CN115435882A - Dynamic weighing method for railway bridge based on axle coupling effect - Google Patents
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Abstract
The invention provides a dynamic weighing method for a railway bridge based on an axle coupling effect. In a time-varying axle system, an extended state space model with the mass and the eccentricity of a wagon as unknown parameters is established, and a wagon mass identification method based on a Kalman filtering theory is provided, so that the weighing efficiency of a railway bridge wagon is improved.
Description
Technical Field
The invention relates to the field of railway bridges, in particular to a dynamic weighing method for a railway bridge based on an axle coupling effect.
Background
The heavy-duty railway wagon is a large direction for the development of transportation. However, the railroad bridge and the infrastructure thereof are easily damaged by fatigue and even destroyed under the repeated action of heavy-duty railway trucks. Therefore, accurate weight information for freight vehicles is critical to railway infrastructure evaluation and maintenance.
Because the on-site vehicle weights are different, on-site vehicle load monitoring has important significance for railway infrastructure management. When the railway freight car is operated, the mass, the rotational inertia and the unbalanced loading condition of the railway freight car are changed due to the change of the quantity of goods and different loading modes. The existing bridge dynamic weighing (BWIM) method has errors when the vehicle speed is large, and the dynamic effect cannot be filtered through signal processing.
Disclosure of Invention
In view of the above, the present invention has been developed to provide a method and system for big data statistics based on urban alien and resident people that overcomes or at least partially solves the above-mentioned problems.
In order to solve the technical problem, the embodiment of the application discloses the following technical scheme:
a railway bridge dynamic weighing method based on an axle coupling effect comprises the following steps:
s100, setting mechanical parameters of a vehicle adopted by truck weighing detection, and arranging an acceleration sensor on a bridge for acquiring bridge vibration acceleration response when the vehicle runs on a line; the mechanical parameters at least include: mass m of vehicle body c Initial coefficient β, bogie mass m t Moment of inertia of bogie J t Wheel pairMass m w Offset distance d c Suspension stiffness k of ct Is a suspension damper c ct Half L of the distance between the centers of gravity of the front and rear bogies 1 And L 2 Two wheels of the same bogie are half L of the distance to the center of gravity t ；
S200, setting the time for the first wheel of the truck to just get on the axle as an initial moment t 0 The time when the first wheel of the railway freight car just leaves the bridge is the termination time t end The discrete time step is delta t, and k =1 is set; at an initial time t 0 In time, the mass m of the truck is set c And truck eccentricity d c Establishing a rigidity matrix K, a damping matrix C, a mass matrix M and a load matrix f of the axle system s And f r Setting the initial value of the expansion state vector of the axle system
Sum covariance matrix initialization value
Constructing coefficient matrixes phi ', theta ', H ' and lambda and nonlinear relations f (eta)) and H (eta)) of the extended state space model;
s300. By
And
Sigma-Point set xi for calculating expansion state vector X of axle system at the moment of t = (k-1) delta t X And process noise
Sigma-Point set xi of sound V V And calculating the weight value of the corresponding Sigma-Point set;
s400, calculating an expansion state vector predicted value at the moment t = k delta t according to the f (.)
Sum covariance
And predict the value from the vector
Sum covariance
Computing predicted value of bridge observation vector through h (.) relation
Sum covariance
S500. Covariance matrix based on prediction
And
computing kalman filter gain matrix K k Based on the current observed value y of the bridge observation vector k Correcting to obtain the optimal estimation of the system state vector at the current t = k Δ t moment
The quality of the truck at the current moment can be obtained
Eccentricity of truck
S600, if the current time t k <t end Repeating S200-S500 until t > t end And the weight and eccentricity identification condition of the railway wagon can be obtained when the front wheel of the wagon leaves the beam section.
Further, in S200, firstly, establishing a dynamic equation of the axle system through a first formula to serve as a basis for subsequent identification; then defining the state of the axle system according to a second formula set, and separating a system state space equationPerforming scattering treatment, namely solving a coefficient matrix phi of the system state equation according to a third formula set based on the obtained M, C and K matrixes k ,Θ k ,H k ,Λ k Performing extended definition according to the state of the axle system of the fourth formula set, and solving a coefficient matrix phi 'of an extended system state equation' k ,Θ' k ,H' k ,Λ k 。
Further, the first formula set for establishing the power equation of the axle system is:
establishing the following time-varying motion equation of the vehicle-bridge coupling system:
wherein M, C and K respectively represent a mass matrix, a damping matrix and a stiffness matrix of the axle system, and f s Representing the static axial load vector, f r Representing a track irregularity vector; the equation of motion can be further written as follows:
wherein, M vv 、C vv 、K vv Representing a mass matrix (to be identified), a damping matrix and a rigidity matrix of the railway wagon; q, a,
Respectively representing the total degree of freedom of the axle system and the first derivative and the second derivative thereof; k vb And K bv A stiffness matrix representing the coupling of the vehicle to the track, C vb And C bv A damping matrix representing a coupling of the vehicle to the track;
and with
Respectively showing the shape of the track unit at the point of contact of the vehicle with the trackA function; p is a radical of v Indicating the load to which the vehicle is subjected, p b Representing the load borne by the lower bridge; the coefficient matrix of the formula (2) can be obtained from the formulas (3) to (4) and the dead axle weight W of the vehicle body j And mass moment of inertia J c Can be expressed as:
J c ＝βm c +m c d c 2 (4)
wherein j (j =1 to 4) is a j-th axis of the vehicle; w j,0 Designing the dead axle weight for the initial; beta is an initial design constant; g is the acceleration of gravity; l is 1 ,L 2 ,L t Respectively represents the distance between the center of gravity of the front bogie and the center of the vehicle body and the distance between two wheels of the same bogie and the center, L 1 ＝L 2 ＝L h 。
Further, the second set of equations defined for the axle system states are:
defining the state vector x is a variable describing the state of the whole axle system, and the specific form is as follows:
where q denotes the total degree of freedom of the axle system,
representing its corresponding first derivative; this state vector satisfies the following system continuous time state equation:
where x (t) represents the time-varying axle system state vector,
showing one order thereofDerivative, f s (t) represents the dead axle weight input load vector, f r (t) represents the track irregularity load vector, and A (t) and B (t) are time-varying coefficient matrices of the specific form:
wherein M, C and K respectively represent a rigidity matrix, a damping matrix and a mass matrix of the vehicle-bridge system, and I represents a unit matrix; this continuous-time equation of state can be converted to a discrete-time equation of state, plus the system noise W k (E(W j W k )＝Π w δ jk ) Comprises the following steps:
x k ＝Φ k-1 x k-1 +Θ k-1 (f s,k-1 +f r,k-1 )+W k (7)
wherein x k Representing the vehicle axle system state vector at the present moment, phi k-1 And Θ k-1 The coefficient matrix in the discrete-time state equation at the previous time is represented.
Further, the coefficient matrix phi of the system state equation is solved k ,Θ k ,H k ,Λ k The third formula set of (1) is:
Φ k-1 and Θ k-1 The coefficient matrix in the discrete-time state equation at the previous moment is represented and can be calculated by the following formula:
a in the formula (8) k-1 And B k-1 Respectively representing corresponding coefficient matrixes A (t) and B (t) in a continuous time state equation at the last moment;
y represents a bridge vertical acceleration observation vector, which can be expressed as a discrete-time observation equation, namely:
y k ＝H k x k +Λ k (f s,k +f r,k )+n k (9)
wherein n is k Represents the observed noise vector at the current moment, isWhite Gaussian noise of zero mean, H k And Λ k Expressing an observation equation coefficient matrix, wherein the specific expression is as follows:
wherein C is a 、C v And C d Respectively representing acceleration, speed and displacement output matrixes of the vehicle-bridge system at the current moment; the coefficient matrix phi of the system state equation of the formula (9) is obtained according to the formula (8) and the formula (10) k ,Θ k ,H k ,Λ k (ii) a Equation 9 contains only the discrete state space model of the axle system for the bridge response, while the coefficient matrix (Φ, Θ, H, and Λ) and the static axle load vector f s,k All are related to the weight of the truck, so that the mass m of the truck with unknown parameters can be used c And mass eccentricity d c And the weight identification problem of the railway freight car is further converted into a system parameter identification problem.
Further, expansion definition is carried out according to the state of the axle system of the fourth formula set, and a coefficient matrix phi 'of an expansion system state equation is solved' k ,Θ' k ,H' k ,Λ k The fourth formula set is: and expanding the state vector in the original axle system as follows:
according to the random walk theory, the unknown parameter vector p is added into the steady-state noise vector with zero mean value and then expressed as:
p k ＝p k-1 +e k-1 (12)
the improved system state space model of the axle can then be expressed as:
wherein the coefficient matrix is:
II is satisfied for the extended process noise k ＝E(V k V j )/δ kj ，Π＝diag(π W ,π e ) Wherein δ kj Is a Kronecker symbol;
the state space model of the axle system relates to the unknown mass and the unknown eccentricity of the truck body in the coefficient matrix, and the expanded state space model has the following characteristics and is obviously different from a traditional structure power system.
Further, in S300, a specific method for calculating a weight value of a corresponding Sigma-Point set includes:
extended state vector X k Respectively, the optimal estimated value and the covariance of
And
by
And
the Sigma-Point set was constructed as follows:
wherein, L =2L X +4，h c For the center difference step length, take
Is p V Column i vector, chol (.) represents the Cholesky decomposition.
Further, in S400, the extended state vector predictor at the time t = k Δ t is calculated from the f (.) relationship
Sum covariance
The calculation method comprises the following steps:
Sigma-Point set under function f ():
finally, a predicted extended state vector of t = (k + 1) Δ t can be obtained
Sum covariance
Wherein the weighting coefficients are:
further, in S400, the predicted value of the bridge observation vector is calculated by the h (.) relationship
Sum covariance
The specific method comprises the following steps:
at time t = (k + 1) Δ t, measured by
And
the constructed observation vector Sigma-Point set is as follows:
wherein N = L X +L y ，h c As a central differential step, still take
Is p n Column i vector, chol (.) represents the Cholesky decomposition;
further, a Sigma-Point set under function h () can be obtained:
finally, a prediction extended observation vector of t = (k + 1) delta t can be obtained
Sum covariance
Wherein the weighting coefficients are:
further, the specific method of S500 includes: using the equations (27), (28) and S400
And
solving a Kalman filter gain matrix K k Reuse of the resulting product of S400
And the measured vibration response observation vector y of the bridge k The system's optimal estimate of the extended state vector is calculated according to equation (29)
And covariance matrix
Obtaining the optimal estimation of the rail wagon at the current moment according to the formula (11)
And
wherein equation (28) and equation (29) are:
system prediction state vector based on t = (k + 1) delta t moment
Covariance matrix with bridge observation vector
The Sigma-Ponit Kalman filtering gain matrix K can be solved k+1 ：
And the optimal estimated value X and the covariance P of the system expansion state vector at the moment t = (k + 1) delta t X And can be determined from the measured y k+1 To update:
further, the truck mass m at the time t = (k + 1) Δ t can be obtained from the equation (11) c And eccentricity d c The optimal estimated value of (c).
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
1. the method provided by the invention can directly install the acceleration sensor on the operation bridge, observe the bridge structure acceleration response data of the railway wagon when the railway wagon runs in the bridge track section, and finish the data collection of the bridge structure response only by arranging the acceleration sensor on the detection beam section during detection.
2. The detection equipment required by the method provided by the invention only comprises the bridge structure vibration response sensor and the computer for data processing, and compared with the existing expensive weighing equipment, the method effectively reduces the detection cost.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a dynamic weighing method for railroad bridges based on axle coupling effect in embodiment 1 of the present invention;
FIG. 2 is a detailed flow chart of the dynamic weighing of the railroad bridge truck in embodiment 1 of the present invention;
FIG. 3 is a schematic view of a vehicle model according to embodiment 1 of the present invention;
FIG. 4 is a graph comparing the dynamic weighing mass identification result of the railroad bridge with the true value in embodiment 1 of the present invention;
fig. 5 is a comparison graph of the dynamic weighing eccentric distance identification result of the railroad bridge and the actual value in embodiment 1 of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
In order to solve the problems in the prior art, the embodiment of the invention provides a dynamic weighing method for a railway bridge based on an axle coupling effect.
Example 1
The embodiment discloses a dynamic weighing method for a railroad bridge based on an axle coupling effect, as shown in fig. 1 and 2, comprising the following steps:
s100, setting mechanical parameters of a vehicle adopted by truck weighing detection, and arranging an acceleration sensor on a bridge for acquiring bridge vibration acceleration response when the vehicle runs on a line; specifically, various parameters of the vehicle are shown in table 1, and the mechanical parameters at least include: mass m of vehicle body c Initial coefficient β, bogie mass m t Moment of inertia of bogie J t Wheel set mass m w Offset distance d c Suspension stiffness k ct Is a suspension damper c ct Half L of the distance between the centers of gravity of the front and rear bogies 1 And L 2 Two wheels of the same bogie are half L of the distance to the center of gravity t (ii) a Specifically, the vehicle model is shown in fig. 2.
In the embodiment, an acceleration sensor is arranged at the bottom of the main beam at the designated position (1/3 span, span-middle span and 2/3 span) of the simply supported beam, and the acceleration response of the bridge when the railway wagon runs is detected. In this embodiment, the railway wagon is set to pass through the simply supported girder bridge at a constant speed of v =80 km/h. Setting system initial state vector
Initial truck mass is
The extended state variable can be set
And its covariance
Watch 1
S200, arranging a first wheel of a truck on a steel frameThe bridge time is the initial time t 0 The time when the first wheel of the railway freight car just leaves the bridge is the termination time t end The discrete time step is delta t, and k =1 is set; at an initial time t 0 In time, set the mass m of the truck c Eccentricity d of the truck c Establishing a rigidity matrix K, a damping matrix C, a mass matrix M and a load matrix f of the axle system s And f r Setting the initial value of the expansion state vector of the axle system
Sum covariance matrix initialization value
Constructing coefficient matrixes phi ', theta ', H ' and Lambda and nonlinear relations f (·) and H (·) of the extended state space model;
in S200 of this embodiment, a dynamic equation of the axle system is first established by a first formula, and is used as a basis for subsequent identification; then defining the state of the axle system according to a second formula set, discretizing a system state space equation, and solving a coefficient matrix phi of the system state equation according to a third formula set on the basis of the obtained M, C and K matrixes k ,Θ k ,H k ,Λ k Performing extended definition according to a fourth formula set axle system state, and solving a coefficient matrix phi 'of an extended system state equation' k ,Θ' k ,H' k ,Λ k 。
Specifically, the first formula set for establishing the dynamic equation of the axle system is as follows:
establishing the following time-varying motion equation of the vehicle-bridge coupling system:
wherein M, C and K respectively represent a mass matrix, a damping matrix and a stiffness matrix of the axle system, and f s Representing the static axial load vector, f r Representing a track irregularity vector; the equation of motion may be further oneThe steps are written as follows:
wherein, M vv 、C vv 、K vv Representing a mass matrix (to be identified), a damping matrix and a rigidity matrix of the railway wagon; q, q,
Respectively representing the total degree of freedom of the axle system and the first derivative and the second derivative thereof; k vb And K bv A stiffness matrix representing the coupling of the vehicle to the track, C vb And C bv A damping matrix representing a coupling of the vehicle to the track;
and with
Respectively representing the shape function of the track unit at the contact point of the vehicle and the track; p is a radical of v Indicating the load to which the vehicle is subjected, p b Representing the load borne by the lower bridge; the coefficient matrix of the formula (2) can be obtained from the formulas (3) to (4), and the dead axle weight W of the vehicle body j And mass moment of inertia J c Can be expressed as:
J c ＝βm c +m c d c 2 (4)
wherein j (j =1 to 4) is a j-th axis of the vehicle; w is a group of j,0 Designing the dead axle weight for the initial; beta is an initial design constant; g is gravity acceleration; l is 1 ,L 2 ,L t Respectively represents the distance between the center of gravity of the front bogie and the center of the vehicle body and the distance between two wheels of the same bogie and the center, L 1 ＝L 2 ＝L h 。
The second set of equations defined for the axle system states are:
defining the state vector x is a variable describing the state of the whole axle system, and the specific form is as follows:
where q represents the total degree of freedom of the axle system,
representing its corresponding first derivative; this state vector satisfies the following system continuous time state equation:
where x (t) represents the time-varying axle system state vector,
represents its first derivative, f s (t) represents the dead axle weight input load vector, f r (t) represents the track irregularity load vector, and A (t) and B (t) are time-varying coefficient matrices of the specific form:
wherein M, C and K respectively represent a rigidity matrix, a damping matrix and a mass matrix of the vehicle-bridge system, and I represents a unit matrix; this continuous-time equation of state can be converted to a discrete-time equation of state, plus the system noise W k (E(W j W k )＝Π w δ jk ) Comprises the following steps:
x k ＝Φ k-1 x k-1 +Θ k-1 (f s,k-1 +f r,k-1 )+W k (7)
wherein x k Representing the vehicle axle system state vector at the present moment, phi k-1 And Θ k-1 The coefficient matrix in the discrete-time state equation at the previous time is represented.
Solving a coefficient matrix phi of a system state equation k ,Θ k ,H k ,Λ k The third formula set of (1) is:
Φ k-1 and Θ k-1 The coefficient matrix in the discrete-time state equation at the previous moment is represented and can be calculated by the following formula:
a in the formula (8) k-1 And B k-1 Respectively representing corresponding coefficient matrixes A (t) and B (t) in a continuous time state equation at the last moment;
y represents a bridge vertical acceleration observation vector, which can be expressed as a discrete-time observation equation, namely:
y k ＝H k x k +Λ k (f s,k +f r,k )+n k (9)
wherein n is k The observed noise vector at the current moment is zero mean Gaussian white noise H k And Λ k Expressing an observation equation coefficient matrix, wherein the specific expression is as follows:
wherein C is a 、C v And C d Respectively representing the acceleration, the speed and the displacement output matrix of the vehicle-bridge system at the current moment; the coefficient matrix phi of the system state equation of the formula (9) is obtained according to the formula (8) and the formula (10) k ,Θ k ,H k ,Λ k (ii) a Equation 9 contains only the discrete state space model of the axle system for the bridge response, while the coefficient matrix (Φ, Θ, H, and Λ) and the static axle load vector f s,k All are related to the weight of the truck, so that the truck mass m with unknown parameters can be used c And mass eccentricity d c The weight identification problem of the railway freight train is further converted into a system parameter identification problem.
According to the fourth publicationThe state of the system of the formula group vehicle axle is extended and defined, and a coefficient matrix phi 'of an extended system state equation is obtained' k ,Θ' k ,H' k ,Λ k The fourth formula set is: and expanding the state vector in the original axle system as follows:
according to the random walk theory, the unknown parameter vector p is added into the steady-state noise vector with zero mean value and then expressed as:
p k ＝p k-1 +e k-1 (12)
the system state space model of the improved axle can then be expressed as:
wherein the coefficient matrix is:
pi is satisfied for the extended process noise k ＝E(V k V j )/δ kj ，Π＝diag(π W ,π e ) Wherein δ kj Is a Kronecker symbol;
the state space model of the axle system relates to the unknown mass and the unknown eccentricity of the truck body in the coefficient matrix, and the expanded state space model has the following characteristics and is obviously different from a traditional structure power system.
S300. The method comprises
And
Sigma-Point set xi for calculating expansion state vector X of axle system at time t = (k-1) delta t X And process noise
Sigma-Point set xi of sound V V And calculating the weight value of the corresponding Sigma-Point set;
in S300 of this embodiment, a specific method for calculating a weight value of a corresponding Sigma-Point set includes:
expanding the state vector X k Respectively, the optimal estimated value and the covariance of
And
by
And
the Sigma-Point set was constructed as follows:
wherein, L =2L X +4，h c As the central difference step length, take
Is p V Column i vector, chol (.) represents the Cholesky decomposition.
S400, calculating an extended state vector predicted value at t = k delta t by using f (.) relation
Sum covariance
And predict the value from the vector
Sum covariance
Computing predicted value of bridge observation vector through h (.) relation
Sum covariance
In S400 of the present embodiment, the extended state vector predictor at the time t = k Δ t is calculated from the f (. -) relationship
Sum covariance
The calculation method comprises the following steps:
Sigma-Point set under function f ():
finally, a predicted extended state vector of t = (k + 1) Δ t can be obtained
Sum covariance
Wherein the weighting coefficients are:
in S400 of the present embodiment, the predicted value of the bridge observation vector is calculated by the h (.) relationship
Sum covariance
The specific method comprises the following steps:
at time t = (k + 1) Δ t, the
And
the constructed observation vector Sigma-Point set is as follows:
wherein N = L X +L y ，h c As a central differential step, still take
Is p n Column i vector, chol (.) represents the Cholesky decomposition;
further, a Sigma-Point set under function h () can be obtained:
finally, a prediction extended observation vector of t = (k + 1) delta t can be obtained
Sum covariance
Wherein the weighting coefficients are:
s500. Covariance matrix based on prediction
And
computing Kalman filter gain matrix K k Based on the current observed value y of the bridge observation vector k Correcting to obtain the optimal estimation of the system state vector at the current t = k Δ t moment
The quality of the truck at the current moment can be obtained
Eccentricity of truck
In this embodiment, the specific method of S500 includes: using the equations (27), (28) and S400
And
solving a Kalman filter gain matrix K k Reuse of the resulting product of S400
And the measured vibration response observation vector y of the bridge k The system's optimal estimate of the extended state vector is calculated according to equation (29)
And covariance matrix
Obtaining the optimal estimation of the rail wagon at the current moment according to the formula (11)
And
wherein equation (28) and equation (29) are:
system prediction state vector based on time t = (k + 1) Δ t
Covariance matrix with bridge observation vector
The Sigma-Ponit Kalman filtering gain matrix K can be solved k+1 ：
And the optimal estimated value X of the system expansion state vector and the covariance P at the time point of t = (k + 1) delta t X And can be determined from the measured y k+1 To update:
further, the truck mass m at the time t = (k + 1) Δ t can be obtained from the equation (11) c And eccentricity d c The optimal estimated value of (a).
S600, if the current time t k <t end Repeating S200-S500 until t > t end And the weight and the eccentricity identification condition of the railway wagon can be obtained when the front wheel of the wagon leaves the beam section.
In this embodiment, after the train speed v =60, 80, 100, 120km/h, the above steps S100-S600 are repeated to obtain the identification of the mass and the eccentricity of the railway wagon at different speeds. The comparison between the quality identification result and the actual truck quality real value is shown in figure 4, and the comparison between the eccentric distance identification result and the actual truck eccentric distance real value is shown in figure 5 (a represents 60km/h, b represents 80km/h, c represents 100km/h, and d represents 120 km/h). It can be seen from fig. 4 and 5 that there is a certain difference between the recognition result and the true value in the initial range, because there is an error between the system state initial value and the true state initial value that are set artificially. After 0.2s, the recognition algorithm is stable, the estimated value and the true value can be matched with each other, a good recognition effect is achieved, and the accuracy and the reliability of the method are verified.
According to the dynamic weighing method for the railway bridge based on the axle coupling effect, disclosed by the embodiment, the acceleration sensor can be directly installed on the operating bridge, the acceleration response data of the bridge structure of the railway wagon when the railway wagon runs in the bridge track section is observed, the data collection of the bridge structure response can be completed only by arranging the acceleration sensor on the detection beam section during detection, and the dynamic weighing of the railway wagon can be rapidly completed in a short time by combining the dynamic weighing method disclosed by the invention. The detection equipment required by the method provided by the invention only comprises the bridge structure vibration response sensor and the computer for data processing, and compared with the existing expensive weighing equipment, the method effectively reduces the detection cost.
It should be understood that the specific order or hierarchy of steps in the processes disclosed is an example of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, invention lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.
Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. Of course, the storage medium may also be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. Of course, the processor and the storage medium may reside as discrete components in a user terminal.
For a software implementation, the techniques described herein may be implemented with modules (e.g., procedures, functions, and so on) that perform the functions described herein. The software codes may be stored in memory units and executed by processors. The memory unit may be implemented within the processor or external to the processor, in which case it can be communicatively coupled to the processor via various means as is known in the art.
What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent that the term "includes" is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or".
Claims (10)
1. A railway bridge dynamic weighing method based on an axle coupling effect is characterized by comprising the following steps:
s100, setting mechanical parameters of a vehicle adopted by truck weighing detection, and arranging an acceleration sensor on a bridge for collecting bridge vibration acceleration response when the vehicle runs on a circuit; the mechanical parameters at least include: mass m of vehicle body c Initial coefficient beta, bogie mass m t Moment of inertia of bogie J t Wheel set mass m w Unbalance loading distance d c Suspension stiffness k ct Is a suspension damper c ct Half L of the distance between the centers of gravity of the front and rear bogies 1 And L 2 Two wheels of the same bogie are half L of the distance to the center of gravity t ；
S200, setting the time for the first wheel of the truck to just get on the axle as an initial moment t 0 The time when the first wheel of the railway freight car just leaves the bridge is the termination time t end The discrete time step is delta t, and k =1 is set; at an initial time t 0 In time, set the mass m of the truck c And truck eccentricity d c Establishing a rigidity matrix K, a damping matrix C, a mass matrix M and a load matrix f of the axle system s And f r Setting the initial value of the expansion state vector of the axle system
Sum covariance matrix initialization value
Constructing coefficient matrixes phi ', theta ', H ' and Lambda and nonlinear relations f (·) and H (·) of the extended state space model;
s300. The method comprises
And
Sigma-Point set xi for calculating expansion state vector X of axle system at time t = (k-1) delta t X Sigma-Point set ξ of process noise V V And calculating the weight value of the corresponding Sigma-Point set;
s400, calculating an extended state vector predicted value at t = k delta t by using f (.) relation
Sum covariance
And predict the value from the vector
Sum covariance
Computing predicted value of bridge observation vector through h (.) relation
Sum covariance
S500. Covariance matrix based on prediction
And
computing kalman filter gain matrix K k Based on the current observed value y of the bridge observation vector k Correcting to obtain the optimal estimation of the system state vector at the current t = k Δ t moment
The quality of the truck at the current moment can be obtained
Eccentricity of truck
S600, if the current time t k <t end Repeating S200-S500 until t > t end And the weight and the eccentricity identification condition of the railway wagon can be obtained when the front wheel of the wagon leaves the beam section.
2. The method for dynamically weighing the railroad bridge based on the axle coupling effect as claimed in claim 1, wherein in S200, a dynamic equation of the axle system is first established by a first formula as a basis for subsequent identification; then defining the state of the axle system according to a second formula set, discretizing a system state space equation, and solving a coefficient matrix phi of the system state equation according to a third formula set on the basis of the obtained M, C and K matrixes k ,Θ k ,H k ,Λ k Performing extended definition according to a fourth formula set axle system state, and solving a coefficient matrix phi 'of an extended system state equation' k ,Θ' k ,H' k ,Λ k 。
3. The method for dynamically weighing a railroad bridge based on the axle coupling effect as claimed in claim 2, wherein the first formula set for establishing the dynamic equation of the axle system is:
establishing the following time-varying motion equation of the vehicle-bridge coupling system:
wherein M, C and K respectively represent a mass matrix, a damping matrix and a rigidity matrix of the axle system, f s Representing the static axial load vector, f r Representing a track irregularity vector; the equation of motion can be further written as follows:
wherein M is vv 、C vv 、K vv Representing a mass matrix (to be identified), a damping matrix and a rigidity matrix of the railway wagon; q, a,
Respectively representing the total degree of freedom of the axle system and the first derivative and the second derivative thereof; k vb And K bv A stiffness matrix representing the coupling of the vehicle to the track, C vb And C bv A damping matrix representing a coupling of the vehicle to the track;
and
respectively representing the shape function of the track unit at the contact point of the vehicle and the track; p is a radical of v Indicating the load to which the vehicle is subjected, p b Representing the load to which the lower bridge is subjected; the coefficient matrix of the formula (2) can be obtained from the formulas (3) to (4) and the dead axle weight W of the vehicle body j And mass moment of inertia J c Can be expressed as:
J c ＝βm c +m c d c 2 (4)
wherein j (j =1 to 4) is a j-th axis of the vehicle; w is a group of j,0 Designing the dead axle weight for the initial; beta is an initial design constant; g is gravity acceleration; l is 1 ,L 2 ,L t Respectively showing the distance between the center of gravity of the front bogie and the center of the vehicle body and the distance between two wheels of the same bogie and the center of gravity of the same bogie，L 1 ＝L 2 ＝L h 。
4. The method for dynamically weighing a railroad bridge based on the axle coupling effect as claimed in claim 2, wherein the second formula set defined for the axle system state is:
defining the state vector x is a variable describing the state of the whole axle system, and the specific form is as follows:
where q represents the total degree of freedom of the axle system,
representing its corresponding first derivative; this state vector satisfies the following system continuous time state equation:
where x (t) represents the time-varying axle system state vector,
representing its first derivative, f s (t) represents the dead axle weight input load vector, f r (t) represents the track irregularity load vector, and A (t) and B (t) are time-varying coefficient matrices of the specific form:
wherein M, C and K respectively represent a rigidity matrix, a damping matrix and a mass matrix of the vehicle-bridge system, and I represents a unit matrix; this continuous-time equation of state can be converted to a discrete-time equation of state, plus the system noise W k (E(W j W k )＝Π w δ jk ) Comprises the following steps:
x k ＝Φ k-1 x k-1 +Θ k-1 (f s,k-1 +f r,k-1 )+W k (7)
wherein x k Representing the vehicle axle system state vector at the present moment, phi k-1 And Θ k-1 The coefficient matrix in the discrete-time state equation at the previous time is represented.
5. The method for dynamically weighing railroad bridge based on axle coupling effect as claimed in claim 2, wherein the coefficient matrix Φ of the system state equation is determined k ,Θ k ,H k ,Λ k The third formula set of (1) is:
Φ k-1 and Θ k-1 The coefficient matrix in the discrete-time state equation at the previous moment is represented and can be calculated by the following formula:
a in the formula (8) k-1 And B k-1 Respectively representing corresponding coefficient matrixes A (t) and B (t) in a continuous time state equation at the last moment;
y represents a bridge vertical acceleration observation vector, which can be expressed as a discrete-time observation equation, namely:
y k ＝H k x k +Λ k (f s,k +f r,k )+n k (9)
wherein n is k The observation noise vector at the current moment is zero mean Gaussian white noise H k And Λ k Expressing an observation equation coefficient matrix, wherein the specific expression is as follows:
wherein C is a 、C v And C d Respectively representing the current time of the vehicle-bridge trainOutputting a matrix of the acceleration, the speed and the displacement of the system; the coefficient matrix phi of the system state equation of the formula (9) is obtained from the formulas (8) and (10) k ,Θ k ,H k ,Λ k (ii) a Equation 9 contains only the discrete state space model of the axle system for the bridge response, while the coefficient matrix (Φ, Θ, H, and Λ) and the static axle load vector f s,k All are related to the weight of the truck, so that the truck mass m with unknown parameters can be used c And mass eccentricity d c The weight identification problem of the railway freight train is further converted into a system parameter identification problem.
6. The method for dynamically weighing a railroad bridge based on the axle coupling effect as claimed in claim 2, wherein the expansion definition is performed according to the fourth formula set axle system state, and the coefficient matrix Φ 'of the expansion system state equation is solved' k ,Θ' k ,H' k ,Λ k The fourth formula set is: and expanding the state vector in the original axle system as follows:
according to the random walk theory, the unknown parameter vector p is added to the steady-state noise vector with zero mean value and then expressed as:
p k ＝p k-1 +e k-1 (12)
the improved system state space model of the axle can then be expressed as:
wherein the coefficient matrix is:
pi is satisfied for the extended process noise k ＝E(V k V j )/δ kj ，Π＝diag(π W ,π e ) Wherein δ kj Is a Kronecker symbol;
the state space model of the axle system relates to the unknown mass and the unknown eccentricity of the truck body in the coefficient matrix, and the expanded state space model has the following characteristics and is obviously different from a traditional structure power system.
7. The method for dynamically weighing railroad bridges based on the axle coupling effect of claim 1, wherein in S300, the specific method for calculating the weight values of the corresponding Sigma-Point sets comprises:
expanding the state vector X k Respectively, the optimal estimated value and the covariance of
And
by
And
the Sigma-Point set was constructed as follows:
wherein L is＝2L X +4，h c As the central difference step length, take
Is p V Column i vector, chol (.) represents the Cholesky decomposition.
8. The method for dynamically weighing a railroad bridge based on the axle coupling effect of claim 1, wherein in S400, the extended state vector predicted value at the time t = k Δ t is calculated from the f (·) relationship
Sum covariance
The calculation method comprises the following steps:
Sigma-Point set under function f ():
finally, a prediction extended state vector of t = (k + 1) delta t can be obtained
Sum covariance
Wherein the weighting coefficients are:
9. the method for dynamically weighing a railroad bridge based on the axle coupling effect of claim 1, wherein in S400, the predicted value of the observation vector of the bridge is calculated according to the h (.) relationship
Sum covariance
The specific method comprises the following steps:
at time t = (k + 1) Δ t, the
And
the constructed observation vector Sigma-Point set is as follows:
wherein N = L X +L y ，h c As a central differential step, still take
Is p n Column i vector, chol (.) represents the Cholesky decomposition;
further, a Sigma-Point set under function h () can be obtained:
finally, a prediction extended observation vector of t = (k + 1) delta t can be obtained
Sum covariance
Wherein the weighting coefficients are:
10. the method for dynamically weighing railroad bridges based on the axle coupling effect as claimed in claim 1, wherein the specific method of S500 comprises: using the equations (27), (28) and S400
And
solving a Kalman filter gain matrix K k Reuse of the resulting product of S400
And the measured vibration response observation vector y of the bridge k Calculating an optimal estimated value of the expanded state vector of the system according to equation (29)
And covariance matrix
Obtaining the optimal estimation of the rail wagon at the current moment according to the formula (11)
And
wherein equations (28) and (29) are:
system prediction state vector based on t = (k + 1) delta t moment
Covariance matrix with bridge observation vector
The Sigma-Ponit Kalman filtering gain matrix K can be solved k+1 ：
And the optimal estimated value X and the covariance P of the system expansion state vector at the moment t = (k + 1) delta t X And can be determined from the measured y k+1 To update:
further, the truck mass m at the time t = (k + 1) Δ t can be obtained from the equation (11) c And eccentricity d c The optimal estimated value of (a).
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