Train passing curve optimal regulation position prediction method based on average superelevation of curve position

Abstract

The application provides a train passing curve optimal adjustment position prediction method based on average superelevation of curve position, relates to the field of train automatic control technology, and comprises the following steps: calculating the adjustment time, the relationship between the adjustment acceleration and the adjustment position according to the current speed, the next curve position and the average superelevation of the curve position; constructing a target optimization function according to the adjustment time and the adjustment acceleration; and then optimizing the adjustment time and the adjustment acceleration according to the target optimization function to calculate the optimal adjustment position. When the train travels to the optimal adjustment position, the train speed is adjusted at the target adjustment acceleration for the target adjustment time. The above-mentioned mode can predict the optimal adjustment position for starting to adjust the train speed before the train passes the curve, so that the whole train passing curve process is as short as possible and the acceleration is as small as possible, thereby ensuring that the passengers do not experience large acceleration and deceleration, guaranteeing the riding experience, and ensuring that the train does not produce schedule delay.

Description

Technical Field

[0001] This invention generally relates to the field of train automatic control technology, and specifically to a method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position. Background Technology

[0002] In recent years, with the continuous advancement of technology and the growth in demand for railway transportation, high-speed rail has become an efficient, safe, comfortable, and environmentally friendly mode of transportation, and has been widely applied and promoted.

[0003] The speed of high-speed trains is controlled through multiple methods, including the track signaling system and the train's automatic driving system. During operation, the train continuously receives signals from the track signaling system, including information such as the train's speed and track curvature. Simultaneously, the train automatically adjusts its straight-line speed to ensure safety and stability during operation.

[0004] Before the train approaches a curve, the train control center receives control instructions from the driver. Based on the curve's radius and the train's speed sensors, the center calculates the train's acceleration and sends instructions to the onboard computer system. The onboard computer system then controls the train's speed and acceleration to ensure the train safely navigates the curve.

[0005] The above-mentioned method of controlling cornering speed requires the train driver to judge the appropriate cornering position based on experience, and then send a command to the onboard computer system to start the above adjustment process, and then the onboard computer system automatically completes the cornering speed adjustment.

[0006] Assuming the speed difference to be adjusted remains constant during cornering speed adjustment, if the initial adjustment position is too close to the corner, the acceleration adjustment will be too large, resulting in a poor passenger experience; if the initial adjustment position is too far from the corner, it will lead to an extension of the train's travel time, potentially causing train delays.

[0007] The existing control methods still rely on the driver's experience to judge the appropriate curve position, which makes it difficult to ensure that the overall time consumption and overall acceleration of the train are at the optimal value when turning. When the driver is inexperienced or driving on unfamiliar road sections, there may be sudden acceleration or deceleration, resulting in a poor passenger experience. Or when deceleration is required when turning, premature deceleration will reduce the average speed of the train and cause train delays. Summary of the Invention

[0008] In view of the above-mentioned defects or deficiencies in the existing technology, it is desirable to provide a method for predicting the optimal adjustment position of trains when cornering based on the average superelevation of the curve position.

[0009] This application provides a method for predicting the optimal adjustment position of a train when cornering based on the average superelevation at the curve position, including:

[0010] Get the train's current speed;

[0011] Obtain the location of the next curve on the railway line and the average superelevation of the curve location; the average superelevation represents the average height difference between two sections of the railway at the curve location;

[0012] Based on the current train speed, curve position, and average superelevation, construct expressions for the adjustment time and acceleration required for the train to adjust its speed from the optimal adjustment position until it reaches the curve position. These expressions include an unknown optimal adjustment position. The optimal adjustment position represents the position where the speed adjustment begins when the weighted sum of the adjustment time and acceleration is minimized.

[0013] Construct a target optimization function based on the adjustment duration expression and the adjustment acceleration expression;

[0014] Based on the target optimization function, the adjustment duration and adjustment acceleration are optimized until the values ​​of the adjustment duration and the adjustment acceleration minimize the target optimization function, thereby obtaining the target adjustment acceleration and the target adjustment duration;

[0015] The optimal adjustment position is calculated based on the target adjustment acceleration and the target adjustment duration.

[0016] Get the train's current position on the railway track;

[0017] Judgment: When the optimal adjustment position is between the current position and the curve position, wait for the train to reach the optimal adjustment position, start adjusting the train speed with the target adjustment acceleration, and continue for the target adjustment duration;

[0018] When the current position is exactly at the optimal adjustment position, the train speed is directly adjusted at the target adjustment acceleration for the target adjustment duration.

[0019] According to the technical solution provided by the present invention, when the current position is between the optimal adjustment position and the curve position, the following steps are performed:

[0020] Based on the current position, curve position, current speed, and average superelevation, the train speed is adjusted from the current position until it reaches the curve position, at which point the required acceleration is obtained, and the compensation acceleration is achieved.

[0021] The train speed is adjusted using the aforementioned compensation acceleration until the train reaches the curve.

[0022] According to the technical solution provided by the present invention, the process of obtaining the location of the next curve on the railway track and the average superelevation of the curve location includes:

[0023] Obtain a railway track database; the railway track database stores at least the locations of all curves of the railway track and the average superelevation corresponding to each curve location;

[0024] Query the railway track database to obtain the locations of all curves on the railway track.

[0025] Based on the train's current position and the positions of all curves, the location of the curve closest to the current position along the railway line is calculated.

[0026] The average superelevation is obtained by querying the railway line database based on the location of the most recent curve.

[0027] According to the technical solution provided by the present invention, the process of obtaining the railway track database includes:

[0028] Obtain the serial numbers of multiple railway locators on the railway track;

[0029] The railway track is divided into multiple track units by using all railway locators on the track; the line connecting the midpoint of each track unit to a railway locator is perpendicular to the direction of the railway track's extension; the length of each track unit is equal to the distance between adjacent railway locators.

[0030] The numbers of the railway locators are matched one-to-one with the numbers of the track units and the railway locators whose lines are perpendicular to the extension direction of the track.

[0031] Equal intervals are sampled within the line unit to measure the superelevation value of multiple sampling points within the line unit;

[0032] The average superelevation of the line unit is calculated by averaging multiple superelevation values.

[0033] Each corresponding track unit, the number of the railway locator corresponding to the track unit, and the average superelevation of the track unit are saved to the database to obtain the railway track database.

[0034] According to the technical solution provided by the present invention, the process of constructing expressions for the adjustment time and adjustment acceleration required for the train from the optimal adjustment position until the train reaches the curve position, based on the current train speed, curve position, and average superelevation, includes:

[0035] Obtain the rail width, the radius of curvature at the curve location, and the total mass of the train;

[0036] The optimal cornering speed is calculated based on the rail width, average superelevation, radius of curvature, and total train mass. The optimal cornering speed represents the centripetal force required for the train to corner, which is the resultant force obtained by the vector superposition of the train's weight and the rail's supporting force on the train.

[0037] Set the starting adjustment position to an unknown parameter;

[0038] The adjustment distance expression from the starting adjustment position to the curve position is calculated based on the starting adjustment position and the curve position; the starting adjustment position is an unknown parameter in the adjustment distance expression.

[0039] Based on the optimal cornering speed, current vehicle speed, and adjustment distance expression, the adjustment duration expression is constructed; in the adjustment duration expression, the start adjustment position and adjustment duration are unknown parameters.

[0040] Based on the optimal cornering speed, the current vehicle speed, and the adjustment duration, an adjustment acceleration expression is constructed; in the adjustment acceleration expression, the start adjustment position, the adjustment duration, and the adjustment acceleration are unknown parameters.

[0041] According to the technical solution provided by the present invention, the objective optimization function represents the weighted sum of the adjustment time and the adjustment acceleration; the objective optimization function is represented by formula (I);

[0042] Formula (1);

[0043] in, f Denotes the objective optimization function. w 1 and w 2 represents weight. Indicates the adjustment duration. a Indicates adjustment of acceleration. It represents the absolute value.

[0044] According to the technical solution provided by the present invention, the process of optimizing the adjustment time and adjustment acceleration based on the target optimization function includes:

[0045] Substituting the average superelevation, current train speed, rail width, radius of curvature at the curve position, total train mass, optimal curve speed, adjustment time expression, and adjustment acceleration expression into the target optimization function yields the expansion of the target optimization function; in the expansion of the target optimization function, only the starting adjustment position is an unknown parameter;

[0046] Differentiate the expansion of the objective optimization function with respect to the initial adjustment position, and calculate the minimum point of the expansion of the objective optimization function;

[0047] The starting adjustment position corresponding to the minimum point is taken as the optimal adjustment position;

[0048] Substituting the optimal adjustment position into the adjustment duration expression and adjustment acceleration expression, the target adjustment acceleration and target adjustment duration are calculated.

[0049] According to the technical solution provided by the present invention, the process of optimizing the adjustment time and adjustment acceleration based on the target optimization function includes:

[0050] The particle swarm optimization algorithm is used to optimize the adjustment time and adjustment acceleration to obtain the target adjustment acceleration and target adjustment time.

[0051] According to the technical solution provided by the present invention, the steps of optimizing the adjustment time and adjustment acceleration using the particle swarm optimization algorithm include:

[0052] S91: Initial settings for particle swarm optimization algorithm parameters: Set the search space for adjusting duration and acceleration; Set the Nth position of multiple particles in the search space, and the Nth velocity of each particle; The initial value of N is set to 1;

[0053] S92: Based on the Nth position, obtain the Nth adjustment duration and Nth adjustment acceleration within the search space;

[0054] S93: Calculate the target optimization function for the current position of the particle based on the Nth adjustment duration and the Nth adjustment acceleration, and obtain the Nth target optimization function;

[0055] S94: Substitute the Nth position of each particle into the position update formula of the particle swarm algorithm; substitute the Nth velocity of each particle into the velocity update formula of the particle swarm algorithm to calculate the (N+1)th position and (N+1)th velocity of each particle in the Nth iteration.

[0056] S95: Judgment: When the termination condition is met, obtain the Nth adjustment duration and Nth adjustment acceleration in the search space based on the final position of the particle, and use the Nth adjustment duration and Nth adjustment acceleration as the target adjustment acceleration and the target adjustment duration; otherwise, increment the value of N by one, and repeat steps S92-S95.

[0057] According to the technical solution provided by the present invention, the search space includes: a first interval and a second interval;

[0058] The first interval is used to represent the search range for adjustment duration; the second interval is used to represent the search range for adjustment acceleration.

[0059] The first interval is shown in formula (II);

[0060] The second interval is shown in formula (III);

[0061] Formula (II);

[0062] Formula (3);

[0063] in, t Indicates the adjustment duration. a Indicates adjustment of acceleration. S 0 represents the total length of the railway track. Indicates the length of the curve at the location of the curve. V max Indicates the train's maximum speed. T This indicates the longest time a train can travel the entire length of the railway track without delaying its scheduled departure. a max This indicates the train's maximum acceleration.

[0064] The beneficial effects of this application are as follows:

[0065] The relationship between adjustment time, adjustment acceleration, and adjustment position is calculated based on the current train speed, the location of the next curve, and the average superelevation at the curve location. A target optimization function is constructed based on the adjustment time and adjustment acceleration, and then these two parameters are optimized using this function. When the adjustment time and adjustment acceleration minimize the target optimization function, the optimal adjustment position is calculated. It is then determined whether the optimal adjustment position lies between the train's current position and the location of the next curve. If the optimal adjustment position does not lie between these two locations, the train's speed is adjusted at the target adjustment acceleration once it reaches the optimal adjustment position, and this adjustment is continued for the target adjustment time. This method can predict the optimal adjustment position for adjusting the train's speed before it enters a curve, resulting in a shorter curve-taking time and less acceleration, thus minimizing passenger acceleration and deceleration and ensuring a smoother ride while preventing train delays. Attached Figure Description

[0066] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0067] Figure 1 A flowchart illustrating the train curve optimal adjustment position prediction method based on average superelevation at curve position provided in this application;

[0068] Figure 2 This is a flowchart of the particle swarm optimization algorithm iteration.

[0069] Figure 3 This is a cross-sectional view of the train as it curves.

[0070] Among them, 1. train; 2. railway track. Detailed Implementation

[0071] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0072] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0073] Specifically, in the current railway system, trains need to obtain electrical energy from the overhead contact line via a pantograph to drive the train's start and stop. In existing technology, this is generally achieved by connecting the overhead contact line to a railway positioner, which then contacts the train's electrical system to transfer power. To ensure continuous train operation, railway positioners need to be laid along the tracks to supply power to the train.

[0074] Specifically, track superelevation is the height difference between two rails. To prevent the train from experiencing lateral displacement relative to the rails when cornering, the rails at the curve are generally designed with unequal heights. This allows the combined force of the rails' support and the train's own weight to provide the centripetal force for the turn.

[0075] For example, when a train turns right, the height of the rail on the left side of the curve is designed to be higher. This way, the train wheels do not generate lateral forces with the rails, reducing wheel wear and lowering the risk of cornering.

[0076] Since the track of a maglev train does not directly contact the train, the risk of derailment is much greater than that of a conventional train. Therefore, the track of a maglev train also needs to be equipped with appropriate superelevation at curves to reduce lateral displacement and lower the risk of derailment.

[0077] The superelevation and radius of curvature of the curve at the same location are constant values, determined during the laying of the railway track. Therefore, the lateral acceleration provided by the centripetal force when a train curves is only related to its speed. In order for the combined force of the rail's support force on the train and the train's own weight to provide the centripetal force for turning, the optimal speed for curve-taking is also a constant value.

[0078] This embodiment assumes the train is traveling smoothly and maintaining a constant speed when cornering. The train is at its optimal cornering speed when the front of the train reaches the beginning of the curve, and speed adjustments can only be made after the rear of the train has passed the end of the curve.

[0079] Specifically, different train models have different maximum speeds. For example, the Harmony train in my country has a steady running speed of 200-380 km / h, while the Fuxing train has a steady running speed of 350 km / h and a maximum speed of 420 km / h.

[0080] As mentioned above, different types of trains have significantly different speeds when traveling smoothly. When different types of trains travel on the same line, the speed difference between adjusting from the smooth driving speed to the optimal cornering speed is also different, and therefore the deceleration distance is also different.

[0081] Based on the above, if a train wants to minimize acceleration and shorten the turning time when turning, it needs to calculate in advance the optimal starting position for speed adjustment before turning, as well as the appropriate acceleration.

[0082] Calculating the acceleration required for speed adjustment requires first determining the distance from the train's front end to the starting point of the curve. Since the curve's location is known, determining the optimal adjustment position before entering the curve is crucial. Accurately predicting the optimal adjustment position is essential for the smoothness of the train's curve-taking process and for controlling the time consumed during curve-taking.

[0083] Please refer to Figure 1 The flowchart of the train curve optimal adjustment position prediction method based on the average superelevation of the curve position provided in this application is shown below, including:

[0084] S1: Get the current speed of the train;

[0085] S2: Obtain the location of the next curve on the railway line and the average superelevation of the curve location; the average superelevation represents the average height difference between the two sections of the railway at the curve location;

[0086] S3: Based on the current train speed, curve position, and average superelevation, construct expressions for the adjustment time and acceleration required for the train to adjust its speed from the optimal adjustment position until it reaches the curve position; the adjustment time and acceleration expressions contain an unknown optimal adjustment position; the optimal adjustment position represents the position where the speed adjustment begins when the weighted sum of the adjustment time and acceleration is minimized.

[0087] S4: Construct the target optimization function based on the adjustment duration expression and the adjustment acceleration expression;

[0088] S5: Based on the target optimization function, optimize the adjustment duration and adjustment acceleration until the values ​​of the adjustment duration and the adjustment acceleration minimize the target optimization function, thereby obtaining the target adjustment acceleration and the target adjustment duration;

[0089] S6: The optimal adjustment position is calculated based on the target adjustment acceleration and the target adjustment duration;

[0090] S7: Get the current position of the train on the railway track;

[0091] S8: Determine the positional relationship between the optimal adjustment position, the current position, and the curve position: When the optimal adjustment position is between the current position and the curve position, wait for the train to reach the optimal adjustment position, start adjusting the train speed with the target adjustment acceleration, and continue for the target adjustment duration;

[0092] When the current position is exactly at the optimal adjustment position, the train speed is directly adjusted at the target adjustment acceleration for the target adjustment duration.

[0093] In this embodiment, the location of a curve refers to the location of the next curve, specifically a curved section of rail with curvature and a non-zero superelevation. The end closer to the front of the train is designated as the starting point of the curve, and the end farther from the front is designated as the ending point.

[0094] Therefore, the following descriptions of the curve locations and the distances to the train all refer to the distance from the starting point of the curve to the front of the train along the rails.

[0095] Specifically, since the train's steady speed is greater than the optimal speed for cornering in most cases, this embodiment takes the case where deceleration is required when cornering as an example.

[0096] In some implementations, the adjustment duration expression is represented by formula (iv);

[0097] Formula (IV);

[0098] The expression for the adjusted acceleration is given by formula (V);

[0099] Formula (5);

[0100] in, Indicates the adjustment duration. a Indicates adjustment of acceleration. x 0 represents the distance from the curve to the end of the railway line. x 1 represents the distance from the optimal adjustment position to the end of the railway line. v Indicates the current vehicle speed. v 0 indicates the optimal cornering speed.

[0101] Optimal adjustment position here x1 represents an unknown quantity. Since the total length of the railway track is fixed and the endpoint position remains unchanged, knowing the total length of the railway track and the endpoint position allows us to calculate the distance from the endpoint of the railway track to the optimal adjustment position, thus determining the optimal adjustment position.

[0102] In some implementations, the weighted sum of the adjustment duration and the adjustment acceleration is represented by multiplying the adjustment duration and adjustment acceleration by their respective weights and then adding them together. The weight values ​​are set according to the actual situation of the train, and the sum of the two weight values ​​equals 100%. For ease of calculation, in this embodiment, the weight of the adjustment duration is set to 50%, and the weight of the adjustment acceleration is set to 50%.

[0103] Specifically, the process of calculating the optimal adjustment position based on the target adjustment acceleration and the target adjustment duration includes:

[0104] Substituting the target adjustment time into formula (iv), the distance from the curve position to the end of the railway line... x 0. Current vehicle speed v and represent the optimal cornering speed v Since all zeros are known, the distance from the optimal adjustment position to the end of the railway line can be calculated. x 1; or substitute the target adjustment acceleration and target adjustment time into the formula (V) to calculate the distance from the optimal adjustment position to the end of the railway line. x 1.

[0105] There are various ways to obtain the current position of a train, such as satellite positioning and inertial navigation system positioning. Due to the high speed of the train, high positioning accuracy is required in this embodiment. After detecting the position information of the train's front, the distance from the train's front to the destination along the rails is calculated using existing technology, combined with the location of the destination and the track alignment. This distance is ultimately used as the current position in this embodiment.

[0106] In some implementations, if the optimal adjustment position is between the train's front and the curve when the prediction calculation begins, it is necessary to wait for the train to reach the optimal adjustment position before adjusting the speed with the target acceleration for the target adjustment duration. This method ensures that the train's front reaches the starting point of the curve at the optimal cornering speed.

[0107] The time to wait for the train to reach the optimal adjustment position can also be calculated, as shown in formula (VI);

[0108] Formula (VI);

[0109] in, t 1 indicates the time it takes for the train to travel from its current position to the optimal adjustment position at its current speed. x This indicates the distance from the current location to the end of the railway line.x 0 represents the distance from the curve to the end of the railway line. v Indicates the current vehicle speed.

[0110] The above method can predict the optimal adjustment position for adjusting the train speed before it turns, so that the entire turning process takes as little time as possible and the acceleration is as small as possible. This ensures that passengers do not experience large acceleration and deceleration, guaranteeing a comfortable ride, while also preventing train delays.

[0111] Furthermore, when the current position is between the optimal adjustment position and the curve position, the following steps are performed:

[0112] Based on the current position, curve position, current speed, and average superelevation, the train speed is adjusted from the current position until it reaches the curve position, at which point the required acceleration is obtained, and the compensation acceleration is achieved.

[0113] The train speed is adjusted using the aforementioned compensation acceleration until the train reaches the curve.

[0114] Specifically, if the train head has already passed the optimal adjustment position, the acceleration is immediately recalculated and the speed is immediately adjusted to ensure that the train is at the optimal cornering speed when the train head reaches the starting point of the curve.

[0115] The above methods can handle some unexpected situations. For example, if the train cannot immediately adjust its speed at the optimal adjustment position due to some unavoidable reasons and instead travels an extra distance, the above procedures are necessary to ensure the train safely navigates the curve.

[0116] Furthermore, the process of obtaining the location of the next curve on the railway line and the average superelevation of the curve location includes:

[0117] Obtain a railway track database; the railway track database stores at least the locations of all curves of the railway track and the average superelevation corresponding to each curve location;

[0118] Query the railway track database to obtain the locations of all curves on the railway track.

[0119] Based on the train's current position and the positions of all curves, the location of the curve closest to the current position along the railway line is calculated.

[0120] The average superelevation is obtained by querying the railway line database based on the location of the most recent curve.

[0121] Specifically, a typical train line between two locations consists of two tracks, each with two rails. The two tracks are for trains traveling in opposite directions, and the direction of travel on one track is fixed. When a train needs to return, it must switch tracks to the other parallel track.

[0122] Based on the above information, knowing the railway line the train is on and its current location, and combining this with the locations of all curves on the railway line stored in the database, we can determine the location of the train's next curve.

[0123] The specific process includes:

[0124] Obtain the distance from all curve positions to the finish line, and get multiple first distances;

[0125] Calculate the distance from the train's current position to the destination to obtain the second distance;

[0126] Then, the first distance, which is less than the second distance and has the smallest difference from the second distance, is calculated.

[0127] The curve position corresponding to the first distance is the next curve position of the train.

[0128] Establishing a railway track database can reduce the amount of computation. When the train speed is high, the onboard computer can make predictions in a timely manner, ensuring the timeliness of the prediction results.

[0129] Furthermore, the process of obtaining the railway track database includes:

[0130] Obtain the serial numbers of multiple railway locators on the railway track;

[0131] The railway track is divided into multiple track units by using all railway locators on the track; the line connecting the midpoint of each track unit to a railway locator is perpendicular to the direction of the railway track's extension; the length of each track unit is equal to the distance between adjacent railway locators.

[0132] The numbers of the railway locators are matched one-to-one with the numbers of the track units and the railway locators whose lines are perpendicular to the extension direction of the track.

[0133] Equal intervals are sampled within the line unit to measure the superelevation value of multiple sampling points within the line unit;

[0134] The average superelevation of the line unit is calculated by averaging multiple superelevation values.

[0135] Each corresponding track unit, the number of the railway locator corresponding to the track unit, and the average superelevation of the track unit are saved to the database to obtain the railway track database.

[0136] Specifically, each railway locator has a number, which is usually printed on the surface facing the train.

[0137] In this embodiment, the railway track is divided into multiple line units according to the interval setting of the railway locator, and the position of the railway locator is set as the midpoint of the line unit.

[0138] During periods when the train is not in operation, the trolley travels at low speed from the starting point to the end point to complete the entire journey; or it only travels around a few curves, experiencing each curve.

[0139] The track-tracking trolley is equipped with a camera and an over-height detection device. When the trolley travels on a curve, the camera captures the numbers of the railway locators on both sides, and the over-height detection device detects multiple over-height values ​​at intervals of 0.2 meters at the curve.

[0140] After the track-tracking trolley finishes collecting data, it inputs the data into the trolley's onboard computer. The onboard computer calculates the average superelevation at this curve location and binds it to the railway locator number. After the track-tracking trolley has inspected all curve locations, the onboard computer binds the average superelevation of all curve locations, the railway locator number, and the curve location together and stores them in the database, thus obtaining the railway track database.

[0141] Specifically, the technical principles and process of measuring railway superelevation using superelevation detection equipment are existing technologies and will not be elaborated upon here. In this embodiment, only the specific value of the superelevation needs to be detected for calculation.

[0142] Because the superelevation of the railway tracks is continuously changing, the starting and ending points of curves are somewhat ambiguous concepts, without fixed standards. In some cases, sections with superelevation greater than 1 cm are designated as curve locations, while in others, sections with superelevation greater than 1 mm are designated as curve locations. These different curve location settings affect the determination of the starting point of the curve from the train's front end, thus impacting the prediction of the optimal adjustment position.

[0143] Since the spacing of railway positioners on the same track is identical, the method of dividing track units based on the spacing of railway positioners can establish a unified division standard, ensuring that the starting and ending points of different curves on the same track are set consistently. This, in turn, guarantees accurate prediction of the optimal adjustment position.

[0144] Furthermore, based on the current train speed, curve position, and average superelevation, the process of constructing expressions for the required adjustment time and acceleration of the train from the optimal adjustment position until it reaches the curve position includes:

[0145] Obtain the rail width, the radius of curvature at the curve location, and the total mass of the train;

[0146] The optimal cornering speed is calculated based on the rail width, average superelevation, radius of curvature, and total train mass. The optimal cornering speed represents the centripetal force required for the train to corner, which is the resultant force obtained by the vector superposition of the train's weight and the rail's supporting force on the train.

[0147] Set the starting adjustment position to an unknown parameter;

[0148] The adjustment distance expression from the starting adjustment position to the curve position is calculated based on the starting adjustment position and the curve position; the starting adjustment position is an unknown parameter in the adjustment distance expression.

[0149] Based on the optimal cornering speed, current vehicle speed, and adjustment distance expression, the adjustment duration expression is constructed; in the adjustment duration expression, the start adjustment position and adjustment duration are unknown parameters.

[0150] Based on the optimal cornering speed, the current vehicle speed, and the adjustment duration, an adjustment acceleration expression is constructed; in the adjustment acceleration expression, the start adjustment position, the adjustment duration, and the adjustment acceleration are unknown parameters.

[0151] In some implementations, if the resultant force obtained by the vector superposition of the train's weight and the rail's supporting force on the train is to provide the centripetal force required for the train to curve, a corresponding mathematical model needs to be constructed first.

[0152] Specifically, such as Figure 3 As shown, Figure 3 Train 1 is positioned on track 2 at a curve. The supporting force of track 2 on train 1 Centripetal force and the total weight of the train The formation of a closed triangle indicates that the train is in a state of dynamic equilibrium, and the total weight of the train... Support force of rail 2 on train 1 The combined force provides centripetal force. α This represents the angle between the line connecting the two rails and the horizontal plane, and is equal to the angle between the total weight of the train and the supporting force. (Total weight of the train) The modulus is equal to the total mass of the train m With gravitational acceleration g The product of. Figure 3 middle, h This indicates that the average is extremely high. d Indicates the width of the railway track.

[0153] Specifically, the centripetal force required for a train to navigate a curve is horizontal, pointing towards the center of the curve. For example, when a train turns right, the centripetal force points towards the right side of the train. The direction of the train's gravity is always vertically downward, and the direction of the supporting force from the rails is perpendicular to the rails. However, due to the difference in rail height on both sides of the curve, the direction of the supporting force will be biased towards the side the train is turning.

[0154] This allows us to construct a mathematical model of the vector superposition of the supporting force, centripetal force, and train weight. According to the geometric relationships of a triangle, the angle between the supporting force and the train weight is equal to the angle between the line connecting the two rails and the horizontal plane.

[0155] The sine of the angle between the line connecting the two rails and the horizontal plane is equal to the ratio of the superelevation to the width between the two rails. Ultimately, the optimal cornering speed can be calculated based on the rail width, average superelevation, radius of curvature, and total train mass. The line connecting the two rails refers to the line perpendicular to the direction of rail extension among any two points on the two sides of the rails.

[0156] The equations for calculating the optimal cornering speed are shown in Equation (VII);

[0157] Formula (VII);

[0158] in, F 1 represents centripetal force. F 2 indicates support force. m Indicates the total mass of the train. g Represents gravitational acceleration. mg This indicates the total weight of the train. v 0 represents the optimal cornering speed. R Indicates the radius of curvature. h This indicates that the average is extremely high. d Indicates the width of the railway track. α It represents the angle between the line connecting the two railway tracks and the horizontal plane.

[0159] According to formula (VII), the support force, the optimal turning speed, the centripetal force, the support force, and the angle between the line connecting the two rails and the horizontal plane can be calculated.

[0160] Further calculations include:

[0161] Start by adjusting the distance from the starting position to the endpoint, setting it to an unknown parameter. y ;

[0162] The adjustment distance expression is represented by formula (8);

[0163] Formula (8);

[0164] Where S represents the adjustment distance. x 0 represents the distance from the curve to the end of the railway line.

[0165] Since the distance from the starting position to the endpoint is set to an unknown parameter. y Formulas (IV) and (V) x 1 replaced with y Substituting the optimal cornering speed calculated in the previous step into formulas (IX) and (X), we can then deduce the adjustment time and adjustment acceleration relative to the starting adjustment position. y The function.

[0166] Specifically, the adjustment duration is related to the starting adjustment position. y The function is represented by formula (IX);

[0167] Formula (IX).

[0168] Adjusting acceleration relative to the starting adjustment position y The function is represented by formula (x);

[0169] Formula (10).

[0170] Furthermore, the objective optimization function represents the weighted sum of the adjustment duration and the adjustment acceleration; the objective optimization function is represented by formula (I);

[0171] Formula (1);

[0172] in, f Denotes the objective optimization function. w 1 and w 2 represents weight. Indicates the adjustment duration. a Indicates adjustment of acceleration. It represents the absolute value.

[0173] In some implementations, the weighted sum of the adjustment duration and the adjustment acceleration is set as the target optimization function. When the target optimization function reaches its minimum value, the corresponding adjustment duration and adjustment acceleration are the target adjustment duration and the target adjustment acceleration.

[0174] The specific weighting values ​​are adjusted based on the actual needs of the train. When the train is used for freight transport and the transport time is relatively urgent, and the goods are not easily affected by acceleration, the influence of acceleration will be considered less, making... w 2 is smaller. For example, w 1 is set to 0.9. w 2 is set to 0.1.

[0175] When applied to sightseeing trains, greater consideration is given to passenger comfort and the sightseeing experience, with less emphasis on time constraints in order to allow passengers to enjoy the scenery more fully. For example, w 1 is set to 0.1. w 2 is set to 0.9.

[0176] The above method allows the train cornering speed optimal starting position prediction method provided by this invention to be applicable to more trains and adapt to more actual situations.

[0177] Furthermore, the process of optimizing the adjustment time and adjustment acceleration according to the objective optimization function includes:

[0178] Substituting the average superelevation, current train speed, rail width, radius of curvature at the curve position, total train mass, optimal curve speed, adjustment time expression, and adjustment acceleration expression into the target optimization function yields the expansion of the target optimization function; in the expansion of the target optimization function, only the starting adjustment position is an unknown parameter;

[0179] Differentiate the expansion of the objective optimization function with respect to the initial adjustment position, and calculate the minimum point of the expansion of the objective optimization function;

[0180] The starting adjustment position corresponding to the minimum point is taken as the optimal adjustment position;

[0181] Substituting the optimal adjustment position into the adjustment duration expression and adjustment acceleration expression, the target adjustment acceleration and target adjustment duration are calculated.

[0182] Specifically, substituting formulas (ix) and (x) into the objective optimization function, it can be derived that the value of the objective optimization function is also about the starting adjustment position. y The function. In this embodiment, the objective optimization function is about... y The function has only one minimum point. The starting adjustment position corresponding to the minimum point, as well as the corresponding adjustment duration and adjustment acceleration, represent the optimal adjustment scheme.

[0183] When the derivative of the objective function is taken as zero, y The value is the distance from the optimal adjustment position to the endpoint.

[0184] This approach is suitable for railway lines with many curves. Since only actual data needs to be substituted for calculation, the overall calculation workload is small, and the optimal adjustment position and feedback adjustment acceleration can be calculated in real time.

[0185] Furthermore, the process of optimizing the adjustment time and adjustment acceleration according to the objective optimization function includes:

[0186] The particle swarm optimization algorithm is used to optimize the adjustment time and adjustment acceleration to obtain the target adjustment acceleration and target adjustment time.

[0187] Further, refer to Figure 2 The steps for optimizing the adjustment time and adjustment acceleration using the particle swarm optimization algorithm include:

[0188] S91: Initial settings for particle swarm optimization algorithm parameters: Set the search space for adjusting duration and acceleration; Set the Nth position of multiple particles in the search space, and the Nth velocity of each particle; The initial value of N is set to 1;

[0189] S92: Based on the Nth position, obtain the Nth adjustment duration and Nth adjustment acceleration within the search space;

[0190] S93: Calculate the target optimization function for the current position of the particle based on the Nth adjustment duration and the Nth adjustment acceleration, and obtain the Nth target optimization function;

[0191] S94: Substitute the Nth position of each particle into the position update formula of the particle swarm algorithm; substitute the Nth velocity of each particle into the velocity update formula of the particle swarm algorithm to calculate the (N+1)th position and (N+1)th velocity of each particle in the Nth iteration.

[0192] S95: Judgment: When the termination condition is met, obtain the Nth adjustment duration and Nth adjustment acceleration in the search space based on the final position of the particle, and use the Nth adjustment duration and Nth adjustment acceleration as the target adjustment acceleration and the target adjustment duration; otherwise, increment the value of N by one, and repeat steps S92-S95.

[0193] Specifically, the algorithm parameters include the number of particles and the learning factor. The number of particles is set to 50-100, and the learning factor is set to 1.25. The initial positions of the particles are randomly set. In some cases, in order to quickly find the optimal result, the mean of the search space can be used as the mean of the particle distribution, and the initial positions of multiple particles are set according to a normal distribution.

[0194] Specifically, the speed update formula is represented by formula (xi);

[0195] Formula (XI);

[0196] in, N 0 represents the number of particles. i Indicates the particle number. i =1,2,..., N 0;

[0197] k Indicates the number of iterations; ω Indicates inertia weight; c 1 represents the individual learning factor. c 2 represents the group learning factor;

[0198] r 1 and r 2 represents a random number within the interval [0,1], used to increase the randomness of the search and avoid getting trapped in a local optimum;

[0199] Indicates the first i The particle in the first k The velocity vector in the next iteration;

[0200] Indicates the first i The particle in the first k The position vector in the next iteration;

[0201] Indicates the first i The particle in the first k The historical best position in the nth iteration, i.e., the position in the nth iteration. k After the nth iteration, the th i The optimal solution found by each particle;

[0202] Indicates the particle swarm in the th k The historical best position in the nth iteration, i.e., the position in the nth iteration. k The optimal solution in the entire particle swarm after the iteration.

[0203] Specifically, the position update formula is represented by formula (twelfth);

[0204] Formula (12);

[0205] in, This indicates the particle position after one iteration. Indicates the current particle position. This represents the velocity of the particles during the iteration process; Indicating that during one iteration, with The displacement of the moving particle at its speed.

[0206] Applying particle swarm optimization (PSO) can more accurately predict the optimal adjustment position, making it suitable for long railway tracks. A longer total distance provides the algorithm with more iteration time to find the optimal adjustment position. Compared to directly inputting data for calculation, the PSO approach avoids errors caused by substituting single data points, as the final optimization structure is the result of the entire particle swarm.

[0207] In some implementations, the optimal adjustment position can be calculated by directly substituting Equation (IX) and Equation (X) into Equation (I) and taking the derivative. The optimal adjustment position can then be obtained by using the particle swarm optimization algorithm. The optimal adjustment position predicted by the two methods can then be provided to the train driver for judgment. Alternatively, the results of the two predictions can be directly averaged to obtain the final optimal adjustment position, and the train speed can be automatically adjusted.

[0208] The above method can adapt to both driver-driven and autonomous driving modes, thus improving applicability.

[0209] Furthermore, the search space includes: a first interval and a second interval;

[0210] The first interval is used to represent the search range for adjustment duration; the second interval is used to represent the search range for adjustment acceleration.

[0211] The first interval is shown in formula (II);

[0212] The second interval is shown in formula (III);

[0213] Formula (II);

[0214] Formula (3);

[0215] in, t Indicates the adjustment duration. a Indicates adjustment of acceleration. S 0 represents the total length of the railway track. Indicates the length of the curve at the location of the curve. V max Indicates the train's maximum speed. T This indicates the longest time a train can travel the entire length of the railway track without delaying its scheduled departure. a max This indicates the train's maximum acceleration.

[0216] Specifically, during the iterative process of the particle swarm optimization algorithm, different particles will seek different results. If the search space is not designed properly, the final result sought by the algorithm may be unrealizable, leading to errors in the overall prediction. To ensure the feasibility of the algorithm's predictions, the specific range of the search space is particularly important.

[0217] In this embodiment, the search space includes setting the range of adjustment duration and setting the range of adjustment acceleration.

[0218] Specifically, disregarding centripetal force during cornering and considering only train performance, the train will minimize its cornering time by traveling at its maximum achievable speed through the curve. This is the ratio of the curve length at the curve location to the train's maximum speed. Under normal circumstances, the train's cornering time is greater than this.

[0219] To ensure the train arrives at its destination without delays, let's assume there's only one curve along the entire route. Except for the curve, the train travels at a lower speed, but at maximum speed throughout. In this scenario, the time spent navigating the curve is the longest possible, calculated as the maximum time the train can travel the entire track without delay, minus the time required to travel the rest of the track at maximum speed. Under normal circumstances, the time spent navigating a curve is less than this.

[0220] The acceleration setting only considers the train's possible acceleration performance, therefore the second interval is set as shown in formula (III). In this embodiment, the maximum acceleration and maximum deceleration of the train are assumed to be the same in magnitude but opposite in direction. When the maximum acceleration and maximum deceleration of the train are the same but different, it is necessary to set the acceleration direction as the positive direction, and the second interval is set to a negative value greater than or equal to the absolute value of the maximum deceleration, and less than or equal to the maximum acceleration.

[0221] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position, characterized in that, include: Get the train's current speed; Obtain the location of the next curve on the railway line and the average superelevation of the curve location; the average superelevation represents the average height difference between two sections of the railway at the curve location; Based on the current train speed, curve position, and average superelevation, construct expressions for the adjustment time and acceleration required for the train to adjust its speed from the optimal adjustment position until it reaches the curve position; the adjustment time and acceleration expressions include an unknown optimal adjustment position. The optimal adjustment position refers to the position where the vehicle speed adjustment begins when the weighted sum of the adjustment duration and the adjustment acceleration is minimized. Construct a target optimization function based on the adjustment duration expression and the adjustment acceleration expression; Based on the target optimization function, the adjustment duration and adjustment acceleration are optimized until the values ​​of the adjustment duration and the adjustment acceleration minimize the target optimization function, thereby obtaining the target adjustment acceleration and the target adjustment duration; The optimal adjustment position is calculated based on the target adjustment acceleration and the target adjustment duration. Get the train's current position on the railway track; Judgment: When the optimal adjustment position is between the current position and the curve position, wait for the train to reach the optimal adjustment position, start adjusting the train speed with the target adjustment acceleration, and continue for the target adjustment duration; When the current position is exactly at the optimal adjustment position, the train speed is directly adjusted at the target adjustment acceleration for the target adjustment duration.

2. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 1, characterized in that, When the current position is between the optimal adjustment position and the curve position, perform the following steps: Based on the current position, curve position, current speed, and average superelevation, the train speed is adjusted from the current position until it reaches the curve position, at which point the required acceleration is obtained, and the compensation acceleration is achieved. The train speed is adjusted using the aforementioned compensation acceleration until the train reaches the curve.

3. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 1, characterized in that, The process of obtaining the location of the next curve on the railway track and the average superelevation of the curve includes: Obtain a railway track database; the railway track database stores at least the locations of all curves of the railway track and the average superelevation corresponding to each curve location; Query the railway track database to obtain the locations of all curves on the railway track. Based on the train's current position and the positions of all curves, the location of the curve closest to the current position along the railway line is calculated. The average superelevation is obtained by querying the railway line database based on the location of the most recent curve.

4. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 3, characterized in that, The process of obtaining the railway track database includes: Obtain the serial numbers of multiple railway locators on the railway track; The railway track is divided into multiple track units by using all railway locators on the track; the line connecting the midpoint of each track unit to a railway locator is perpendicular to the direction of the railway track's extension; the length of each track unit is equal to the distance between adjacent railway locators. The numbers of the railway locators are matched one-to-one with the numbers of the track units and the railway locators whose lines are perpendicular to the extension direction of the track. Equal intervals are sampled within the line unit to measure the superelevation value of multiple sampling points within the line unit; The average superelevation of the line unit is calculated by averaging multiple superelevation values. Each corresponding track unit, the number of the railway locator corresponding to the track unit, and the average superelevation of the track unit are saved to the database to obtain the railway track database.

5. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 1, characterized in that, Based on the current train speed, curve position, and average superelevation, the process of constructing expressions for the required adjustment time and acceleration of the train from the optimal adjustment position until it reaches the curve position includes: Obtain the rail width, the radius of curvature at the curve location, and the total mass of the train; The optimal cornering speed is calculated based on the rail width, average superelevation, radius of curvature, and total train mass. The optimal cornering speed represents the centripetal force required for the train to corner, which is the resultant force obtained by the vector superposition of the train's weight and the rail's supporting force on the train. Set the starting adjustment position to an unknown parameter; The adjustment distance expression from the starting adjustment position to the curve position is calculated based on the starting adjustment position and the curve position; the starting adjustment position is an unknown parameter in the adjustment distance expression. Based on the optimal cornering speed, current vehicle speed, and adjustment distance expression, the adjustment duration expression is constructed; in the adjustment duration expression, the start adjustment position and adjustment duration are unknown parameters. Based on the optimal cornering speed, the current vehicle speed, and the adjustment duration, an adjustment acceleration expression is constructed; in the adjustment acceleration expression, the start adjustment position, the adjustment duration, and the adjustment acceleration are unknown parameters.

6. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 5, characterized in that, The objective optimization function represents the weighted sum of the adjustment time and the adjustment acceleration; the objective optimization function is expressed by formula (I); Formula (1); in, f Denotes the objective optimization function. w 1 and w 2 represents weight. Indicates the adjustment duration. a Indicates adjustment of acceleration. It represents the absolute value.

7. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 6, characterized in that, The process of optimizing the adjustment time and adjustment acceleration according to the objective optimization function includes: Substituting the average superelevation, current train speed, rail width, radius of curvature at the curve position, total train mass, optimal curve speed, adjustment time expression, and adjustment acceleration expression into the target optimization function yields the expansion of the target optimization function; in the expansion of the target optimization function, only the starting adjustment position is an unknown parameter; Differentiate the expansion of the objective optimization function with respect to the initial adjustment position, and calculate the minimum point of the expansion of the objective optimization function; The starting adjustment position corresponding to the minimum point is taken as the optimal adjustment position; Substituting the optimal adjustment position into the adjustment duration expression and adjustment acceleration expression, the target adjustment acceleration and target adjustment duration are calculated.

8. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 1, characterized in that, The process of optimizing the adjustment time and adjustment acceleration according to the objective optimization function includes: The particle swarm optimization algorithm is used to optimize the adjustment time and adjustment acceleration to obtain the target adjustment acceleration and target adjustment time.

9. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 8, characterized in that, The steps for optimizing the adjustment time and adjustment acceleration using the particle swarm optimization algorithm include: S91: Initial settings for particle swarm optimization algorithm parameters: Set the search space for adjusting duration and acceleration; Set the Nth position of multiple particles in the search space, and the Nth velocity of each particle; The initial value of N is set to 1; S92: Based on the Nth position, obtain the Nth adjustment duration and Nth adjustment acceleration within the search space; S93: Calculate the target optimization function for the current position of the particle based on the Nth adjustment duration and the Nth adjustment acceleration, and obtain the Nth target optimization function; S94: Substitute the Nth position of each particle into the position update formula of the particle swarm algorithm; substitute the Nth velocity of each particle into the velocity update formula of the particle swarm algorithm to calculate the (N+1)th position and (N+1)th velocity of each particle in the Nth iteration. S95: Judgment: When the termination condition is met, obtain the Nth adjustment duration and Nth adjustment acceleration in the search space based on the final position of the particle, and use the Nth adjustment duration and Nth adjustment acceleration as the target adjustment acceleration and the target adjustment duration; otherwise, increment the value of N by one, and repeat steps S92-S95.

10. The method for predicting the optimal adjustment position of a train when cornering based on the average superelevation of the curve position according to claim 9, characterized in that, The search space includes: a first interval and a second interval; The first interval is used to represent the search range for adjustment duration; the second interval is used to represent the search range for adjustment acceleration. The first interval is shown in formula (II); The second interval is shown in formula (III); Formula (II); Formula (3); in, t Indicates the adjustment duration. a Indicates adjustment of acceleration. S 0 represents the total length of the railway track. Indicates the length of the curve at the location of the curve. V max Indicates the train's maximum speed. T This indicates the longest time a train can travel the entire length of the railway track without delaying its scheduled departure. a max This indicates the train's maximum acceleration.

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