Optimization method for long downhill maneuvering of heavy-load trains based on air brakes

Abstract

The invention discloses a method for optimizing the operation of a heavy-load train on a long downhill slope based on air brakes. The method comprises the following steps: obtaining basic data of the heavy-load train, constructing a longitudinal dynamics model of the train, and performing parameter verification on the longitudinal dynamics model of the train according to the basic data; and constructing a multi-objective optimization calculation model of the train based on the verified longitudinal dynamics model of the train; completing the construction of a standard quadratic form of the multi-objective optimization calculation model of the train, solving it using a standard QP model, and obtaining an optimized operation sequence; the invention establishes a more accurate dynamics simulation model of the heavy-load train by refining the air brake model, quantitatively characterizing the changing law of the air brake performance of the heavy-load train on a long downhill slope, thereby obtaining an optimized operation sequence based on the standard QP model, effectively supporting and optimizing the operation strategy of the heavy-load train on a long downhill slope, and ensuring the safe and stable operation of the heavy-load train.

Description

Technical Field

[0001] The invention relates to the field of train operation optimization, and in particular to a long downhill operation optimization method for a heavy-load train based on air braking. Background Art

[0002] In recent years, as the traction weight and marshaling length of heavy-load freight trains continue to increase, their advantages of low cost and large transportation capacity continue to stand out. However, due to the restrictions of train traction weight, marshaling length, line speed limit and continuous long downhill slopes during operation, heavy-load trains have more stringent safety and smooth operation requirements than ordinary freight trains. Taking the Shuohuang Railway Line as an example, its railway longitudinal section is high in the west and low in the east, with an altitude difference of nearly 2000m. The maximum downhill slope in the heavy vehicle direction is -12‰, the minimum curve radius is 400m, and the downhill section accounts for almost 47% of the entire line. Especially in the continuous long downhill sections in the heavy vehicle direction, the driver needs to perform periodic air braking and relief operations. Since the appropriate braking and relief points are difficult to judge, the poor air braking operation may cause unplanned stops between stations, thereby reducing the transportation efficiency of the entire line; in extreme cases, the coupler may even break and the train derail, which greatly affects the safety of train operation. Therefore, it is necessary to conduct research on multi-objective control optimization methods from the perspective of air brake mechanism analysis and model in-depth analysis, with the goal of ensuring the safety and stability of heavy-load trains in the long downhill periodic braking process.

[0003] Since heavy-loaded trains must use air brakes to adjust their speed during operation, and during the air brake process, the air brake wave transmission time increases and the train pipe charging and exhaust are nonlinear, making it difficult for the driver to predict the braking / relieving timing of the air brake during driving. At the same time, the long formation, large inertia, and relative movement between vehicles of heavy-loaded trains make longitudinal impulses prone to occur during train operation. In order to ensure safe and smooth operation in long and long downhill sections, the evaluation of air brake performance has become the first problem to be solved. The existing evaluation of air brake performance is mainly based on the analysis and summary of the operation experience and operation rules of excellent drivers. In order to ensure the effect of the optimization of the operation strategy, it is also necessary to evaluate the performance of air brakes based on the model.

[0004] In summary, the standard indicators for heavy-load train operation on long downhill slopes established at this stage are general indicators that are generally applicable to the safe operation of trains on the entire line. However, they still lack specificity and accuracy for long downhill sections. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art: the currently established standard indicators for the operation of heavy-loaded trains on long downhill slopes are general indicators that are generally applicable to the safe operation of trains on the entire line, but they are still lacking in specificity and accuracy for long downhill sections. The present invention provides an optimization method for the long downhill operation of heavy-loaded trains based on air braking.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for optimizing the long downhill operation of a heavy-loaded train based on air braking, comprising the following steps:

[0007] S1. Obtain basic data of heavy-load trains;

[0008] S2. constructing a longitudinal dynamics model of the train, and performing parameter verification on the longitudinal dynamics model of the train according to basic data to obtain a verified longitudinal dynamics model of the train;

[0009] S3. Constructing a multi-objective optimization calculation model for a train based on the verified longitudinal dynamics model of the train;

[0010] S4. Construct a standard quadratic form based on the train multi-objective optimization calculation model, and solve it using the standard QP model to obtain the optimized operation sequence.

[0011] The present invention has the following beneficial effects:

[0012] In the present invention, the basic data of heavy-load trains are obtained to construct a longitudinal dynamics model of the train, and the parameters of the longitudinal dynamics model of the train are verified according to the basic data to obtain the verified longitudinal dynamics model of the train. The mathematical formula can be used to characterize the braking / relieving transient process and the performance stabilization process, and the time-space distribution relationship of the air brake performance is fitted by combining the influencing factors such as the recharging time, the air-drying gate, the number of cycle braking and the long-distance gate braking. A multi-objective optimization calculation model of the train is constructed based on the verified longitudinal dynamics model of the train. Starting from the safety and stability requirements of the long downhill operation process of the heavy-load train, a target function is established with the optimization target of the control quantity change rate and the coupler force size. number to ensure the safety and stability of heavy-load train's periodic braking on a long downhill slope; then complete the construction of standard quadratic form for the multi-objective optimization calculation model of the train, use the standard QP model to solve it, and get the optimized operation sequence. The quadratic form is used to consider the linear expression of various nonlinear constraints, and the linear expression problem of the quadratic solver is solved. The present invention establishes a more accurate heavy-load train dynamics simulation model by refining the air brake model, and quantitatively characterizes the change law of the air brake performance of the heavy-load train on a long downhill slope, so as to obtain the optimized operation sequence based on the standard QP model, effectively support and optimize the operation strategy of the heavy-load train on a long downhill slope, and ensure the safe and stable operation of the heavy-load train.

[0013] Further, step S2 includes the following sub-steps:

[0014] S21, constructing a train coupling model, and calculating the front and rear coupling forces of a heavy-load train based on basic data;

[0015] S22, constructing a train air braking transient process model;

[0016] S23, constructing a steady-state process model of train air braking;

[0017] S24. Calculate the air braking force of each carriage of the heavy-load train according to the train air braking transient process model and the train air braking steady-state process model, expressed as:

[0018] F Bi (t) = β c *φ h *K h *B para,i (t)

[0019]

[0020] Among them, F Bi is the air braking force of the i-th train compartment, β c is the braking coefficient, φ h To convert the friction coefficient, K h To convert the brake shoe pressure, B para,i (t) is the power utilization rate of the i-th train car, λ is the characteristic parameter of the brake control valve, γ is the characteristic parameter of the brake wave propagation speed, n is the total number of train cars, t d,i is the time when the brake cylinder of the i-th train compartment starts to charge, t Δ,i Q is the time difference between the brake cylinder filling of the i-th train carriage and the first train carriage, py is the offset inflection point of the S function rise, L is the S function discreteness, T BRA is the total braking time of the brake, t BRA is the real-time braking time, e is a constant, t m is the end time of the transient process, T1 is the filling time of the brake cylinder of the first vehicle;

[0021] S25, constructing a longitudinal dynamics model of the train according to the air braking force of each carriage of the heavy-load train and the front and rear hook forces of the heavy-load train;

[0022] S26. Perform parameter verification on the train longitudinal dynamics model according to the basic data to obtain a verified train longitudinal dynamics model.

[0023] The further beneficial effects are:

[0024] Mathematical formulas are used to characterize the braking / relief transient process and the performance stabilization process, and the time-space distribution relationship of the air brake performance is fitted based on influencing factors such as recharging time, brake drying, number of cyclic braking, and long brake down, laying the foundation for building a train multi-objective optimization calculation model based on the calibrated train longitudinal dynamics model to ensure the safety and stability of heavy-load trains in long downhill periodic braking.

[0025] Further, step S23 is specifically as follows:

[0026] The influencing factors are parameterized and the mathematical description of the train air brake steady-state process is introduced to obtain the train air brake steady-state process model, and its mathematical description is expressed as follows:

[0027]

[0028] Among them, P is the steady-state characteristic coefficient.

[0029] The further beneficial effects are:

[0030] The influence of factors such as the current braking time on the air braking force is taken into consideration, and the train air braking steady-state process model in the air braking model is refined.

[0031] Further, step S25 is specifically as follows:

[0032] The differential equations are constructed by the air braking force of each carriage of the heavy-load train and the front and rear coupler forces of the heavy-load train to obtain the longitudinal dynamics model of the train, where the differential equations are expressed as:

[0033]

[0034] Among them, m i is the mass of the i-th train carriage; is the longitudinal displacement of the i-th train carriage; F TEi is the traction force of the i-th train carriage; F ci-1 ,F cn are the front and rear coupler forces of the i-th train carriage respectively; F DBi is the electric braking force of the i-th train carriage; F wi is the total resistance of the i-th train compartment; F Bi is the air braking force of the i-th train car.

[0035] The further beneficial effects are:

[0036] The effects of electric traction / braking force, coupler force, running resistance, and air braking force on the locomotive and the effects of coupler force, running resistance, and air braking force on the vehicle are taken into consideration, so as to refine the air brake model and obtain the longitudinal dynamics model of the train.

[0037] Furthermore, step S3 specifically includes the following sub-steps:

[0038] Step S3 specifically includes the following sub-steps:

[0039] S31. Construct an optimization objective function based on the basic data model, expressed as:

[0040]

[0041] Among them, J is the optimization objective function, t f is the optimization end time, t0 is the optimization start time, λ f is the train longitudinal force weight coefficient, λ u is the weight coefficient of locomotive traction / braking force change rate, λ e is the train operation energy consumption weight coefficient, v r is the train speed, u i is the locomotive traction or braking force of the i-th train carriage, u i-1 is the locomotive traction / braking force of the i-1 train carriage, f in is the coupler force of the train carriage;

[0042] S32, constructing a motion state equation according to the verified train longitudinal dynamics model;

[0043] S33. According to the optimization objective function and basic data, the operation boundary and operation constraints are constructed, and the train characteristic constraints are preset according to the safety and stability indicators to obtain the train multi-objective optimization calculation model.

[0044] The further beneficial effects are:

[0045] Based on the safety and stability requirements of heavy-load trains running on long downhill slopes, an objective function is established with the optimization objectives of the control variable change rate and the coupler force to ensure the safety and stability of heavy-load trains in periodic braking on long downhill slopes.

[0046] Furthermore, the motion state equation in step S31 is expressed as:

[0047]

[0048] Among them, m i is the mass of the i-th train carriage, is the acceleration of the i-th train carriage, v i is the speed of the i-th train carriage, v i+1 is the speed between carriages of the i+1th train, is the relative speed between the i-th train carriage and the i+1-th train carriage, is the coupling force of the i-th train carriage, is the coupling force of the i-1 train carriage, is the total resistance of the i-th train carriage.

[0049] The further beneficial effects are:

[0050] The equations of motion are constructed using each locomotive and vehicle as a point mass, which is a set of equations of motion that is more sophisticated than the existing equations of motion that treat the train as a single point mass or a homogeneous rod model.

[0051] Furthermore, the train multi-objective optimization calculation model in step S33 is expressed as:

[0052]

[0053] Optimization boundaries and operational constraints:

[0054] v i (x0) = v0 t(x0) = t0

[0055] v i (x f )=v f t(x f ) = t f

[0056] v i (x)≤min{v lim1 (x),v lim2 (x),v lim3 (x),…}

[0057] Among them, v i (x0) = v0 is the initial velocity of the initial position x0 defined as v0, t(x0) = t0 is the initial time of the initial position x0 defined as t0, v i (x f )=v f To change the end point position x f The terminal velocity is defined as v f , t(x f ) = t f To change the end point position x f The end time is defined as t f , v lim1 (x),v lim2 (x),v lim3 (x) etc. respectively represent the speed limits during operation;

[0058] Constraints on the fluctuation of coupler force:

[0059] 0≤f in ≤F SET

[0060] Locomotive traction / braking force constraints:

[0061] 0≤u i ≤F max (v i )

[0062] And air brakes relieve recharge time constraints:

[0063] T charge ≥T SET

[0064] Among them, f in is the train coupler force, F SET is the constraint on the coupler force, u i is the locomotive traction or braking force, F max (v i ) is the locomotive traction or braking force constraint, T charge The actual air filling time of the train compartment is relieved, T SET This can actually alleviate the time constraints on air filling for train carriages.

[0065] The further beneficial effects are:

[0066] Based on the safety and stability requirements of heavy-load trains running downhill, an objective function is established with the optimization objectives of the control variable change rate and the coupler force to ensure the safety and stability of heavy-load trains' periodic braking on long downhill slopes. The model constraints and boundaries are set through the actual train system and running line to ensure that the solution based on the model is within a reasonable range.

[0067] Step S4 includes the following sub-steps:

[0068] S41. The nonlinear part in the multi-objective optimization calculation model is linearized to obtain a standard train state equation, which is expressed as:

[0069]

[0070] Among them, k i-1 x i-1 The simplified coupling force of the i-1 train carriage, k i x i The simplified coupling force of the i-th train carriage, m i is the mass of the i-th train carriage, u′ i is the equivalent train control quantity, δ i is the equivalent partial resistance of the i-th train carriage, is the relative speed between the i-th train carriage and the i+1-th train carriage; v i is the speed of the i-th train carriage, v i+1is the speed between carriages of the i+1th train, are the basic resistance coefficients of the i-th train compartment, f pi is the resistance of the i-th train car related to its position, is the acceleration of the i-th train carriage;

[0071] S42, discretizing the standard train state equation using the step size to obtain a discretized train state equation;

[0072] S43, using the discretized train state equation to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, and obtain a quadratically standardized train multi-objective optimization calculation model;

[0073] S44. The multi-objective optimization calculation model of the train after the second normalization is brought into the standard QP model for solution to obtain the optimized operation sequence.

[0074] The further beneficial effects are:

[0075] By considering the linear expression of various nonlinear realization constraints through quadratic forms, the linear expression problem of the quadratic solver is solved, which effectively supports and optimizes the operation strategy of heavy-load trains on long and steep downhill slopes, ensuring the safe and smooth operation of heavy-load trains.

[0076] Further, step S42 is specifically as follows:

[0077] The sampling period is preset, and the standard train state equation is discretized in the continuous time domain using a zero-order holder to obtain the discretized train state equation, which is expressed as:

[0078] x(k+1)=Ax(k)+Bu'(k)

[0079] Among them, x(k+1) is the discretized train state equation, u'(k) is the equivalent train control quantity, k is the discretized sampling point, T s is the sampling period, e is a constant, and τ is the time variable.

[0080] The further beneficial effects are:

[0081] The continuous state quantity is discretized using a certain sampling period to form a train state matrix, which facilitates numerical calculations using computers.

[0082] Further, step S43 is specifically as follows:

[0083] The discretized train state equation is used to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, which is expressed as:

[0084]

[0085] Among them, J * is the objective function after the standard quadratic form, x is the train state, (·) T is the vector transpose, Q is the weight coefficient λ of the longitudinal force of the train f and locomotive traction / braking force change rate weight coefficient λ u The coefficient matrix of the train operation energy consumption is λ, diag[·] is a diagonal matrix, and R is a weighted matrix containing the train operation energy consumption coefficient λ. e The coefficient matrix, F1 T is the weight coefficient λ of the locomotive traction / braking force change rate u The first coefficient matrix, F2 T is the weight coefficient λ of train operation energy consumption e The second coefficient matrix, I nxn is the n-order unit matrix, δ n is the equivalent partial resistance of the nth train carriage, u i-1 is the traction / braking force actually exerted by the locomotive at the previous moment, k n-1 is the proportional coefficient in the hook-buffer model.

[0086] The further beneficial effects are:

[0087] In practice, the practical problem that the nonlinear characteristics of the train electric locomotive's traction / electric braking characteristics, coupler model, air brake model, train motion equations, etc., conflict with the linear constraints of the quadratic programming problem and cannot be directly matched is effectively solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A flowchart of the steps of a method for optimizing the long downhill maneuvering of a heavy-load train based on air brakes provided by the present invention;

[0089] Figure 2 This is a flowchart of the steps in step S2 of the present invention;

[0090] Figure 3 is a step-by-step flow chart of step S3 in the present invention;

[0091] Figure 4 It is a step-by-step flow chart of step S4 in the present invention. DETAILED DESCRIPTION

[0092] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0093] like Figure 1 As shown, in an embodiment of the present invention, a method for optimizing downhill maneuvering of a heavy-loaded train based on air braking is provided, comprising the following steps S1 to S4:

[0094] S1. Obtain basic data of heavy-load trains;

[0095] In practice, the basic data of heavy-load trains obtained include: heavy-load train data (train formation information, locomotive traction / braking characteristics); line data (speed limit, slope, curve, station kilometer mark); timetable data (departure interval, stop time, section operation time), etc.

[0096] S2. constructing a longitudinal dynamics model of the train, and performing parameter verification on the longitudinal dynamics model of the train according to basic data to obtain a verified longitudinal dynamics model of the train;

[0097] like Figure 2 As shown, in the embodiment of the present invention, step S2 includes the following sub-steps:

[0098] S21, constructing a train coupling model, and calculating the front and rear coupling forces of a heavy-load train based on basic data;

[0099] In practice, the train coupler-buffer device can be equivalent to a mathematical coupler-buffer model to construct a train coupler-buffer model, and the front and rear coupler forces of the heavy-load train can be calculated based on the basic data based on the constructed train coupler-buffer model.

[0100] S22, constructing a train air braking transient process model;

[0101] In practice, the construction of the train air brake transient process model focuses on the brake control valve characteristics, brake cylinder inflation characteristics, brake wave propagation velocity characteristics and other factors of the heavy-load train. During the decompression process of the heavy-load train pipe, that is, the train air brake transient process described in the present invention, the complex pneumatic process in the brake cylinder and the train pipe can be abstracted into a mathematical description, that is:

[0102]

[0103]

[0104]

[0105] Among them, P n (t) is the braking efficiency coefficient of the nth vehicle in the transient process, λ is the characteristic parameter of the brake control valve, γ is the characteristic parameter of the brake wave propagation speed, K is the characteristic parameter of the brake cylinder inflation, n is the total number of train carriages, t d,i is the time when the brake cylinder of the i-th train compartment starts to charge, in seconds / s, t Δ,i is the time difference between the brake cylinder of the ith train car and the first train car, in seconds / s, t1 is the time when the brake cylinder of the first car starts to be inflated, in seconds / s, t N The time when the brake cylinder of the Nth vehicle starts to fill, in seconds / s, T N is the inflation time of the brake cylinder of the Nth vehicle, in seconds / s; T1 is the inflation time of the brake cylinder of the 1st vehicle, in seconds / s.

[0106] S23, constructing a steady-state process model of train air braking;

[0107] In the embodiment of the present invention, step S23 is specifically as follows:

[0108] Step S23 is specifically as follows:

[0109] The influencing factors are parameterized and the mathematical description of the train air brake steady-state process is introduced to obtain the train air brake steady-state process model, and its mathematical description is expressed as follows:

[0110]

[0111] Among them, P is the steady-state characteristic coefficient.

[0112] In practice, the braking force is not stable in the steady-state process of air braking (i.e., the effective air braking process of the train), because there will be a certain fluctuation in the dynamic process. Therefore, when considering the historical braking release time of the train, the influence of factors such as the current braking time on the air braking force is taken into consideration, and the above-mentioned influencing factors are quantified as parameters, and the steady-state process of air braking is introduced. Its mathematical description is expressed as follows:

[0113]

[0114]

[0115] Q py =k1*B shoe_tmp +k2

[0116]

[0117] Among them, P is the steady-state characteristic coefficient, T REL_Lastis the release time of the upper gate, in seconds / s, L is the discreteness of the S function, i.e. the initial value of the S function, T REL_Set Time reserved for complete relief, unit: seconds / s, t BRA is the real-time braking time, in seconds / s, T BRA is the total braking time of the brake, in seconds / s, Q py is the offset inflection point of the S function rise; B shoe_tmp The unit of the brake shoe temperature is: Celsius / ℃, e is a constant, k1 is the proportional coefficient of the rising inflection point fitting function, k2 is the constant part of the rising inflection point fitting function, and a, b, c, and d are the correlation coefficients of the temperature fitting function of the brake shoe respectively.

[0118] S24. Calculate the air braking force of each carriage of the heavy-load train according to the train air braking transient process model and the train air braking steady-state process model, expressed as:

[0119] F Bi (t) = β c *φ h *K h *B para,i (t)

[0120]

[0121] Among them, F Bi is the air braking force of the i-th train compartment, β c is the braking coefficient, φ h To convert the friction coefficient (high friction), K h To convert the brake shoe pressure (high friction), B para,i (t) is the power utilization rate of the i-th train car, λ is the characteristic parameter of the brake control valve, γ is the characteristic parameter of the brake wave propagation speed, n is the total number of train cars, t d,i is the time when the brake cylinder of the i-th train compartment starts to charge, t Δ,i Q is the time difference between the brake cylinder filling of the i-th train carriage and the first train carriage, py is the offset inflection point of the S function rise, L is the S function discreteness, T BRA is the total braking time of the brake, t BRA is the real-time braking time, e is a constant, t m is the end time of the transient process, T1 is the filling time of the brake cylinder of the first vehicle;

[0122] S25, constructing a longitudinal dynamics model of the train according to the air braking force of each carriage of the heavy-load train and the front and rear hook forces of the heavy-load train;

[0123] In practice, the above analysis shows that during operation, the locomotive will be affected by the electric traction / braking force, coupler force, running resistance, and air braking force; the vehicle will be affected by the coupler force, running resistance, and air braking force. Therefore, the air braking force F of the i-th train car can be solved by the air brake model. Bi Substitute it into the differential form, construct the force analysis of the locomotive and vehicle, and construct a mathematical description of the train state, that is, the longitudinal dynamics model of the train.

[0124] In the embodiment of the present invention, step S25 is specifically as follows:

[0125] The differential equations are constructed by the air braking force of each carriage of the heavy-load train and the front and rear coupler forces of the heavy-load train to obtain the longitudinal dynamics model of the train, where the differential equations are expressed as:

[0126]

[0127] Among them, m i is the mass of the i-th train carriage, unit: ton / t; is the longitudinal displacement of the i-th train carriage, unit: mm; F TEi is the traction force of the i-th train carriage, unit: kN; F ci-1 ,F cn are the front and rear hook forces of the i-th train carriage, in kN; F DBi is the electric braking force of the i-th train carriage, unit: kN; F wi is the total resistance of the i-th train compartment, unit: kN; F Bi is the air braking force of the i-th train compartment, unit: kN;

[0128] S26. Perform parameter verification on the train longitudinal dynamics model according to the basic data to obtain a verified train longitudinal dynamics model.

[0129] In practice, the present invention imports actual train operation data into the constructed train longitudinal dynamics model, uses the same operating conditions as the actual vehicle to perform traction calculations to reproduce the train's operating status and adjusts parameters to make the simulation results of the train longitudinal dynamics model consistent with the actual results, and verifies the size and distribution of the coupler force in the simulation results, and evaluates the application and changes of the braking performance based on the calculated air braking force.

[0130] S3. Constructing a multi-objective optimization calculation model for a train based on the verified longitudinal dynamics model of the train;

[0131] like Figure 3 As shown, in the embodiment of the present invention, step S3 specifically includes the following sub-steps:

[0132] S31. Construct an optimization objective function based on the basic data model, expressed as:

[0133]

[0134] Among them, J is the optimization objective function, t f is the optimization end time, t0 is the optimization start time, λ f is the train longitudinal force weight coefficient, λ u is the weight coefficient of locomotive traction / braking force change rate, λ e is the train operation energy consumption weight coefficient, v r is the train speed, u i is the locomotive traction or braking force of the i-th train carriage, u i-1 is the locomotive traction / braking force of the i-1 train carriage, f in is the coupler force of the train carriage;

[0135] In practice, taking into account the characteristics of heavy-load trains operating on long downhill slopes, an evaluation function based on safety, stability and energy saving was established.

[0136] S32, constructing a motion state equation according to the verified train longitudinal dynamics model;

[0137] In the embodiment of the present invention, the motion state equation in step S32 is expressed as:

[0138]

[0139] Among them, m i is the mass of the i-th train carriage, is the acceleration of the i-th train carriage, v i is the speed of the i-th train carriage, v i+1 is the speed between carriages of the i+1th train, is the relative speed between the i-th train carriage and the i+1-th train carriage, is the coupling force of the i-th train carriage, is the coupling force of the i-1 train carriage, is the total resistance of the i-th train carriage;

[0140] In practice, in order to satisfy the standard quadratic form used in the present invention, the kinematic equation of the heavy-duty train needs to be converted into a state equation form that conforms to the quadratic programming algorithm. The specific conversion steps are as follows:

[0141] First, since heavy-load trains are centralized power trains, only locomotives can provide traction and electric braking force, while freight cars only have air braking force, so the locomotive control amount u can be constructed. l The limited range, that is, u l ∈[-BBmax ,F Tmax ], where B Bmax In order for the locomotive to exert maximum electric braking force, F Tmax The locomotive can exert the maximum electric traction force, and the freight car control amount u w The limited range, that is, u w ∈[-B Bmin ,-B Bmax ], where B Bmin To provide the locomotive with the minimum electric braking force;

[0142] Secondly, the resistance of the train can be expressed as: Among them, f ri is the total resistance of the i-th train carriage, in kN, m i is the mass of the i-th train carriage, in kN, are the basic resistance coefficients of the i-th train compartment, f pi is the resistance of the i-th train car related to its position, v i is the speed of the i-th train carriage;

[0143] Since the train coupler force depends on the relative displacement and relative speed of the two adjacent carriages, its expression can be simplified as: in, is the coupler force of the i-th train carriage, in kN; k i 、b i are the coupler force coefficients of the i-th train carriage, is the relative speed of two adjacent cars, n is the total number of train cars;

[0144] Therefore, the kinematic equation for a single train carriage can be transformed into:

[0145]

[0146] The relative speed of two adjacent train carriages can be converted into:

[0147]

[0148] Therefore, the motion state equations can be obtained together. This set of equations is constructed with each train locomotive and carriage as a mass point, which is more refined than the motion equations in the existing technical solution that regards the train as a single mass point or a homogeneous rod model.

[0149] S33. According to the optimization objective function and basic data, the operation boundary and operation constraints are constructed, and the train characteristic constraints are preset according to the safety and stability indicators to obtain the train multi-objective optimization calculation model.

[0150] In this embodiment, the train multi-objective optimization calculation model in step S33 is expressed as:

[0151]

[0152] Optimization boundaries and operational constraints:

[0153] v i (x0) = v0 t(x0) = t0

[0154] v i (x f )=v f t(x f ) = t f

[0155] v i (x)≤min{v lim1 (x),v lim2 (x),v lim3 (x),…}

[0156] Among them, v i (x0) = v0 is the initial velocity of the initial position x0 defined as v0, t(x0) = t0 is the initial time of the initial position x0 defined as t0, v i (x f )=v f To change the end point position x f The terminal velocity is defined as v f , t(x f ) = t f To change the end point position x f The end time is defined as t f , v lim1 (x),v lim2 (x),v lim3 (x) etc. respectively represent the speed limits during operation;

[0157] Constraints on the fluctuation of coupler force:

[0158] 0≤f in ≤F SET

[0159] Locomotive traction / braking force constraints:

[0160] 0≤u i ≤F max (v i )

[0161] And air brakes relieve recharge time constraints:

[0162] T ch arge ≥T SET

[0163] Among them, f in is the train coupler force, unit: kN, F SET is the constraint of the coupler force, u i is the locomotive traction / braking force, unit: kN, F max (v i ) is the locomotive traction / braking force constraint, unit: kN, T charge The actual air-filling time of the train compartment, unit: second / S, T SET It is the actual relief of air filling time constraint for train compartments, unit: second / S;

[0164] In practice, the optimization boundaries and operation constraints can be clearly defined according to the route conditions in the basic data to increase the safety of train operation. Secondly, various constraints determined according to safety and stability indicators can be integrated to complete the construction of the multi-objective optimization calculation model of the train.

[0165] The size of the constraint conditions can be selected according to the actual situation.

[0166] S4. Construct a standard quadratic form based on the train multi-objective optimization calculation model, and solve it using the standard QP model to obtain the optimized operation sequence.

[0167] like Figure 4 As shown, in the embodiment of the present invention, step S4 includes the following sub-steps:

[0168] S41. The nonlinear part in the multi-objective optimization calculation model is linearized to obtain a standard train state equation, which is expressed as:

[0169]

[0170] Among them, k i-1 x i-1 The simplified coupling force of the i-1 train carriage, k i x i The simplified coupling force of the i-th train carriage, m i is the mass of the i-th train carriage, u′ i is the equivalent train control quantity, unit: kN, δ i is the equivalent partial resistance of the ith train carriage, in kN, is the relative speed between the i-th train carriage and the i+1-th train carriage; v i is the speed of the i-th train carriage, v i+1 is the speed between carriages of the i+1th train, are the basic resistance coefficients of the i-th train compartment, f pi is the resistance of the i-th train car related to its position;

[0171] In practice, in the actual operation of heavy-load trains, the damping effect of the coupler buffer will bring about nonlinear characteristics of the train model that are difficult to measure directly. Therefore, the train model needs to be linearized and b can be ignored. i Item (i.e., let b i =0), the total running resistance is split and assigned to the locomotive traction / braking force, thereby obtaining the standard train state equation;

[0172] The train speed and the relative displacement of two adjacent trains can be taken as the state quantity x, that is: The control variable is u'=[u'1, u'2,...,u' n ], then the vector form can be expressed as: A and B are preset coefficients respectively.

[0173] S42, discretizing the standard train state equation using the step size to obtain a discretized train state equation;

[0174] In the embodiment of the present invention, step S42 is specifically as follows:

[0175] The sampling period is preset, and the standard train state equation is discretized in the continuous time domain using a zero-order holder to obtain the discretized train state equation, which is expressed as:

[0176] x(k+1)=Ax(k)+Bu'(k)

[0177] Among them, x(k+1) is the discretized train state equation, u'(k) is the equivalent train control quantity, k is the discretized sampling point, T s is the sampling period, e is a constant, and τ is the time variable;

[0178] S43, using the discretized train state equation to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, and obtain a quadratically standardized train multi-objective optimization calculation model;

[0179] In the embodiment of the present invention, step S43 is specifically as follows:

[0180] The discretized train state equation is used to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, which is expressed as:

[0181]

[0182] Among them, J *is the objective function after the standard quadratic form, x is the train state, (·) T is the vector transpose, Q is the weight coefficient λ of the longitudinal force of the train f and locomotive traction / braking force change rate weight coefficient λ u The coefficient matrix of the train operation energy consumption is λ, diag[·] is a diagonal matrix, and R is a weighted matrix containing the train operation energy consumption coefficient λ. e The coefficient matrix, F1 T is the weight coefficient λ of the locomotive traction / braking force change rate u The first coefficient matrix, F2 T is the weight coefficient λ of train operation energy consumption e The second coefficient matrix, I nxn is the n-order unit matrix, δ n is the equivalent partial resistance of the nth train carriage, u i-1 is the traction / braking force actually exerted by the locomotive at the previous moment, k n-1 is the proportional coefficient in the hook-buffer model;

[0183] In practice, the simultaneous state equations equate the objective function and ignore the constant term, classifying it as a standard quadratic form.

[0184] S44. The multi-objective optimization calculation model of the train after the second normalization is brought into the standard QP model for solution to obtain the optimized operation sequence.

[0185] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0186] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0187] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0188] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0189] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for optimizing the long downhill maneuvering of a heavy-load train based on air brakes, characterized in that: The following steps are involved: S1. Obtain basic data of heavy-load trains; S2. constructing a longitudinal dynamics model of the train, and performing parameter verification on the longitudinal dynamics model of the train according to basic data to obtain a verified longitudinal dynamics model of the train; include The following steps: S21, constructing a train coupling model, and calculating the front and rear coupling forces of a heavy-load train based on basic data; S22, constructing a train air braking transient process model; S23, constructing a steady-state process model of train air braking; specifically: The influencing factors are parameterized and the mathematical description of the train air brake steady-state process is introduced to obtain the train air brake steady-state process model, and its mathematical description is expressed as follows: Where, P is the steady-state characteristic coefficient; S24. Calculate the air braking force of each carriage of the heavy-load train according to the train air braking transient process model and the train air braking steady-state process model, expressed as: F Bi (t)=β c *f h *K h *B para,i (t) Among them, F Bi is the air braking force of the i-th train compartment, β c is the braking coefficient, φ h To convert the friction coefficient, K h To convert the brake shoe pressure, B para,i (t) is the power utilization rate of the i-th train car, λ is the characteristic parameter of the brake control valve, t d,i is the time when the brake cylinder of the i-th train compartment starts to charge, t Δ,i Q is the time difference between the brake cylinder filling of the i-th train carriage and the first train carriage, py is the offset inflection point of the S function rise, L is the S function discreteness, T BRA is the total braking time of the brake, t BRA is the real-time braking time, e is a constant, t m is the end time of the transient process, T1 is the filling time of the brake cylinder of the first vehicle; S25. Construct a longitudinal dynamics model of the train based on the air braking force of each carriage of the heavy-load train and the front and rear coupler forces of the heavy-load train; specifically: The differential equations are constructed by the air braking force of each carriage of the heavy-load train and the front and rear coupler forces of the heavy-load train to obtain the longitudinal dynamics model of the train, where the differential equations are expressed as: Among them, m i is the mass of the i-th train carriage; is the longitudinal displacement of the i-th train carriage; F TEi is the traction force of the i-th train carriage; F ci-1 ,F cn are the front and rear coupler forces of the i-th train carriage respectively; F DBi is the electric braking force of the i-th train carriage; F wi is the total resistance of the i-th train compartment; F Bi is the air braking force of the i-th train carriage; S26, performing parameter verification on the train longitudinal dynamics model according to the basic data to obtain a verified train longitudinal dynamics model; S3. Constructing a multi-objective optimization calculation model for a train based on the verified longitudinal dynamics model of the train; S4. Construct a standard quadratic form based on the train multi-objective optimization calculation model, and solve it using the standard QP model to obtain the optimized operation sequence.

2. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brake according to claim 1, characterized in that: Step S3 specifically includes the following sub-steps: S31. Construct an optimization objective function based on the basic data model, expressed as: Among them, J is the optimization objective function, tf To optimize the termination time, t0 To optimize the starting time, λ f is the weight coefficient of the longitudinal force of the train, λ u is the weight coefficient of locomotive traction / braking force change rate, λ e is the train operation energy consumption weight coefficient, v r is the train speed, u i is the locomotive traction or braking force of the i-th train carriage, u i-1 is the locomotive traction / braking force of the i-1 train carriage, f in is the coupler force of the train carriage; S32, constructing a motion state equation according to the verified train longitudinal dynamics model; S33. According to the optimization objective function and basic data, the operation boundary and operation constraints are constructed, and the train characteristic constraints are preset according to the safety and stability indicators to obtain the train multi-objective optimization calculation model.

3. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brake according to claim 2, characterized in that: The motion state equation in step S31 is expressed as: Among them, m i is the mass of the i-th train carriage, is the acceleration of the i-th train carriage, v i is the speed of the i-th train carriage, v i+1 is the speed between carriages of the i+1th train, is the relative speed between the i-th train carriage and the i+1-th train carriage, is the coupling force of the i-th train carriage, is the coupling force of the i-1 train carriage, is the total resistance of the i-th train carriage.

4. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brake according to claim 2, characterized in that: The train multi-objective optimization calculation model in step S33 is expressed as: Optimization boundaries and operational constraints: v i (x0)=v0 t(x0)=t0 v i (x f )=v f t(x f )=t f v i (x)≤min{v lim1 (x),v lim2 (x),v lim3 (x),…} Among them, v i (x0) = v0 is the initial velocity of the initial position x0 defined as v0, t(x0) = t0 is the initial time of the initial position x0 defined as t0, v i (x f )=v f To change the end point position x f The terminal velocity is defined as v f , t(x f ) = t f To change the end point position x f The end time is defined as t f , v lim1 (x),v lim2 (x),v lim3 (x) etc. respectively represent the speed limits during operation; Constraints on the fluctuation of coupler force: 0≤f in ≤F SET Locomotive traction / braking force constraints: 0≤u i ≤F max (in i ) And air brakes relieve recharge time constraints: T charge ≥T SET Among them, f in is the train coupler force, F SET is the constraint on the coupler force, u i is the locomotive traction or braking force, F max (v i ) is the locomotive traction or braking force constraint, T charge The actual air filling time of the train compartment is relieved, T SET This can actually alleviate the time constraints on air filling for train carriages.

5. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brake according to claim 1, characterized in that: Step S4 includes the following sub-steps: S41. The nonlinear part in the multi-objective optimization calculation model is linearized to obtain a standard train state equation, which is expressed as: Among them, k i-1 x i-1 The simplified coupling force of the i-1 train carriage, k i x i The simplified coupling force of the i-th train carriage, m i is the mass of the i-th train carriage, u' i is the equivalent train control quantity, δ i is the equivalent partial resistance of the i-th train carriage, is the relative speed between the i-th train carriage and the i+1-th train carriage; v i is the speed of the i-th train carriage, v i+1 is the speed between carriages of the i+1th train, are the basic resistance coefficients of the i-th train compartment, f pi is the resistance of the i-th train car related to its position, is the acceleration of the i-th train carriage; S42, discretizing the standard train state equation using the step size to obtain a discretized train state equation; S43, using the discretized train state equation to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, and obtain a quadratically standardized train multi-objective optimization calculation model; S44. The multi-objective optimization calculation model of the train after the second normalization is brought into the standard QP model for solution to obtain the optimized operation sequence.

6. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brake according to claim 5, characterized in that: Step S42 is specifically as follows: The sampling period is preset, and the standard train state equation is discretized in the continuous time domain using a zero-order holder to obtain the discretized train state equation, which is expressed as: x(k+1)=Ax(k)+Bu'(k) Among them, x(k+1) is the discretized train state equation, u'(k) is the equivalent train control quantity, k is the discretized sampling point, T s is the sampling period, e is a constant, and τ is the time variable.

7. The method for optimizing the long downhill maneuvering of a heavy-load train based on air brakes according to claim 6, characterized in that: Step S43 is specifically as follows: The discretized train state equation is used to classify the optimization objective function in the train multi-objective optimization calculation model into a standard quadratic form, which is expressed as: Among them, J* is the objective function after the standard quadratic form, x is the train state quantity, (·) T is the vector transpose, Q is the weight coefficient λ of the longitudinal force of the train f and locomotive traction / braking force change rate weight coefficient λ u The coefficient matrix of the train operation energy consumption is λ, diag[·] is a diagonal matrix, and R is a weighted matrix containing the train operation energy consumption coefficient λ. e The coefficient matrix, F1 T is the weight coefficient λ of the locomotive traction / braking force change rate u The first coefficient matrix of is the weight coefficient λ of train operation energy consumption e The second coefficient matrix, I nxn is the n-order unit matrix, δ n is the equivalent partial resistance of the nth train carriage, u i-1 is the traction / braking force actually exerted by the locomotive at the previous moment, k n-1 is the proportional coefficient in the hook-buffer model.

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