A train braking distance evaluation method based on a periodic maintenance strategy

Abstract

The application discloses a kind of train braking distance evaluation methods based on periodic maintenance strategy, collect train braking system data and calculate braking system state probability, by establishing the Markov state space of train braking system, the failure of braking system is described using continuous time Markov chain, the Markov state transition matrix of braking system working phase is calculated, then the braking system state probability before periodic maintenance and the braking system state probability after periodic maintenance are calculated respectively, then braking system data and train operation data are collected to calculate train braking distance, finally the braking system state probability before and after periodic maintenance and train braking distance are coupled to obtain the relationship between braking distance and braking motor state within periodic maintenance cycle and braking distance expectation, so as to realize the train braking distance evaluation under periodic maintenance strategy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of train braking technology, and more particularly to a train braking distance evaluation method based on periodic maintenance strategy. BACKGROUND

[0002] In recent years, China's rail transit construction has been in full swing. By the end of 2020, the total mileage of rail transit in mainland cities reached 7969.7 kilometers. Among them, the mileage of metro operating lines reached 6280.8 kilometers. The passenger volume in 2020 reached 175.9 billion person-times, which means that more than 24 million people take the subway every day. With the rapid increase in the operating mileage of the subway, train safety has become one of the inevitable problems.

[0003] The braking system is one of the most important subsystems related to the safety of subway travel, and untimely braking is the biggest safety hazard in the process of subway operation. The braking activities of the subway are divided into general braking and emergency braking. General braking is the braking when the subway stops at the station, while emergency braking is the braking under abnormal conditions during the subway travel. Now, the main braking force of general braking and emergency braking comes from the electric braking system. After the train control system issues a braking instruction, the electric braking system is activated. And ensure that the subway vehicle immediately decelerates. The braking force of the electric braking system is provided by the torque generated by the braking motor and the corresponding mechanical mechanism, and the braking output can be adjusted. Under emergency braking conditions, the braking system needs to provide maximum output. The integrity of the emergency braking function will affect the safety of the train, while the general braking will not.

[0004] The braking motor constitutes part of the braking system as a component and dominates the key functions of the braking system. Multiple motors work together to provide the braking force required for braking. If one or more motors fail to work, the maximum braking force provided by the braking system will decrease. When the maximum braking force drops to a certain level, the emergency braking distance of the train will not meet the safety braking distance. Therefore, in order to meet this requirement of safety braking distance, there needs to be a sufficient number of braking motors working properly. And before the braking system fails, the greater the remaining redundancy, the better the braking effect. Therefore, the number of working braking motors is set according to the evaluation of the train braking distance.

[0005] Before the brake system fails, maintenance can restore the degraded brake system performance. And the brake system is part of the train system, and its maintenance features are also included in the maintenance of the train system. In order to ensure the continuous safety and reliable operation of the system, the train will arrange regular maintenance. Regular maintenance will generally perform a comprehensive inspection and replacement of the system, repair the performance of each unit including the motor that has failed, and restore the system to an optimal or suboptimal state, thereby maintaining the performance of the brake system. And through the quantitative relationship between the train braking distance and the state of the brake system, the train braking distance can be coupled with the state probability before and after regular maintenance.

[0006] Therefore, how to realize the evaluation of the train brake system braking distance under the regular maintenance strategy is a problem that those skilled in the art need to solve. SUMMARY

[0007] Therefore, the present application provides a train braking distance evaluation method based on regular maintenance strategy, which realizes the evaluation of train braking distance under regular maintenance strategy, can ensure that the effective brake distance of the brake system is calculated and analyzed according to the fault state of the brake motor in the brake system under the condition that the brake system does not fail, provides an effective method support for train safety design analysis, and helps to ensure train operation safety.

[0008] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0009] A train braking distance evaluation method based on regular maintenance strategy, that is, to find an evaluation method to evaluate the braking distance, the specific steps are as follows:

[0010] Step 1: Collect the motor installed scale of the train brake system and the minimum number of motors required for the operation of the brake system, calculate the number of motor working states, and obtain the state probability of the brake system;

[0011] Step 2: Establish the Markov state space of the brake system, use continuous time Markov chain to describe the failure of the brake system, collect the motor failure rate, calculate the state transition process of the brake system working stage, and obtain the Markov state transition matrix of the brake system working stage; According to the brake system failure rate λ, the state transition relationship before regular maintenance is derived;

[0012] Step 3: According to the brake system state probability and the Markov state transition matrix, the brake system state probability before regular maintenance is calculated and obtained;

[0013] Step 4: Obtain the brake system repair result, i.e. brake system repair effect, according to the periodic maintenance strategy, and calculate the brake system state probability after periodic maintenance according to the brake system repair result; given the periodic maintenance cycle, calculate the number of periodic maintenance at the current time according to the periodic maintenance cycle; calculate the brake system state probability after periodic maintenance according to the number of periodic maintenance and the Markov state transition matrix;

[0014] Step 5: Collect motor data and train data in the brake system, and calculate the train braking distance; the motor data includes motor power, and the train data includes train weight, train running speed, etc.; the train braking distance is the sum of the train braking lag distance and the effective braking distance;

[0015] Step 6: Determine the brake system state probability at the current time according to the brake system state probability before periodic maintenance and the brake system state probability after periodic maintenance, and couple the current brake system state probability and the train braking distance to obtain the relationship between the braking distance and the brake motor state in the periodic maintenance cycle, i.e. to obtain the braking distance under the mapping of the random fault state of the motor;

[0016] Step 7: According to the number of normal working motors and the relationship between the braking distance and the brake motor state in the periodic maintenance cycle, the expected braking distance in the periodic maintenance cycle is calculated as the train braking distance evaluation result. It can be judged whether the current train braking system matches the safety braking distance design target.

[0017] Preferably, in step 1, the number of motor working states I = n-k+1; wherein n is the total number of brake motors, indicating the motor installed capacity; k is the minimum number of motors required for the operation of the brake system; the motor working state is counted from the state of all n motors working normally, that is, state 1; when n-i+1 motors can work normally, the state is i; until only k motors can work normally, that is, state n-k+1;

[0018] The probability of the system I states, i.e. the state probability of the system, can be expressed as P t (i) is the probability of state i; the initial state probability

[0019] Preferably, in step 2, the elements in the brake system working stage Markov state transition matrix C are:

[0020]

[0021] Wherein, i and j represent the motor working state, indicating the element position in the Markov state transition matrix; λ is the motor failure rate; n is the total number of brake motors; k is the minimum number of motors required for the operation of the brake system.

[0022] Preferably, in step 3, when the current time t satisfies t∈[0,T), the brake system state probability before the periodic maintenance is represented as:

[0023]

[0024] Wherein, is the initial state probability in the brake system state probability, C is the Markov state transition matrix; t is the current time.

[0025] Preferably, in step 4, the brake system state probability at the end of the periodic maintenance is represented as:

[0026]

[0027] Wherein, I represents the number of motor working states;

[0028]

[0029] Wherein, i represents the motor working state; n o represents the motor working state corresponding to the number of available motors after the periodic maintenance;

[0030] At any time t after the periodic maintenance, and t>T, T is the periodic maintenance interval, then the brake system state probability after the periodic maintenance is represented as:

[0031]

[0032] Wherein, C represents the Markov state transition matrix of the brake system working phase; s represents the number of periodic maintenances experienced within t time.

[0033] Preferably, in step 5, the beta utilization rate of a single motor braking force, train load, train running speed, train braking lag time and brake force is collected;

[0034] The train braking distance d b is:

[0035] d b =d k +d e

[0036] Wherein, d k is the train braking lag distance; d e is the effective braking distance;

[0037]

[0038] Wherein, tk is the train braking lag time; v0 is the train running speed;

[0039] The effective braking distance of the braking system when n-i+1 motors are working normally is represented as:

[0040]

[0041] wherein B m is the braking force of a single motor; β is the beta utilization rate of the braking force; G is the train load, in t; w0 is the basic resistance, in N / kN; g is the acceleration of gravity.

[0042] Preferably, in step 6, the current braking system state probability is coupled into the braking distance calculation, and the coupling expression is:

[0043]

[0044] wherein d b (t) represents the braking distance at time t; P t (i) represents the braking system state probability at time t, which can be the braking system state probability before maintenance or the braking system state probability after maintenance, depending on the time; I is the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; t k is the train braking lag time; v0 is the train running speed.

[0045] Preferably, in step 7, the number of normally working motors is n-i+1, and the expectation of the braking distance within the periodic maintenance cycle is represented as:

[0046]

[0047] wherein T represents the cycle interval of periodic maintenance; P t (i) represents the braking system state probability at time t; I is the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; i represents the motor working state.

[0048] Compared with the prior art, the train braking distance evaluation method based on the periodic maintenance strategy provided by the present application can collect train braking system data to calculate braking system state probability, establish a Markov state space of the train braking system, use a continuous time Markov chain to describe the failure of the braking system, calculate a Markov state transition matrix of the working phase of the braking system, then calculate the braking system state probability before and after periodic maintenance, collect braking system data and train operation data to calculate the train braking distance, and finally couple the braking system state probability before and after periodic maintenance and the train braking distance to obtain the relationship between the braking distance and the braking motor state within the periodic maintenance cycle and the braking distance expectation, so that the train braking distance evaluation under the periodic maintenance strategy can be realized in combination with the requirement of the safety braking distance. Meanwhile, the influence of the periodic maintenance cycle on the train safety can be balanced, and the safety of the braking system can be ensured by reasonably arranging the periodic maintenance. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only constitute a part of the embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor based on the provided drawings.

[0050] Figure 1 The accompanying drawings are a flowchart of the train braking distance evaluation method based on the periodic maintenance strategy provided by the present application.

[0051] Figure 2 The accompanying drawings are a braking cycle-time variation diagram of the actual train braking distance provided by the present application. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments only constitute a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0053] The embodiment of the present application discloses a train braking distance evaluation method based on a periodic maintenance strategy, which comprises the following specific steps:

[0054] S1: Determine the motor installed capacity of the train braking system, and establish a Markov state space of the braking system.

[0055] In the braking system, the total number of braking motors is n, and all the braking motors are perfect at the beginning, all the braking motors have the same output and failure rate, and cannot be maintained during operation, so the redundancy of the braking motor will only gradually decrease due to failure, and the braking system needs to meet the condition of safe braking distance, that is, to ensure that k braking motors can work normally, and the parameter k depends on the size of the safe braking distance, such a system is a typical K-N:G system.

[0056] When a braking motor in the train braking system fails, if the remaining redundancy of the braking motor is not completely lost, that is, there is still remaining available redundancy, the system can still be used; if the failed braking motor is not completely repaired, the remaining available redundancy of the braking motor will continue to decrease, and during this period, the system is in an incomplete running state, therefore, the normal running state of the train braking system depends on the number of normally working braking motors;

[0057] S2: A continuous-time Markov chain is used to describe the failure of the braking system, and the state transition relationship before periodic maintenance is derived according to the failure rate λ of the braking system.

[0058] The redundancy of the system will only gradually decrease during operation, and such a process is similar to a finite pure death process, which can be described by an absorbing state Markov chain, for which the state probability will be in the absorbing state after some steps, regardless of which state they start from;

[0059] The failure rate of the motor during operation is λ, and the failure process follows an exponential distribution with respect to t, for such a braking system, the total number of states can be represented as I=n-k+1, which includes n-k operating states and one shutdown state that cannot work normally, the motor operating state starts from n motors all working normally, that is, state 1; when there are n-i+1 motors that can work normally, the state is i; to k motors that can work normally, that is, state n-k+1; therefore, the probability of the I states of the system, that is, the state probability of the system, can be represented as P t (i) is the probability of state i; in the initial state of the braking system, all the motors are perfect, so the initial state probability is

[0060] When the system is in the working stage, the elements in the Markov state transition matrix C during operation can be represented as:

[0061]

[0062] Where i and j represent the motor working state, and in the Markov state transition matrix, i and j represent the element position in the transition matrix; λ is the motor failure rate; n is the total number of braking motors; and k is the minimum number of motors required for the operation of the braking system;

[0063] S3: The instantaneous state probability of the braking system at different times can be represented as This is obtained from the above state transition matrix, and the state probability of each stage depends on the state transition matrix of the stage, and the state probability at the beginning of each stage is the state probability at the end of the previous stage. Therefore, the state probability of the braking system before periodic maintenance, that is, when t∈[0, T), can be represented as:

[0064]

[0065] S4: Considering the repair effect of the braking system after periodic maintenance, the state probability of the braking system after periodic maintenance is obtained;

[0066] After periodic maintenance, the system will recover to what state depends on the degree of repair. According to the different degrees of repair, these preventive maintenance strategies can be generally divided into complete repair and incomplete repair; complete repair restores the system to its original state; incomplete repair ensures that the system is restored between the original state and the minimum operating state;

[0067] At the end of complete repair, the system will recover to its initial state, and its state probability is determined at this time point:

[0068]

[0069] After incomplete repair, the state at the repair time point is still determined, but it depends on the degree of repair; assuming that each periodic maintenance will repair the number of available motors to n-n0+1, then the state probability of the braking system at the end of periodic maintenance is:

[0070]

[0071] At the end of periodic maintenance, the state probability can be represented as , where s is the number of periodic maintenance experienced within t time, and the braking state probability after periodic maintenance can be represented as follows:

[0072]

[0073] S5: Collect the data of motor power, train load, train running speed, etc. of the braking system to determine the braking distance;

[0074] Train braking distance d b The train braking lag distance d k And the effective braking distance d e ;

[0075] d b = d k + d e

[0076] Braking lag distance d k Depends on the train braking lag time t k And the train running speed v0, the train travels at a uniform speed during the lag braking process;

[0077]

[0078] The effective braking distance d e Of the train (i) is the deceleration distance of n-i+1 normal working brake motors after the brake is started, the formula is:

[0079]

[0080] Where v0 is the train running speed, unit: km / h; Beta is the beta utilization rate of brake force; i is the number of normal working motors; B m Is the braking force of a single motor, unit: MN; G is the train load, unit: t; w0 is the basic resistance, unit: N / kN; g is the acceleration of gravity, unit: m / s 2 ;

[0081] S6: Coupling the brake motor state probability obtained by S3-S5 with the train braking distance to obtain the relationship between the braking distance and the brake motor state in the periodic maintenance cycle;

[0082] The safety risk of the train braking system is related to the braking distance, when the braking distance of the train exceeds the given safety braking distance, at this time it can be considered that the braking system has safety risk; The braking force of the electric brake equipment is provided by multiple motors, according to the description in S1, the electric brake equipment equipped with n motors needs k normal output to provide enough braking force to meet the safety braking distance, each motor in the braking system provides the same braking output B m , then if the effective braking distance of the system at time t is represented as follows:

[0083]

[0084] Where P t (i) represents the braking system state probability at time t; d e(i) is the effective braking distance when n-i+1 motors are working normally; I represents the number of motor working states;

[0085] The braking lag distance d obtained in S5 k Substituting, we can get the braking distance d at a certain moment. b (t):

[0086]

[0087] Among them, d b (t) represents the braking distance at time t; P t (i) represents the state probability of the braking system at time t; I is the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; t k is the train braking delay time; v0 is the train running speed;

[0088] S7: Considering n-i+1 as the number of motors in normal operation, the expected braking distance within the regular maintenance cycle is expressed as follows:

[0089]

[0090] Where T represents the periodic maintenance interval, in hours; P t (i) represents the state probability of the braking system at time t; I is the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; the expected braking distance is used as the train braking distance evaluation result.

[0091] Example

[0092] The motor installed capacity N of a braking system is collected to determine the minimum number of motors k required for normal operation. The Markov space is then divided and the Markov state transition relationship is derived based on the motor failure rate. Data such as the output power of a single motor, train load, and train speed are collected to determine the regular maintenance cycle. The train braking distance under the regular maintenance strategy is obtained by coupling the motor state probability with the braking distance. The specific calculation process is as follows:

[0093] S1: The collected motor installed capacity N = 6, and the minimum number of motors k = 2 required for the operation of the braking system is determined. Therefore, the braking system contains I = N - k + 1 = 5 states;

[0094] The braking system state probability can be expressed as In the initial state of the braking system, all motors are intact, so the initial state probability is

[0095] S2: Collect the failure rate data λ = 0.0005h of the braking motor -1 When the braking system is in the working phase, the Markov state transition matrix can be expressed as:

[0096]

[0097] S3: When the periodic maintenance has not yet occurred, that is, when t ∈ [0, T), the system state probability can be expressed as:

[0098]

[0099] S4: When the periodic maintenance ends, it is determined that the periodic maintenance will repair the number of available motors to 5, corresponding to the motor working state i = 2, and then the system state probability after periodic maintenance is:

[0100]

[0101] Given the periodic maintenance cycle T = 720h, let s be the number of periodic maintenance experienced within t time, and the periodic maintenance number s is expressed as:

[0102] s = t mod T

[0103] State probability can be expressed as

[0104]

[0105] S5: Determine the braking force B of a single motor of the braking system m = 61.67MN, the train load is G = 370.06t, the train running speed v0 = 80km / h, the train braking buffer time t k = 5s, the gravitational acceleration g = 9.81m / s 2 , the braking utilization rate β = 1, and the basic resistance coefficient w0 is taken as follows:

[0106]

[0107] Then the braking lag distance d k is obtained as follows:

[0108]

[0109] If the system has n-i+1 normally working motors in the current state, then the effective braking distance d e (i) of the system can be expressed as:

[0110]

[0111] S6: Combine the state probabilities obtained in S2 and S3 to obtain the effective braking distance d of the train at a certain time e (t):

[0112]

[0113] The braking lag distance d obtained in S4 k Substituting into S5, we can find the braking distance at a certain moment:

[0114]

[0115] S7: Considering i as the number of motors in normal operation, the expected braking distance within the regular maintenance cycle is expressed as follows:

[0116]

[0117] The variation of braking cycle with time is obtained as Figure 2 As shown in the figure, the pink line represents the safe braking distance, and the blue line represents the actual braking distance of the train; the expected braking distance is used as the train braking distance evaluation result.

[0118] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0119] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A train braking distance evaluation method based on a periodic maintenance strategy, characterized in that: The specific steps include: Step 1: Collect the motor installed capacity of the train braking system and the minimum number of motors required for the operation of the braking system, calculate the number of motor working states, and obtain the braking system state probability; Step 2: Establish the Markov state space of the braking system, collect the motor failure rate, calculate the state transition process of the braking system working stage, and obtain the Markov state transfer matrix of the braking system working stage; Step 3: Calculate the brake system state probability before scheduled maintenance based on the brake system state probability and the Markov state transition matrix; Step 4: Obtain the brake system maintenance results according to the regular maintenance strategy, and calculate the brake system state probability after the regular maintenance based on the brake system maintenance results; Step 5: Collect motor data and train data in the braking system and calculate the train braking distance; Step 6: Determine the current brake system state probability based on the brake system state probability before and after scheduled maintenance. Couple the current brake system state probability with the train braking distance to obtain the relationship between the braking distance and the brake motor state during the scheduled maintenance period. Step 7: Based on the number of normally working motors and the relationship between the braking distance during the regular maintenance period and the change in the state of the brake motor, calculate the expected braking distance during the regular maintenance period as the train braking distance assessment result.

2. A train braking distance evaluation method based on a periodic maintenance strategy according to claim 1, characterized in that: In step 1, the number of motor working states I=n-k+1; wherein n is the total number of brake motors, indicating the installed capacity of the motors; k is the minimum number of motors required for the operation of the brake system; the motor working state starts from when all n brake motors are working normally, which is state 1; when n-i+1 brake motors are working normally, it is state i; until only k brake motors are working normally, it is state n-k+1; the corresponding system has I state probabilities, and the state probability of the system is expressed as P t (i) is the probability of state i; the probability of the initial state 3. The train braking distance evaluation method based on the periodic maintenance strategy according to claim 1 is characterized in that: The elements in the Markov state transfer matrix C of the braking system working phase in step 2 are: Wherein, i and j represent the working state of the motor and the position of the element in the Markov state transition matrix; λ is the motor failure rate; n is the total number of brake motors; and k is the minimum number of motors required for the operation of the brake system.

4. The train braking distance evaluation method based on periodic maintenance strategy according to claim 1 is characterized in that: In step 3, the interval between regular maintenance cycles is T. At the current time t∈[0,T), it is before regular maintenance. The probability of the brake system state before regular maintenance is expressed as: in, is the initial state probability in the braking system state probability, C is the Markov state transition matrix; t is the current time.

5. The train braking distance evaluation method based on periodic maintenance strategy according to claim 1 is characterized in that: In step 4, the probability of the brake system state at the end of regular maintenance is expressed as: Wherein, I represents the number of motor working states; Among them, i represents the working state of the motor; n o Indicates the motor working status corresponding to the number of available motors after regular maintenance; At any time t after regular maintenance, the probability of the brake system state after regular maintenance is expressed as: Where T is the interval between scheduled maintenance cycles; C represents the Markov state transition matrix of the braking system during the working phase; and s represents the number of scheduled maintenance operations during the time t.

6. The train braking distance evaluation method based on periodic maintenance strategy according to claim 2 is characterized in that: In step 5, the beta utilization rate of the braking force of a single motor, train load, train running speed, train braking lag time and braking force is collected; Train braking distance d b for: d b =d k +d e Among them, d k is the train braking lag distance; d e is the effective braking distance; Among them, t k is the train braking delay time; v0 is the train running speed; The effective braking distance of the braking system when n-i+1 motors are working normally is expressed as: Among them, B m is the braking force of a single motor; β is the beta utilization rate of the braking force; G is the train load; w0 is the basic resistance; g is the acceleration due to gravity.

7. The train braking distance evaluation method based on periodic maintenance strategy according to claim 6 is characterized in that: In step 6, the current braking system state probability is substituted into the braking distance calculation for coupling. The coupling expression is: Among them, d b (t) represents the braking distance at time t; P t (i) represents the probability of the braking system state at time t; I represents the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; t k is the train braking delay time; v0 is the train running speed.

8. The method for evaluating train braking distance based on a periodic maintenance strategy according to claim 2, characterized in that: In step 7, the expected braking distance within the regular maintenance period is expressed as: Where T represents the regular maintenance period interval; P t (i) represents the probability of the braking system state at time t; I represents the number of motor working states; d e (i) represents the effective braking distance when n-i+1 motors are working normally; i represents the working status of the motor.

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