition is defined by the quantity of goods h, the longitudinal loading offset x, and the lateral loading offset y; the operating condition is defined by the radius of the track curve R and the vehicle cruising speed v; the vehicle's operating safety and energy efficiency are represented by the wheel load reduction rate (UN) and the operating resistance energy consumption (ECMR), respectively.

4. The speed-saving control method for a subway logistics system considering cargo loading conditions according to claim 1, characterized in that, In step S2, the random forest surrogate model is extended from the standard random forest model architecture, encoding the characteristic relationship between freight volume and longitudinal loading offset into the model; the input of the random forest surrogate model is curve radius R, cruising speed v, lateral loading offset y, freight quantity h and longitudinal loading offset x, and the output is UN and ECMR; the random forest surrogate models used to predict UN and ECMR contain 500 and 70 trees respectively, and the maximum tree depths are 18 and 13 respectively.

5. The speed-saving control method for a subway logistics system considering cargo loading conditions according to claim 1, characterized in that, In step S3, for a specific subway section, it is divided into several operating units based on loading and track conditions. Utilizing the difference in the impact of cruising speed on vehicle performance under different operating conditions, a dual-objective optimization is performed on the cruising speed of vehicles within these operating units. This dual-objective optimization model treats UN and ECMR as conflicting optimization objectives, specifically: In the formula, and Let UN and ECMR be the regression functions derived from the surrogate model, respectively. Indicates the vehicle's cruising speed. The vector represents the track radius, h represents the freight volume, and x and y represent the off-center freight load. Indicates the number of units within a segment and limits the effective range of cruising speed: In the formula, and These represent the lower and upper limits of speed, respectively. The AR-MOEA algorithm is used to solve the Pareto solution for cruise speed under multiple operating conditions.

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