CN113536531A - Train operation risk prediction method based on mutation theory - Google Patents

Train operation risk prediction method based on mutation theory Download PDF

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CN113536531A
CN113536531A CN202110603244.9A CN202110603244A CN113536531A CN 113536531 A CN113536531 A CN 113536531A CN 202110603244 A CN202110603244 A CN 202110603244A CN 113536531 A CN113536531 A CN 113536531A
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CN113536531B (en
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刘学文
张文静
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Shanghai University of Engineering Science
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Abstract

The invention belongs to the technical field of rail transit safe operation, and discloses a train operation risk prediction method based on a mutation theory, which is applied to a train running on a curve section track, wherein a point mutation model is established by taking transverse offset, transverse vibration acceleration and a train body gravity center deflection angle which are suffered by the train in operation as influence parameters, and the point mutation model is analyzed to obtain a value range of the influence parameters, so that the operation state of the train is predicted, dangerous accidents such as derailment and the like of the train are avoided, and the safe operation of the train is ensured. The method provides data basis for platform staff to control the safe operation of the train, and plays an important role in improving the management level of the large passenger flow in the train station and ensuring the safety of the passengers in trip.

Description

Train operation risk prediction method based on mutation theory
Technical Field
The invention belongs to the technical field of rail transit safe operation, and particularly relates to a train operation risk prediction method based on a mutation theory.
Background
The problem of derailment of vehicles is always troubling people and is a main research subject of expert and scholars for over a hundred years. The operation safety of vehicles is related to the life and property safety of people of all countries, and attention must be paid. Two methods, namely a Nadal derailment coefficient and a wheel load shedding rate, are mostly adopted in the standard for judging vehicle derailment at home and abroad, for example, Wangjing and the like research on the influence of the transverse shift of the gravity center of goods on the curve passing by a train, and the larger the transverse shift of the gravity center can be judged according to the derailment coefficient and the wheel load shedding rate, the more dangerous the vehicle is; zhang Mo Yan and the like establish a train-rail dynamic model to study the influence of a small-radius curve section wheel polygon on the safety of a train, and analyze the change of a derailment coefficient and a wheel load shedding rate under the action of different wave depths and orders; wei and the like carry out stress analysis on the wheel pairs to deduce an expression of lateral force of a wheel axle and vertical force of a wheel rail, and the running safety of the train is comprehensively judged by adopting two methods of derailment coefficient and load shedding rate; wangkang mainly uses parameters such as derailment coefficient, wheel load shedding rate and the like as evaluation indexes to analyze the influence of transverse wind on the safe running of a high-speed train at a curve; cheng et al, established a railway vehicle model, and compared the effects of suspension system parameters, different wheel tapers and nominal rolling radii on derailment coefficients, load shedding ratios, compliance indicators, and the like by analysis.
Most of the train derailment judgment criteria adopted in the articles are derailment coefficient and wheel load shedding rate judgment methods, but when the criteria are used for evaluation, researchers find that the derailment coefficient and the wheel load shedding rate of the train are not larger than the safety value of the existing judgment criteria when the actual vehicle is derailed; on the contrary, when the numerical values of the derailment coefficient and the wheel load shedding rate are far larger than the critical values, the train is unlikely to derail, so that the traditional criterion for judging the derailment of the vehicle can not accurately warn the running state of the train under certain conditions, and the accuracy is poor. Therefore, a new evaluation method needs to be considered to research the operation safety problem of the train.
Disclosure of Invention
The invention provides a train operation risk prediction method based on a mutation theory, and solves the problems that the traditional criterion for judging the derailment of a train cannot accurately early warn the operation state of the train under certain conditions, the accuracy is poor and the like.
The invention can be realized by the following technical scheme:
a train operation risk prediction method based on a mutation theory is applied to a train running on a curve section track, a sharp point mutation model is established by taking transverse offset, transverse vibration acceleration and a train body gravity center deflection angle which are suffered by the train in the running process as influence parameters, the sharp point mutation model is analyzed, and a value range of the influence parameters is obtained, so that the running state of the train is predicted, and the safe running of the train is ensured.
Further, by carrying out stress analysis on the running train, according to the principle of the total potential energy invariable value of the elastic system and the moment balance principle, a functional relation equation between the transverse offset, the transverse vibration acceleration and the gravity center deflection angle of the train body when the train derails on the curve section track is obtained, namely the function equation of the sudden change potential of the train derail is obtained, and thus the sharp point sudden change model is established.
Further, obtaining corresponding bifurcation set functions according to the cusp mutation model, setting the bifurcation set functions as functional relation equations between the lateral offset and the lateral vibration acceleration and the gravity center deflection angle of the vehicle body respectively, obtaining the value ranges of the lateral offset and the lateral vibration acceleration by combining the bifurcation set functions through analyzing the cusp mutation model, and obtaining the value ranges of the gravity center deflection angle of the vehicle body by combining the functions corresponding to the cusp mutation model.
Further, the function corresponding to the cusp mutation model is set as
Figure BDA0003093591310000021
Wherein M iscThe total weight of the train, i is the half length of the axle of the train, H is the height of the gravity center of the train body, and H iswThe height of the wind force action point from the rail surface is defined as a, the transverse vibration acceleration of the gravity center of the train body is defined as a, the transverse offset of the gravity center of the train body is defined as y, and FwIs the wind power, P1、P2Is the vertical force of the wheel track of the train, alpha is the gravity center deflection angle of the train body of the train,v is the running speed of the train, and R is the radius of the track curve;
corresponding bifurcation set function set to
Figure BDA0003093591310000031
In the form of its decomposition
Figure BDA0003093591310000032
The beneficial technical effects of the invention are as follows:
by carrying out stress analysis on a train running on a curve section track, selecting transverse offset of the gravity center of the train body and transverse vibration acceleration of the gravity center of the train body as control variables, and selecting a gravity center deflection angle of the train body as a state variable, taking the state variable as an influence parameter, obtaining a sudden change potential function equation according to a total potential energy invariant value principle and a moment balance principle of an elastic system, establishing a sharp point sudden change model, explaining a derailment mechanism of the train and giving a dangerous area for running of the train, and therefore, the train can always keep safe and stable running as long as the value range of the influence parameter is ensured to be within a safe value. The application of the mutation theory in the vehicle derailment assessment provides a new theoretical idea for the research of the vehicle derailment mechanism, has certain guiding significance, provides data basis for platform workers to control the safe operation of the train, and has important effects on improving the management level of subway station passenger flow and guaranteeing the safety of passenger travel.
Drawings
FIG. 1 is a schematic overview of the process of the present invention;
FIG. 2 is a schematic view of the force analysis of the present invention during a derailment of a train operating on a curved section of track;
FIG. 3 is a schematic diagram of a point jump model during train derailment according to the present invention;
FIG. 4 is a schematic diagram of a bifurcation set corresponding to a sharp point mutation model for train derailment according to the present invention;
FIG. 5 is a schematic illustration of a simulation model of a model C64k train in accordance with the present invention;
FIG. 6 is a schematic diagram showing the variation of lateral offset and lateral vibration acceleration of the vehicle body under different track irregularity excitations according to the present invention;
FIG. 7 is a graph showing simulation graphs under American class six rail irregularity excitation, including lateral vibration acceleration and change of gravity center deflection angle with lateral offset, according to the present invention.
Detailed Description
The following detailed description of the preferred embodiments will be made with reference to the accompanying drawings.
The mutation theory is proposed by French mathematician Ren Thom, and is mainly used for researching the phenomenon of sudden change of a dynamic system in the continuous development process, explaining the reason of the sudden change, explaining the interrelation among all influencing factors and finding out the change rule. The mutation theory is about singularity (critical point), and the phenomenon and the law presented when a thing undergoes mutation are explained through the established system potential function equation. Whether the system has mutation or not is mainly determined by the fact that the potential function has a plurality of extreme points, and when the number of the extreme points is large, the system has mutation. The catastrophe model has five basic features, snap, unreachability, multi-modal, hysteresis, and divergence.
The phenomenon of mutation is ubiquitous in nature, and a sudden change in the state or property of any one thing is a mutation, and the change is completed in a moment, but before the moment, the continuous change of each factor in the system is the key point for causing the mutation. Therefore, the research on the change rule of the influencing factors is the foundation of mutation theory and is the main entry point for explaining the mutation phenomenon.
When a train runs on an actual curve road, the vehicle-track system is in a dynamic balance state, and when the train encounters severe external environment interference or poor road condition and begins to derail until the train completely derails, the system state is suddenly changed. Therefore, the invention utilizes the basic characteristics of the mutation theory to research the mutation phenomenon in the train running process, explains the train derailment mechanism according to the characteristic parameters, provides the safe running area of the train and provides a guarantee and early warning method for the safe running of the train.
As shown in figure 1, the invention provides a train operation risk prediction method based on a mutation theory, which is applied to a train running on a curve section track, a sharp point mutation model is established by taking transverse offset, transverse vibration acceleration and a train body gravity center deflection angle which are suffered by the train in the running process as influence parameters, the sharp point mutation model is analyzed, and a value range of the influence parameters is obtained, so that the train is prevented from derailing, and the safe running of the train is ensured. The method comprises the following specific steps:
first, selecting the influencing parameter
By analyzing the stress of the vehicle running on the track, as shown in fig. 2, the train is subjected to the combined action of a plurality of forces when running on a curved road and has a certain gravity center offset. Under normal conditions, the forces are mutually balanced to achieve a balanced state so as to ensure the stable and safe running of the vehicle. However, when the vehicle is influenced by other factors and the center of gravity offset of the vehicle body exceeds a reasonable range, the center of gravity of the whole vehicle is deviated to the inner side of a curve, and under the condition, when the action direction of the transverse inertia force of the vehicle body is consistent with the center of gravity offset direction, the whole vehicle can incline to the inner side more under the action of transverse vibration acceleration, and at the moment, the train is likely to be separated from a track, so that serious accidents occur. In order to avoid the derailment phenomenon, considering state parameters and control variables influencing the running safety of the vehicle, the invention determines and selects three influencing parameters of transverse offset, transverse vibration acceleration and gravity center deflection angle of the vehicle body to research the running safety of the train on the curve section track.
Secondly, establishing a cusp mutation model
By combining a sudden change theory, a stress analysis is carried out on a running train, and a functional relation equation between the transverse offset, the transverse vibration acceleration and the gravity center deflection angle of the train body when the train derails on a curve section track is obtained according to the principle of the total potential energy constant value of the elastic system and the moment balance principle, namely the sudden change potential function equation of the train derailing, so that a sharp point sudden change model is established.
The following assumptions are made for the mechanical modeling of a train traveling on a curved section of track:
(1) the change of the vertical position of the gravity center of the vehicle body is not considered;
(2) neglecting the vertical inertia force on the vehicle;
(3) neglecting the unsprung mass of the train;
(4) neglecting the transverse inertial force of the unsprung mass;
(5) neglecting the wind force on the unsprung portion.
The force analysis of the derailed vehicle on the curve is shown in fig. 2, and the vehicle is acted by a plurality of forces such as gravity, transverse inertia force, wind force, centrifugal force and the like, wherein M iscThe total weight of the train, i is the half length of the axle of the train, H is the height of the gravity center of the train body, and H iswThe height of the wind force action point from the rail surface is defined as a, the transverse vibration acceleration of the gravity center of the train body is defined as a, the transverse offset of the gravity center of the train body is defined as y, and FwIs the wind power, P1、P2The vertical force of the wheel track of the train is shown, alpha is the gravity center deflection angle of the train body of the train, v is the running speed of the train, and R is the radius of a track curve.
From fig. 2, the sum of the lateral forces experienced by the train when derailing on the curve is:
Figure BDA0003093591310000061
the potential energy sum of the transverse force obtained according to the principle of the total potential energy invariable value of the elastic system and the moment balance principle is as follows:
Figure BDA0003093591310000062
Figure BDA0003093591310000063
transforming equation (3) can obtain:
Figure BDA0003093591310000064
substituting equation (4) into equation (2) yields:
Figure BDA0003093591310000065
considering that the equivalence is infinitesimally small, equation (5) can be simplified to:
Figure BDA0003093591310000066
the potential function equation of the train derailing at the curve can be obtained as follows:
Figure BDA0003093591310000067
the expression of the balance surface M according to equation (7) is:
Figure BDA0003093591310000068
the equation for solving the biorder derivative singularity set S for equation (7) is:
Figure BDA0003093591310000069
simultaneous formulas (8) and (9):
Figure BDA0003093591310000071
the expression of α is:
Figure BDA0003093591310000072
substituting equation (10) into (9) reduces the equation into a bifurcation set as:
Figure BDA0003093591310000073
writing equation (11) in decomposed form is as follows:
Figure BDA0003093591310000074
thirdly, analyzing the cusp mutation model
And obtaining corresponding bifurcation set functions according to the sharp point mutation model, wherein the bifurcation set functions are set as functional relation equations between the lateral offset and the lateral vibration acceleration and the gravity center deflection angle of the train body respectively, obtaining the value ranges of the lateral offset and the lateral vibration acceleration by combining the bifurcation set functions through analyzing the sharp point mutation model, and obtaining the value range of the gravity center deflection angle of the train body by combining the functions corresponding to the sharp point mutation model, so that the safe operation of the train can be ensured as long as the related influence parameters of the train are controlled within the corresponding value ranges.
The application of the abrupt change model in the train operation safety early warning is described in detail below by taking the example of establishing the abrupt change model for the train which operates on the curve section track with the radius of 1200 m.
The C64k train is selected, and the main technical parameters are as follows:
Figure BDA0003093591310000075
Figure BDA0003093591310000081
substituting the parameters into the formula (7) to obtain a potential function equation of the train with sudden change at the curve, wherein the potential function equation is as follows:
Figure BDA0003093591310000082
the expression of the balance surface M is:
Figure BDA0003093591310000083
the equation for the singularity set S is:
V″＝202500α2-145800a (15)
simultaneous equations (14) and (15),
Figure BDA0003093591310000084
the expression of α is:
Figure BDA0003093591310000085
substituting equation (16) into equation (15) and simplifying into a bifurcation set equation:
Figure BDA0003093591310000086
writing equation (17) in decomposed form is as follows:
Figure BDA0003093591310000087
from the equations (14) and (18), a sharp point abrupt model map and a bifurcation set of train derailment at a curve track radius of 1200m can be constructed, as shown in fig. 3 and 4.
FIG. 3 shows the process of the train having a sudden change of state on a curve, wherein the curved surface in the three-dimensional space represents the balance curved surface of the vehicle system during the operation, the vertical coordinate is the gravity center deflection angle of the train body for estimating the operation state of the train, and the change range is-2 rad; the curve on the control space is a bifurcation set, represents the value range of the transverse offset of the gravity center of the train body and the transverse vibration acceleration at the middle lobe fold, and provides the conditions for the occurrence of the train derailment accident. As can be seen from fig. 3, the upper and lower lobes of the balance curve are smooth and flat, which indicates that the vehicle system is in a stable state within the range of the upper and lower lobes; and a fold curved surface exists at the middle leaf, which indicates that the system has sudden jump and is unstable, and the value range of the gravity center deflection angle is-1 rad. According to the sudden change theory, when the lateral offset of the gravity center of the vehicle body and the vibration acceleration are taken as values outside the bifurcation set, only one point is arranged on the corresponding balance curved surface, namely, the potential function has only one extreme value; when the control variable changes in the bifurcation cluster area, two points exist on the corresponding balance curved surface, namely the potential function has two extreme values, and the two extreme values are mutually dragged to finally cause the state of the system to change suddenly, namely the deflection angle changes suddenly. Therefore, the fold part on the balance curved surface corresponds to the unstable state of the system, namely when the control variables (the lateral offset and the lateral acceleration of the gravity center of the train body) in the vehicle system fall into the bifurcation set, the on-track running state of the train is changed due to the sudden change of the state variables (the deflection angle of the gravity center of the train body) of the system, and the train is separated from the track in serious cases to cause accidents. The train derails, which is the most dangerous process in train operation and needs to be avoided, is changed from a stable operation state to another stable equilibrium state after derailment.
In the running process of a train on a curve, the phenomenon that the gravity center deflection angle of the train body changes suddenly under the action of the lateral offset and the lateral vibration acceleration of the gravity center of the train body can be theoretically explained by a sharp point sudden change model in a sudden change theory. The running state of the train is represented by points on a three-dimensional space, the points form a balance curved surface, and when the train runs stably on a curved road, the points fall on an upper lobe; when the vehicle reaches a stable state after derailment, the points all fall on the lower leaves; when the point gradually moves to the edge of the upper and lower lobes, the point in the space directly crosses the unstable state of the middle lobe and then jumps to another stable equilibrium position due to the unreachable characteristic of the abrupt change, which indicates that the running state of the vehicle system is abrupt.
As can be seen from fig. 3 and 4, when the value of the lateral offset is less than zero, it indicates that the train changes from the jump-jump state to the stable operation state; when the value of the transverse offset is larger than zero, the change of the train from the stable operation to the derailment state is represented. Analyzing fig. 3, the state of the vehicle after derailment corresponds to the lower lobe of the curved surface, and the value of the control variable at this time falls in the area above the right curve of the bifurcation set on the control space, so that the area is a dangerous area where the vehicle may derail. If the running state of the train is suddenly changed under the action of the transverse offset and the transverse acceleration of the gravity center of the train body to cause derailment accidents, the sudden change is a harmful sudden change, so that the phenomenon is avoided as much as possible, namely the condition that the value range of the transverse offset and the transverse vibration acceleration of the gravity center of the train body exceeds the right curve of the bifurcation set is avoided.
As can be seen from the bifurcation cluster graph, the possibility of train derailment is increased along with the increase of the lateral offset and the lateral acceleration of the gravity center of the train body. In the right part of the bifurcation set, when the offset is 0 m-0.25 m, the running safety of the train is influenced by the lateral vibration acceleration, if the phase point falls in the right side area, the system is suddenly changed, but the vehicle can not derail, and if the phase point falls out of the area, the possibility of the vehicle derailing is increased. When the offset continues to increase and is greater than 0.25m, the train can break away from the track, and an accident occurs. Therefore, the transverse offset of the gravity center of the train body is reduced, the possibility of train derailment can be reduced, and the train derailment accident can be effectively prevented. In the left area of the bifurcation set, the train jumps on the rail surface under the action of the control variable and the control variable to run for a period of time and then falls back to the rail to enter the stable running state again, and during the period, the wheel pair does not break away from the rail although the wheel pair jumps suddenly, so the sudden change is beneficial.
Fourth, simulation verification
According to the technical parameters of the C64k type train and partial assumption in simulation modeling, a vehicle system simulation model shown in 5 is established, the running condition of the vehicle is set, and track irregularity excitation is applied to verify the accuracy of the simulation model.
In order to better illustrate the accuracy of the simulation model, the invention considers the change conditions of the transverse vibration acceleration, the vertical vibration acceleration, the stability index and the derailment coefficient of the vehicle body under the actions of the American five-level rail irregularity excitation, the American six-level rail irregularity excitation and the German rail irregularity excitation, and contrasts and analyzes the running states of the vehicle under different rail excitations.
TABLE 1 vehicle simulation model verification data
Figure BDA0003093591310000101
Comparing the values obtained by simulation in the table 1 with the specific parameters in the evaluation and test identification Specification for the dynamics performance of the locomotive vehicle (GB/T5599-2019) in the tables 2-4, the vehicle model simulation verification results established by the SIMPACK are all within the range of national standard requirements, so that the accuracy of the established model can be demonstrated.
TABLE 2 evaluation criteria for vehicle vibration acceleration
Figure BDA0003093591310000111
TABLE 3 evaluation criteria for vehicle smoothness
Figure BDA0003093591310000112
TABLE 4 derailment coefficient evaluation criteria
Figure BDA0003093591310000113
Therefore, through the established vehicle simulation model, the vehicle system safety under three different working conditions (no excitation, American six-grade rail irregularity excitation and Germany rail irregularity excitation) is analyzed by considering the changes of the transverse vibration acceleration and the gravity center deflection angle of the train under different gravity center transverse offsets of the train. Will simulate to obtainThe data of the road condition data and the mutation model bifurcation set are compared, the feasibility of the application of the mutation theory in the vehicle running safety is judged in two directions according to the derailment coefficient, and the intersection point coordinates of the simulation data and the mutation theory bifurcation set on the right side curve under the three road conditions can be obtained according to the graph 6 and the table 5. When no track excitation, the intersection point is y equal to 0.17m and a equal to 0.616m/s2Only when the value of the transverse offset is larger than 0.17m, the vehicle is possibly dangerous, and the derailment coefficient is 1.224; the lower intersection point of the American six-grade track irregularity excitation is y equal to 0.16m and a equal to 0.586m/s2The derailment coefficient is 1.08, the German irregularity excitation lower intersection point is y equal to 0.16m, and a equal to 0.593m/s2The derailment coefficient is 1.332, and when the lateral offset is larger than 0.16m, the probability of the derailment of the train is increased.
TABLE 5 parameter values of theoretical and simulation data at critical points under three conditions
Figure BDA0003093591310000121
The simulation of FIG. 7 shows the variation pattern of lateral vibration acceleration and gravity center deflection angle with lateral offset under the U.S. six-stage track irregularity excitation. As can be seen from FIG. 7, the maximum value of the lateral vibration acceleration is 1.15m/s at different lateral offsets2And the variation range is not large, and the gravity center deflection angle of the vehicle body is increased along with the increase of the lateral offset. As can be seen from FIGS. 7(b) and (c), when the lateral offset is increased from 0.15m to 0.16m, the maximum body center of gravity deflection angle is from 3.52X 10 at 0.4s-3rad suddenly changed to 8.21X 10-3rad, at this time, the yaw angle is increased by more than 2 times as much as the original angle, and therefore, it is known that when the offset amount is 0.16m, the state of the vehicle system may suddenly change. Thereafter, as the lateral offset continues to increase, the maximum body center of gravity deflection angle remains 8.96 × 10-3Near rad, much greater than 3.52X 10-3rad。
As can be seen from fig. 6 and table 5, the simulation data and the theoretical model intersect at the critical point, and values of the lateral offset and the lateral vibration acceleration of the center of gravity of the vehicle body under different line conditions are shown in table 5. At the critical point, the magnitude of the derailment coefficient is also greater than the second limit of 1.0 specified in the locomotive vehicle dynamics performance assessment and test identification Specification (GB/T5599-2019). With reference to fig. 7, under excitation of the american track spectrum, when the lateral offset is 0.16m, the gravity center deflection angle of the train body changes abruptly, so that it can be determined that the values of the lateral offset and the lateral vibration acceleration of the gravity center of the train body at the critical point are parameter values that enable the train to be in a critical state, and thus it can be demonstrated that the operation safety of the train can be determined according to the selected parameters, i.e., the feasibility and the accuracy of the application of the abrupt change theory on the train operation safety evaluation are verified.
Although specific embodiments of the present invention have been described above, it will be appreciated by those skilled in the art that these are merely examples and that many variations or modifications may be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is therefore defined by the appended claims.

Claims (4)

1. A train operation risk prediction method based on a mutation theory is characterized by comprising the following steps: the method is applied to the train running on the curve section track, a sharp point mutation model is established by taking the transverse offset, the transverse vibration acceleration and the gravity center deflection angle of the train body, which are suffered by the train in the running process, as influence parameters, the sharp point mutation model is analyzed, and the value range of the influence parameters is obtained, so that the running state of the train is predicted, and the safe running of the train is ensured.
2. The train operation risk prediction method based on the mutation theory as claimed in claim 1, wherein: by carrying out stress analysis on a running train, and according to the principle of the total potential energy invariable value of an elastic system and the moment balance principle, a functional relation equation between the transverse offset, the transverse vibration acceleration and the gravity center deflection angle of a train body when the train derails on a curve section track is obtained, namely the function equation of the sudden change potential of the train derail is obtained, and thus a sharp point sudden change model is established.
3. The train operation risk prediction method based on the mutation theory as claimed in claim 2, wherein: and obtaining corresponding bifurcation set functions according to the cusp mutation model, wherein the bifurcation set functions are set as functional relation equations between the lateral offset and the lateral vibration acceleration and the gravity center deflection angle of the vehicle body respectively, obtaining the value ranges of the lateral offset and the lateral vibration acceleration by combining the bifurcation set functions through analyzing the cusp mutation model, and obtaining the value ranges of the gravity center deflection angle of the vehicle body by combining the functions corresponding to the cusp mutation model.
4. The train operation risk prediction method based on the mutation theory as claimed in claim 2, wherein: the function corresponding to the cusp mutation model is set as
Figure FDA0003093591300000011
Wherein M iscThe total weight of the train, i is the half length of the axle of the train, H is the height of the gravity center of the train body, and H iswThe height of the wind force action point from the rail surface is defined as a, the transverse vibration acceleration of the gravity center of the train body is defined as a, the transverse offset of the gravity center of the train body is defined as y, and FwIs the wind power, P1、P2The method comprises the following steps of (1) taking a wheel track vertical force of a train, wherein alpha is a gravity center deflection angle of a train body of the train, v is a running speed of the train, and R is a radius of a track curve;
corresponding bifurcation set function set to
Figure FDA0003093591300000012
In the form of its decomposition
Figure FDA0003093591300000021
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