Fine Simulation Calculation Method for Evaluating the Driving Safety and Passenger Comfort on High-Speed Railway Bridges

Abstract

The present invention discloses a refined simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges, comprising the following steps: establishing a digital twin simulation calculation model of the bridge structure; establishing a digital twin simulation calculation model of the high-speed train; establishing a digital twin simulation calculation model of the passenger seat; establishing a complete human-vehicle-bridge coupling simulation system; establishing a digital twin simulation calculation module for random track irregularities; establishing a digital twin simulation calculation module for additional track irregularities caused by bridge structure damage; establishing the coupling dynamic relationship between the high-speed train and the track at the wheel-rail contact surface; obtaining a digital twin calculation module for the safety evaluation indexes of driving safety and passenger comfort on the high-speed railway bridge structure; and obtaining the quantitative mapping relationship between bridge structure damage and driving safety and passenger comfort. The present invention solves the underlying key technical problems of accurate mapping modeling, design, analysis, diagnosis, and decision-making of the physical model and data-driven model for evaluating the driving safety and passenger comfort on high-speed railway bridges.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic safety, and particularly relates to a fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges. Background Art

[0002] By the end of 2021, the national high-speed railway operating mileage had reached 40,000 kilometers, and the bridge structure accounted for more than 50% in most high-speed railway lines. With the continuous and rapid development of high-speed railways, they inevitably pass through special areas such as seismic zones, extreme climates, and poor geological conditions, which are bound to cause various deformation and damage modes such as pier settlement, beam end rotation, beam body offset, and bearing deformation of the bridge structure. Based on the interlayer mechanics and deformation coordination between the track and the bridge, most of these deformations will be mapped to the rail surface, causing additional track irregularities and affecting the train operation safety. The deformation of the bridge structure is one of the extremely key factors affecting the geometric shape of the rail surface.

[0003] Due to the characteristics of the ballastless track-bridge system of high-speed railways, such as structural complexity, disease diversity, and working condition time-variation, the existing research bases and means cannot keep up with the development needs, resulting in the increasingly prominent problem of the service safety of vehicle structures. It is urgent to study the key scientific problems involved and propose reasonable prevention and control measures to solve these engineering problems and improve the service safety performance of high-speed railway lines. On the other hand, when current scholars conduct research, they mostly rely on the combined use of multiple types of commercial software, and there is no completely applicable independent integrated fine simulation calculation system.

[0004] In view of the above problems, it is very necessary to develop a set of independent and controllable fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges to systematically solve the fine simulation calculation problems of driving safety and passenger comfort under the condition of accurately simulating and comprehensively considering the track random irregularities and the additional track irregularities caused by the damage of bridge components. Summary of the Invention

[0005] The present invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges.

[0006] The technical solution of the present invention is: a fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges, including the following steps:

[0007] A. Establish a digital twin simulation calculation model of the bridge structure;

[0008] B. Establish a digital twin simulation calculation model of the high-speed train;

[0009] C. Establish a digital twin simulation calculation model of the passenger seat;

[0010] D. Establish a complete human-vehicle-bridge coupling simulation system;

[0011] E. Establish a digital twin simulation calculation module for random track irregularities;

[0012] F. Establish a digital twin simulation calculation module for additional track irregularities caused by bridge structure damage;

[0013] G. Establish the coupled dynamic relationship between high-speed trains and tracks at the wheel-rail contact surface;

[0014] H. Based on the digital twin simulation calculation module for random track irregularities and the digital twin simulation calculation module for additional track irregularities caused by bridge structure damage, obtain the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on high-speed railway bridge structures;

[0015] I. Based on the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on high-speed railway bridge structures, obtain the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort.

[0016] Furthermore, in step A, establish a digital twin simulation calculation model for bridge structures, and the specific process is as follows:

[0017] First, determine the component members of the bridge structure;

[0018] Then, use the finite element method to establish a digital twin simulation calculation model for the bridge structure;

[0019] Next, the geometric dimensions of the component members are input using custom arbitrary cross-section input;

[0020] Finally, the bearings in the bridge structure are simulated using six-direction support springs.

[0021] Furthermore, in step B, establish a digital twin simulation calculation model for high-speed trains, and the specific process is as follows:

[0022] First, establish digital twin simulation calculation models for high-speed trains with different degrees of freedom for different high-speed trains;

[0023] Then, different degrees-of-freedom high-speed trains establish vibration motion equations according to the principle of Lagrange's equation.

[0024] Furthermore, in step C, establish a digital twin simulation calculation model for passenger seats, and the specific process is as follows:

[0025] First, establish a human body model, regarding the human body as a biological elastic body, and the biological elastic body includes the head, viscera, and torso, and the head, viscera, and torso are all represented by two degrees of freedom;

[0026] Then, establish a seat model, and the seat model is represented by two degrees of freedom;

[0027] Finally, a complete digital twin simulation calculation model of the passenger chair is formed by the human body model and the seat model;

[0028] Furthermore, in step D, a complete vehicle-bridge coupling simulation system is established, and the specific process is as follows:

[0029] First, the vehicle-bridge coupling simulation system is constructed by the digital twin simulation calculation model of the bridge structure established in step A and the digital twin simulation calculation model of the high-speed train established in step B;

[0030] Then, the digital twin simulation calculation model of the passenger chair established in step C is added to the vehicle-bridge coupling simulation system to obtain a complete vehicle-bridge coupling simulation system.

[0031] Furthermore, in step E, a digital twin simulation calculation module for track random irregularities is established, and the specific process is as follows:

[0032] First, the composition of track random irregularities is determined. Track random irregularities include vertical alignment, alignment, gauge, level, and cross-level;

[0033] Then, the track random irregularities are converted into time history curves as the self-excitation of the vehicle-bridge coupling simulation system;

[0034] Next, based on the self-excited track random irregularities and the vehicle-bridge coupling simulation system, a digital twin simulation calculation module for track random irregularities is obtained;

[0035] Finally, the trigonometric series method is used as the main algorithm of the digital twin simulation calculation module for track random irregularities to obtain an array of track random irregularities.

[0036] Furthermore, in step F, a digital twin simulation calculation module for additional track irregularities caused by bridge structure damage is established, and the specific process is as follows:

[0037] First, bridge structure damage includes pier settlement, beam offset, beam end rotation, bearing detachment, fastener breakage, and bottom slab mortar layer detachment;

[0038] Then, pier settlement, beam offset, beam end rotation, bearing detachment, fastener breakage, and bottom slab mortar layer detachment result in additional irregularities on the rail surface;

[0039] Finally, a general array of additional track irregularities caused by damage with a freely expandable array dimension is obtained.

[0040] Furthermore, in step G, the coupling dynamic relationship between the high-speed train and the track at the wheel-rail contact surface is established, and the specific process is as follows:

[0041] First, the wheel-rail normal force between the high-speed train and the track is obtained using the non-linear Hertz contact theory;

[0042] Then, the wheel-rail tangential creep force between the high-speed train and the track is calculated using the Kaller theory.

[0043] Furthermore, step H is based on the digital twin simulation calculation module of track random irregularities and the digital twin simulation calculation module of additional track irregularities caused by bridge structure damage, and obtains the digital twin calculation module of safety evaluation indexes for train operation safety and passenger comfort on the high-speed railway bridge structure. The specific process is as follows:

[0044] First, the array of track random irregularities obtained in step E and the array of additional track irregularities caused by general damage obtained in step F are superimposed and then substituted into the vehicle-bridge coupling simulation system formed in step D.

[0045] Then, the calculation results of the vehicle-bridge coupling dynamic response are obtained. The calculation results of the vehicle-bridge coupling dynamic response include train operation safety indexes and passenger comfort indexes.

[0046] Furthermore, step I is based on the digital twin calculation module of safety evaluation indexes for train operation safety and passenger comfort on the high-speed railway bridge structure, and obtains the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort. The specific process is as follows:

[0047] First, the calculation results of the vehicle-bridge coupling dynamic response obtained in step H are used as the first response result.

[0048] Then, the calculation results of the vehicle-bridge coupling dynamic response calculated from the array of track random irregularities are used as the second response result.

[0049] Then, the third response result is obtained by subtracting the second response result from the first response result. The third response result is used as the calculation result of the vehicle-bridge coupling dynamic response corresponding to the array of additional track irregularities caused by bridge structure damage.

[0050] Then, the second-order derivative of the additional track irregularities caused by bridge structure damage with respect to the track mileage is calculated.

[0051] Then, the least squares fitting method is used to establish the quantitative relationship between the above second-order derivative and the third response result.

[0052] Finally, according to the quantitative relationship, a damage threshold of the bridge structure to ensure train operation safety and passenger comfort is established.

[0053] The beneficial effects of the present invention are as follows:

[0054] Aiming at the problem of fine simulation calculation of train operation safety and passenger comfort evaluation on high-speed railway bridges, the present invention establishes a complete set of fine simulation calculation methods and technologies for train operation safety and passenger comfort evaluation on high-speed railway bridges that are completely independently controllable.

[0055] The present invention can digitally construct a fine simulation calculation for the evaluation of train operation safety and passenger comfort in the field of traffic safety technology, and solve the underlying key technical problems of accurate mapping modeling, design, analysis, diagnosis, and decision-making of the physical model and data-driven model for train operation safety and passenger comfort evaluation on high-speed railway bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a schematic diagram of the module of the present invention;

[0057] Figure 2 is a schematic cross-sectional view of the box girder of the present invention;

[0058] Figure 3 is an arbitrary cross-section input interface of the cross-section of the box girder of the present invention;

[0059] Figure 4 is a schematic diagram of the calculation model of a high-speed train of the present invention;

[0060] Figure 5 is a schematic diagram of the human-chair calculation model of the present invention;

[0061] Figure 6 is a schematic diagram of track irregularity of the present invention;

[0062] Figure 7 is a schematic diagram of train operation and component damage on a high-speed railway bridge of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] Hereinafter, the present invention will be described in detail with reference to the drawings and embodiments:

[0064] As Figures 1 to 7 shown, a fine simulation calculation method for train operation safety and passenger comfort evaluation on a high-speed railway bridge includes the following steps:

[0065] A. Establish a digital twin simulation calculation model of the bridge structure;

[0066] B. Establish a digital twin simulation calculation model of the high-speed train;

[0067] C. Establish a digital twin simulation calculation model of the passenger-chair;

[0068] D. Establish a complete human-vehicle-bridge coupling simulation system;

[0069] E. Establish a digital twin simulation calculation module for random track irregularity;

[0070] F. Establish a digital twin simulation calculation module for additional track irregularity caused by bridge structure damage;

[0071] G. Establish the coupled dynamic relationship between the high-speed train and the track at the wheel-rail contact surface;

[0072] H. Based on the digital twin simulation calculation module for track random unevenness and the digital twin simulation calculation module for additional track unevenness caused by bridge structure damage, obtain the digital twin calculation module for the safety evaluation indexes of train operation safety and passenger comfort on the high-speed railway bridge structure;

[0073] I. Based on the digital twin calculation module for the safety evaluation indexes of train operation safety and passenger comfort on the high-speed railway bridge structure, obtain the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort.

[0074] Furthermore, in step A, establish the digital twin simulation calculation model of the bridge structure, and the specific process is as follows:

[0075] First, determine the component parts of the bridge structure;

[0076] Then, establish the digital twin simulation calculation model of the bridge structure by using the finite element method;

[0077] Next, the geometric dimensions of the component parts are input by using the custom arbitrary cross-section input;

[0078] Finally, the bearings in the bridge structure are simulated by using six-direction support springs.

[0079] Furthermore, in step B, establish the digital twin simulation calculation model of the high-speed train, and the specific process is as follows:

[0080] First, establish the digital twin simulation calculation model of the high-speed train with different degrees of freedom for different high-speed trains;

[0081] Then, the vibration equations of motion are established for the high-speed trains with different degrees of freedom according to the Lagrange equation principle.

[0082] Furthermore, in step C, establish the digital twin simulation calculation model of the passenger seat, and the specific process is as follows:

[0083] First, establish the human body model. The human body is regarded as a biological elastic body, and the biological elastic body includes the head, internal organs and torso, and the head, internal organs and torso are all represented by two degrees of freedom;

[0084] Then, establish the seat model, and the seat model is represented by two degrees of freedom;

[0085] Finally, the human body model and the seat model form a complete digital twin simulation calculation model of the passenger seat;

[0086] Furthermore, in step D, establish the complete human-vehicle-bridge coupling simulation system, and the specific process is as follows:

[0087] First, construct the vehicle-bridge coupling simulation system by integrating the digital twin simulation calculation model of the bridge structure established in step A and the digital twin simulation calculation model of the high-speed train established in step B;

[0088] Then, add the digital twin simulation calculation model of the passenger seat established in step C to the vehicle-bridge coupling simulation system to obtain a complete human-vehicle-bridge coupling simulation system.

[0089] Furthermore, in step E, establish the digital twin simulation calculation module for track random irregularities, and the specific process is as follows:

[0090] First, determine the composition of track random irregularities, which include vertical alignment, track direction, gauge and level, and cross-level;

[0091] Then, convert the track random irregularities into time-history curves as the self-excitation of the vehicle-bridge coupling simulation system;

[0092] Next, based on the self-excited track random irregularities and the vehicle-bridge coupling simulation system, obtain the digital twin simulation calculation module for track random irregularities;

[0093] Finally, use the trigonometric series method as the main algorithm of the digital twin simulation calculation module for track random irregularities to obtain the track random irregularity array.

[0094] Furthermore, in step F, establish the digital twin simulation calculation module for additional track irregularities caused by bridge structure damage, and the specific process is as follows:

[0095] First, bridge structure damage includes pier settlement, beam offset, beam end rotation, bearing disengagement, fastener breakage, and bottom slab mortar layer disengagement;

[0096] Then, pier settlement, beam offset, beam end rotation, bearing disengagement, fastener breakage, and bottom slab mortar layer disengagement cause additional irregularities on the rail surface;

[0097] Finally, obtain a general array of additional track irregularities caused by damage with a freely expandable array dimension.

[0098] Furthermore, in step G, establish the coupling dynamic relationship between the high-speed train and the track at the wheel-rail contact surface, and the specific process is as follows:

[0099] First, the wheel-rail normal force between the high-speed train and the track is obtained using the non-linear Hertz contact theory;

[0100] Then, the wheel-rail tangential creep force between the high-speed train and the track is calculated using the Kaller theory.

[0101] Furthermore, step H is based on the digital twin simulation calculation module of track random irregularity and the digital twin simulation calculation module of additional track irregularity caused by bridge structure damage to obtain the digital twin calculation module of safety evaluation indexes for train operation safety and passenger comfort on high-speed railway bridge structures. The specific process is as follows:

[0102] First, the track random irregularity array obtained in step E and the general damage-induced additional track irregularity array obtained in step F are superimposed and then substituted into the human-vehicle-bridge coupling simulation system formed in step D;

[0103] Then, the calculation results of the human-vehicle-bridge coupling dynamic response are obtained. The calculation results of the human-vehicle-bridge coupling dynamic response include train operation safety indexes and passenger comfort indexes.

[0104] Furthermore, step I is based on the digital twin calculation module of safety evaluation indexes for train operation safety and passenger comfort on high-speed railway bridge structures to obtain the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort. The specific process is as follows:

[0105] First, the calculation results of the human-vehicle-bridge coupling dynamic response obtained in step H are used as the first response result;

[0106] Then, the calculation results of the human-vehicle-bridge coupling dynamic response calculated from the track random irregularity array are used as the second response result;

[0107] Next, the third response result is obtained by subtracting the second response result from the first response result. The third response result is used as the calculation result of the human-vehicle-bridge coupling dynamic response corresponding to the additional track irregularity array caused by bridge structure damage;

[0108] Next, calculate the second derivative of the additional track irregularity caused by bridge structure damage with respect to the track mileage;

[0109] Next, use the least squares fitting method to establish the quantitative relationship between the above second derivative and the third response result;

[0110] Finally, according to the quantitative relationship, establish the damage threshold of the bridge structure to ensure train operation safety and passenger comfort.

[0111] Specifically, in step A of establishing the digital twin simulation calculation model of the bridge structure, the beam body of the simply supported beam is simulated by using the equal-section space beam element, and the beam body of the continuous beam is simulated by using the variable-section space beam element.

[0112] Specifically, in step B of establishing the digital twin simulation calculation model of the high-speed train, the degrees of freedom of the digital twin simulation calculation model of the high-speed train are 21, 23, 31, 35, and 42.

[0113] Specifically, in step E of establishing the digital twin simulation calculation module for track random irregularities, when calculating the dynamic responses of the vehicle and the human body, the track irregularity spectrum specified in the Code for Track Irregularity Spectrum of Ballastless High-Speed Railways (TB / T 3352-2014) (hereinafter referred to as the "irregularity spectrum code") is used as the basis.

[0114] Specifically, in step F of establishing the digital twin simulation calculation module for additional track irregularities caused by bridge structure damage, in order to be compatible with different types of structural damage and the differences in additional track surface irregularities caused by damage to simply supported beams and continuous beams, a general array for additional track irregularities caused by damage with freely expandable array dimensions is proposed.

[0115] Specifically, in step A, a digital twin simulation calculation model of the bridge structure composed of bridge piers, beam bodies, and pile foundations is established, and the geometric dimensions of the component parts are input using a custom arbitrary cross-section input mode.

[0116] The custom arbitrary cross-section input rules are as follows:

[0117] a. Each side is input in a counterclockwise direction and separated by a semicolon ";".

[0118] b. The information of each side contains 5 parameters, separated by a comma "," in the middle.

[0119] c. The physical meanings of the 5 parameters are as follows:

[0120] ① Section number, >0 for the outer contour, <0 for the inner contour

[0121] ② Starting endpoint x coordinate

[0122] ③ Starting endpoint z coordinate

[0123] ④ Radius r, =0 for a straight line segment, >0 for the radius of an arc

[0124] ⑤ Arc indication, =0 for a full circle, >0 for a minor arc, <0 for a major arc.

[0125] The digital twin simulation calculation model of the bridge structure is established using the finite element method, and the bearings are simulated using six-direction support springs. For the simply supported beam body, an equal-section space beam element is used for simulation, and for the continuous beam body, a variable-section space beam element is used for simulation.

[0126] Specifically, the relevant technical content in the Chinese invention patent application CN202210511550.4 can be adopted for the part of the stiffness matrix involving the variable-section space beam element.

[0127] Specifically, in step B of establishing the digital twin simulation calculation model of the high-speed train, the vibration motion equations of high-speed trains with different degrees of freedom are established according to the principle of Lagrange's equation. Among them, the expression of Lagrange's equation is:

[0128] (1)

[0129] In formula (1), T, V, and Q are the total kinetic energy, total elastic potential energy, and total damping dissipation energy of the system, respectively;

[0130] are the degrees of freedom of each part of the high-speed train;

[0131] is the derivative of;

[0132] represent the degrees of freedom of the car body, bogie, and wheel set;

[0133] represents the total derivative with respect to time;

[0134] represents the partial derivative operator.

[0135] More specifically, taking the vibration equation of a 31-degree-of-freedom high-speed train as an example, the degrees of freedom of the car body, bogie, and wheel set are as follows:

[0136] Degrees of freedom of the car body :

[0137] (2)

[0138] Degrees of freedom of the bogie :

[0139] (3)

[0140] Degrees of freedom of the wheel set :

[0141] (4)

[0142] In formulas (2), (3), and (4), , , represent the degrees of freedom of the car body, bogie, and wheel set, respectively;

[0143] represents yaw, represents heave, represents roll, represents pitch, represents shake;

[0144] The subscript c represents the car body, ti represents the bogie, and wij represents the wheel set;

[0145] T is the transpose operator of the matrix.

[0146] Based on the degrees of freedom in Equations (2) to (4), the total kinetic energy, total potential energy, and damping dissipation energy of the vehicle are calculated respectively, and then substituting them into Equation (1), the vibration motion equation of the 31-degree-of-freedom high-speed train can be obtained.

[0147] Specifically, in step C for establishing the digital twin simulation calculation model of the passenger chair, the digital twin simulation calculation model of the passenger chair has a total of 8 degrees of freedom, and the specific expressions are as follows:

[0148] The specific expressions of the degrees of freedom of the passenger chair are as follows:

[0149] (5)

[0150] In Equation (5), 、 represent the degrees of freedom in two directions of the seat;

[0151] 、 represent the degrees of freedom in two directions of the torso;

[0152] 、 represent the degrees of freedom in two directions of the internal organs;

[0153] 、 represent the degrees of freedom in two directions of the head.

[0154] Specifically, in step D for establishing the complete human-vehicle-bridge coupling simulation system, the digital twin simulation calculation model of the passenger chair established in step C is added to the vehicle-bridge coupling simulation system, thus forming a complete human-vehicle-bridge coupling simulation system.

[0155] Taking the dynamic balance equation corresponding to the human-vehicle system in the human-vehicle-bridge coupling simulation system as an example, its equation is expressed as follows:

[0156] (6)

[0157] In Equation (6), 、 、 、 represent the mass matrices of the car body, bogie, wheel set, and passenger respectively;

[0158] 、 、 、 represent the acceleration vector matrices of the car body, bogie, wheel set, and passenger respectively;

[0159] 、 , , represent the speed vector matrices of the car body, bogie, wheel set, and passengers respectively;

[0160] , , , represent the displacement vector matrices of the car body, bogie, wheel set, and passengers respectively;

[0161] , represent the damping matrix and the elastic matrix respectively, where the subscripts vv, tt, ww, and pp in the matrix represent the matrices on the main diagonals of the car body, bogie, wheel set, and passengers; the subscript vt(tv) represents the correlation matrix between the car body and the bogie; the subscript vp(pv) represents the correlation matrix between the car body and the passengers; the subscript tw(wt) represents the correlation matrix between the bogie and the wheel set;

[0162] represents the load column vector acting on the wheels.

[0163] For the specific degrees of freedom of the car body, bogie, and wheel set, please refer to the above formulas (2) to (4), and for the specific degrees of freedom of the passengers, please refer to formula (5).

[0164] Specifically, in step E of establishing the digital twin simulation calculation module for track random irregularities, the track random irregularity spectrum is piecewise fitted using a power function, and its formula is:

[0165] (7)

[0166] In formula (7), represents the spatial frequency;

[0167] , represent the coefficients of the fitting formula.

[0168] It is converted into a time history curve using a numerical algorithm and used as the self-excitation for the vehicle-bridge coupling dynamic analysis. Here, the trigonometric series method is used as the main algorithm for the irregularity digital twin simulation calculation module to calculate the track random irregularity array. The specific calculation formula is:

[0169] (8)

[0170] In formula (8), is the generated track irregularity sequence;

[0171] is the distance of the generated track irregularity sequence;

[0172] is the power spectral density function of the given track irregularity;

[0173] (k = 1, 2, … n) are the considered frequencies, where 、 are the upper and lower limits of the considered frequencies respectively;

[0174] n is the order of the upper frequency limit;

[0175] is the bandwidth of the frequency interval;

[0176] is the phase of the corresponding k-th frequency, which can generally be uniformly distributed between 0 and 2π.

[0177] Specifically, in step F of establishing the digital twin simulation calculation module for the additional track irregularity caused by bridge structure damage, the main modes of bridge structure damage include pier settlement, beam body offset, beam end rotation, bearing disengagement, etc. These structural damages will all cause a certain degree of additional track irregularity on the rail surface. To be compatible with different types of structural damages and the differences in the additional track irregularity on the rail surface caused by the damages of simply supported beams and continuous beams, a general array for the additional track irregularity caused by damage with freely expandable array dimensions is proposed here.

[0178] When different types of damages occur, the calculated array of the additional track irregularity is different, and the array of the additional track irregularity obtained by real-time calculation can be assigned to the general array for the additional track irregularity caused by damage with freely expandable array dimensions.

[0179] Specifically, when calculating the additional track irregularity on the rail surface caused by common damages of simply supported beams such as pier settlement, beam end rotation, broken fastener bars, and debonding of the mortar layer under the slab, the calculation method can adopt the relevant technology of Chinese invention patent application CN201910810980.4. When calculating the additional track irregularity on the rail surface caused by uneven settlement of the side piers of continuous beam bridges, the calculation method can adopt the paper by Feng Yulin et al. Coordination relationship between track layer deformations and dynamic applications under uneven settlement of side piers of continuous beam bridges, Engineering Mechanics, 2021, Vol. 38 (No. 4), pp. 179 - 190.

[0180] After calculating the additional track irregularity on the rail surface caused by specific types of damages using different methods, it can be assigned to the general array for the additional track irregularity caused by damage with freely expandable array dimensions.

[0181] Specifically, in step G of establishing the coupled dynamic relationship between the high-speed train and the track at the wheel-rail contact surface, the specific process is as follows:

[0182] The wheel-rail normal force between the high-speed train and the track is calculated using the non-linear Hertz contact theory, and the calculation formula is as follows:

[0183] (9)

[0184] In Equation (9), is the wheel-rail contact constant, which is related to factors such as the wheel-rail tread, and the unit is ;

[0185] is the Hertz normal contact force;

[0186] is the normal relative deformation value between the wheel and the rail.

[0187] The wheel-rail tangential creep force between the high-speed train and the track adopts the Kaller theory, and the relationship with the creep rate can be expressed as:

[0188] (10)

[0189] In Equation (10), 、 are the longitudinal and lateral creep forces;

[0190] is the rotational creep moment;

[0191] 、 are the longitudinal and lateral creep coefficients;

[0192] are the rotational and lateral creep coefficients;

[0193] is the rotational creep coefficient;

[0194] 、 、 represent the longitudinal, lateral, and vertical creep rates, respectively.

[0195] Specifically, in step H, the calculation results of the human-vehicle-bridge coupled dynamic response in the digital twin calculation module for the train operation safety and passenger comfort safety evaluation indicators on the high-speed railway bridge structure include train operation safety indicators and passenger comfort indicators.

[0196] The train operation safety indicators mainly include train vertical acceleration, wheel-rail vertical force, wheel weight reduction rate, derailment coefficient, lateral force, car body acceleration indicators, etc.

[0197] The passenger comfort indicator evaluates the comfort level based on the root mean square of the total weighted acceleration of the human body. The root mean square value of the total weighted acceleration is calculated according to the following formula:

[0198] (11)

[0199] In Equation (11), 、 、 are respectively the root mean square values of the weighted acceleration in each direction (x, y, and z directions).

[0200] According to ISO2631-1, the relationship between the root mean square weighted value of acceleration and the subjective human feeling level is given in Table 1. The larger the value, the worse the comfort felt by the passengers.

[0201]

[0202] Specifically, in step I, the quantitative mapping relationship between bridge structure damage, driving safety, and passenger comfort is obtained as follows:

[0203] Take the calculation result of the vehicle-bridge coupling dynamic response obtained in step H as the first response result, and take the calculation result of the vehicle-bridge coupling dynamic response calculated from the track random unevenness array as the second response result.

[0204] Subtract the second response result from the first response result to obtain the third response result, and use the third response result as the calculation result of the vehicle-bridge coupling dynamic response corresponding to the additional track unevenness array caused by bridge structure damage. It can be expressed by the formula as follows:

[0205] (12)

[0206] In Equation (12), is the vehicle-bridge coupling dynamic response obtained in step H;

[0207] is the vehicle-bridge coupling dynamic response calculated from the track random unevenness array;

[0208] is the vehicle-bridge coupling dynamic response corresponding to the additional track unevenness array caused by bridge structure damage.

[0209] Calculate the second derivative of the additional track unevenness caused by bridge structure damage with respect to the track mileage, and use the least squares fitting method to establish the quantitative relationship between this second derivative and the third response result, which can be expressed as:

[0210] (13)

[0211] In Equation (13), is the second derivative of the additional track unevenness caused by bridge structure damage with respect to the track mileage;

[0212] and is the fitting coefficient obtained by the least squares fitting method;

[0213] is the track mileage.

[0214] Using the quantitative relationship established by Equation (13), various bridge structure damage thresholds that ensure train operation safety and passenger comfort can be established. For example represents the wheel load reduction rate of high-speed railways. According to the "Code for Design of High-Speed Railways" (TB 10621-2014), its limit value is 0.6. Assume that the calculated value of the wheel load reduction rate caused by random track unevenness is , then the limit value of is . Combining with Equation (13), we get:

[0215] (14)

[0216] In Equation (14), is the calculated value of the wheel load reduction rate caused by random track unevenness.

[0217] Using Equation (14), the bridge structure damage threshold that meets the wheel load reduction rate limit requirement can be established. When takes other remaining dynamic response indicators, the complete bridge structure damage thresholds that ensure train operation safety and passenger comfort can be established.

[0218] As a specific implementation

[0219] A fine simulation calculation method for evaluating train operation safety and passenger comfort on high-speed railway bridges includes the following steps:

[0220] Step A. Establish a digital twin simulation calculation model of the bridge structure.

[0221] Establish a digital twin simulation calculation model of the bridge structure composed of components such as bridge piers, girders, and pile foundations. The geometric dimensions of the components are input using a custom arbitrary cross-section input mode. The custom arbitrary cross-section input rules are as follows:

[0222] a. Each side is input in the counterclockwise direction and separated by a semicolon ";";

[0223] b. The information of each side contains 5 parameters, separated by a comma "," in the middle;

[0224] c. The physical meanings of the 5 parameters are as follows:

[0225] ① Section number, >0 for outer contour, <0 for inner contour

[0226] ② Starting endpoint x coordinate

[0227] ③ Starting endpoint z coordinate

[0228] ④ Radius r, =0 for straight line segment, >0 for arc radius

[0229] ⑤ Arc indication, =0 for full circle, >0 for minor arc, <0 for major arc.

[0230] As shown in the Figure 2 box girder cross-section shown, using any of the above cross-section input rules, the specific data can be seen in the following table. The box girder cross-section input interface of the digital twin simulation platform based on any cross-section input rule is as Figure 3 shown.

[0231] Box Girder Cross-Section Input Data Table

[0232]

[0233] The digital twin simulation calculation model of the bridge structure is established using the finite element method, and the bearings are simulated using six-direction support springs. For simply supported beam bodies, equal-section space beam elements are used for simulation, and for continuous beam bodies, variable-section space beam elements are used for simulation.

[0234] The stiffness matrix of the variable-section space beam element adopts the relevant technology of Chinese invention patent application CN 202210511550.4.

[0235] Step B. Establish a digital twin simulation calculation model of high-speed trains.

[0236] Establish different degrees-of-freedom digital twin simulation calculation models of high-speed trains of different types (such as Figure 4 ). The common degrees of freedom of the train models are 21, 23, 31, 35, and 42. The vibration equations of motion of each degree-of-freedom high-speed train are established according to the principle of Lagrange's equation.

[0237] The expression of Lagrange's equation is:[[]]

[0238] (1)

[0239] In equation (1), T , V , Q are the total kinetic energy, total elastic potential energy, and total damping dissipation energy of the system respectively;

[0240] are the degrees of freedom of each part of the high-speed train;

[0241] is the derivative of;

[0242] Represent the degrees of freedom of the carbody, bogie, and wheelset;

[0243] Represent the total derivative with respect to time;

[0244] Represent the partial derivative operator;

[0245] Taking the vibration equation of a 31-degree-of-freedom high-speed train as an example, the specific symbols of the carbody, bogie, and wheelset are as follows:

[0246] Degrees of freedom of the carbody :

[0247] (2)

[0248] Degrees of freedom of the bogie :

[0249] (3)

[0250] Degrees of freedom of the wheelset :

[0251] (4)

[0252] In equations (2), (3), and (4), , , respectively represent the degrees of freedom of the carbody, bogie, and wheelset;

[0253] represents yaw, represents heave, represents roll, represents pitch, represents shake;

[0254] The subscript c represents the carbody, ti represents the bogie, and wij represents the wheelset;

[0255] T is the transpose operator of the matrix.

[0256] Based on the degrees of freedom in equations (2) to (4), the total kinetic energy, total potential energy, and damping dissipation energy of the vehicle are calculated respectively, and then substituted into equation (1), and the vibration motion equation of the 31-degree-of-freedom high-speed train can be obtained.

[0257] Step C. Establish a digital twin simulation calculation model for the passenger seat.

[0258] Establish a complete digital twin simulation calculation model for the passenger seat consisting of four parts: the head, viscera, torso, and seat (as shown in Figure 5), where the human body is regarded as a biological elastic system, including three parts: the head, viscera, and torso. Each part is represented by two degrees of freedom, so the human-seat digital twin simulation calculation model has a total of eight degrees of freedom.

[0259] Degrees of freedom of the human-seat:

[0260] (5)

[0261] In equation (5), and represent the degrees of freedom of the seat in two directions;

[0262] and represent the degrees of freedom of the torso in two directions;

[0263] and represent the degrees of freedom of the internal organs in two directions;

[0264] and represent the degrees of freedom of the head in two directions.

[0265] Specifically, in step D of establishing a complete human-vehicle-bridge coupling simulation system, the passenger-seat digital twin simulation calculation model established in step C is added to the vehicle-bridge coupling simulation system, thus forming a complete human-vehicle-bridge coupling simulation system.

[0266] Taking the dynamic equilibrium equation corresponding to the human-vehicle system in the human-vehicle-bridge coupling simulation system as an example, its equation is expressed as follows:

[0267] (6)

[0268] In equation (6), and and and represent the mass matrices of the car body, bogie, wheel set, and passenger respectively;

[0269] and and and represent the acceleration vector matrices of the car body, bogie, wheel set, and passenger respectively;

[0270] and and and represent the velocity vector matrices of the car body, bogie, wheel set, and passenger respectively;

[0271] and , , represent the displacement vector matrices of the car body, bogie, wheel set, and passengers respectively;

[0272] , represent the damping matrix and the elastic matrix respectively. In the matrix, the subscripts vv, tt, ww, and pp represent the matrices on the main diagonals of the car body, bogie, wheel set, and passengers; the subscript vt (tv) represents the correlation matrix between the car body and the bogie; the subscript vp (pv) represents the correlation matrix between the car body and the passengers; the subscript tw (wt) represents the correlation matrix between the bogie and the wheel set;

[0273] represents the load column vector acting on the wheel.

[0274] For the specific degrees of freedom of the car body, bogie, and wheel set, refer to the above formulas (2) to (4), and for the specific degrees of freedom of the passengers, refer to formula (5).

[0275] Step E, establish a digital twin simulation calculation module for track random irregularities.

[0276] Track random irregularities, as the self-excitation of the vehicle-bridge coupling analysis system, mainly include several types of track irregularities such as vertical alignment, horizontal alignment, gauge, level, and cross-level (attached Figure 6 ). When calculating the dynamic responses of the vehicle and the human body, it is necessary to be based on the track irregularity spectrum specified in the specification "Spectrum of Ballastless Track Irregularities for High-Speed Railways" (TB / T 3352-2014) (hereinafter referred to as the "irregularity spectrum specification"). The track irregularity spectrum is fitted in segments using a power function, and its formula is:

[0277] (7)

[0278] In formula (7), represents the spatial frequency;

[0279] , represent the coefficients of the fitting formula.

[0280] It is converted into a time history curve using a numerical algorithm to serve as the self-excitation for vehicle-bridge coupling dynamic analysis. Here, the trigonometric series method is used as the main algorithm for the digital twin simulation calculation module of irregularities, and the track random irregularity array is calculated. The specific calculation formula is:

[0281] (8)

[0282] In formula (8), is the generated track irregularity sequence;

[0283] is the distance of the generated track irregularity sequence;

[0284] is the power spectral density function of the given track irregularity;

[0285] (k = 1, 2, … n) are the considered frequencies, where and are the upper and lower limits of the considered frequencies respectively;

[0286] n is the order of the upper frequency limit;

[0287] is the bandwidth of the frequency interval;

[0288] is the phase of the corresponding k-th frequency, which generally takes values uniformly distributed between 0 and 2π.

[0289] Step F. Establish a digital twin simulation calculation module for the additional track irregularity caused by bridge structure damage.

[0290] The main modes of bridge structure damage include pier settlement, beam offset, beam end rotation, support disengagement, fastener bar breakage, and bottom slab mortar layer disengagement. These structural damages will all cause a certain degree of additional track irregularity on the rail surface (attached Figure 7 ). To be compatible with different types of structural damage and the differences in the additional track irregularity on the rail surface caused by the damage of simply supported beams and continuous beams, a general damage-induced additional track irregularity array with freely extensible array dimensions is proposed here. When different types of damage occur, the calculated additional track irregularity arrays are different, and the real-time calculated additional track irregularity array can be assigned to the general damage-induced additional track irregularity array with freely extensible array dimensions.

[0291] After calculating the additional track irregularity on the rail surface caused by a specific type of damage using different methods, it can be assigned to the general damage-induced additional track irregularity array with freely extensible array dimensions.

[0292] Step G. Establish the coupled dynamic relationship between the high-speed train and the track at the wheel-rail contact surface.

[0293] Establish the coupled dynamic relationship between the train and the track at the wheel-rail contact surface. The wheel-rail normal force between the train and the bridge is calculated using the non-linear Hertz contact theory, and the wheel-rail tangential creep force is calculated using the Kaller theory. The specific description is as follows:

[0294] The wheel-rail normal force between the high-speed train and the track is calculated using the non-linear Hertz contact theory, and the calculation formula is as follows:

[0295] (9)

[0296] In Equation (9), is the wheel-rail contact constant, which is related to factors such as the wheel-rail tread surface, and the unit ;

[0297] is the Hertz normal contact force;

[0298] is the normal relative deformation value between the wheel and the rail.

[0299] The wheel-rail tangential creep force between the high-speed train and the track adopts the Kaller theory, and the relationship with the creep rate can be expressed as:

[0300] (10)

[0301] In Equation (10), , are the longitudinal and lateral creep forces;

[0302] is the rotational creep moment;

[0303] , are the longitudinal and lateral creep coefficients;

[0304] is the rotational / lateral creep coefficient;

[0305] is the rotational creep coefficient;

[0306] , , respectively represent the longitudinal, lateral, and vertical creep rates.

[0307] Step H. Obtain the digital twin calculation module for the safety evaluation indexes of train operation safety and passenger comfort on the high-speed railway bridge structure.

[0308] The train operation safety indexes mainly include train vertical acceleration, wheel-rail vertical force, wheel weight reduction rate, derailment coefficient, lateral force, car body acceleration index, etc.

[0309] The passenger comfort index evaluates the comfort level by the root mean square of the total weighted acceleration of the human body. The root mean square value of the total weighted acceleration is calculated according to the following formula:

[0310] (11)

[0311] In Equation (11), , , The root mean square values of the weighted accelerations in each direction (x, y, and z directions), respectively.

[0312] According to ISO2631-1, the relationship between the root mean square weighted value of acceleration and the level of human subjective feeling is given in Table 1. The larger the value, the worse the comfort felt by the passengers.

[0313]

[0314] Step I. Establish the quantitative mapping relationship between bridge structure damage, driving safety, and passenger comfort.

[0315] Take the calculation result of the vehicle-bridge coupling dynamic response obtained in Step H as the first response result, and take the calculation result of the vehicle-bridge coupling dynamic response calculated from the track random unevenness array as the second response result.

[0316] Subtract the second response result from the first response result to obtain the third response result, and use the third response result as the calculation result of the vehicle-bridge coupling dynamic response corresponding to the additional track unevenness array caused by bridge structure damage. It can be expressed by the formula as follows:

[0317] (12)

[0318] In Equation (12), is the vehicle-bridge coupling dynamic response obtained in Step H;

[0319] is the vehicle-bridge coupling dynamic response calculated from the track random unevenness array;

[0320] is the vehicle-bridge coupling dynamic response corresponding to the additional track unevenness array caused by bridge structure damage.

[0321] Calculate the second derivative of the additional track unevenness caused by bridge structure damage with respect to the track mileage, and use the least squares fitting method to establish the quantitative relationship between this second derivative and the third response result, which can be expressed as:

[0322] (13)

[0323] In Equation (13), is the second derivative of the additional track unevenness caused by bridge structure damage with respect to the track mileage;

[0324] 、 are the fitting coefficients obtained by the least squares fitting method;

[0325] is the track mileage.

[0326] Using the quantitative relationship established by Equation (13), various bridge structure damage thresholds that ensure driving safety and passenger comfort can be established. For example represents the wheel load reduction rate of high-speed railways. According to the "Code for Design of High-Speed Railways" (TB 10621-2014), its limit value is 0.6. Assume that the calculated value of the wheel load reduction rate caused by random track irregularities is , then The limit value of is . Combining with Equation (13), we get:

[0327] (14)

[0328] In Equation (14), is the calculated value of the wheel load reduction rate caused by random track irregularities.

[0329] Using Equation (14), the bridge structure damage threshold that meets the requirements of the wheel load reduction rate limit can be established. When takes other remaining dynamic response indicators, various bridge structure damage thresholds that ensure driving safety and passenger comfort can be established completely.

[0330] The present invention aims at the problem of fine simulation calculation for the evaluation of driving safety and passenger comfort on high-speed railway bridges, and establishes a complete set of fine simulation calculation method technology for the evaluation of driving safety and passenger comfort on high-speed railway bridges that is completely independently controllable.

[0331] The present invention can digitally construct the fine simulation calculation for the evaluation of driving safety and passenger comfort on high-speed railway bridges in the field of traffic safety technology, and solve the underlying key technical problems of accurate mapping modeling, design, analysis, diagnosis, and decision-making of the physical model and data-driven model for the evaluation of driving safety and passenger comfort on high-speed railway bridges.

Claims

1. A fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges, characterized in that: It includes the following steps: (A)Establish a digital twin simulation calculation model for the bridge structure; (B)Establish a digital twin simulation calculation model for the high-speed train; (C)Establish a digital twin simulation calculation model for the passenger chair; (D)Establish a complete human-vehicle-bridge coupling simulation system; (E)Establish a digital twin simulation calculation module for track random unevenness; (F)Establish a digital twin simulation calculation module for additional track unevenness caused by bridge structure damage; (G)Establish the coupling dynamic relationship between the high-speed train and the track at the wheel-rail contact surface; (H)Based on the digital twin simulation calculation module for track random unevenness and the digital twin simulation calculation module for additional track unevenness caused by bridge structure damage, obtain the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on the high-speed railway bridge structure; (I)Based on the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on the high-speed railway bridge structure, obtain the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort; Step (H)Based on the digital twin simulation calculation module for track random unevenness and the digital twin simulation calculation module for additional track unevenness caused by bridge structure damage, obtain the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on the high-speed railway bridge structure. The specific process is as follows: First, superimpose the track random unevenness array obtained in step (E) and the general additional track unevenness array caused by damage obtained in step (F), and then substitute them into the human-vehicle-bridge coupling simulation system formed in step (D); Then, calculate the calculation results of the human-vehicle-bridge coupling dynamic response. The calculation results of the human-vehicle-bridge coupling dynamic response include train operation safety indicators and passenger comfort indicators; Step (I)Based on the digital twin calculation module for safety evaluation indicators of train operation safety and passenger comfort on the high-speed railway bridge structure, obtain the quantitative mapping relationship between bridge structure damage and train operation safety and passenger comfort. The specific process is as follows: First, take the calculation results of the human-vehicle-bridge coupling dynamic response obtained in step (H) as the first response result; Then, take the calculation results of the human-vehicle-bridge coupling dynamic response calculated from the track random unevenness array as the second response result; Next, subtract the second response result from the first response result to obtain the third response result. The third response result is used as the calculation result of the human-vehicle-bridge coupling dynamic response corresponding to the additional track unevenness array caused by bridge structure damage; Next, calculate the second derivative of the additional track unevenness caused by bridge structure damage with respect to the track mileage; Next, use the least squares fitting method to establish the quantitative relationship between the above second derivative and the third response result; Finally, according to the quantitative relationship, establish the damage threshold of the bridge structure to ensure train operation safety and passenger comfort.

2. The fine simulation calculation method for evaluating the train operation safety and passenger comfort on high-speed railway bridges according to claim 1, wherein: Step (A)Establish a digital twin simulation calculation model for the bridge structure. The specific process is as follows: First, determine the component members of the bridge structure; Then, use the finite element method to establish a digital twin simulation calculation model for the bridge structure; Next, the geometric dimensions of the component members are input using custom arbitrary cross-section input; Finally, the bearings in the bridge structure are simulated using six-direction support springs.

3. The fine simulation calculation method for evaluating the train operation safety and passenger comfort on high-speed railway bridges according to claim 1, wherein: Step (B) Establish a digital twin simulation calculation model for high-speed trains, and the specific process is as follows: First, establish digital twin simulation calculation models with different degrees of freedom for different high-speed trains; Then, different degrees-of-freedom high-speed trains establish vibration equations of motion based on the Lagrange equation principle.

4. The fine simulation calculation method for evaluating the train operation safety and passenger comfort on high-speed railway bridges according to claim 1, wherein: Step (D) Establish a complete human-vehicle-bridge coupling simulation system, and the specific process is as follows: First, construct the vehicle-bridge coupling simulation system by using the digital twin simulation calculation model of the bridge structure established in step (A) and the digital twin simulation calculation model of the high-speed train established in step (B); Then, add the digital twin simulation calculation model of the passenger chair established in step (C) to the vehicle-bridge coupling simulation system to obtain a complete human-vehicle-bridge coupling simulation system.

5. The fine simulation calculation method for evaluating the driving safety and passenger comfort on high-speed railway bridges according to claim 1, characterized in that: Step (E) Establish a digital twin simulation calculation module for track random irregularities, and the specific process is as follows: First, determine the composition of track random irregularities, which include elevation, alignment, gauge, level, and cross-level; Then, convert the track random irregularities into time history curves as the self-excitation of the vehicle-bridge coupling simulation system; Next, based on the self-excited track random irregularities and the vehicle-bridge coupling simulation system, obtain the digital twin simulation calculation module for track random irregularities; Finally, use the trigonometric series method as the main algorithm of the digital twin simulation calculation module for track random irregularities to obtain the track random irregularity array.

6. The fine simulation calculation method for evaluating the train operation safety and passenger comfort on high-speed railway bridges according to claim 1, characterized in that: Step (F) Establish a digital twin simulation calculation module for additional track irregularities caused by bridge structure damage, and the specific process is as follows: First, bridge structure damage includes pier settlement, beam offset, beam end rotation, bearing disengagement, fastener breakage, and bottom slab mortar layer disengagement; Then, pier settlement, beam offset, beam end rotation, bearing disengagement, fastener breakage, and bottom slab mortar layer disengagement cause additional irregularities on the track surface; Finally, obtain a general array for additional track irregularities caused by damage with a freely expandable array dimension.

7. The fine simulation calculation method for evaluating the train operation safety and passenger comfort on high-speed railway bridges according to claim 1, characterized in that: Step (G) Establish the coupling dynamic relationship between the high-speed train and the track at the wheel-rail contact surface, and the specific process is as follows: First, the wheel-rail normal force between the high-speed train and the track is obtained by using the nonlinear Hertz contact theory; Then, the wheel-rail tangential creep force between the high-speed train and the track is calculated by using the Kaller theory.

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