CN107679265B - Train emergency braking modeling and model identification method - Google Patents
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Abstract
The invention discloses a method for modeling and identifying a train emergency brake, which comprises the following steps: analyzing the relationship among braking force, resistance, speed and acceleration in the emergency braking process of the train; discretizing the state according to Newton second theorem, and establishing a parameterized emergency braking model of the train; constructing a mathematical expectation of train conditions based on a maximum expectation identification algorithm, and maximizing the mathematical expectation of conditions; and obtaining the optimal estimated value of the emergency braking parameter by adopting a gradient optimization method. Experimental results show that the train emergency braking model established by the method disclosed by the invention is more suitable for the actual running environment of the train, and the braking model is high in identification speed and high in accuracy.
Description
Technical Field
The invention belongs to the technical field of rail transit operation safety, and relates to a train emergency braking modeling and model identification method.
Background
The train has become a green vehicle preferentially developed in China due to various advantages such as strong transportation capacity, high running speed, little environmental pollution, high economic benefit and the like. With the development of economy and the vigorous increase of riding demands of people, the operation speed of trains is improved, and a plurality of safety problems are caused. Therefore, basic research on trains is crucial.
The safe running process of the train consists of a plurality of parts, namely a train traction process, a train inertia process and a train braking process. The traction process consists of a starting process and an accelerating process, and the braking process comprises a service brake which comprehensively acts in a plurality of braking modes and a train emergency brake which mainly comprises pure air brake. As an important component in the train running process, the traction process has already been researched more maturely, and an accurate train running traction model is established. However, the braking process is another important part of the safe operation of the train, and the research on the braking process is not deep enough, and various problems occurring in the braking process still need to be solved. The emergency braking is one of the most critical devices in a train braking system, and is the last barrier for ensuring the safe and stable operation of a train when a major fault or an accident condition affecting the safety occurs in the train operation process, so that effective modeling and identification of braking parameters in the train emergency braking process are particularly important.
Disclosure of Invention
The invention aims to provide a method for modeling and identifying a model for train emergency braking, which solves the problems of inaccurate modeling and low model identification effect precision in the process of train emergency braking in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for modeling and identifying a train emergency brake comprises the following steps:
step 1: train braking force analysis: the train braking force is the force which is generated by a braking device arranged on a train body and used for decelerating and stopping the train, friction braking is used as a main device for emergency braking of the train, the main realization mode of the friction braking is that air pressure is generated through a brake cylinder, then the air pressure is effectively acted on a brake pad of the train body through various transmission modes, and the brake pad and a brake disc of the train generate effective friction, so that the train braking force for decelerating and stopping the train is generated, when the train is in an emergency braking state, the maximum air pressure is acted on the brake pad by a train brake cylinder, the maximum braking force is generated, and the train is stopped in the shortest time;
braking force B generated by each brake pad of the disc brake:
in the formula dzBrake cylinder diameter (mm); pzFor brake cylinder air pressure (kPa); ηzCalculating a transmission efficiency for the foundation braking device; gamma rayzThe brake multiplying power; r iszBrake disc friction radius (mm); rcVehicle wheel diameter (mm); mu is a friction coefficient; n is the total number of the vehicle brake pads;
step 2: train basic resistance analysis: the basic resistance W of the train exists under any working condition of the train, and the size of the basic resistance is related to a plurality of factors, including the structure and the technical state of the train, the axle weight, the line condition, the climate condition and the running speed of the train; the basic resistance of the train adopts the following formula:
W＝M·(c0+c1·v+c2·v2)·g·10-3
wherein M is the train weight, c0，c1，c2Is train resistance coefficient, v is train running speed (km/h), g is gravity acceleration 9.8m/s2；
And step 3: train additional resistance analysis: when the train passes through some special roads, including ramps, curves, tunnelsThe extra resistance is called train additional resistance I, and the common additional resistance is ramp additional resistance omegaiCurve additional resistance omegarAdditional resistance omega of tunnelsFully consider multiple additional resistance, make the train model of establishing more press close to the actual running state of train, the train additional resistance is promptly:
I＝M·(ωi+ωr+ωs)·g·10-3
wherein M is the train weight, omegai，ωr，ωsRespectively unit ramp additional resistance, unit curve additional resistance and unit tunnel additional resistance;
and 4, step 4: the resultant force applied to the train is as follows: f ═ B + W + I;
and 5: according to Newton's second theorem, the deceleration a of the train braking process is calculated as follows:
step 6: discretizing the speed v and the displacement S to obtain a difference form:
vt+1＝vt-3.6·a·T
in the formula vtIs the velocity value (m/S) at time t, StDisplacement value (m) at time t; t is a sampling interval(s);
and 7: establishing a space model of an emergency braking state of the high-speed train:
yt＝[1 0]xt+et
in the formula xtIs a 2-dimensional vector, the first dimension represents the braking distance, the other dimension represents the braking speed, ytAn observed value representing the time t of the train, namely:
wtrepresenting the interference of the complexity of the running environment of the train on the displacement and speed of the train during the emergency braking of the train, etRepresenting errors in the train displacement measurement; in order to enable the train emergency braking model established by the invention to be closer to the actual running state of the train, wtAnd etAre all set to non-Gaussian noise, wtAnd etThe specific distribution of the system is determined according to the running condition of the train;
and 8: observing and recording train output displacement vector sequence YN＝{y1,…,yNAnd setting a parameter vector theta to be estimated as [ P ═ P }z,ηz,γz,μ]T；
And step 9: due to train state XNContains an unobservable braking parameter vector, so that a state sequence X consisting of train displacement and speed is formedN＝{x1,…,xNConsider the data as not fully measurable, calculate XNAnd YNCombined logarithmic probability density function L of all data of compositionθ(XN,YN)：
In the formula pθ(Ω | Δ) represents the probability density of the random vector Ω in the case of Δ when the braking parameter of the train is θ, and is obtained according to the markov property of the model;
step 10: setting the parameter estimation value of the current train as thetakCalculating Lθ(XN,YN) Desired value of Q (theta )k) Analytic solution of (2):
Q(θ,θk)＝I1+I2+I3
step 11: computing Q (theta ) using particle filtering and particle smoothingk) Numerical solution of (a):
Q(θ,θk)＝I1+I2+I3
in the formula (I), the compound is shown in the specification,
represents the filtered weight of the ith particle at time t,
indicating all output sequences Y of trainNConditioned particles
The smoothing weight of (2);
step 12: calculating conditional mathematical expectation using a gradient optimization method
The maximum parameter vector estimation value theta;
step 13: if the estimated value of the parameter meets the precision requirement, stopping the algorithm and outputting the parameter; otherwise, returning to step 11 to continue iterative computation.
The invention has the beneficial effects that: aiming at the actual dynamic behavior of the train in the emergency braking process, a parameterized train emergency braking model is established by analyzing the train emergency braking mechanism, and the train emergency braking parameters are identified based on the maximum expectation algorithm (EM), so that the identification result is high in precision, high in convergence speed, strong in transportability and high in practicability and feasibility.
Drawings
FIG. 1 is a flow chart of a high-speed train emergency brake modeling and model identification method of the invention;
FIG. 2 is a diagram of the transmission efficiency recognition results obtained by the method of the present invention.
FIG. 3 is a diagram of the air pressure identification result of the brake cylinder obtained by the method of the present invention.
FIG. 4 is a diagram of the brake multiplying power recognition result obtained by the method of the present invention.
FIG. 5 is a graph of the coefficient of friction identification results obtained by the method of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A train emergency brake modeling and model identification method comprises the following steps: analyzing the relationship among braking force, resistance, speed and acceleration in the emergency braking process of the train; discretizing the state according to Newton second theorem, and establishing a parameterized emergency braking model of the train; constructing a mathematical expectation of train conditions based on a maximum expectation identification algorithm, and maximizing the mathematical expectation of conditions; and obtaining the optimal estimated value of the emergency braking parameter by adopting a gradient optimization method. The method is implemented according to the following steps:
step 1: train braking force analysis: the train braking force is a force generated by a braking device mounted on a train body to decelerate and stop the train; the invention adopts friction braking as a main device for emergency braking of a train, and the main realization mode of the friction braking is to generate air pressure through a brake cylinder, then the air pressure is effectively acted on a brake pad of a train body through various transmission modes, and the brake pad and a brake disc of the train generate effective friction, so that train braking force for decelerating and stopping the train is generated. When the train is in an emergency braking state, the train brake cylinder can apply the maximum air pressure to the brake pad to generate the maximum braking force, so that the train is stopped in the shortest time.
Braking force B generated by each brake pad of the disc brake:
in the formula dzBrake cylinder diameter (mm); pzFor brake cylinder air pressure (kPa); ηzCalculating a transmission efficiency for the foundation braking device; gamma rayzThe brake multiplying power; r iszBrake disc friction radius (mm); rcVehicle wheel diameter (mm); mu is a friction coefficient; n is the total number of the vehicle brake pads;
step 2: train basic resistance analysis: the basic resistance W of the train exists in any working condition of the train, and the size of the basic resistance is related to a plurality of factors, such as the structure and the technical state of the train, the axle weight, the line condition, the climate condition, the running speed of the train and the like. The basic resistance of the train varies with the speed, as follows:
W＝M·(c0+c1·v+c2·v2)·g·10-3
wherein M is the train weight, c0，c1，c2Is train resistance coefficient, v is train running speed (km/h), g is gravity acceleration 9.8m/s2；
And step 3: train additional resistance analysis: the extra resistance generated by the train when passing through some special roads, such as ramps, curves, tunnels, etc., is called the additional resistance I of the train. Common additional resistance is ramp additional resistance ωiCurve additional resistance omegarAdditional resistance omega of tunnelsAnd the like. The invention fully considers various additionsResistance, the established train model is closer to the actual running state of the train, namely
I＝M·(ωi+ωr+ωs)·g·10-3
Wherein M is the train weight, omegai，ωr，ωsRespectively unit ramp additional resistance, unit curve additional resistance and unit tunnel additional resistance;
and 4, step 4: the resultant force applied to the train is as follows: f ═ B + W + I;
and 5: according to Newton's second theorem, the deceleration a of the train braking process is calculated as follows:
step 6: discretizing the speed v and the displacement S to obtain a difference form:
vt+1＝vt-3.6·a·T
in the formula vtIs the velocity value (m/S) at time t, StDisplacement value (m) at time t; t is a sampling interval(s);
and 7: establishing a space model of an emergency braking state of the high-speed train:
yt＝[1 0]xt+et
in the formula xtIs a 2-dimensional vector, the first dimension represents the braking distance, the other dimension represents the braking speed, ytAn observed value representing the time t of the train, namely:
wtrepresenting the complexity of the running environment of the train to the train displacement in the emergency braking process of the trainInterference with velocity, etRepresenting errors in the train displacement measurement; in order to enable the train emergency braking model established by the invention to be closer to the actual running state of the train, wtAnd etAre all set to non-Gaussian noise, wtAnd etThe specific distribution of the system is determined according to the running condition of the train;
and 8: observing and recording train output displacement vector sequence YN＝{y1,…,yNAnd setting a parameter vector theta to be estimated as [ P ═ P }z,ηz,γz,μ]T；
And step 9: due to train state XNContains an unobservable braking parameter vector, so that a state sequence X consisting of train displacement and speed is formedN＝{x1,…,xNConsider the data as not fully measurable, calculate XNAnd YNCombined logarithmic probability density function L of all data of compositionθ(XN,YN)：
In the formula pθ(Ω | Δ) represents the probability density of the random vector Ω under Δ when the braking parameter of the train is θ, and can be obtained according to the markov property of the model;
step 10: setting the parameter estimation value of the current train as thetakCalculating Lθ(XN,YN) Desired value of Q (theta )k) Analytic solution of (2):
Q(θ,θk)＝I1+I2+I3
step 11: computing Q (theta ) using particle filtering and particle smoothingk) Numerical solution of (a):
Q(θ,θk)＝I1+I2+I3
in the formula (I), the compound is shown in the specification,
represents the filtered weight of the ith particle at time t,
indicating all output sequences Y of trainNConditioned particles
The smoothing weight of (1).
Step 12: calculating conditional mathematical expectation using a gradient optimization method
The largest parameter vector estimate θ.
Step 13: if the estimated value of the parameter meets the precision requirement, stopping the algorithm and outputting the parameter; otherwise, returning to step 11 to continue iterative computation.
The following experiments demonstrate that the process of the present invention is effective.
FIG. 2 is a graph showing the results of transmission efficiency identification obtained by the method of the present invention; FIG. 3 is a diagram showing the air pressure identification result of the brake cylinder obtained by the method of the present invention; FIG. 4 is a diagram showing the result of identifying the braking magnification by the method of the present invention; FIG. 5 is a graph showing the results of identifying the coefficient of friction obtained by the method of the present invention. As can be clearly seen from the observation of fig. 2 to 5, the identification method provided by the invention can effectively and accurately identify the braking parameters of the train.
The method aims at the actual dynamic behavior of the train in the emergency braking process, establishes the parameterized train emergency braking model by analyzing the train emergency braking mechanism, identifies the train emergency braking parameters based on the maximum Expectation algorithm (EM), and has the advantages of high identification result precision, high convergence speed, strong transportability and strong practicability and feasibility.
The foregoing is a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that variations, modifications, substitutions and alterations can be made in the embodiment without departing from the principles and spirit of the invention.
Claims (1)
1. A method for modeling and identifying a train emergency brake is characterized by comprising the following steps: analyzing the relationship among braking force, resistance, speed and acceleration in the emergency braking process of the train; discretizing the state according to Newton second theorem, and establishing a parameterized emergency braking model of the train; constructing a mathematical expectation of train conditions based on a maximum expectation identification algorithm, and maximizing the mathematical expectation of conditions; obtaining an optimal estimated value of the emergency braking parameter by adopting a gradient optimization method; the method comprises the following specific steps:
step 1: train braking force analysis: the train braking force is the force which is generated by a braking device arranged on a train body and used for decelerating and stopping the train, friction braking is used as a main device for emergency braking of the train, the main realization mode of the friction braking is that air pressure is generated through a brake cylinder, then the air pressure is effectively acted on a brake pad of the train body through various transmission modes, and the brake pad and a brake disc of the train generate effective friction, so that the train braking force for decelerating and stopping the train is generated, when the train is in an emergency braking state, the maximum air pressure is acted on the brake pad by a train brake cylinder, the maximum braking force is generated, and the train is stopped in the shortest time;
braking force B generated by each brake pad of the disc brake:
in the formula dzThe diameter of the brake cylinder is mm; pzFor brake cylinder air pressure kPa ηzCalculating a transmission efficiency for the foundation braking device; gamma rayzThe brake multiplying power; r iszThe friction radius of the brake disc is mm; rcThe diameter of the vehicle wheel is mm; mu is a friction coefficient; n is the total number of the vehicle brake pads;
step 2: train basic resistance analysis: the basic resistance W of the train exists under any working condition of the train, and the size of the basic resistance is related to a plurality of factors, including the structure and the technical state of the train, the axle weight, the line condition, the climate condition and the running speed of the train; the basic resistance of the train adopts the following formula:
W＝M·(c0+c1·v+c2·v2)·g·10-3
wherein M is the train weight, c0，c1，c2Is train resistance coefficient, v is train running speed km/h, and g is gravity acceleration 9.8m/s2；
And step 3: train additional resistance analysis: when a train passes through a certain special road, the additional resistance generated is called as additional train resistance I, the common additional resistance comprises additional ramp resistance, additional curve resistance and additional tunnel resistance, a plurality of additional resistances are fully considered, an established train model is closer to the actual running state of the train, and the additional train resistance is that:
I＝M·(ωi+ωr+ωs)·g·10-3
wherein M is the train weight, omegai，ωr，ωsRespectively unit ramp additional resistance, unit curve additional resistance and unit tunnel additional resistance;
and 4, step 4: the resultant force applied to the train is as follows: f ═ B + W + I;
and 5: according to Newton's second theorem, the deceleration a of the train braking process is calculated as follows:
step 6: discretizing the speed v and the displacement S to obtain a difference form:
vt+1＝vt-3.6·a·T
in the formula vtIs the velocity value m/S at time t, StIs the displacement value m at the time t; t is a sampling interval s;
and 7: establishing a space model of an emergency braking state of the high-speed train:
yt＝[1 0]xt+et
in the formula xtIs a 2-dimensional vector, the first dimension represents the braking distance, the other dimension represents the braking speed, ytAn observed value representing the time t of the train, namely:
wtrepresenting the interference of the complexity of the running environment of the train on the displacement and speed of the train during the emergency braking of the train, etRepresenting errors in the train displacement measurement; in order to make the inventionThe established train emergency braking model is closer to the actual running state of the train, wtAnd etAre all set to non-Gaussian noise, wtAnd etThe specific distribution of the system is determined according to the running condition of the train;
and 8: observing and recording train output displacement vector sequence YN＝{y1,…,yNAnd setting a parameter vector theta to be estimated as [ P ═ P }z,ηz,γz,μ]T；
And step 9: due to train state XNContains an unobservable braking parameter vector, so that a state sequence X consisting of train displacement and speed is formedN＝{x1,…,xNConsider the data as not fully measurable, calculate XNAnd YNCombined logarithmic probability density function L of all data of compositionθ(XN,YN)：
In the formula pθ(Ω | Δ) represents the probability density of the random vector Ω in the case of Δ when the braking parameter of the train is θ, and is obtained according to the markov property of the model;
step 10: setting the parameter estimation value of the current train as thetakCalculating Lθ(XN,YN) Desired value of Q (theta )k) Analytic solution of (2):
Q(θ,θk)＝I1+I2+I3
step 11: computing Q (theta ) using particle filtering and particle smoothingk) Numerical solution of (a):
Q(θ,θk)＝I1+I2+I3
in the formula (I), the compound is shown in the specification,
represents the filtered weight of the ith particle at time t,
indicating all output sequences Y of trainNConditioned particles
The smoothing weight of (2);
step 12: calculating conditional mathematical expectation using a gradient optimization method
The maximum parameter vector estimation value theta;
step 13: if the estimated value of the parameter meets the precision requirement, stopping the algorithm and outputting the parameter; otherwise, returning to step 11 to continue iterative computation.
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| CN108647435A (en) * | 2018-05-10 | 2018-10-12 | 西安理工大学 | A kind of train model on-line parameter discrimination method based on gaussian sum filtering |
| CN109407713A (en) * | 2018-11-02 | 2019-03-01 | 中国铁路总公司 | A kind of train deceleration degree closed loop control method and system |
| CN110321587B (en) * | 2019-05-10 | 2023-06-02 | 中车青岛四方车辆研究所有限公司 | Rail vehicle tunnel air additional resistance calculation method based on numerical simulation |
| CN113104067A (en) * | 2021-05-14 | 2021-07-13 | 中国铁道科学研究院集团有限公司 | Method and device for generating train emergency operation strategy |
| CN113420256B (en) * | 2021-07-27 | 2023-06-20 | 北京建筑大学 | Method and device for determining performance of vehicle braking system |
| CN113591229B (en) * | 2021-09-01 | 2023-05-26 | 北京建筑大学 | Method and system for calculating braking distance of high-speed train |
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